Quadruple-well ferroelectricity and moderate switching barrier in defective wurtzite α-Al2S3: a first-principles study

Quadruple-well ferroelectricity and moderate switching barrier in defective wurtzite α-Al2S3: a first-principles study | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Quadruple-well ferroelectricity and moderate switching barrier in defective wurtzite α-Al2S3: a first-principles study Hirofumi Akamatsu, Yuto Shimomura, Saneyuki Ohno, Katsuro Hayashi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4680101/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 17 Feb, 2025 Read the published version in npj Computational Materials → Version 1 posted 12 You are reading this latest preprint version Abstract Wurtzite-type ferroelectrics are highly promising for next-generation microelectronic devices due to their ferroelectric properties and integration with exiting semiconductors. However, their high coercive fields, which are close to breakdown electric fields, need to be lowered. To deal with this issue and secure device reliability, much effort has been devoted to exploring novel wurtzite compounds with lower polarization switching barriers and implementing doping strategies. Here, we report first-principles calculations on polarization switching in cation-vacancy ordered wurtzite α-Al 2 S 3 , unveiling its uniaxial quadruple-well ferroelectricity and moderate switching barrier, 51 meV/cation, which is much lower than that of conventional wurtzite ferroelectrics. There are three important features relevant to the Al vacancies leading to the uncommon quadruple-well ferroelectricity and the moderate switching barrier: mitigation of cation-cation repulsion, structural flexibility that alleviates an in-plane lattice expansion, and formation of s-like bonding states consisting of Al 3p z and S 3p z orbitals. Biaxial compressive strain and Ga doping lower the switching barriers by up to 40%. This study encourages experimental investigation of the ferroelectric properties for defective wurtzite α-Al 2 S 3 as a new promising material with unconventional and intriguing ferroelectricity and suggests a potential strategy for reducing switching barriers in wurtzite ferroelectrics: introducing cation vacancies . Physical sciences/Materials science/Materials for devices/Electronic devices Physical sciences/Chemistry/Materials chemistry/Electronic materials Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 1. Introduction Ferroelectric materials, characterized by electrically and/or mechanically switchable spontaneous polarization, are utilized in various devices such as piezoelectric actuators, pyroelectric sensors, and capacitors 1–3 . Recently, wurtzite-type compounds have been attracting much attention. This class of materials was known to be piezoelectric and pyroelectric owing to their polar crystal structures with P 6 3 mc space group symmetry. The possible ferroelectricity of wurtzite-type compounds is highly promising for cutting-edge computing and data storage devices due to their high spontaneous polarization. However, their ferroelectricity was not observed prior to dielectric breakdown because of their high coercive fields until Fichtner et al . clearly demonstrated ferroelectric switching for wurtzite-type Sc-doped AlN in 2019 4 . Their work hinted at doping strategies that facilitate ferroelectric switching and ignited rapid progress in the exploration of wurtzite ferroelectrics. Consequently, ferroelectric switching has been reported for other doped wurtzite compounds such as Al 1- x B x N, Ga 1- x Sc x N, Zn x Mg 1- x O, and Al 1- x Y x N 5–8 . However, their high coercive fields, close to breakdown electric fields, reduce device reliability 9,10 . To address this issue, considerable effort has been made to explore novel wurtzite compounds with lower switching barriers and substantial breakdown electric fields 10–12 as well as to implement the doping strategy as mentioned above 4–8 . Wurtzite structures consist of an hcp anion arrangement with cations occupying half of the 4-fold coordinated tetrahedral sites (Fig. 1 b and d). The filled tetrahedra are all oriented upwards (or all oriented downwards), sharing a vertex. It is commonly considered that upon ferroelectric switching in typical wurtzite-type compounds such as pristine AlN, all the cations move collectively from the upwards-oriented tetrahedra to neighboring downwards-oriented tetrahedra along the c -axis direction by passing through anion basal triangles, which involves a bottleneck of switching 13–15 . The saddle point of the minimum energy pathway (MEP) is a nonpolar hexagonal-boron nitride (h-BN)-like structure with space group symmetry of P 6 3 / mmc , in which all the cations locate at 5-fold coordinated trigonal bipyramidal sites 14 . Doping isovalent cations and applying biaxial tensile strain reduce the switching barriers by destabilizing the polar wurtzite structures and/or stabilizing the saddle-point h-BN-like structures to achieve switching prior to breakdown 16,17 . Recently, Lee et al . reported a first-principles study suggesting that certain ternary wurtzite-type compounds containing two types of cations exhibit polarization switching not in a "collective" way via a h-BN-like structure, but in an "individual" or "stepwise" way via multiple local-minimum intermediate structures 18 , highlighting that avoiding the saddle-point h-BN-like structures enables those multinary wurtzite compounds to have low switching barriers. Here, we propose introducing cation vacancies as a potential strategy to lower the switching barriers through a first-principles study on the polarization switching in a defective wurtzite compound. γ-In 2 Se 3 is known as a cation-vacancy ordered wurtzite (Fig. 1 a and c) 19,20 . About 30 compounds with γ-In 2 Se 3 -type structures are registered in the Inorganic Crystal Structure Database (ICSD). In this study, we focus on α-Al 2 S 3 , which consists of the most abundant elements found in the γ-In 2 Se 3 -type compounds. Our first-principles calculations in conjunction with solid-state nudged elastic band (SS-NEB) methods 21 unveiled MEPs for polarization switching in α-Al 2 S 3 , which manifest itself as uniaxial quadruple-well potential curves with four local-minimum states. The intermediate local-minimum structures encompass 5-fold trigonal bipyramidal coordination. The calculated switching barrier is much lower than that of conventional wurtzite ferroelectrics. Detailed analysis of the evolution of the atomic arrangements and chemical bonding during the polarization switching indicates that the Al vacancies play important roles in yielding the unconventional quadruple-well ferroelectricity and the moderate switching barrier. Our calculations also predict that biaxial compressive strain and Ga doping enable the tunability of switching barriers. The calculated piezoelectric constants suggest that piezoresponse force microscopy (PFM) allows us to distinguish the four local-minimum states with different polarization values experimentally. This work showcases introducing cation vacancies as a potential route to lower the switching barriers in wurtzite ferroelectrics as well as predicts the unconventional ferroelectricity in α-Al 2 S 3 . 2. Result and Discussion 2.1 Crystal Structure of α-Al 2 S 3 and Polarization Switching Behavior The crystal structures of cation-vacancy ordered wurtzite α-Al 2 S 3 and conventional wurtzite ZnS are summarized in Fig. 1 . α-Al 2 S 3 shows a polar and chiral P 6 1 space group symmetry. Two-thirds of the tetrahedral sites in wurtzite-type structures are occupied by the Al atoms, while the remaining one-third are vacant 22,23 . In contrast to conventional wurtzite-type compounds, α-Al 2 S 3 has two kinds of crystallographically inequivalent cation sites, both of which are located at Wyckoff positions 6a. These sites can be readily distinguished based on the position of the nearest-neighbor Al vacant sites, i.e., whether it locates either in the sulfur vertex or basal-triangle side along the c axis. Figure 1 e and f extract a column of the coordination tetrahedra along the c axis from the whole structure of α-Al 2 S 3 and ZnS, respectively. Hereafter, the tetrahedral sites with a nearest-neighbor vacant site in the vertex or basal-triangle side are referred to as T1 and T2, respectively. The suffixes "u" and "d" indicate the upwards-oriented or downwards-oriented tetrahedra, respectively. The calculated lattice constants ( a = 6.41 Å, c = 17.80 Å) for α-Al 2 S 3 are in good agreement with the experimental ones ( a = 6.44 Å, c = 17.90 Å) 23 , substantiating that the GGA-PBEsol functional used in this study well reproduces crystal structures. The calculated electric polarization of α-Al 2 S 3 , 66 µC/cm 2 , is comparable to or smaller than those of wurtzite ferroelectrics (e.g., 65 and 135 µC/cm 2 for ZnS and AlN, respectively) 13,15 . An MEP between the two oppositely polarized states with all the tetrahedra oriented upwards or downwards was calculated by using SS-NEB methods to elucidate the switching barrier and behavior (Fig. 2 a). Interestingly, α-Al 2 S 3 has four local energy minima in the MEP, referred to as + HP, +LP, –LP, and –HP in the order of the magnitude of polarization. Here, the states with high, low, and zero absolute polarization values are denoted as HP, LP, and ZP, respectively, and the prefix "+" and "–" symbols indicate positive and negative polarization values, respectively. Figure 3 illustrates these five structures providing the local energy minima and the saddle point. (An animation of the structural evolution associated with the switching is available in the Supporting Information and would help to understand the switching behavior.) Both + HP and + LP states possess P 6 1 space group symmetry. The P 6 1 symmetry is preserved during the switching pathway, except in the saddle-point ZP state, which has zero polarization and nonpolar P 6 1 22 symmetry. The 6 1 symmetry element is preserved during the entire polarization switching process, indicating that the polarization direction remains along the c axis. In contrast to quadruple-well ferroelectrics such as BiFeO 3 , which have multiple independent polarization axes 24 , the four local-minimum states in the MEP of α-Al 2 S 3 are polarized along the c axis, revealing that α-Al 2 S 3 is an unusual ferroelectric with a uniaxial quadruple-well potential as observed in CuInP 2 S 6 25 . Figure 2 b illustrates the structural evolution of α-Al 2 S 3 during the polarization switching as the columns of coordination tetrahedra along the c axis for simplicity. All the six columns included in the unit cell are related to each other by the 6 1 symmetry operation, which is preserved during the polarization switching. The atomic displacement in the column reflects the entire polarization switching process. In the initial high-polarization + HP state, the two inequivalent Al atoms, denoted as Al1 and Al2, occupy the T1u and T2u sites, respectively, enclosed by the upwards-oriented tetrahedra. Beyond a small potential hill, there emerges the + LP state with lower total energy and polarization (+ 30 µC/cm 2 ), where the Al1 atoms occupy the T1u sites whereas the Al2 atoms occupy 5-fold coordinated bipyramidal sites, referred to as B1 sites. In the structural evolution from the + HP to + LP states, the Al2 atoms move from the T2u sites towards the vacant sites and migrate to the bipyramidal B1 sites, whereas the Al1 atoms remain at the T1u sites. Upon transitioning from the + LP to ZP states, the Al2 atoms move from the bipyramidal B1 sites to the T1d sites in the downward-oriented tetrahedra, whereas the Al1 atoms still remain at the T1u sites, resulting in a half-switched state where half of the tetrahedra and the other half are oriented upward and downward with the polarization canceled out. In the latter half of polarization switching from the ZP state to the –LP state to the final –HP state, the Al1 atoms at the T1u sites migrate to the T2d sites via the bipyramidal B2 sites. It should be noted that the Al1 (Al2) atoms sitting at the T1u (T2u) sites in the initial + HP state occupy the T2d (T1d) sites in the final –HP states, indicating the swapping of the crystallographically inequivalent sites during the polarization switching between the T1 and T2 sites. This highlights the nonconventional ferroelectricity of α-Al 2 S 3 . Our first-principles phonon calculation revealed that both the HP and LP states were dynamically stable (Figure S1 and S2). Notably, Al 2 S 3 with the LP structure has been synthesized by chemical vapor transport 23 , while solid-state reaction methods yield α-Al 2 S 3 , which adopts the HP structure. These facts imply that these isosymmetric polymorphs are energetically antagonized at room temperature or above, although our first-principles calculations predict that the LP state is more stable than the HP state at 0 K. 2.2 Comparison of Switching Behavior and Barriers in Wurtzite Compounds In this study, the switching barriers for quadruple-well potential surfaces are defined as the highest energy barrier between a valley and its neighboring peak towards the switching direction 18 . The switching barrier of α-Al 2 S 3 corresponds to the total energy difference between the LP and ZP states. The switching barrier of α-Al 2 S 3 , 51 meV/cation, is approximately one-tenth that of AlN (523 meV/cation) and one-third that of Al 15/16 B 1/16 N (150 meV/cation) 26 . The moderate switching barrier is anticipated to enable polarization switching prior to electric breakdown. We compare the switching behavior in α-Al 2 S 3 and other wurtzite ferroelectrics to understand the moderate switching barrier in α-Al 2 S 3 below. In the binary wurtzite ferroelectrics such as pristine AlN, all the cations displace collectively from the upwards-oriented to the downwards-oriented tetrahedra during polarization switching 12,14 . In ternary wurtzite systems such as Li 2 SiO 3 , for which two-step polarization switching has been predicted by first-principles calculations, more electronegative atoms move first, followed by the migration of less electronegative atoms, with the first switching barrier being the highest 18 . In contrast to these cases, in α-Al 2 S 3 , consisting of only one type of cations, the Al atoms situated at the crystallographically different sites exhibit individual motion; the Al2 atoms exhibit displacement preceding that of the Al1 atoms, as shown in Fig. 2 b, predominantly because the Al2 atoms can displace towards the vacancy sites apart from the Al1 atoms, thereby mitigating cation-cation electrostatic repulsion. In the saddle-point structures for MEPs in binary and ternary wurtzite-type compounds, cations locate at the trigonal bipyramidal sites 10,12,26 . The basal triangles of the bipyramids do not offer enough space for accommodating the cations, resulting in the expansion of the anion triangles. The resultant in-plane lattice expansion destabilizes the saddle-point structures. In sharp contrast, α-Al 2 S 3 has the lowest total energy when half of the Al atoms locate at the bipyramidal sites (i.e., the LP states), highlighting the switching behavior quite different from that for other wurtzite ferroelectrics. Upon transitioning from the + HP to + LP states, the Al2 atoms move to the center of S triangles, accompanying an expansion of the triangle (See Figure S3). In conventional wurtzite ferroelectrics, such triangle expansion increases the in-plane lattice constants typically by 5% 14,16 , destabilizing the h-BN-like saddle-point structures. In α-Al 2 S 3 , the in-plane lattice constant for the LP state is only 1% larger than that of the HP state (See Figure S4). Figure 3 b and d depict the LP structure, in which the AlS 5 and AlS 4 polyhedra tilt with respect to the c axis, resulting in the buckling of close-packed sulfur basal planes, i.e., non-flat sulfur basal planes. The buckling alleviates the in-plane lattice expansion. In conventional wurtzite-type compounds, four anion tetrahedra are connected to each other via an S atom, "locking" the anion polyhedral network. Meanwhile, in α-Al 2 S 3 , just two or three tetrahedra are connected to each other due to the Al vacancies, leading to a flexibility of the polyhedral network. Thus, in contrast to conventional wurtzite-type ferroelectrics, the cation vacancies mitigate the electrostatic repulsion between cations in α-Al 2 S 3 (Fig. 2 b). Also, the disconnection of polyhedral network induced by the Al vacancies produces structural flexibility alleviating the in-plane lattice expansion. These features are considered as the primary reasons why the switching barrier of the defective wurtzite α-Al 2 S 3 is much smaller than those of "filled" wurtzite-type compounds. 2.3 Stabilization Mechanism of AlS 5 Trigonal Bipyramidal Coordination We have discussed above how the Al vacancies stabilize the intermediate structures including the LP states from the structural aspects. The half of Al atoms occupy the trigonal bipyramidal sites in the most stable intermediate LP structures for α-Al 2 S 3 , whereas, in binary and ternary wurtzite ferroelectrics, cations occupy the trigonal bipyramidal sites in the unstable saddle-point structures. It remains unclear why the LP states are stable in α-Al 2 S 3 from the viewpoint of chemical bonding. To elucidate the underlying stabilization mechanism of the AlS 5 bipyramids in terms of chemical bonding, bond valence (BV) and crystal orbital Hamilton population (COHP) between the Al and S atoms were calculated. Here, BV and COHP describe the strength of chemical bonding based on the bond length and the interactions between atomic orbitals, respectively. The negative and positive values of COHP indicate bonding and antibonding interactions, respectively. We utilize negative COHP (–COHP) integrated with respect to energy (–ICOHP) within the valence bands, which indicates the magnitude of net energy gain due to bonding and anti-bonding interactions. Figure 4 a labels the S atoms composing of AlS 4 tetrahedra or AlS 5 bipyramids as follows: the axial S atoms located at the + c and – c sides with respect to the Al atoms as ax1 and ax2, respectively, and the equatorial S atoms composing of basal triangles as Eq. 1 , Eq. 2, and Eq. 3. Figure 4 b and c present the BVs and –ICOHP, respectively, for the Al1 and Al2 atoms against the S atoms for the ZP, +LP, and + HP states. Transitioning from the + HP to + LP states, the Al2 atoms migrate from the tetrahedral T2u sites to the bipyramidal B1 sites (Fig. 2 b), as described above. In the + HP state, the BV sums and –ICOHP of both Al1 and Al2 atoms are primarily contributed to by four S atoms, ax1, Eq. 1 , Eq. 2, and Eq. 3, with minimal contribution from ax2, confirming 4-fold tetragonal coordination (Fig. 4 b and c). In contrast, in the + LP state, the BV sum and –ICOHP of Al2 atom are significantly contributed to by the five S atoms, corroborating 5-fold coordination rather than 3-fold coordination. Let us pay attention to the chemical bonding evolution for the Al2 atoms, as it is crucial to understand the stabilization mechanism of the + LP state. Figure 4 b reveals that the BV sum of the Al2 atoms is significantly smaller for the + LP state than for the + HP state, indicating that the ionic bonding between Al2 and S atoms become weaker upon transitioning from the + HP to + LP states. As shown in Fig. 4 c, however, the sum of –ICOHP for the Al2 atom is comparable in the + LP and + HP states, revealing that the energy gain due to covalent bonding remains upon the structural evolution. This motivates us to unravel the Al2-S covalent bonding that compensates for the poor ionic bonding in more detail. Figure 4 d and e depict the –COHP for the Al2-S bonds as a function of energy in the + LP and + HP states, respectively. A remarkable difference is seen just below the Fermi level; the axial and equatorial S atoms show bonding and antibonding contributions, respectively, in the energy range from − 1 to 0 eV for the + LP state, yielding a net bonding contribution, whereas negligible –COHP is found in this energy range for the + HP state, indicating no bonding contribution. This remarkable difference is considered as a major factor stabilizing the LP states. Figure 4 f and g illustrate the wavefunctions of eigenstates just below the Fermi level for the + LP and + HP states, respectively, both of which mainly consist of S 3p z orbitals. In the eigenstate of the + LP state, the 3p z orbitals of the ax2 S atoms elongate towards the Al2 atoms to overlap with the Al2 3p z orbitals, clearly indicating a s-like bonding interaction between these orbitals. Meanwhile, the S 3p z orbitals of the ax2 S atoms are localized and nonbonding in the eigenstate for the + HP state. The ax2 S atoms are 2-fold coordinated by Al atoms in the + HP state, rendering one of the 3p orbitals nonbonding. The Al2 displacements to the bipyramidal sites yield an additional Al coordination to the ax2 S atoms, causing the ax2 S 3p z orbitals to take part in the bonding states with the Al 3p z states. The formation of the bonding states in the LP states is considered as another factor stabilizing the LP state with respect to the HP state. 2.4 Effects of Epitaxial Strain and Chemical Doping on Switching Barriers For wurtzite ferroelectrics, lowering the switching barrier is a key priority for wider practical applications. It has been demonstrated that epitaxial biaxial strain and chemical doping lower the switching barriers for ZnO and AlN by theory and experiments 16,17,27 . Here, the effects of biaxial strain and chemical doping on MEPs are investigated for Al 2 S 3 to give insights into the experimental control of ferroelectric switching. The reduction of switching barrier in α-Al 2 S 3 requires the stabilization of the ZP states and/or the destabilization of the LP states. Without the constraint of strain, the in-plane lattice constant of the LP state is larger than that of the ZP state, as shown in Figure S4, implying that the MEP can be controlled by harnessing biaxial strain. Figure 5 a shows calculated MEPs under biaxial strain. The total energies of the LP states become higher with respect to those of the ZP states under compressive (negative) biaxial strain, which is consistent with the in-plane lattice constant of the LP state larger than that of the ZP state (Figure S4). Figure 5 b shows the switching barriers under strain, which correspond to the total energy difference between the LP and ZP states. The switching barriers decrease by 8.5% with 2% compressive strain. The biaxial strain dependence of switching barriers for α-Al 2 S 3 is contrary to that for wurtzite ferroelectrics such as ZnO and AlN, where the switching barriers are reduced by tensile biaxial strain 14 . This is because the in-plane lattice constant decreases in α-Al 2 S 3 and increases in typical wurtzite ferroelectrics when climbing the potential hills for the polarization switching. Next, we consider the chemical doping effects on the switching barriers. It has been reported that the switching barrier is successfully reduced for AlN by doping B atoms, which favor planar triangle coordination. It is not likely that B-atom doping helps lower the switching barrier for α-Al 2 S 3 , because it can stabilize the LP states with trigonal bipyramidal coordination. Here, we focus on doping of Ga atoms. Ga is considered as a prime candidate for the following three reasons; ( 1 ) Ga atoms are isovalent to Al. ( 2 ) α-Ga 2 S 3 adopts γ-In 2 Se 3 structure similarly to α-Al 2 S 3 28 . ( 3 ) The ionic radius of Ga 3+ is bigger than that of Al 3+ . The cation-anion radius ratio of Al to S ( r Al / r S = 0.212) is less than 0.225, which is the minimum value for 4-fold tetrahedral coordination according to the Pauling's third rule. Meanwhile, r Ga / r S is 0.255, indicating that Ga atoms favor tetrahedral coordination of S atoms 29 . It is expected from these facts that Ga-doping stabilize the ZP and HP states and destabilize the LP states, reducing the switching barrier. Figure 5 c shows the MEPs for representative structural models of Al (12-x)/6 Ga x/6 S 3 with x = 0, 2, 4, 6, 8, 10, 12. An increase in x stabilizes the ZP and HP states with respect to the LP states, as expected. In the low- x range (0 \(\:\text{≤}\) x \(\:\text{≤}\) 6), the pathway from the +LP to ZP to –LP states corresponds to the highest potential hill, whereas, in the high- x range (6 \(\:\text{≤}\) x \(\:\text{≤}\) 12), the +HP-+LP pathway includes the highest potential hill. Figure 5 d shows the box-and-whisker plot of the switching barriers against doping concentration x in Al (12- x )/6 Ga x /6 S 3 . The switching barrier decreases with an increase in x , and shows a minimum at x = 6, followed by an increase in the barrier above x = 6. The barrier is about 40% smaller for x = 6 compared to pristine α-Al 2 S 3 . Thus, our calculations predict that Ga-doping facilitates the polarization switching for α-Al 2 S 3 . Furthermore, Ga-doping modulates the relative energy relationship of the four different polarization states, which enables the control of stable phases. 2.5 Piezoelectric Constants α-Al 2 S 3 was found to be a quite rare example of quadruple-well ferroelectrics. Its polarization is always oriented along the c axis in the MEP with four local energy minima. The four polar states ( \(\:\text{±}\) HP and \(\:\text{±}\) LP) can be distinguished by PFM if they have distinct piezoelectric constants. Here, we calculated the piezoelectric constants for the +HP and +LP states. Table 1 summarizes the piezoelectric stress constants ( e 33 ), elastic stiffness coefficients ( C 33 ), and piezoelectric constants ( d 33 ) for the + HP and + LP states. Their piezoelectric constants are comparable to that of pristine AlN (~5 pC/N) 30,31 . The piezoelectric constants of the LP and HP states are distinctly different so that these two states are distinguished for the c -plane cleaved single crystal samples by PFM, as in CuInP 2 S 6 25 . The four polar states can be detected by PFM since the positively and negatively polarized states show piezoresponse with opposite signs. Table 1 Piezoelectric stress constants ( e 33 ), elastic stiffness coefficients ( C 33 ), and piezoelectric constants ( d 33 ) for the + HP and + LP states of α-Al 2 S 3 . State e 33 (C/m 2 ) C 33 (GPa) d 33 (pC/N) +HP 0.654 90 7.3 +LP 0.246 65 3.8 3. Conclusions We unveiled an unusual ferroelectricity in a defective wurtzite α-Al 2 S 3 using first-principles calculations. α-Al 2 S 3 is predicted to be a rare example of quadruple-well ferroelectrics, which have four local energy minima in the MEPs. The intermediate lower-polarization states contain 5-fold coordinated AlS 5 trigonal bipyramids. The polarization switching barrier of α-Al 2 S 3 (51 meV/cation, 1.0 meV/Å 3 ) is one order of magnitude smaller than that of a typical wurtzite ferroelectric AlN. The Al vacancies alleviate electrostatic repulsion between Al atoms and bring into structural flexibility mitigating elastic energy penalty during the polarization switching. The bonding interactions between Al and S 3p z states play a role in stabilizing the AlS 5 bipyramidal coordination. Biaxial compressive strain and Ga-atom doping destabilize the intermediate lower-polarization structures, facilitating the polarization switching. In particular, 50% Ga substitution is predicted to reduce the switching barrier by about 40%. Our calculated piezoelectric constants revealed that PFM enables to distinguish the four polarized states. Overall, this study encourages the experimental investigation of an unconventional ferroelectric Al 2 S 3 as a new ferroelectric material promising for computing and data storage devices. Notably, the predicted quadruple-well potential surface as well as its fine tunability with chemical doping enables innovative devices such as a multi-valued high-density memory. This work also provides a new strategy for reducing the switching barrier in wurtzite ferroelectrics: introducing cation defects. 4. Method 4.1 Density functional theory calculations First-principles calculations were carried out based on density functional theory (DFT). We used the projector augmented-wave (PAW) method 32,33 and the GGA-PBEsol functional 34–36 as implemented in the Vienna Ab-initio Simulation Package (VASP 5.4.4) 37–40 . A plane-wave cutoff energy of 300 eV was used. The radial cutoffs of PAW data sets for Al, Ga, and S are of 1.4, 1.2, and 1.2 Å, respectively. Al 3s, 3p; Ga 3d, 4s, 4p; and S 3s, 3p states are treated as valence electrons. Γ-centered 3 × 3 × 2 k-point mesh sampling was employed. The lattice constants and internal coordinates were optimized until residual stress and forces converged to 0.01 GPa and 1 meV/Å, respectively. Born effective charge tensors and piezoelectric stress tensors were obtained by using density functional perturbation theory (DFPT) calculations. For DFPT calculations, a plane-wave cutoff energy of 600 eV and Γ-centered 6 × 6 × 4 k-point mesh sampling were used. 4.2 Minimum energy pathways First, the higher symmetry structure of α-Al 2 S 3 was searched using the spglib code 41 . The atomic displacements of the polar structure with respect to the higher symmetric structure were obtained using the STRUCTURE RELATIONS code in BCS 42–44 . By reversing the displacements, the polar structural models with polarization in the opposite direction were created. Structural relaxation was performed for the polar end structures. The intermediate images were generated by linear interpolation between the relaxed end structures. To represent a complicated pathway, we employed 32 intermediate images 11 . Solid-state nudged elastic band (SS-NEB) method 21 was employed to determine the switching pathways and barriers using VASP Transition State Theory (VTST) tools (VTST code-198) developed by Henkelman and Jonsson 45,46 except for the calculations under biaxial epitaxial strain. The polarization was calculated for each image using its structure and Born effective charges. The effects of Ga doping on the switching barriers were also examined. Ga-doped structures were thoroughly searched using the CLUPAN code 47 . As mentioned above, the polarization switching in α-Al 2 S 3 involves site exchange between the T1 and T2 sites. Depending on doped structural models, the initial structures are not equivalent to the final structures, leading to asymmetric MEPs. In this study, for simplicity, we chose the doped structural models for which the initial and final structures are equivalent to each other, and calculated MEPs by SS-NEB to obtain the switching barriers. We used the algorithm implemented in the pymatgen code 48 to check the consistence of the structures before and after the switching. Structural relaxation was performed for the obtained end structural models. After preparing initial pathways by the linear interpolation of the end structures, MEPs and switching barriers were calculated using SS-NEB methods. The number of data is 6 for x = 2 and 10; 15 for x = 4 and 8; and 14 for x = 6. To examine the strain dependence of the switching barriers, MEPs were also calculated under the constraint of fixed in-plane lattice constants using NEB methods implemented in the VASP code. We defined in-plane biaxial stain as s = ( a – a 0 )/ a 0 , where a 0 is the in-plane lattice constant of the unstrained α-Al 2 S 3 structure. The calculations were carried out within the s range from − 2 to 2%. Out-of-plane lattice constants and internal coordinates were optimized for the polar end structures of the switching pathways with fixed in-plane lattice constants. The initial pathways were created by the linear interpolation of the end structures. 4.3 Piezoelectric constants In this study, we focused on the diagonal component of piezoelectric (strain) constant, d 33 . The piezoelectric constants were derived from piezoelectric stress tensors and elastic constants according to the procedure described in Ref. 49 . We calculated elastic constants using the strain-energy relationship. In the Voigt notation, the elastic energy can be written as 50,51 $$\:E=\:\frac{1}{2}{\epsilon\:}_{p}{C}_{pq}{\epsilon\:}_{p}$$ 1 , where C pq is the elastic constants, and e p is the strain. Consider the point group 6 for α-Al 2 S 3 , the elastic constant matrix C is represented as 52 \(\:\left(\begin{array}{cccccc}{C}_{11}&\:{C}_{12}&\:{C}_{13}&\:0&\:0&\:0\\\:{C}_{12}&\:{C}_{11}&\:{C}_{13}&\:0&\:0&\:0\\\:{C}_{13}&\:{C}_{13}&\:{C}_{33}&\:0&\:0&\:0\\\:0&\:0&\:0&\:{C}_{44}&\:0&\:0\\\:0&\:0&\:0&\:0&\:{C}_{44}&\:0\\\:0&\:0&\:0&\:0&\:0&\:\frac{1}{2}\left({C}_{11}-{C}_{12}\right)\end{array}\right)\) ( 2 ). The strain tensor \(\:\epsilon\:=\left({\epsilon\:}_{1},\:{\epsilon\:}_{2},\:{\epsilon\:}_{3},\:{\epsilon\:}_{4},\:{\epsilon\:}_{5},\:{\epsilon\:}_{6}\right)\) is defined as \(\:\epsilon\:=\left(\begin{array}{ccc}{\epsilon\:}_{1}&\:\frac{{\epsilon\:}_{6}}{2}&\:\frac{{\epsilon\:}_{5}}{2}\\\:\frac{{\epsilon\:}_{6}}{2}&\:{\epsilon\:}_{2}&\:\frac{{\epsilon\:}_{4}}{2}\\\:\frac{{\epsilon\:}_{5}}{2}&\:\frac{{\epsilon\:}_{4}}{2}&\:{\epsilon\:}_{3}\end{array}\right)\) ( 3 ). By applying monoaxial strain \(\:\epsilon\:=\left(0,\:0,\:\delta\:,\:0,\:0,\:0\right)\) to the crystal, we obtained the elastic energy: \(\:E=\:\frac{1}{2}{C}_{33}{\delta\:}^{2}\) ( 4 ). Therefore, the elastic constants \(\:{C}_{33}\) was determined from total energies versus strain along the c axis. 4.4 Others We used the LOBSTER code to perform COHP analysis 53–57 . Bond valence was calculated using the bond valence parameters reported by Brese and O'Keeffe 58 . Phonon band structures were calculated using the PHONOPY code 59,60 . Space group symmetry was determined using the spglib code 41 . The VESTA code was used to visualize crystal structures 61 . ASSOCIATED CONTENT Declarations Supporting Information . The Supporting Information is available free of charge at the website. It includes calculated phonon band structures of α-Al 2 S 3 in the +HP and +LP states and changes in the area of the basal triangles involved with the Al1 and Al2 atoms and the lattice constants a and c during the polarization switching in α-Al 2 S 3 (PDF). An animation of structural evolution during the polarization switching of α-Al 2 S 3 is also available (MP4). AUTHOR CONTRIBUTIONS Y.S. conducted the calculations under the supervision of H.A. Y.S. and H.A. drafted the manuscript, and all authors edited it. ACKNOWLEDGMENT This research was supported by Japan Society of the Promotion of Science (JSPS) KAKENHI Grants Nos. JP17K19172, JP18H01892, JP19H00883, JP21K19027, JP21H05568, JP21H04619, JP23H02069, and JP23H01869. H.A. appreciates Murata Science Foundation and Collaborative Research Project of Laboratory for Materials and Structures, Institute of Innovative Research, Tokyo Institute of Technology. S.O. gratefully acknowledges the Toyota Riken for financial support through a Rising Fellow Program. The computation was carried out using the computer resource offered under the category of General Projects by Research Institute for Information Technology, Kyushu University. COMPETING INTERESTS The authors declare that they have no competing interests. DATA AVAILABILITY The datasets used and/or analysed during the current study available from the corresponding author on reasonable request. References Kishi, H., Mizuno, Y. & Chazono, H. Base-metal electrode-multilayer ceramic capacitors: Past, present and future perspectives. Japanese Journal of Applied Physics, Part 1: Regular Papers and Short Notes and Review Papers 42 , 1–5 (2003). Setter, N. et al. Ferroelectric thin films: Review of materials, properties, and applications. J Appl Phys 100 , 51606 (2006). Kohli, M. et al. Pyroelectric thin-film sensor array. Sens Actuators A Phys 60 , 147–153 (1997). Fichtner, S., Wolff, N., Lofink, F., Kienle, L. & Wagner, B. AlScN: A III-V semiconductor based ferroelectric. J Appl Phys 125 , 114103 (2019). Hayden, J. et al. Ferroelectricity in boron-substituted aluminum nitride thin films. Phys Rev Mater 5 , 044412 (2021). Wang, D., Wang, P., Wang, B. & Mi, Z. Fully epitaxial ferroelectric ScGaN grown on GaN by molecular beam epitaxy. Appl Phys Lett 119 , 111902 (2021). Ferri, K. et al. Ferroelectrics everywhere: Ferroelectricity in magnesium substituted zinc oxide thin films. J Appl Phys 130 , (2021). Wang, D. et al. Ferroelectric YAlN grown by molecular beam epitaxy. Appl Phys Lett 123 , (2023). Kim, K. H., Karpov, I., Olsson, R. H. & Jariwala, D. Wurtzite and fluorite ferroelectric materials for electronic memory. Nature Nanotechnology 2023 18:5 18 , 422–441 (2023). Moriwake, H. et al. A computational search for wurtzite-structured ferroelectrics with low coercive voltages. APL Mater 8 , 121102 (2020). Lee, C.-W. et al. Emerging Materials and Design Principles for Wurtzite-type Ferroelectrics. (2023) doi:10.26434/CHEMRXIV-2023-HF60W. Dai, Y. & Wu, M. Covalent-like bondings and abnormal formation of ferroelectric structures in binary ionic salts. Sci Adv 9 , (2023). Moriwake, H. et al. Ferroelectricity in wurtzite structure simple chalcogenide. Appl Phys Lett 104 , 242909 (2014). Konishi, A. et al. Mechanism of polarization switching in wurtzite-structured zinc oxide thin films. Appl Phys Lett 109 , 102903 (2016). Dreyer, C. E., Janotti, A., Van de Walle, C. G. & Vanderbilt, D. Correct implementation of polarization constants in wurtzite materials and impact on III-nitrides. Phys Rev X 6 , 021038 (2016). Liu, Z., Wang, X., Ma, X., Yang, Y. & Wu, D. Doping effects on the ferroelectric properties of wurtzite nitrides. Appl Phys Lett 122 , 122901 (2023). Noor-A-Alam, M., Olszewski, O. Z. & Nolan, M. Ferroelectricity and Large Piezoelectric Response of AlN/ScN Superlattice. ACS Appl Mater Interfaces 11 , 20482–20490 (2019). Lee, C.-W., Yazawa, K., Zakutayev, A., Brennecka, G. L. & Gorai, P. Switching it Up: New Mechanisms Revealed in Wurtzite-type Ferroelectrics. (2023) doi:10.26434/CHEMRXIV-2023-XDP95. Likforman, A., Carré, D., Hillel, R. & IUCr. Structure cristalline du séléniure d’indium In2Se3. urn:issn:0567-7408 34 , 1–5 (1978). Pfitzner, A. & Lutz, H. D. Redetermination of the Crystal Structure of γ-In2Se3by Twin Crystal X-Ray Method. J Solid State Chem 124 , 305–308 (1996). Sheppard, D., Xiao, P., Chemelewski, W., Johnson, D. D. & Henkelman, G. A generalized solid-state nudged elastic band method. Journal of Chemical Physics 136 , (2012). Eisenmann, B. Crystal structure of a-dialuminium trisulfide, Al2S3. Zeitschrift fur Kristallographie - New Crystal Structures 198 , 307–308 (1992). Krebs, B., Schiemann, A. & Läge, M. Synthese und Kristallstruktur einer Neuen hexagonalen Modifikation von Al2S3 mit fünffach koordiniertem Aluminium. Z Anorg Allg Chem 619 , 983–988 (1993). Baek, S. H. et al. Ferroelastic switching for nanoscale non-volatile magnetoelectric devices. Nature Materials 2010 9:4 9 , 309–314 (2010). Brehm, J. A. et al. Tunable quadruple-well ferroelectric van der Waals crystals. Nature Materials 2019 19:1 19 , 43–48 (2019). Sebastian Calderon, V. et al. Atomic-scale polarization switching in wurtzite ferroelectrics. Science (1979) 380 , 1034–1038 (2023). Clima, S. et al. Strain and ferroelectricity in wurtzite ScxAl1−xN materials. Appl Phys Lett 119 , 172905 (2021). Tomas, A., Pardo, M. P., Guittard, M., Guymont, M. & Famery, R. Determination des structures des formes α et β de Ga2S3 structural determination of α and β Ga2S3. Mater Res Bull 22 , 1549–1554 (1987). Shannon, R. D. Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides. Acta Crystallographica Section A 32 , 751–767 (1976). Lueng, C. M., Chan, H. L. W., Surya, C. & Choy, C. L. Piezoelectric coefficient of aluminum nitride and gallium nitride. J Appl Phys 88 , 5360–5363 (2000). Akiyama, M. et al. Enhancement of Piezoelectric Response in Scandium Aluminum Nitride Alloy Thin Films Prepared by Dual Reactive Cosputtering. Advanced Materials 21 , 593–596 (2009). Blöchl, P. E. Projector augmented-wave method. Phys Rev B 50 , 17953 (1994). Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys Rev B 59 , 1758 (1999). Perdew, J. P. et al. Restoring the density-gradient expansion for exchange in solids and surfaces. Phys Rev Lett 100 , 136406 (2008). Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized Gradient Approximation Made Simple [Phys. Rev. Lett. 77, 3865 (1996)]. Phys Rev Lett 78 , 1396 (1997). Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys Rev Lett 77 , 3865 (1996). Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys Rev B 54 , 11169 (1996). Kresse, G. & Hafner, J. Ab initio molecular dynamics for open-shell transition metals. Phys Rev B 48 , 13115 (1993). Kresse, G. & Hafner, J. Ab initio molecular dynamics for liquid metals. Phys Rev B 47 , 558 (1993). Kresse, G. & Furthmüller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput Mater Sci 6 , 15–50 (1996). Togo, A., Shinohara, K. & Tanaka, I. $\texttt{Spglib}$: a software library for crystal symmetry search. (2018). Aroyo, M. I. et al. Crystallography online: Bilbao crystallographic server. Bulgarian Chemical Communications 43 , 183–197 (2011). Aroyo, M. I. et al. Bilbao Crystallographic Server: I. Databases and crystallographic computing programs. Zeitschrift fur Kristallographie 221 , 15–27 (2006). Aroyo, M. I., Kirov, A., Capillas, C., Perez-Mato, J. M. & Wondratschek, H. Bilbao Crystallographic Server. II. Representations of crystallographic point groups and space groups. urn:issn:0108-7673 62 , 115–128 (2006). Henkelman, G., Uberuaga, B. P. & Jónsson, H. A climbing image nudged elastic band method for finding saddle points and minimum energy paths. J Chem Phys 113 , 9901–9904 (2000). Henkelman, G. & Jónsson, H. Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points. J Chem Phys 113 , 9978–9985 (2000). Seko, A., Koyama, Y. & Tanaka, I. Cluster expansion method for multicomponent systems based on optimal selection of structures for density-functional theory calculations. Phys Rev B Condens Matter Mater Phys 80 , 165122 (2009). Ong, S. P. et al. Python Materials Genomics (pymatgen): A robust, open-source python library for materials analysis. Comput Mater Sci 68 , 314–319 (2013). Wu, X., Vanderbilt, D. & Hamann, D. R. Systematic treatment of displacements, strains, and electric fields in density-functional perturbation theory. Phys Rev B 72 , 035105 (2005). Sarasamak, K., Limpijumnong, S. & Lambrecht, W. R. L. Pressure-dependent elastic constants and sound velocities of wurtzite SiC, GaN, InN, ZnO, and CdSe, and their relation to the high-pressure phase transition: A first-principles study. Phys Rev B Condens Matter Mater Phys 82 , 035201 (2010). Wright, A. F. Elastic properties of zinc-blende and wurtzite AlN, GaN, and InN. J Appl Phys 82 , 2833–2839 (1997). Newnham, R. E. Properties of Materials: Anisotropy, Symmetry, Structure. (2004) doi:10.1093/OSO/9780198520757.001.0001. Dronskowski, R. & Blöchl, P. E. Crystal orbital hamilton populations (COHP). Energy-resolved visualization of chemical bonding in solids based on density-functional calculations. Journal of Physical Chemistry 97 , 8617–8624 (1993). Deringer, V. L., Tchougréeff, A. L. & Dronskowski, R. Crystal orbital Hamilton population (COHP) analysis as projected from plane-wave basis sets. Journal of Physical Chemistry A 115 , 5461–5466 (2011). Maintz, S., Deringer, V. L., Tchougréeff, A. L. & Dronskowski, R. Analytic projection from plane-wave and PAW wavefunctions and application to chemical-bonding analysis in solids. J Comput Chem 34 , 2557–2567 (2013). Maintz, S., Deringer, V. L., Tchougréeff, A. L. & Dronskowski, R. LOBSTER: A tool to extract chemical bonding from plane-wave based DFT. J Comput Chem 37 , 1030–1035 (2016). Nelson, R. et al. LOBSTER: Local orbital projections, atomic charges, and chemical-bonding analysis from projector-augmented-wave-based density-functional theory. J Comput Chem 41 , 1931–1940 (2020). Brese, N. E. & O’Keeffe, M. Bond-valence parameters for solids. Acta Crystallographica Section B 47 , 192–197 (1991). Togo, A. First-principles Phonon Calculations with Phonopy and Phono3py. https://doi.org/10.7566/JPSJ.92.012001 92 , (2022). Togo, A., Chaput, L., Tadano, T. & Tanaka, I. Implementation strategies in phonopy and phono3py. Journal of Physics: Condensed Matter 35 , 353001 (2023). Momma, K. & Izumi, F. VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data. urn:issn:0021-8898 44 , 1272–1276 (2011). Additional Declarations (Not answered) Supplementary Files Al2S3switching.mp4 An animation of structural evolution during the polarization switching of α-Al2S3 Al2S3SIShimomuraetal.pdf Supplemental Material Cite Share Download PDF Status: Published Journal Publication published 17 Feb, 2025 Read the published version in npj Computational Materials → Version 1 posted Editorial decision: revise 03 Sep, 2024 Review # 2 received at journal 01 Sep, 2024 Review # 3 received at journal 01 Sep, 2024 Review # 1 received at journal 18 Aug, 2024 Reviewer # 3 agreed at journal 16 Aug, 2024 Reviewer # 2 agreed at journal 01 Aug, 2024 Reviewer # 1 agreed at journal 31 Jul, 2024 Reviewers invited by journal 27 Jul, 2024 Submission checks completed at journal 11 Jul, 2024 First submitted to journal 10 Jul, 2024 Unknown event 10 Jul, 2024 Editor assigned by journal 03 Jul, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4680101","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":332649817,"identity":"66de4238-2858-4951-91ac-fd5bf39420a1","order_by":0,"name":"Hirofumi Akamatsu","email":"data:image/png;base64,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","orcid":"","institution":"Kyushu University","correspondingAuthor":true,"prefix":"","firstName":"Hirofumi","middleName":"","lastName":"Akamatsu","suffix":""},{"id":332649818,"identity":"c9f04085-75ac-433c-8eb9-9b40920008dc","order_by":1,"name":"Yuto Shimomura","email":"","orcid":"","institution":"Kyushu University","correspondingAuthor":false,"prefix":"","firstName":"Yuto","middleName":"","lastName":"Shimomura","suffix":""},{"id":332649819,"identity":"f82cfcad-e554-47c5-8ad2-9d31189d0d49","order_by":2,"name":"Saneyuki Ohno","email":"","orcid":"","institution":"Tohoku Universuty","correspondingAuthor":false,"prefix":"","firstName":"Saneyuki","middleName":"","lastName":"Ohno","suffix":""},{"id":332649820,"identity":"e77f9236-d98a-4800-bbd3-bce866edca14","order_by":3,"name":"Katsuro Hayashi","email":"","orcid":"","institution":"Kyushu University","correspondingAuthor":false,"prefix":"","firstName":"Katsuro","middleName":"","lastName":"Hayashi","suffix":""}],"badges":[],"createdAt":"2024-07-03 11:35:26","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4680101/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4680101/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41524-025-01519-3","type":"published","date":"2025-02-17T05:00:00+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":63097831,"identity":"f5d55c2c-7727-40d8-b235-9ef03ab86bbd","added_by":"auto","created_at":"2024-08-23 06:14:49","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":616608,"visible":true,"origin":"","legend":"\u003cp\u003eCrystal structures of \u003cstrong\u003e(a, c)\u003c/strong\u003e cation-vacancy ordered wurtzite α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e with a γ-In\u003csub\u003e2\u003c/sub\u003eSe\u003csub\u003e3\u003c/sub\u003e-type structure (space group: \u003cem\u003eP\u003c/em\u003e6\u003csub\u003e1\u003c/sub\u003e) and \u003cstrong\u003e(b, d)\u003c/strong\u003e wurtzite ZnS (space group: \u003cem\u003eP\u003c/em\u003e6\u003csub\u003e3\u003c/sub\u003e\u003cem\u003emc\u003c/em\u003e).\u0026nbsp; The solid lines indicate unit cells. \u0026nbsp;The abbreviated illustrations of columns of coordination tetrahedra along the \u003cem\u003ec\u003c/em\u003e axis for \u003cstrong\u003e(e)\u003c/strong\u003e α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e and \u003cstrong\u003e(f)\u003c/strong\u003e ZnS.\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-4680101/v1/2e19ada871dd6d21029fa0dd.png"},{"id":63097835,"identity":"60c3654b-f8ff-4884-b9d1-487404c2882c","added_by":"auto","created_at":"2024-08-23 06:14:49","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":480083,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003e(a)\u003c/strong\u003e Calculated minimum energy pathway associated with polarization switching in α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e.\u0026nbsp; \u003cstrong\u003e(b)\u003c/strong\u003e Structural evolution during the polarization switching.\u0026nbsp; For simplicity, the columns of coordination tetrahedra along the \u003cem\u003ec\u003c/em\u003e axis are shown.\u0026nbsp; The gray-colored region indicates the Al vacancy sites.\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-4680101/v1/04acdd4cca8956b692fa4b7e.png"},{"id":63098257,"identity":"b440bcf8-1611-41c5-be7f-7ccad03a4c0c","added_by":"auto","created_at":"2024-08-23 06:22:49","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":518341,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic structures for (a) –HP, (b) –LP, (c) ZP, (d) +LP, and (e) +HP states.\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-4680101/v1/672218e577cb4bd61bd0490d.png"},{"id":63097833,"identity":"82cd876e-02d1-4435-a2ca-bc40b0af2199","added_by":"auto","created_at":"2024-08-23 06:14:49","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":2895045,"visible":true,"origin":"","legend":"\u003cp\u003eChemical bonding in α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e.\u0026nbsp; \u003cstrong\u003e(a)\u003c/strong\u003e Labeling of the S atoms surrounding the Al atom.\u0026nbsp; \u003cstrong\u003e(b)\u003c/strong\u003e BV sums and \u003cstrong\u003e(c)\u003c/strong\u003e –ICOHPs between the Al and S atoms for the Al1 and Al2 atoms in the ZP, +LP, and +HP states of α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e.\u0026nbsp; They are decomposed into the contributions from each bond.\u0026nbsp; –COHPs plotted as a function of energy for the Al2-S bonds in the \u003cstrong\u003e(d)\u003c/strong\u003e +LP and \u003cstrong\u003e(e)\u003c/strong\u003e +HP states.\u0026nbsp; They are decomposed into the contributions from axial and equatorial S atoms.\u0026nbsp; Real part of the wave function for the bonding state just below the Fermi levels in the \u003cstrong\u003e(f)\u003c/strong\u003e +LP and \u003cstrong\u003e(g)\u003c/strong\u003e +HP states.\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-4680101/v1/4a86ba55b258cf3df8bba8cf.png"},{"id":63097836,"identity":"7a46b713-a081-4c5f-9016-7a090c45c80b","added_by":"auto","created_at":"2024-08-23 06:14:49","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":525817,"visible":true,"origin":"","legend":"\u003cp\u003eSwitching barrier control by biaxial strain and chemical doping.\u003cstrong\u003e\u0026nbsp;\u0026nbsp; (a)\u003c/strong\u003e Total energy evolution in the MEPs of α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e under biaxial strain ranging from –2 to 2 %.\u0026nbsp; The highest total energies in each MEP are set to 0 meV/cation.\u0026nbsp; \u003cstrong\u003e(b)\u003c/strong\u003e Switching barriers plotted against biaxial strain.\u0026nbsp; \u003cstrong\u003e(c)\u003c/strong\u003e Total energy evolution in the MEPs for the representative structural models of Al\u003csub\u003e(12-x)/6\u003c/sub\u003eGa\u003csub\u003ex/6\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e with \u003cem\u003ex\u003c/em\u003e = 0, 2, 4, 6, 8, 10, and 12. \u0026nbsp;\u003cstrong\u003e(d)\u003c/strong\u003e Box plot of the switching barriers as a function of doping concentration \u003cem\u003ex\u003c/em\u003e.\u0026nbsp; The whiskers extend to the maximum and minimum data points.\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-4680101/v1/5110dc08198ba7fe3eb4d50c.png"},{"id":76539771,"identity":"0e0a26ef-0c6a-42e5-93a9-3a53b4089f90","added_by":"auto","created_at":"2025-02-18 08:09:48","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":7518293,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4680101/v1/ef38303c-5367-473c-a45d-702aa2b77e73.pdf"},{"id":63098256,"identity":"9b5cb177-91ae-4fb5-8894-fcdbaaf918be","added_by":"auto","created_at":"2024-08-23 06:22:49","extension":"mp4","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":1064522,"visible":true,"origin":"","legend":"An animation of structural evolution during the polarization switching of \u0026#x03B1;-Al2S3","description":"","filename":"Al2S3switching.mp4","url":"https://assets-eu.researchsquare.com/files/rs-4680101/v1/54a1fd01267ac2b466879805.mp4"},{"id":63097837,"identity":"9c989b87-e1a1-4c7e-a0a6-fb90ef72c48b","added_by":"auto","created_at":"2024-08-23 06:14:49","extension":"pdf","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":2469115,"visible":true,"origin":"","legend":"\u003cp\u003eSupplemental Material\u003c/p\u003e","description":"","filename":"Al2S3SIShimomuraetal.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4680101/v1/737da2b7b66979207606c462.pdf"}],"financialInterests":"(Not answered)","formattedTitle":"Quadruple-well ferroelectricity and moderate switching barrier in defective wurtzite α-Al2S3: a first-principles study","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eFerroelectric materials, characterized by electrically and/or mechanically switchable spontaneous polarization, are utilized in various devices such as piezoelectric actuators, pyroelectric sensors, and capacitors \u003csup\u003e1\u0026ndash;3\u003c/sup\u003e. Recently, wurtzite-type compounds have been attracting much attention. This class of materials was known to be piezoelectric and pyroelectric owing to their polar crystal structures with \u003cem\u003eP\u003c/em\u003e6\u003csub\u003e3\u003c/sub\u003e\u003cem\u003emc\u003c/em\u003e space group symmetry. The possible ferroelectricity of wurtzite-type compounds is highly promising for cutting-edge computing and data storage devices due to their high spontaneous polarization. However, their ferroelectricity was not observed prior to dielectric breakdown because of their high coercive fields until Fichtner \u003cem\u003eet al\u003c/em\u003e. clearly demonstrated ferroelectric switching for wurtzite-type Sc-doped AlN in 2019 \u003csup\u003e4\u003c/sup\u003e. Their work hinted at doping strategies that facilitate ferroelectric switching and ignited rapid progress in the exploration of wurtzite ferroelectrics. Consequently, ferroelectric switching has been reported for other doped wurtzite compounds such as Al\u003csub\u003e1-\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN, Ga\u003csub\u003e1-\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eSc\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN, Zn\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eMg\u003csub\u003e1-\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eO, and Al\u003csub\u003e1-\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eY\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN \u003csup\u003e5\u0026ndash;8\u003c/sup\u003e. However, their high coercive fields, close to breakdown electric fields, reduce device reliability \u003csup\u003e9,10\u003c/sup\u003e. To address this issue, considerable effort has been made to explore novel wurtzite compounds with lower switching barriers and substantial breakdown electric fields\u003csup\u003e10\u0026ndash;12\u003c/sup\u003e as well as to implement the doping strategy as mentioned above \u003csup\u003e4\u0026ndash;8\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eWurtzite structures consist of an hcp anion arrangement with cations occupying half of the 4-fold coordinated tetrahedral sites (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb and d). The filled tetrahedra are all oriented upwards (or all oriented downwards), sharing a vertex. It is commonly considered that upon ferroelectric switching in typical wurtzite-type compounds such as pristine AlN, all the cations move collectively from the upwards-oriented tetrahedra to neighboring downwards-oriented tetrahedra along the \u003cem\u003ec\u003c/em\u003e-axis direction by passing through anion basal triangles, which involves a bottleneck of switching \u003csup\u003e13\u0026ndash;15\u003c/sup\u003e. The saddle point of the minimum energy pathway (MEP) is a nonpolar hexagonal-boron nitride (h-BN)-like structure with space group symmetry of \u003cem\u003eP\u003c/em\u003e6\u003csub\u003e3\u003c/sub\u003e/\u003cem\u003emmc\u003c/em\u003e, in which all the cations locate at 5-fold coordinated trigonal bipyramidal sites \u003csup\u003e14\u003c/sup\u003e. Doping isovalent cations and applying biaxial tensile strain reduce the switching barriers by destabilizing the polar wurtzite structures and/or stabilizing the saddle-point h-BN-like structures to achieve switching prior to breakdown \u003csup\u003e16,17\u003c/sup\u003e. Recently, Lee \u003cem\u003eet al\u003c/em\u003e. reported a first-principles study suggesting that certain ternary wurtzite-type compounds containing two types of cations exhibit polarization switching not in a \"collective\" way via a h-BN-like structure, but in an \"individual\" or \"stepwise\" way via multiple local-minimum intermediate structures \u003csup\u003e18\u003c/sup\u003e, highlighting that avoiding the saddle-point h-BN-like structures enables those multinary wurtzite compounds to have low switching barriers.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eHere, we propose \u003cem\u003eintroducing cation vacancies\u003c/em\u003e as a potential strategy to lower the switching barriers through a first-principles study on the polarization switching in a defective wurtzite compound. γ-In\u003csub\u003e2\u003c/sub\u003eSe\u003csub\u003e3\u003c/sub\u003e is known as a cation-vacancy ordered wurtzite (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea and c) \u003csup\u003e19,20\u003c/sup\u003e. About 30 compounds with γ-In\u003csub\u003e2\u003c/sub\u003eSe\u003csub\u003e3\u003c/sub\u003e-type structures are registered in the Inorganic Crystal Structure Database (ICSD). In this study, we focus on α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e, which consists of the most abundant elements found in the γ-In\u003csub\u003e2\u003c/sub\u003eSe\u003csub\u003e3\u003c/sub\u003e-type compounds. Our first-principles calculations in conjunction with solid-state nudged elastic band (SS-NEB) methods\u003csup\u003e21\u003c/sup\u003e unveiled MEPs for polarization switching in α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e, which manifest itself as uniaxial quadruple-well potential curves with four local-minimum states. The intermediate local-minimum structures encompass 5-fold trigonal bipyramidal coordination. The calculated switching barrier is much lower than that of conventional wurtzite ferroelectrics. Detailed analysis of the evolution of the atomic arrangements and chemical bonding during the polarization switching indicates that the Al vacancies play important roles in yielding the unconventional quadruple-well ferroelectricity and the moderate switching barrier. Our calculations also predict that biaxial compressive strain and Ga doping enable the tunability of switching barriers. The calculated piezoelectric constants suggest that piezoresponse force microscopy (PFM) allows us to distinguish the four local-minimum states with different polarization values experimentally. This work showcases introducing cation vacancies as a potential route to lower the switching barriers in wurtzite ferroelectrics as well as predicts the unconventional ferroelectricity in α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e.\u003c/p\u003e"},{"header":"2. Result and Discussion","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Crystal Structure of α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e and Polarization Switching Behavior\u003c/h2\u003e \u003cp\u003eThe crystal structures of cation-vacancy ordered wurtzite α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e and conventional wurtzite ZnS are summarized in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e shows a polar and chiral \u003cem\u003eP\u003c/em\u003e6\u003csub\u003e1\u003c/sub\u003e space group symmetry. Two-thirds of the tetrahedral sites in wurtzite-type structures are occupied by the Al atoms, while the remaining one-third are vacant \u003csup\u003e22,23\u003c/sup\u003e. In contrast to conventional wurtzite-type compounds, α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e has two kinds of crystallographically inequivalent cation sites, both of which are located at Wyckoff positions 6a. These sites can be readily distinguished based on the position of the nearest-neighbor Al vacant sites, i.e., whether it locates either in the sulfur vertex or basal-triangle side along the \u003cem\u003ec\u003c/em\u003e axis. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ee and f extract a column of the coordination tetrahedra along the \u003cem\u003ec\u003c/em\u003e axis from the whole structure of α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e and ZnS, respectively. Hereafter, the tetrahedral sites with a nearest-neighbor vacant site in the vertex or basal-triangle side are referred to as T1 and T2, respectively. The suffixes \"u\" and \"d\" indicate the upwards-oriented or downwards-oriented tetrahedra, respectively.\u003c/p\u003e \u003cp\u003eThe calculated lattice constants (\u003cem\u003ea\u003c/em\u003e\u0026thinsp;=\u0026thinsp;6.41 \u0026Aring;, \u003cem\u003ec\u003c/em\u003e\u0026thinsp;=\u0026thinsp;17.80 \u0026Aring;) for α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e are in good agreement with the experimental ones (\u003cem\u003ea\u003c/em\u003e\u0026thinsp;=\u0026thinsp;6.44 \u0026Aring;, \u003cem\u003ec\u003c/em\u003e\u0026thinsp;=\u0026thinsp;17.90 \u0026Aring;) \u003csup\u003e23\u003c/sup\u003e, substantiating that the GGA-PBEsol functional used in this study well reproduces crystal structures. The calculated electric polarization of α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e, 66 \u0026micro;C/cm\u003csup\u003e2\u003c/sup\u003e, is comparable to or smaller than those of wurtzite ferroelectrics (e.g., 65 and 135 \u0026micro;C/cm\u003csup\u003e2\u003c/sup\u003e for ZnS and AlN, respectively) \u003csup\u003e13,15\u003c/sup\u003e. An MEP between the two oppositely polarized states with all the tetrahedra oriented upwards or downwards was calculated by using SS-NEB methods to elucidate the switching barrier and behavior (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea). Interestingly, α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e has four local energy minima in the MEP, referred to as +\u0026thinsp;HP, +LP, \u0026ndash;LP, and \u0026ndash;HP in the order of the magnitude of polarization. Here, the states with high, low, and zero absolute polarization values are denoted as HP, LP, and ZP, respectively, and the prefix \"+\" and \"\u0026ndash;\" symbols indicate positive and negative polarization values, respectively. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e illustrates these five structures providing the local energy minima and the saddle point. (An animation of the structural evolution associated with the switching is available in the Supporting Information and would help to understand the switching behavior.) Both +\u0026thinsp;HP and +\u0026thinsp;LP states possess \u003cem\u003eP\u003c/em\u003e6\u003csub\u003e1\u003c/sub\u003e space group symmetry. The \u003cem\u003eP\u003c/em\u003e6\u003csub\u003e1\u003c/sub\u003e symmetry is preserved during the switching pathway, except in the saddle-point ZP state, which has zero polarization and nonpolar \u003cem\u003eP\u003c/em\u003e6\u003csub\u003e1\u003c/sub\u003e22 symmetry. The 6\u003csub\u003e1\u003c/sub\u003e symmetry element is preserved during the entire polarization switching process, indicating that the polarization direction remains along the \u003cem\u003ec\u003c/em\u003e axis. In contrast to quadruple-well ferroelectrics such as BiFeO\u003csub\u003e3\u003c/sub\u003e, which have multiple independent polarization axes \u003csup\u003e24\u003c/sup\u003e, the four local-minimum states in the MEP of α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e are polarized along the \u003cem\u003ec\u003c/em\u003e axis, revealing that α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e is an unusual ferroelectric with a uniaxial quadruple-well potential as observed in CuInP\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e6\u003c/sub\u003e \u003csup\u003e25\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb illustrates the structural evolution of α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e during the polarization switching as the columns of coordination tetrahedra along the \u003cem\u003ec\u003c/em\u003e axis for simplicity. All the six columns included in the unit cell are related to each other by the 6\u003csub\u003e1\u003c/sub\u003e symmetry operation, which is preserved during the polarization switching. The atomic displacement in the column reflects the entire polarization switching process. In the initial high-polarization\u0026thinsp;+\u0026thinsp;HP state, the two inequivalent Al atoms, denoted as Al1 and Al2, occupy the T1u and T2u sites, respectively, enclosed by the upwards-oriented tetrahedra. Beyond a small potential hill, there emerges the +\u0026thinsp;LP state with lower total energy and polarization (+\u0026thinsp;30 \u0026micro;C/cm\u003csup\u003e2\u003c/sup\u003e), where the Al1 atoms occupy the T1u sites whereas the Al2 atoms occupy 5-fold coordinated bipyramidal sites, referred to as B1 sites. In the structural evolution from the +\u0026thinsp;HP to +\u0026thinsp;LP states, the Al2 atoms move from the T2u sites towards the vacant sites and migrate to the bipyramidal B1 sites, whereas the Al1 atoms remain at the T1u sites. Upon transitioning from the +\u0026thinsp;LP to ZP states, the Al2 atoms move from the bipyramidal B1 sites to the T1d sites in the downward-oriented tetrahedra, whereas the Al1 atoms still remain at the T1u sites, resulting in a half-switched state where half of the tetrahedra and the other half are oriented upward and downward with the polarization canceled out.\u003c/p\u003e \u003cp\u003eIn the latter half of polarization switching from the ZP state to the \u0026ndash;LP state to the final \u0026ndash;HP state, the Al1 atoms at the T1u sites migrate to the T2d sites via the bipyramidal B2 sites. It should be noted that the Al1 (Al2) atoms sitting at the T1u (T2u) sites in the initial\u0026thinsp;+\u0026thinsp;HP state occupy the T2d (T1d) sites in the final \u0026ndash;HP states, indicating the swapping of the crystallographically inequivalent sites during the polarization switching between the T1 and T2 sites. This highlights the nonconventional ferroelectricity of α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e.\u003c/p\u003e \u003cp\u003eOur first-principles phonon calculation revealed that both the HP and LP states were dynamically stable (Figure \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e and S2). Notably, Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e with the LP structure has been synthesized by chemical vapor transport \u003csup\u003e23\u003c/sup\u003e, while solid-state reaction methods yield α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e, which adopts the HP structure. These facts imply that these isosymmetric polymorphs are energetically antagonized at room temperature or above, although our first-principles calculations predict that the LP state is more stable than the HP state at 0 K.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Comparison of Switching Behavior and Barriers in Wurtzite Compounds\u003c/h2\u003e \u003cp\u003eIn this study, the switching barriers for quadruple-well potential surfaces are defined as the highest energy barrier between a valley and its neighboring peak towards the switching direction \u003csup\u003e18\u003c/sup\u003e. The switching barrier of α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e corresponds to the total energy difference between the LP and ZP states. The switching barrier of α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e, 51 meV/cation, is approximately one-tenth that of AlN (523 meV/cation) and one-third that of Al\u003csub\u003e15/16\u003c/sub\u003eB\u003csub\u003e1/16\u003c/sub\u003eN (150 meV/cation) \u003csup\u003e26\u003c/sup\u003e. The moderate switching barrier is anticipated to enable polarization switching prior to electric breakdown. We compare the switching behavior in α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e and other wurtzite ferroelectrics to understand the moderate switching barrier in α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e below.\u003c/p\u003e \u003cp\u003eIn the binary wurtzite ferroelectrics such as pristine AlN, all the cations displace collectively from the upwards-oriented to the downwards-oriented tetrahedra during polarization switching \u003csup\u003e12,14\u003c/sup\u003e. In ternary wurtzite systems such as Li\u003csub\u003e2\u003c/sub\u003eSiO\u003csub\u003e3\u003c/sub\u003e, for which two-step polarization switching has been predicted by first-principles calculations, more electronegative atoms move first, followed by the migration of less electronegative atoms, with the first switching barrier being the highest \u003csup\u003e18\u003c/sup\u003e. In contrast to these cases, in α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e, consisting of only one type of cations, the Al atoms situated at the crystallographically different sites exhibit individual motion; the Al2 atoms exhibit displacement preceding that of the Al1 atoms, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb, predominantly because the Al2 atoms can displace towards the vacancy sites apart from the Al1 atoms, thereby mitigating cation-cation electrostatic repulsion.\u003c/p\u003e \u003cp\u003eIn the saddle-point structures for MEPs in binary and ternary wurtzite-type compounds, cations locate at the trigonal bipyramidal sites \u003csup\u003e10,12,26\u003c/sup\u003e. The basal triangles of the bipyramids do not offer enough space for accommodating the cations, resulting in the expansion of the anion triangles. The resultant in-plane lattice expansion destabilizes the saddle-point structures. In sharp contrast, α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e has the lowest total energy when half of the Al atoms locate at the bipyramidal sites (i.e., the LP states), highlighting the switching behavior quite different from that for other wurtzite ferroelectrics. Upon transitioning from the +\u0026thinsp;HP to +\u0026thinsp;LP states, the Al2 atoms move to the center of S triangles, accompanying an expansion of the triangle (See Figure S3). In conventional wurtzite ferroelectrics, such triangle expansion increases the in-plane lattice constants typically by 5% \u003csup\u003e14,16\u003c/sup\u003e, destabilizing the h-BN-like saddle-point structures. In α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e, the in-plane lattice constant for the LP state is only 1% larger than that of the HP state (See Figure S4). Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb and d depict the LP structure, in which the AlS\u003csub\u003e5\u003c/sub\u003e and AlS\u003csub\u003e4\u003c/sub\u003e polyhedra tilt with respect to the \u003cem\u003ec\u003c/em\u003e axis, resulting in the buckling of close-packed sulfur basal planes, i.e., non-flat sulfur basal planes. The buckling alleviates the in-plane lattice expansion. In conventional wurtzite-type compounds, four anion tetrahedra are connected to each other via an S atom, \"locking\" the anion polyhedral network. Meanwhile, in α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e, just two or three tetrahedra are connected to each other due to the Al vacancies, leading to a flexibility of the polyhedral network.\u003c/p\u003e \u003cp\u003eThus, in contrast to conventional wurtzite-type ferroelectrics, the cation vacancies mitigate the electrostatic repulsion between cations in α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb). Also, the disconnection of polyhedral network induced by the Al vacancies produces structural flexibility alleviating the in-plane lattice expansion. These features are considered as the primary reasons why the switching barrier of the defective wurtzite α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e is much smaller than those of \"filled\" wurtzite-type compounds.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3 Stabilization Mechanism of AlS\u003csub\u003e5\u003c/sub\u003e Trigonal Bipyramidal Coordination\u003c/h2\u003e \u003cp\u003eWe have discussed above how the Al vacancies stabilize the intermediate structures including the LP states from the structural aspects. The half of Al atoms occupy the trigonal bipyramidal sites in the most stable intermediate LP structures for α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e, whereas, in binary and ternary wurtzite ferroelectrics, cations occupy the trigonal bipyramidal sites in the unstable saddle-point structures. It remains unclear why the LP states are stable in α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e from the viewpoint of chemical bonding. To elucidate the underlying stabilization mechanism of the AlS\u003csub\u003e5\u003c/sub\u003e bipyramids in terms of chemical bonding, bond valence (BV) and crystal orbital Hamilton population (COHP) between the Al and S atoms were calculated. Here, BV and COHP describe the strength of chemical bonding based on the bond length and the interactions between atomic orbitals, respectively. The negative and positive values of COHP indicate bonding and antibonding interactions, respectively. We utilize negative COHP (\u0026ndash;COHP) integrated with respect to energy (\u0026ndash;ICOHP) within the valence bands, which indicates the magnitude of net energy gain due to bonding and anti-bonding interactions. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea labels the S atoms composing of AlS\u003csub\u003e4\u003c/sub\u003e tetrahedra or AlS\u003csub\u003e5\u003c/sub\u003e bipyramids as follows: the axial S atoms located at the +\u0026thinsp;\u003cem\u003ec\u003c/em\u003e and \u0026ndash;\u003cem\u003ec\u003c/em\u003e sides with respect to the Al atoms as ax1 and ax2, respectively, and the equatorial S atoms composing of basal triangles as Eq.\u0026nbsp;\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, Eq.\u0026nbsp;2, and Eq.\u0026nbsp;3. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb and c present the BVs and \u0026ndash;ICOHP, respectively, for the Al1 and Al2 atoms against the S atoms for the ZP, +LP, and +\u0026thinsp;HP states.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTransitioning from the +\u0026thinsp;HP to +\u0026thinsp;LP states, the Al2 atoms migrate from the tetrahedral T2u sites to the bipyramidal B1 sites (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb), as described above. In the +\u0026thinsp;HP state, the BV sums and \u0026ndash;ICOHP of both Al1 and Al2 atoms are primarily contributed to by four S atoms, ax1, Eq.\u0026nbsp;\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, Eq.\u0026nbsp;2, and Eq.\u0026nbsp;3, with minimal contribution from ax2, confirming 4-fold tetragonal coordination (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb and c). In contrast, in the +\u0026thinsp;LP state, the BV sum and \u0026ndash;ICOHP of Al2 atom are significantly contributed to by the five S atoms, corroborating 5-fold coordination rather than 3-fold coordination.\u003c/p\u003e \u003cp\u003eLet us pay attention to the chemical bonding evolution for the Al2 atoms, as it is crucial to understand the stabilization mechanism of the +\u0026thinsp;LP state. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb reveals that the BV sum of the Al2 atoms is significantly smaller for the +\u0026thinsp;LP state than for the +\u0026thinsp;HP state, indicating that the ionic bonding between Al2 and S atoms become weaker upon transitioning from the +\u0026thinsp;HP to +\u0026thinsp;LP states. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ec, however, the sum of \u0026ndash;ICOHP for the Al2 atom is comparable in the +\u0026thinsp;LP and +\u0026thinsp;HP states, revealing that the energy gain due to covalent bonding remains upon the structural evolution. This motivates us to unravel the Al2-S covalent bonding that compensates for the poor ionic bonding in more detail.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ed and e depict the \u0026ndash;COHP for the Al2-S bonds as a function of energy in the +\u0026thinsp;LP and +\u0026thinsp;HP states, respectively. A remarkable difference is seen just below the Fermi level; the axial and equatorial S atoms show bonding and antibonding contributions, respectively, in the energy range from \u0026minus;\u0026thinsp;1 to 0 eV for the +\u0026thinsp;LP state, yielding a net bonding contribution, whereas negligible \u0026ndash;COHP is found in this energy range for the +\u0026thinsp;HP state, indicating no bonding contribution. This remarkable difference is considered as a major factor stabilizing the LP states. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ef and g illustrate the wavefunctions of eigenstates just below the Fermi level for the +\u0026thinsp;LP and +\u0026thinsp;HP states, respectively, both of which mainly consist of S 3p\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e orbitals. In the eigenstate of the +\u0026thinsp;LP state, the 3p\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e orbitals of the ax2 S atoms elongate towards the Al2 atoms to overlap with the Al2 3p\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e orbitals, clearly indicating a s-like bonding interaction between these orbitals. Meanwhile, the S 3p\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e orbitals of the ax2 S atoms are localized and nonbonding in the eigenstate for the +\u0026thinsp;HP state. The ax2 S atoms are 2-fold coordinated by Al atoms in the +\u0026thinsp;HP state, rendering one of the 3p orbitals nonbonding. The Al2 displacements to the bipyramidal sites yield an additional Al coordination to the ax2 S atoms, causing the ax2 S 3p\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e orbitals to take part in the bonding states with the Al 3p\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e states. The formation of the bonding states in the LP states is considered as another factor stabilizing the LP state with respect to the HP state.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e2.4 Effects of Epitaxial Strain and Chemical Doping on Switching Barriers\u003c/h2\u003e \u003cp\u003eFor wurtzite ferroelectrics, lowering the switching barrier is a key priority for wider practical applications. It has been demonstrated that epitaxial biaxial strain and chemical doping lower the switching barriers for ZnO and AlN by theory and experiments \u003csup\u003e16,17,27\u003c/sup\u003e. Here, the effects of biaxial strain and chemical doping on MEPs are investigated for Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e to give insights into the experimental control of ferroelectric switching.\u003c/p\u003e \u003cp\u003eThe reduction of switching barrier in α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e requires the stabilization of the ZP states and/or the destabilization of the LP states. Without the constraint of strain, the in-plane lattice constant of the LP state is larger than that of the ZP state, as shown in Figure S4, implying that the MEP can be controlled by harnessing biaxial strain. Figure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ea shows calculated MEPs under biaxial strain. The total energies of the LP states become higher with respect to those of the ZP states under compressive (negative) biaxial strain, which is consistent with the in-plane lattice constant of the LP state larger than that of the ZP state (Figure S4). Figure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eb shows the switching barriers under strain, which correspond to the total energy difference between the LP and ZP states. The switching barriers decrease by 8.5% with 2% compressive strain. The biaxial strain dependence of switching barriers for α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e is contrary to that for wurtzite ferroelectrics such as ZnO and AlN, where the switching barriers are reduced by tensile biaxial strain \u003csup\u003e14\u003c/sup\u003e. This is because the in-plane lattice constant decreases in α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e and increases in typical wurtzite ferroelectrics when climbing the potential hills for the polarization switching.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eNext, we consider the chemical doping effects on the switching barriers. It has been reported that the switching barrier is successfully reduced for AlN by doping B atoms, which favor planar triangle coordination. It is not likely that B-atom doping helps lower the switching barrier for α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e, because it can stabilize the LP states with trigonal bipyramidal coordination. Here, we focus on doping of Ga atoms. Ga is considered as a prime candidate for the following three reasons; (\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e) Ga atoms are isovalent to Al. (\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e) α-Ga\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e adopts γ-In\u003csub\u003e2\u003c/sub\u003eSe\u003csub\u003e3\u003c/sub\u003e structure similarly to α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e \u003csup\u003e28\u003c/sup\u003e. (\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e) The ionic radius of Ga\u003csup\u003e3+\u003c/sup\u003e is bigger than that of Al\u003csup\u003e3+\u003c/sup\u003e. The cation-anion radius ratio of Al to S (\u003cem\u003er\u003c/em\u003e\u003csub\u003eAl\u003c/sub\u003e/\u003cem\u003er\u003c/em\u003e\u003csub\u003eS\u003c/sub\u003e = 0.212) is less than 0.225, which is the minimum value for 4-fold tetrahedral coordination according to the Pauling's third rule. Meanwhile, \u003cem\u003er\u003c/em\u003e\u003csub\u003eGa\u003c/sub\u003e/\u003cem\u003er\u003c/em\u003e\u003csub\u003eS\u003c/sub\u003e is 0.255, indicating that Ga atoms favor tetrahedral coordination of S atoms \u003csup\u003e29\u003c/sup\u003e. It is expected from these facts that Ga-doping stabilize the ZP and HP states and destabilize the LP states, reducing the switching barrier.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ec shows the MEPs for representative structural models of Al\u003csub\u003e(12-x)/6\u003c/sub\u003eGa\u003csub\u003ex/6\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e with \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0, 2, 4, 6, 8, 10, 12. An increase in \u003cem\u003ex\u003c/em\u003e stabilizes the ZP and HP states with respect to the LP states, as expected. In the low-\u003cem\u003ex\u003c/em\u003e range (0 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{\u0026le;}\\)\u003c/span\u003e\u003c/span\u003e \u003cem\u003ex\u003c/em\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{\u0026le;}\\)\u003c/span\u003e\u003c/span\u003e 6), the pathway from the +LP to ZP to \u0026ndash;LP states corresponds to the highest potential hill, whereas, in the high-\u003cem\u003ex\u003c/em\u003e range (6 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{\u0026le;}\\)\u003c/span\u003e\u003c/span\u003e \u003cem\u003ex\u003c/em\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{\u0026le;}\\)\u003c/span\u003e\u003c/span\u003e 12), the +HP-+LP pathway includes the highest potential hill. Figure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ed shows the box-and-whisker plot of the switching barriers against doping concentration \u003cem\u003ex\u003c/em\u003e in Al\u003csub\u003e(12-\u003cem\u003ex\u003c/em\u003e)/6\u003c/sub\u003eGa\u003csub\u003e\u003cem\u003ex\u003c/em\u003e/6\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e. The switching barrier decreases with an increase in \u003cem\u003ex\u003c/em\u003e, and shows a minimum at \u003cem\u003ex\u003c/em\u003e = 6, followed by an increase in the barrier above \u003cem\u003ex\u003c/em\u003e = 6. The barrier is about 40% smaller for \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;6 compared to pristine α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e. Thus, our calculations predict that Ga-doping facilitates the polarization switching for α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e. Furthermore, Ga-doping modulates the relative energy relationship of the four different polarization states, which enables the control of stable phases.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e2.5 Piezoelectric Constants\u003c/h2\u003e \u003cp\u003eα-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e was found to be a quite rare example of quadruple-well ferroelectrics. Its polarization is always oriented along the \u003cem\u003ec\u003c/em\u003e axis in the MEP with four local energy minima. The four polar states (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{\u0026plusmn;}\\)\u003c/span\u003e\u003c/span\u003eHP and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{\u0026plusmn;}\\)\u003c/span\u003e\u003c/span\u003eLP) can be distinguished by PFM if they have distinct piezoelectric constants. Here, we calculated the piezoelectric constants for the +HP and +LP states. Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e summarizes the piezoelectric stress constants (\u003cem\u003ee\u003c/em\u003e\u003csub\u003e33\u003c/sub\u003e), elastic stiffness coefficients (\u003cem\u003eC\u003c/em\u003e\u003csub\u003e33\u003c/sub\u003e), and piezoelectric constants (\u003cem\u003ed\u003c/em\u003e\u003csub\u003e33\u003c/sub\u003e) for the +\u0026thinsp;HP and +\u0026thinsp;LP states. Their piezoelectric constants are comparable to that of pristine AlN (~5 pC/N) \u003csup\u003e30,31\u003c/sup\u003e. The piezoelectric constants of the LP and HP states are distinctly different so that these two states are distinguished for the \u003cem\u003ec\u003c/em\u003e-plane cleaved single crystal samples by PFM, as in CuInP\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e6\u003c/sub\u003e \u003csup\u003e25\u003c/sup\u003e. The four polar states can be detected by PFM since the positively and negatively polarized states show piezoresponse with opposite signs.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003ePiezoelectric stress constants (\u003cem\u003ee\u003c/em\u003e\u003csub\u003e33\u003c/sub\u003e), elastic stiffness coefficients (\u003cem\u003eC\u003c/em\u003e\u003csub\u003e33\u003c/sub\u003e), and piezoelectric constants (\u003cem\u003ed\u003c/em\u003e\u003csub\u003e33\u003c/sub\u003e) for the +\u0026thinsp;HP and +\u0026thinsp;LP states of α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eState\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003ee\u003c/em\u003e\u003csub\u003e33\u003c/sub\u003e (C/m\u003csup\u003e2\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eC\u003c/em\u003e\u003csub\u003e33\u003c/sub\u003e (GPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003ed\u003c/em\u003e\u003csub\u003e33\u003c/sub\u003e (pC/N)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e+HP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.654\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7.3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e+LP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.246\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e65\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3.8\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"3. Conclusions","content":"\u003cp\u003eWe unveiled an unusual ferroelectricity in a defective wurtzite α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e using first-principles calculations. α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e is predicted to be a rare example of quadruple-well ferroelectrics, which have four local energy minima in the MEPs. The intermediate lower-polarization states contain 5-fold coordinated AlS\u003csub\u003e5\u003c/sub\u003e trigonal bipyramids. The polarization switching barrier of α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e (51 meV/cation, 1.0 meV/\u0026Aring;\u003csup\u003e3\u003c/sup\u003e) is one order of magnitude smaller than that of a typical wurtzite ferroelectric AlN. The Al vacancies alleviate electrostatic repulsion between Al atoms and bring into structural flexibility mitigating elastic energy penalty during the polarization switching. The bonding interactions between Al and S 3p\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e states play a role in stabilizing the AlS\u003csub\u003e5\u003c/sub\u003e bipyramidal coordination. Biaxial compressive strain and Ga-atom doping destabilize the intermediate lower-polarization structures, facilitating the polarization switching. In particular, 50% Ga substitution is predicted to reduce the switching barrier by about 40%. Our calculated piezoelectric constants revealed that PFM enables to distinguish the four polarized states. Overall, this study encourages the experimental investigation of an unconventional ferroelectric Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e as a new ferroelectric material promising for computing and data storage devices. Notably, the predicted quadruple-well potential surface as well as its fine tunability with chemical doping enables innovative devices such as a multi-valued high-density memory. This work also provides a new strategy for reducing the switching barrier in wurtzite ferroelectrics: introducing cation defects.\u003c/p\u003e"},{"header":"4. Method","content":"\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e4.1 Density functional theory calculations\u003c/h2\u003e \u003cp\u003eFirst-principles calculations were carried out based on density functional theory (DFT). We used the projector augmented-wave (PAW) method\u003csup\u003e32,33\u003c/sup\u003e and the GGA-PBEsol functional\u003csup\u003e34\u0026ndash;36\u003c/sup\u003e as implemented in the Vienna Ab-initio Simulation Package (VASP 5.4.4) \u003csup\u003e37\u0026ndash;40\u003c/sup\u003e. A plane-wave cutoff energy of 300 eV was used. The radial cutoffs of PAW data sets for Al, Ga, and S are of 1.4, 1.2, and 1.2 \u0026Aring;, respectively. Al 3s, 3p; Ga 3d, 4s, 4p; and S 3s, 3p states are treated as valence electrons. Γ-centered 3 \u0026times; 3 \u0026times; 2 k-point mesh sampling was employed. The lattice constants and internal coordinates were optimized until residual stress and forces converged to 0.01 GPa and 1 meV/\u0026Aring;, respectively. Born effective charge tensors and piezoelectric stress tensors were obtained by using density functional perturbation theory (DFPT) calculations. For DFPT calculations, a plane-wave cutoff energy of 600 eV and Γ-centered 6 \u0026times; 6 \u0026times; 4 k-point mesh sampling were used.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e4.2 Minimum energy pathways\u003c/h2\u003e \u003cp\u003eFirst, the higher symmetry structure of α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e was searched using the spglib code \u003csup\u003e41\u003c/sup\u003e. The atomic displacements of the polar structure with respect to the higher symmetric structure were obtained using the STRUCTURE RELATIONS code in BCS \u003csup\u003e42\u0026ndash;44\u003c/sup\u003e. By reversing the displacements, the polar structural models with polarization in the opposite direction were created. Structural relaxation was performed for the polar end structures. The intermediate images were generated by linear interpolation between the relaxed end structures. To represent a complicated pathway, we employed 32 intermediate images \u003csup\u003e11\u003c/sup\u003e. Solid-state nudged elastic band (SS-NEB) method\u003csup\u003e21\u003c/sup\u003e was employed to determine the switching pathways and barriers using VASP Transition State Theory (VTST) tools (VTST code-198) developed by Henkelman and Jonsson\u003csup\u003e45,46\u003c/sup\u003e except for the calculations under biaxial epitaxial strain. The polarization was calculated for each image using its structure and Born effective charges.\u003c/p\u003e \u003cp\u003eThe effects of Ga doping on the switching barriers were also examined. Ga-doped structures were thoroughly searched using the CLUPAN code \u003csup\u003e47\u003c/sup\u003e. As mentioned above, the polarization switching in α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e involves site exchange between the T1 and T2 sites. Depending on doped structural models, the initial structures are not equivalent to the final structures, leading to asymmetric MEPs. In this study, for simplicity, we chose the doped structural models for which the initial and final structures are equivalent to each other, and calculated MEPs by SS-NEB to obtain the switching barriers. We used the algorithm implemented in the pymatgen code\u003csup\u003e48\u003c/sup\u003e to check the consistence of the structures before and after the switching. Structural relaxation was performed for the obtained end structural models. After preparing initial pathways by the linear interpolation of the end structures, MEPs and switching barriers were calculated using SS-NEB methods. The number of data is 6 for \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2 and 10; 15 for \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;4 and 8; and 14 for \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;6.\u003c/p\u003e \u003cp\u003eTo examine the strain dependence of the switching barriers, MEPs were also calculated under the constraint of fixed in-plane lattice constants using NEB methods implemented in the VASP code. We defined in-plane biaxial stain as \u003cem\u003es\u003c/em\u003e = (\u003cem\u003ea\u003c/em\u003e \u0026ndash; \u003cem\u003ea\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e)/\u003cem\u003ea\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e, where \u003cem\u003ea\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e is the in-plane lattice constant of the unstrained α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e structure. The calculations were carried out within the \u003cem\u003es\u003c/em\u003e range from \u0026minus;\u0026thinsp;2 to 2%. Out-of-plane lattice constants and internal coordinates were optimized for the polar end structures of the switching pathways with fixed in-plane lattice constants. The initial pathways were created by the linear interpolation of the end structures.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e4.3 Piezoelectric constants\u003c/h2\u003e \u003cp\u003eIn this study, we focused on the diagonal component of piezoelectric (strain) constant, \u003cem\u003ed\u003c/em\u003e\u003csub\u003e33\u003c/sub\u003e. The piezoelectric constants were derived from piezoelectric stress tensors and elastic constants according to the procedure described in Ref. \u003csup\u003e49\u003c/sup\u003e. We calculated elastic constants using the strain-energy relationship. In the Voigt notation, the elastic energy can be written as \u003csup\u003e50,51\u003c/sup\u003e\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:E=\\:\\frac{1}{2}{\\epsilon\\:}_{p}{C}_{pq}{\\epsilon\\:}_{p}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e,\u003c/p\u003e \u003cp\u003ewhere \u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003epq\u003c/em\u003e\u003c/sub\u003e is the elastic constants, and \u003cem\u003ee\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e is the strain. Consider the point group 6 for α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e, the elastic constant matrix \u003cem\u003eC\u003c/em\u003e is represented as \u003csup\u003e52\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:\\left(\\begin{array}{cccccc}{C}_{11}\u0026amp;\\:{C}_{12}\u0026amp;\\:{C}_{13}\u0026amp;\\:0\u0026amp;\\:0\u0026amp;\\:0\\\\\\:{C}_{12}\u0026amp;\\:{C}_{11}\u0026amp;\\:{C}_{13}\u0026amp;\\:0\u0026amp;\\:0\u0026amp;\\:0\\\\\\:{C}_{13}\u0026amp;\\:{C}_{13}\u0026amp;\\:{C}_{33}\u0026amp;\\:0\u0026amp;\\:0\u0026amp;\\:0\\\\\\:0\u0026amp;\\:0\u0026amp;\\:0\u0026amp;\\:{C}_{44}\u0026amp;\\:0\u0026amp;\\:0\\\\\\:0\u0026amp;\\:0\u0026amp;\\:0\u0026amp;\\:0\u0026amp;\\:{C}_{44}\u0026amp;\\:0\\\\\\:0\u0026amp;\\:0\u0026amp;\\:0\u0026amp;\\:0\u0026amp;\\:0\u0026amp;\\:\\frac{1}{2}\\left({C}_{11}-{C}_{12}\\right)\\end{array}\\right)\\)\u003c/span\u003e \u003c/span\u003e (\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe strain tensor \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\epsilon\\:=\\left({\\epsilon\\:}_{1},\\:{\\epsilon\\:}_{2},\\:{\\epsilon\\:}_{3},\\:{\\epsilon\\:}_{4},\\:{\\epsilon\\:}_{5},\\:{\\epsilon\\:}_{6}\\right)\\)\u003c/span\u003e\u003c/span\u003e is defined as\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:\\epsilon\\:=\\left(\\begin{array}{ccc}{\\epsilon\\:}_{1}\u0026amp;\\:\\frac{{\\epsilon\\:}_{6}}{2}\u0026amp;\\:\\frac{{\\epsilon\\:}_{5}}{2}\\\\\\:\\frac{{\\epsilon\\:}_{6}}{2}\u0026amp;\\:{\\epsilon\\:}_{2}\u0026amp;\\:\\frac{{\\epsilon\\:}_{4}}{2}\\\\\\:\\frac{{\\epsilon\\:}_{5}}{2}\u0026amp;\\:\\frac{{\\epsilon\\:}_{4}}{2}\u0026amp;\\:{\\epsilon\\:}_{3}\\end{array}\\right)\\)\u003c/span\u003e \u003c/span\u003e (\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eBy applying monoaxial strain \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\epsilon\\:=\\left(0,\\:0,\\:\\delta\\:,\\:0,\\:0,\\:0\\right)\\)\u003c/span\u003e\u003c/span\u003e to the crystal, we obtained the elastic energy:\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:E=\\:\\frac{1}{2}{C}_{33}{\\delta\\:}^{2}\\)\u003c/span\u003e \u003c/span\u003e (\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eTherefore, the elastic constants \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{C}_{33}\\)\u003c/span\u003e\u003c/span\u003e was determined from total energies versus strain along the \u003cem\u003ec\u003c/em\u003e axis.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003e4.4 Others\u003c/h2\u003e \u003cp\u003eWe used the LOBSTER code to perform COHP analysis \u003csup\u003e53\u0026ndash;57\u003c/sup\u003e. Bond valence was calculated using the bond valence parameters reported by Brese and O'Keeffe \u003csup\u003e58\u003c/sup\u003e. Phonon band structures were calculated using the PHONOPY code \u003csup\u003e59,60\u003c/sup\u003e. Space group symmetry was determined using the spglib code \u003csup\u003e41\u003c/sup\u003e. The VESTA code was used to visualize crystal structures \u003csup\u003e61\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eASSOCIATED CONTENT\u003c/p\u003e \u003c/div\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eSupporting Information\u003c/strong\u003e.\u003c/p\u003e\n\u003cp\u003eThe Supporting Information is available free of charge at the website. \u0026nbsp;It includes calculated phonon band structures of \u0026alpha;-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e in the +HP and +LP states and changes in the area of the basal triangles involved with the Al1 and Al2 atoms and the lattice constants \u003cem\u003ea\u003c/em\u003e and \u003cem\u003ec\u003c/em\u003e during the polarization switching in \u0026alpha;-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e (PDF). \u0026nbsp; An animation of structural evolution during the polarization switching of \u0026alpha;-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e is also available (MP4).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eAUTHOR CONTRIBUTIONS\u003c/p\u003e\n\u003cp\u003eY.S. conducted the calculations under the supervision of H.A. \u0026nbsp;Y.S. and H.A. drafted the manuscript, and all authors edited it.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eACKNOWLEDGMENT\u003c/p\u003e\n\u003cp\u003eThis research was supported by Japan Society of the Promotion of Science (JSPS) KAKENHI Grants Nos. JP17K19172, JP18H01892, JP19H00883, JP21K19027, JP21H05568, JP21H04619, JP23H02069, and JP23H01869. \u0026nbsp;H.A. appreciates Murata Science Foundation and Collaborative Research Project of Laboratory for Materials and Structures, Institute of Innovative Research, Tokyo Institute of Technology. \u0026nbsp;S.O. gratefully acknowledges the Toyota Riken for financial support through a Rising Fellow Program. \u0026nbsp;The computation was carried out using the computer resource offered under the category of General Projects by Research Institute for Information Technology, Kyushu University.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eCOMPETING INTERESTS\u003c/p\u003e\n\u003cp\u003eThe authors declare that they have no competing interests.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eDATA AVAILABILITY\u003c/p\u003e\n\u003cp\u003eThe datasets used and/or analysed during the current study available from the corresponding author on reasonable request.\u003c/p\u003e\n\u003cdiv id=\"_com_1\" language=\"JavaScript\"\u003e\n \u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n\u003c/div\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eKishi, H., Mizuno, Y. \u0026amp; Chazono, H. Base-metal electrode-multilayer ceramic capacitors: Past, present and future perspectives. \u003cem\u003eJapanese Journal of Applied Physics, Part 1: Regular Papers and Short Notes and Review Papers\u003c/em\u003e \u003cstrong\u003e42\u003c/strong\u003e, 1\u0026ndash;5 (2003).\u003c/li\u003e\n\u003cli\u003eSetter, N. \u003cem\u003eet al.\u003c/em\u003e Ferroelectric thin films: Review of materials, properties, and applications. \u003cem\u003eJ Appl Phys\u003c/em\u003e \u003cstrong\u003e100\u003c/strong\u003e, 51606 (2006).\u003c/li\u003e\n\u003cli\u003eKohli, M. \u003cem\u003eet al.\u003c/em\u003e Pyroelectric thin-film sensor array. \u003cem\u003eSens Actuators A Phys\u003c/em\u003e \u003cstrong\u003e60\u003c/strong\u003e, 147\u0026ndash;153 (1997).\u003c/li\u003e\n\u003cli\u003eFichtner, S., Wolff, N., Lofink, F., Kienle, L. \u0026amp; Wagner, B. AlScN: A III-V semiconductor based ferroelectric. \u003cem\u003eJ Appl Phys\u003c/em\u003e \u003cstrong\u003e125\u003c/strong\u003e, 114103 (2019).\u003c/li\u003e\n\u003cli\u003eHayden, J. \u003cem\u003eet al.\u003c/em\u003e Ferroelectricity in boron-substituted aluminum nitride thin films. \u003cem\u003ePhys Rev Mater\u003c/em\u003e \u003cstrong\u003e5\u003c/strong\u003e, 044412 (2021).\u003c/li\u003e\n\u003cli\u003eWang, D., Wang, P., Wang, B. \u0026amp; Mi, Z. Fully epitaxial ferroelectric ScGaN grown on GaN by molecular beam epitaxy. \u003cem\u003eAppl Phys Lett\u003c/em\u003e \u003cstrong\u003e119\u003c/strong\u003e, 111902 (2021).\u003c/li\u003e\n\u003cli\u003eFerri, K. \u003cem\u003eet al.\u003c/em\u003e Ferroelectrics everywhere: Ferroelectricity in magnesium substituted zinc oxide thin films. \u003cem\u003eJ Appl Phys\u003c/em\u003e \u003cstrong\u003e130\u003c/strong\u003e, (2021).\u003c/li\u003e\n\u003cli\u003eWang, D. \u003cem\u003eet al.\u003c/em\u003e Ferroelectric YAlN grown by molecular beam epitaxy. \u003cem\u003eAppl Phys Lett\u003c/em\u003e \u003cstrong\u003e123\u003c/strong\u003e, (2023).\u003c/li\u003e\n\u003cli\u003eKim, K. H., Karpov, I., Olsson, R. H. \u0026amp; Jariwala, D. Wurtzite and fluorite ferroelectric materials for electronic memory. \u003cem\u003eNature Nanotechnology 2023 18:5\u003c/em\u003e \u003cstrong\u003e18\u003c/strong\u003e, 422\u0026ndash;441 (2023).\u003c/li\u003e\n\u003cli\u003eMoriwake, H. \u003cem\u003eet al.\u003c/em\u003e A computational search for wurtzite-structured ferroelectrics with low coercive voltages. \u003cem\u003eAPL Mater\u003c/em\u003e \u003cstrong\u003e8\u003c/strong\u003e, 121102 (2020).\u003c/li\u003e\n\u003cli\u003eLee, C.-W. \u003cem\u003eet al.\u003c/em\u003e Emerging Materials and Design Principles for Wurtzite-type Ferroelectrics. (2023) doi:10.26434/CHEMRXIV-2023-HF60W.\u003c/li\u003e\n\u003cli\u003eDai, Y. \u0026amp; Wu, M. Covalent-like bondings and abnormal formation of ferroelectric structures in binary ionic salts. \u003cem\u003eSci Adv\u003c/em\u003e \u003cstrong\u003e9\u003c/strong\u003e, (2023).\u003c/li\u003e\n\u003cli\u003eMoriwake, H. \u003cem\u003eet al.\u003c/em\u003e Ferroelectricity in wurtzite structure simple chalcogenide. \u003cem\u003eAppl Phys Lett\u003c/em\u003e \u003cstrong\u003e104\u003c/strong\u003e, 242909 (2014).\u003c/li\u003e\n\u003cli\u003eKonishi, A. \u003cem\u003eet al.\u003c/em\u003e Mechanism of polarization switching in wurtzite-structured zinc oxide thin films. \u003cem\u003eAppl Phys Lett\u003c/em\u003e \u003cstrong\u003e109\u003c/strong\u003e, 102903 (2016).\u003c/li\u003e\n\u003cli\u003eDreyer, C. E., Janotti, A., Van de Walle, C. G. \u0026amp; Vanderbilt, D. Correct implementation of polarization constants in wurtzite materials and impact on III-nitrides. \u003cem\u003ePhys Rev X\u003c/em\u003e \u003cstrong\u003e6\u003c/strong\u003e, 021038 (2016).\u003c/li\u003e\n\u003cli\u003eLiu, Z., Wang, X., Ma, X., Yang, Y. \u0026amp; Wu, D. Doping effects on the ferroelectric properties of wurtzite nitrides. \u003cem\u003eAppl Phys Lett\u003c/em\u003e \u003cstrong\u003e122\u003c/strong\u003e, 122901 (2023).\u003c/li\u003e\n\u003cli\u003eNoor-A-Alam, M., Olszewski, O. Z. \u0026amp; Nolan, M. Ferroelectricity and Large Piezoelectric Response of AlN/ScN Superlattice. \u003cem\u003eACS Appl Mater Interfaces\u003c/em\u003e \u003cstrong\u003e11\u003c/strong\u003e, 20482\u0026ndash;20490 (2019).\u003c/li\u003e\n\u003cli\u003eLee, C.-W., Yazawa, K., Zakutayev, A., Brennecka, G. L. \u0026amp; Gorai, P. Switching it Up: New Mechanisms Revealed in Wurtzite-type Ferroelectrics. (2023) doi:10.26434/CHEMRXIV-2023-XDP95.\u003c/li\u003e\n\u003cli\u003eLikforman, A., Carr\u0026eacute;, D., Hillel, R. \u0026amp; IUCr. Structure cristalline du s\u0026eacute;l\u0026eacute;niure d\u0026rsquo;indium In2Se3. \u003cem\u003eurn:issn:0567-7408\u003c/em\u003e \u003cstrong\u003e34\u003c/strong\u003e, 1\u0026ndash;5 (1978).\u003c/li\u003e\n\u003cli\u003ePfitzner, A. \u0026amp; Lutz, H. D. Redetermination of the Crystal Structure of \u0026gamma;-In2Se3by Twin Crystal X-Ray Method. \u003cem\u003eJ Solid State Chem\u003c/em\u003e \u003cstrong\u003e124\u003c/strong\u003e, 305\u0026ndash;308 (1996).\u003c/li\u003e\n\u003cli\u003eSheppard, D., Xiao, P., Chemelewski, W., Johnson, D. D. \u0026amp; Henkelman, G. A generalized solid-state nudged elastic band method. \u003cem\u003eJournal of Chemical Physics\u003c/em\u003e \u003cstrong\u003e136\u003c/strong\u003e, (2012).\u003c/li\u003e\n\u003cli\u003eEisenmann, B. Crystal structure of a-dialuminium trisulfide, Al2S3. \u003cem\u003eZeitschrift fur Kristallographie - New Crystal Structures\u003c/em\u003e \u003cstrong\u003e198\u003c/strong\u003e, 307\u0026ndash;308 (1992).\u003c/li\u003e\n\u003cli\u003eKrebs, B., Schiemann, A. \u0026amp; L\u0026auml;ge, M. Synthese und Kristallstruktur einer Neuen hexagonalen Modifikation von Al2S3 mit f\u0026uuml;nffach koordiniertem Aluminium. \u003cem\u003eZ Anorg Allg Chem\u003c/em\u003e \u003cstrong\u003e619\u003c/strong\u003e, 983\u0026ndash;988 (1993).\u003c/li\u003e\n\u003cli\u003eBaek, S. H. \u003cem\u003eet al.\u003c/em\u003e Ferroelastic switching for nanoscale non-volatile magnetoelectric devices. \u003cem\u003eNature Materials 2010 9:4\u003c/em\u003e \u003cstrong\u003e9\u003c/strong\u003e, 309\u0026ndash;314 (2010).\u003c/li\u003e\n\u003cli\u003eBrehm, J. A. \u003cem\u003eet al.\u003c/em\u003e Tunable quadruple-well ferroelectric van der Waals crystals. \u003cem\u003eNature Materials 2019 19:1\u003c/em\u003e \u003cstrong\u003e19\u003c/strong\u003e, 43\u0026ndash;48 (2019).\u003c/li\u003e\n\u003cli\u003eSebastian Calderon, V. \u003cem\u003eet al.\u003c/em\u003e Atomic-scale polarization switching in wurtzite ferroelectrics. \u003cem\u003eScience (1979)\u003c/em\u003e \u003cstrong\u003e380\u003c/strong\u003e, 1034\u0026ndash;1038 (2023).\u003c/li\u003e\n\u003cli\u003eClima, S. \u003cem\u003eet al.\u003c/em\u003e Strain and ferroelectricity in wurtzite ScxAl1\u0026minus;xN materials. \u003cem\u003eAppl Phys Lett\u003c/em\u003e \u003cstrong\u003e119\u003c/strong\u003e, 172905 (2021).\u003c/li\u003e\n\u003cli\u003eTomas, A., Pardo, M. P., Guittard, M., Guymont, M. \u0026amp; Famery, R. Determination des structures des formes \u0026alpha; et \u0026beta; de Ga2S3 structural determination of \u0026alpha; and \u0026beta; Ga2S3. \u003cem\u003eMater Res Bull\u003c/em\u003e \u003cstrong\u003e22\u003c/strong\u003e, 1549\u0026ndash;1554 (1987).\u003c/li\u003e\n\u003cli\u003eShannon, R. D. Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides. \u003cem\u003eActa Crystallographica Section A\u003c/em\u003e \u003cstrong\u003e32\u003c/strong\u003e, 751\u0026ndash;767 (1976).\u003c/li\u003e\n\u003cli\u003eLueng, C. M., Chan, H. L. W., Surya, C. \u0026amp; Choy, C. L. Piezoelectric coefficient of aluminum nitride and gallium nitride. \u003cem\u003eJ Appl Phys\u003c/em\u003e \u003cstrong\u003e88\u003c/strong\u003e, 5360\u0026ndash;5363 (2000).\u003c/li\u003e\n\u003cli\u003eAkiyama, M. \u003cem\u003eet al.\u003c/em\u003e Enhancement of Piezoelectric Response in Scandium Aluminum Nitride Alloy Thin Films Prepared by Dual Reactive Cosputtering. \u003cem\u003eAdvanced Materials\u003c/em\u003e \u003cstrong\u003e21\u003c/strong\u003e, 593\u0026ndash;596 (2009).\u003c/li\u003e\n\u003cli\u003eBl\u0026ouml;chl, P. E. Projector augmented-wave method. \u003cem\u003ePhys Rev B\u003c/em\u003e \u003cstrong\u003e50\u003c/strong\u003e, 17953 (1994).\u003c/li\u003e\n\u003cli\u003eKresse, G. \u0026amp; Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. \u003cem\u003ePhys Rev B\u003c/em\u003e \u003cstrong\u003e59\u003c/strong\u003e, 1758 (1999).\u003c/li\u003e\n\u003cli\u003ePerdew, J. P. \u003cem\u003eet al.\u003c/em\u003e Restoring the density-gradient expansion for exchange in solids and surfaces. \u003cem\u003ePhys Rev Lett\u003c/em\u003e \u003cstrong\u003e100\u003c/strong\u003e, 136406 (2008).\u003c/li\u003e\n\u003cli\u003ePerdew, J. P., Burke, K. \u0026amp; Ernzerhof, M. Generalized Gradient Approximation Made Simple [Phys. Rev. Lett. 77, 3865 (1996)]. \u003cem\u003ePhys Rev Lett\u003c/em\u003e \u003cstrong\u003e78\u003c/strong\u003e, 1396 (1997).\u003c/li\u003e\n\u003cli\u003ePerdew, J. P., Burke, K. \u0026amp; Ernzerhof, M. Generalized Gradient Approximation Made Simple. \u003cem\u003ePhys Rev Lett\u003c/em\u003e \u003cstrong\u003e77\u003c/strong\u003e, 3865 (1996).\u003c/li\u003e\n\u003cli\u003eKresse, G. \u0026amp; Furthm\u0026uuml;ller, J. Efficient iterative schemes for \u003cem\u003eab initio\u003c/em\u003e total-energy calculations using a plane-wave basis set. \u003cem\u003ePhys Rev B\u003c/em\u003e \u003cstrong\u003e54\u003c/strong\u003e, 11169 (1996).\u003c/li\u003e\n\u003cli\u003eKresse, G. \u0026amp; Hafner, J. \u003cem\u003eAb initio\u003c/em\u003e molecular dynamics for open-shell transition metals. \u003cem\u003ePhys Rev B\u003c/em\u003e \u003cstrong\u003e48\u003c/strong\u003e, 13115 (1993).\u003c/li\u003e\n\u003cli\u003eKresse, G. \u0026amp; Hafner, J. \u003cem\u003eAb initio\u003c/em\u003e molecular dynamics for liquid metals. \u003cem\u003ePhys Rev B\u003c/em\u003e \u003cstrong\u003e47\u003c/strong\u003e, 558 (1993).\u003c/li\u003e\n\u003cli\u003eKresse, G. \u0026amp; Furthm\u0026uuml;ller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. \u003cem\u003eComput Mater Sci\u003c/em\u003e \u003cstrong\u003e6\u003c/strong\u003e, 15\u0026ndash;50 (1996).\u003c/li\u003e\n\u003cli\u003eTogo, A., Shinohara, K. \u0026amp; Tanaka, I. $\\texttt{Spglib}$: a software library for crystal symmetry search. (2018).\u003c/li\u003e\n\u003cli\u003eAroyo, M. I. \u003cem\u003eet al.\u003c/em\u003e Crystallography online: Bilbao crystallographic server. \u003cem\u003eBulgarian Chemical Communications\u003c/em\u003e \u003cstrong\u003e43\u003c/strong\u003e, 183\u0026ndash;197 (2011).\u003c/li\u003e\n\u003cli\u003eAroyo, M. I. \u003cem\u003eet al.\u003c/em\u003e Bilbao Crystallographic Server: I. Databases and crystallographic computing programs. \u003cem\u003eZeitschrift fur Kristallographie\u003c/em\u003e \u003cstrong\u003e221\u003c/strong\u003e, 15\u0026ndash;27 (2006).\u003c/li\u003e\n\u003cli\u003eAroyo, M. I., Kirov, A., Capillas, C., Perez-Mato, J. M. \u0026amp; Wondratschek, H. Bilbao Crystallographic Server. II. Representations of crystallographic point groups and space groups. \u003cem\u003eurn:issn:0108-7673\u003c/em\u003e \u003cstrong\u003e62\u003c/strong\u003e, 115\u0026ndash;128 (2006).\u003c/li\u003e\n\u003cli\u003eHenkelman, G., Uberuaga, B. P. \u0026amp; J\u0026oacute;nsson, H. A climbing image nudged elastic band method for finding saddle points and minimum energy paths. \u003cem\u003eJ Chem Phys\u003c/em\u003e \u003cstrong\u003e113\u003c/strong\u003e, 9901\u0026ndash;9904 (2000).\u003c/li\u003e\n\u003cli\u003eHenkelman, G. \u0026amp; J\u0026oacute;nsson, H. Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points. \u003cem\u003eJ Chem Phys\u003c/em\u003e \u003cstrong\u003e113\u003c/strong\u003e, 9978\u0026ndash;9985 (2000).\u003c/li\u003e\n\u003cli\u003eSeko, A., Koyama, Y. \u0026amp; Tanaka, I. Cluster expansion method for multicomponent systems based on optimal selection of structures for density-functional theory calculations. \u003cem\u003ePhys Rev B Condens Matter Mater Phys\u003c/em\u003e \u003cstrong\u003e80\u003c/strong\u003e, 165122 (2009).\u003c/li\u003e\n\u003cli\u003eOng, S. P. \u003cem\u003eet al.\u003c/em\u003e Python Materials Genomics (pymatgen): A robust, open-source python library for materials analysis. \u003cem\u003eComput Mater Sci\u003c/em\u003e \u003cstrong\u003e68\u003c/strong\u003e, 314\u0026ndash;319 (2013).\u003c/li\u003e\n\u003cli\u003eWu, X., Vanderbilt, D. \u0026amp; Hamann, D. R. Systematic treatment of displacements, strains, and electric fields in density-functional perturbation theory. \u003cem\u003ePhys Rev B\u003c/em\u003e \u003cstrong\u003e72\u003c/strong\u003e, 035105 (2005).\u003c/li\u003e\n\u003cli\u003eSarasamak, K., Limpijumnong, S. \u0026amp; Lambrecht, W. R. L. Pressure-dependent elastic constants and sound velocities of wurtzite SiC, GaN, InN, ZnO, and CdSe, and their relation to the high-pressure phase transition: A first-principles study. \u003cem\u003ePhys Rev B Condens Matter Mater Phys\u003c/em\u003e \u003cstrong\u003e82\u003c/strong\u003e, 035201 (2010).\u003c/li\u003e\n\u003cli\u003eWright, A. F. Elastic properties of zinc-blende and wurtzite AlN, GaN, and InN. \u003cem\u003eJ Appl Phys\u003c/em\u003e \u003cstrong\u003e82\u003c/strong\u003e, 2833\u0026ndash;2839 (1997).\u003c/li\u003e\n\u003cli\u003eNewnham, R. E. Properties of Materials: Anisotropy, Symmetry, Structure. (2004) doi:10.1093/OSO/9780198520757.001.0001.\u003c/li\u003e\n\u003cli\u003eDronskowski, R. \u0026amp; Bl\u0026ouml;chl, P. E. Crystal orbital hamilton populations (COHP). Energy-resolved visualization of chemical bonding in solids based on density-functional calculations. \u003cem\u003eJournal of Physical Chemistry\u003c/em\u003e \u003cstrong\u003e97\u003c/strong\u003e, 8617\u0026ndash;8624 (1993).\u003c/li\u003e\n\u003cli\u003eDeringer, V. L., Tchougr\u0026eacute;eff, A. L. \u0026amp; Dronskowski, R. Crystal orbital Hamilton population (COHP) analysis as projected from plane-wave basis sets. \u003cem\u003eJournal of Physical Chemistry A\u003c/em\u003e \u003cstrong\u003e115\u003c/strong\u003e, 5461\u0026ndash;5466 (2011).\u003c/li\u003e\n\u003cli\u003eMaintz, S., Deringer, V. L., Tchougr\u0026eacute;eff, A. L. \u0026amp; Dronskowski, R. Analytic projection from plane-wave and PAW wavefunctions and application to chemical-bonding analysis in solids. \u003cem\u003eJ Comput Chem\u003c/em\u003e \u003cstrong\u003e34\u003c/strong\u003e, 2557\u0026ndash;2567 (2013).\u003c/li\u003e\n\u003cli\u003eMaintz, S., Deringer, V. L., Tchougr\u0026eacute;eff, A. L. \u0026amp; Dronskowski, R. LOBSTER: A tool to extract chemical bonding from plane-wave based DFT. \u003cem\u003eJ Comput Chem\u003c/em\u003e \u003cstrong\u003e37\u003c/strong\u003e, 1030\u0026ndash;1035 (2016).\u003c/li\u003e\n\u003cli\u003eNelson, R. \u003cem\u003eet al.\u003c/em\u003e LOBSTER: Local orbital projections, atomic charges, and chemical-bonding analysis from projector-augmented-wave-based density-functional theory. \u003cem\u003eJ Comput Chem\u003c/em\u003e \u003cstrong\u003e41\u003c/strong\u003e, 1931\u0026ndash;1940 (2020).\u003c/li\u003e\n\u003cli\u003eBrese, N. E. \u0026amp; O\u0026rsquo;Keeffe, M. Bond-valence parameters for solids. \u003cem\u003eActa Crystallographica Section B\u003c/em\u003e \u003cstrong\u003e47\u003c/strong\u003e, 192\u0026ndash;197 (1991).\u003c/li\u003e\n\u003cli\u003eTogo, A. First-principles Phonon Calculations with Phonopy and Phono3py. \u003cem\u003ehttps://doi.org/10.7566/JPSJ.92.012001\u003c/em\u003e \u003cstrong\u003e92\u003c/strong\u003e, (2022).\u003c/li\u003e\n\u003cli\u003eTogo, A., Chaput, L., Tadano, T. \u0026amp; Tanaka, I. Implementation strategies in phonopy and phono3py. \u003cem\u003eJournal of Physics: Condensed Matter\u003c/em\u003e \u003cstrong\u003e35\u003c/strong\u003e, 353001 (2023).\u003c/li\u003e\n\u003cli\u003eMomma, K. \u0026amp; Izumi, F. VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data. \u003cem\u003eurn:issn:0021-8898\u003c/em\u003e \u003cstrong\u003e44\u003c/strong\u003e, 1272\u0026ndash;1276 (2011).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"npj-computational-materials","isNatureJournal":false,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"npjcompumats","sideBox":"Learn more about [npj Computational Materials](http://www.nature.com/npjcompumats/)","snPcode":"41524","submissionUrl":"https://mts-npjcompumats.nature.com/","title":"npj Computational Materials","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"NPJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-4680101/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4680101/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWurtzite-type ferroelectrics are highly promising for next-generation microelectronic devices due to their ferroelectric properties and integration with exiting semiconductors. However, their high coercive fields, which are close to breakdown electric fields, need to be lowered. To deal with this issue and secure device reliability, much effort has been devoted to exploring novel wurtzite compounds with lower polarization switching barriers and implementing doping strategies. Here, we report first-principles calculations on polarization switching in cation-vacancy ordered wurtzite α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e, unveiling its uniaxial quadruple-well ferroelectricity and moderate switching barrier, 51 meV/cation, which is much lower than that of conventional wurtzite ferroelectrics. There are three important features relevant to the Al vacancies leading to the uncommon quadruple-well ferroelectricity and the moderate switching barrier: mitigation of cation-cation repulsion, structural flexibility that alleviates an in-plane lattice expansion, and formation of s-like bonding states consisting of Al 3p\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e and S 3p\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e orbitals. Biaxial compressive strain and Ga doping lower the switching barriers by up to 40%. This study encourages experimental investigation of the ferroelectric properties for defective wurtzite α-Al\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003e as a new promising material with unconventional and intriguing ferroelectricity and suggests a potential strategy for reducing switching barriers in wurtzite ferroelectrics: \u003cem\u003eintroducing cation vacancies\u003c/em\u003e.\u003c/p\u003e","manuscriptTitle":"Quadruple-well ferroelectricity and moderate switching barrier in defective wurtzite α-Al2S3: a first-principles study","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-08-23 06:14:44","doi":"10.21203/rs.3.rs-4680101/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"revise","date":"2024-09-03T11:43:51+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"This content is not available.","date":"2024-09-01T23:31:55+00:00","index":2,"fulltext":"This content is not available."},{"type":"editorInvitedReview","content":"This content is not available.","date":"2024-09-01T06:29:31+00:00","index":3,"fulltext":"This content is not available."},{"type":"editorInvitedReview","content":"This content is not available.","date":"2024-08-18T21:31:00+00:00","index":1,"fulltext":"This content is not available."},{"type":"reviewerAgreed","content":"This content is not available.","date":"2024-08-16T18:14:55+00:00","index":3,"fulltext":"This content is not available."},{"type":"reviewerAgreed","content":"This content is not available.","date":"2024-08-01T06:45:14+00:00","index":2,"fulltext":"This content is not available."},{"type":"reviewerAgreed","content":"This content is not available.","date":"2024-07-31T11:46:37+00:00","index":1,"fulltext":"This content is not available."},{"type":"reviewersInvited","content":"","date":"2024-07-28T02:43:39+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-07-11T18:16:49+00:00","index":"","fulltext":""},{"type":"submitted","content":"npj Computational Materials","date":"2024-07-10T09:35:16+00:00","index":"","fulltext":""},{"type":"checksFailed","content":"","date":"2024-07-10T08:15:35+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-07-03T11:32:00+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"npj-computational-materials","isNatureJournal":false,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"npjcompumats","sideBox":"Learn more about [npj Computational Materials](http://www.nature.com/npjcompumats/)","snPcode":"41524","submissionUrl":"https://mts-npjcompumats.nature.com/","title":"npj Computational Materials","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"NPJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"facbdaea-c753-4e63-8b95-72af4a6f0ae2","owner":[],"postedDate":"August 23rd, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":35222069,"name":"Physical sciences/Materials science/Materials for devices/Electronic devices"},{"id":35222070,"name":"Physical sciences/Chemistry/Materials chemistry/Electronic materials"}],"tags":[],"updatedAt":"2025-02-18T08:09:01+00:00","versionOfRecord":{"articleIdentity":"rs-4680101","link":"https://doi.org/10.1038/s41524-025-01519-3","journal":{"identity":"npj-computational-materials","isVorOnly":false,"title":"npj Computational Materials"},"publishedOn":"2025-02-17 05:00:00","publishedOnDateReadable":"February 17th, 2025"},"versionCreatedAt":"2024-08-23 06:14:44","video":"","vorDoi":"10.1038/s41524-025-01519-3","vorDoiUrl":"https://doi.org/10.1038/s41524-025-01519-3","workflowStages":[]},"version":"v1","identity":"rs-4680101","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4680101","identity":"rs-4680101","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}