Design and Predict Tetragonal van der Waals Layered Quantum Materials of MPd5I2 (M=Ga, In and 3d Transition Metals)

Design and Predict Tetragonal van der Waals Layered Quantum Materials of MPd5I2 (M=Ga, In and 3d Transition Metals) | 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 Design and Predict Tetragonal van der Waals Layered Quantum Materials of MPd5I2 (M=Ga, In and 3d Transition Metals) Niraj Nepal, Tyler Slade, Joanna Blawat, Andrew Eaton, Johanna Palmstrom, and 6 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4830029/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 19 Feb, 2025 Read the published version in npj 2D Materials and Applications → Version 1 posted 11 You are reading this latest preprint version Abstract Quantum materials with stacking van der Waals (vdW) layers that can host non-trivial band structure topology and magnetism have shown many interesting properties. Here using high-throughput density functional theory calculations, we design and predict tetragonal vdW-layered quantum materials in the MPd 5 I 2 structure (M = Ga, In and 3 d transition metals). Our study shows that besides the known AlPd 5 I 2 , the -MPd 5 - structural motif of three-layer slabs separated by two I layers can host a variety of metal elements giving arise to topological interesting features and highly tunable magnetic properties in both bulk and single layer 2D structures. Among them, TiPd 5 I 2 and InPd 5 I 2 host a pair of Dirac points and a likely strong topological insulator state for the band manifolds just above and below the top valence band, respectively, with their single layers possibly hosting quantum spin Hall states. CrPd 5 I 2 is a ferromagnet with a large out-of-plane magneto-anisotropy energy, desirable for rare-earth-free permanent magnets. Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 I. Introduction Design and discovery of novel 2D van der Waals (vdW) layered topological and magnetic materials containing 3 d transition metals (TM) can be essential for advancing both fundamental science and applied technology. For example, understanding and manipulating itinerant 3 d TM magnetism in intermetallics are crucial to understand many emergent states including superconductivity 1–5 . At the same time, rare-earth-free permanent magnets with 3 d TM having large coercivity and saturation moment are sought after for renewable energy technologies 6–11 . When combining these two features in the same material, it is rare to find families of magnetic 2D vdW materials with only a handful examples such as CrX 3 (X = I, Br, Cl) 12–17 , VI 3 18 , Cr 2 Si 2 Te 6 19 , Cr 2 Ge 2 Te 6 20, 21 , Fe 3 GeTe 2 22 and MnBi 2n Te 3n + 1 (MBT) 23 . The MBT systems are particularly interesting because most of them are intrinsic antiferromagnetic (AF) topological insulator (TI) that can be exfoliated to a few layers. The discovery of these magnetic 2D vdW materials have galvanized extensive research activities to study their unique properties. The recent discovery 24–29 of magnetic materials with the structural motif of -MPt 5 - and -MPd 5 - slabs in the tetragonal anti-CeCo 5 In structure has attracted wide attention for incorporating 3 d TM magnetism of Cr, Mn and Fe into slabs of Pd and Pt with large spin-orbit coupling (SOC). Ferromagnetic (FM) CrPt 5 P 28 and MnPd 5 P 29 have shown large magneto-anisotropy energy (MAE) for possible rare-earth-free permanent magnet applications, however, the easy axis is in-plane. These 1-5-1 compounds with separation of -MPd 5 - and -MPt 5 - slabs by a single layer of P or As are not exfoliable due to the strong bonding of P or As to Pd or Pt on both sides. But it hints at a new way to design 2D vdW materials by inserting more anion layers to separate the well-structured atomic metal slabs. On the other hand, non-magnetic (NM) 2D vdW materials that can be exfoliated to a single layer are in high demand to realize a range of emergent quantum states from superconductivity 30 to fractional quantum Hall effect 31–33 by twisting few-layer systems, as well as charge density wave (CDW) induced quantum spin Hall (QSH) effect 34 by gating. These new tetragonal vdW-layered materials predicted here can potentially provide a platform for the twisted few-layer systems with a tetragonal lattice 35 besides the twisted hexagonal and orthorhombic lattices. Here we report the design and prediction of 2D vdW-layered I-separated -MPd 5 - slabs in the body-centered tetragonal crystal structure of MPd 5 I 2 with (M = Ga, In and 3d TMs) by first-principles calculations. The phase stability calculations based on density functional theory 36, 37 (DFT) show that the NM ones are on the ground state (GS) hull and thermodynamically stable, similar to the already existing AlPd 5 I 2 38 , and a few magnetic ones are close to the GS hull and thus metastable. These materials have either topologically non-trivial band structures or interesting magnetic properties. In the two band manifolds near the Fermi energy (E F ), the NM compounds host a pair of bulk Dirac points (BDPs) and a possible strong TI state just above and below the highest valence band, respectively. While TiPd 5 I 2 is a Dirac semimetal (DSM) with a relatively clean Fermi surface (FS), InPd 5 I 2 has a half-filled top valence band with the surface Dirac point (SDP) from the strong TI state appearing at the E F . This combined feature results in the surface states with both the BDP projection and SDP appearing at the \(\:{\Gamma\:}\) point in a narrow energy window of 0.1–0.2 eV around the E F in TiPd 5 I 2 and InPd 5 I 2 . The single layer (1L) TiPd 5 I 2 is a QSH insulator with an indirect global band gap of 30 meV or a narrow-gap semiconductor with a small direct gap of 100 meV depending on the DFT exchange-correlation (XC) functional, while InPd 5 I 2 hosts two QSH states just above and below the half-filled top valence band. Among the magnetic ones, CrPd 5 I 2 stands out for having the highest MAE of 2.88 meV/f.u. with the FM easy axis along the c -axis giving the desirable out-of-plane magnetic anisotropy needed for rare-earth-free permanent magnet. The large MAE remains for the 1L FM CrPd 5 I 2 . From the many band crossings around E F in both bulk and 1L CrPd 5 I 2 , there are Weyl nodal lines protected by the horizontal mirror plane as the FM magnetic moment is along the c -axis. II. Results and Discussion II-a. Structural motif and phase stability Figure 1 (a) summaries the design of layered compounds based on the -MPd 5 - slab. Without layer separation, the -MPd 5 - slab with shared plane boundary is in the Cu 3 Au-type structure in space group (SG) Pm-3m (221) with M being surrounded by 12 nearest-neighbor Pd in a local close-packed face-centered cubic (FCC) structure. As shown by the successful synthesis of MPd 5 P and MPd 5 As compounds 27, 29 , an anionic layer can be inserted between the -MPd 5 - slabs to make new structures in the SG P4/mmm (123). With P/As in the nominal valence of 3–, it is possible to have two I to replace P and more importantly it becomes vdW layered, as shown by the existence of AlPd 5 I 2 38 , the only reported compound in this structure so far. It replaces P with two I and shifts the -MPd 5 - slabs in-plane for every other layer, which results in a body-centered tetragonal (tI16) structure in SG I4/mmm (139). Here we design and predict new vdW layered compounds in this structure by replacing Al with other group III elements and also 3 d TMs via high throughput DFT calculations. As plotted in Fig. 1 (b) for the projected density of states (PDOS) of NM InPd 5 I 2 , TiPd 5 I 2 and FM CrPd 5 I 2 , most of the I 5 p orbitals hybridize with the bottom of Pd 4 d orbitals from − 6 to − 4 eV to form the p-d bonding states. The p-d anti-bonding states are pushed to above 1 eV as empty states to gain more cohesion for the ternary compounds with additional bonding hybridization between Pd 5 s (not shown) and I 5 p orbitals in the same low-energy range. In contrast to I 5 p , the p orbitals of group III elements at M site, for example In, mostly hybridizes with Pd 4 d states at a higher energy range (–4 to − 2 eV), reflecting their electron positive character. But the states near the E F in InPd 5 I 2 are dominated by Pd 4 d and I 5 p orbitals. Next moving to 3 d TM, Ti 3 d orbitals hybridize extensively with Pd 4 d orbitals giving the broader and lower Pd 4 d -derived bands than InPd 5 I 2 below the E F . There is also a large empty anti-bonding DOS peak just above the E F due to the 3 d -4 d hybridization. Then for Cr with two more 3 d electrons, these empty states get partially filled and induce a large exchange interaction shown as the two splitting DOS peaks at 0 and + 2 eV. This interaction gives a sizable magnetic moment on Cr of 2.80 \(\:{\mu\:}_{B}\) to prefer FM and importantly the easy axis is along the c -axis with a large MAE of 2.88 meV/f.u. The PDOS for other magnetic 3 d TM MPd 5 I 2 are similar in terms of band hybridizations. The NM TiPd 5 I 2 is an interesting case with the right number of valence electrons that the anti-bonding states are almost completely empty giving a minimum DOS at E F to form a DSM, whose topological band structure will be detailed later. The GS convex hull energy (E h ) for all the MPd 5 I 2 compounds studied are plotted in Fig. 1 (c) for PBEsol 39 and also with vdW exchange functional of optB86b 40 . To confirm that the introduction of I prefers two anion layers instead of one, besides the MPd 5 I 2 in the I4/mmm structure, we have also calculated the hypothetical MPd 5 I in the P4/mmm structure. As shown in Fig. 1 (c), E h for MPd 5 I are all above 0.10 eV/atom, much higher than MPd 5 I 2 , confirming the qualitative argument that the broken metallic interactions in separating -MPd 5 - slabs need to be compensated by a strong ionic interaction with enough anionic valence. For group III elements, Al, Ga and In, the E h of MPd 5 I 2 are all zero for PBEsol and slightly below 0.01 eV/atom for optB86b, which shows they are all thermodynamically stable as AlPd 5 I 2 has already been found in experiment 38 , although optB86b gives a small positive E h of 0.006 eV/atom. InPd 5 I 2 has the smallest E h , thus the most stable among the group III compounds. For the 3 d TMs, first TiPd 5 I 2 is quite stable on the GS hull even for optB86b and we found it is a DSM with a clean FS. Next for V and Cr, E h becomes positive, but smaller than 0.10 eV/atom. Then E h decreases for Mn and Fe at the middle of 3 d TM series, and increases again for the late 3 d Co and Ni, which are the least stable among the 3 d TM MPd 5 I 2 . Overall, optB86b gives a higher E h than PBEsol, showing a systematic shift between the different XC functionals. But the trends for the variation in E h across the whole series for both MPd 5 I 2 and MPd 5 I are the same for different XC functionals showing the results are well converged. The magnetic properties across the 3 d TM series for MPd5I2 are quite interesting and tabulated at the top of Fig. 1 (c). Except for Ti being NM, the magnetic moment size increases first starting with V, reaching the maximum of 3.92 \(\:{\mu\:}_{B}\) for Mn before decreases at the end of the series for Co and Ni. With the gradual filling of the 3 d orbitals, V, Cr and Mn prefer FM, while Fe, Co and Ni prefer AF. Importantly, both V and Cr prefer easy axis along the c -axis with Cr having the largest MAE of 2.88 meV/f.u., much higher than the 0.30 meV/f.u. for VPd 5 I 2 and the rest. In contrast, FM Mn prefers the in-plane easy-axis, although with the largest moment. Then for AF, first Fe moments prefers in-plane and then Co and Ni prefer out-of-plane directions. To study phase stability and construct GS hull, all the existing binary and ternary compounds together with the elemental ones in the ternary phase diagrams have been computed and their stability are calculated via different possible reaction paths. Although PBEsol gives AlPd 5 I 2 on the GS hull agreeing with experiment, Fig. 2 (a) shows the calculated volume per atom is underestimated when compared to available experimental data. This underestimation of volume with PBEsol is improved by using optB86b exchange functional. Also, to explicitly include vdW interaction for the 1-5-2 compounds, we have chosen optB86b vdW exchange functional for the phase stability plots in Fig. 2 , as well as the band structure and magnetic property calculations. The GS hulls with PBEsol are similar and can be found in Fig. S1 of SM. As shown in Fig. 2 , for Pd-I binary, there is only one stable line compound of PdI 2 . For M-I binaries, there are many stable line compounds for Ga, In, Ti and V. For the rest, there is only one stable binary M-I compound including CrI 3 for Cr-I. For M-Pd, Al, Ga, In, Ti, V and Mn have many stable line compounds. Interestingly, for the -MPd 5 - motif in MPd 3 or the Cu 3 Au-type, this binary line compound structure exists for In, Ti, V, Cr, Mn and Fe with Pd. But for Ni and Co, they form random alloy or solid solution with Pd. Because CoPd 3 and NiPd 3 both are only slightly above the GS hull at 0.06 eV/atom, they can be used as good representatives for the binary solid solution. We also include them in calculating the stability of the MPd 5 I 2 . Among the calculated MPd 5 I 2 , the NM compounds are more stable than the magnetic ones. Given AlPd 5 I 2 with the E h of 0.006 eV/atom in optB86b has already been synthesized, we predict the existence of GaPd 5 I 2 , InPd 5 I 2 and TiPd 5 I 2 because they are on the GS hull. For magnetic ones, Mn and Fe have the smallest E h above GS hull and then followed by V and Cr. Considering the approximations used in DFT calculations, we predict these four magnetic ternaries are metastable, also because the binary MPd 3 line compounds with the -MPd 5 - motif are stable and found in experiments. Lastly for Co and Ni, they have the largest E h above GS hull even with PBEsol and because the solid solution of MPd 3 , it is also possible to form solid solution for the ternary compounds. We predict these two are possible ternaries but with solid solution tendency, which needs to be further studied in the future. From an experimental viewpoint, these MPd 5 I 2 compounds are much more challenging to synthesize than MPd 5 P and MPd 5 As because of the higher vapor pressure or lower sublimation temperature of I than P and As. II-b. Topological features of non-magnetic 1-5-2 compounds For the band structures of NM MPd 5 I 2 , we chose TiPd 5 I 2 and InPd 5 I 2 to present the topological band features of both the bulk and 1L structures. Bulk band structures of other MPd 5 I 2 can be found in Fig.S2 of SM. Figure 3 (a) plots the band structure of bulk TiPd 5 I 2 without SOC with the body-centered tetragonal Brillouin zone (BZ) and high symmetry k-points shown in Fig. 3 (c). The highest valence band (N) and band below (N–2) according to simple filling are shown in red and blue, respectively. Above the highest valence band, there is a sizable gap in most of the BZ, except for around the Z point in the \(\:{\Gamma\:}\) -Z, Z-S 1 and Y 1 -Z directions. Along the \(\:{\Gamma\:}\) -Z direction, band N and N–2 are degenerate, giving triple degeneracy (or six-fold including spin) at the crossing point between the highest valence and lowest conduction band in the middle of \(\:{\Gamma\:}\) -Z. From the triple degeneracy point to the Z point, a doubly degenerated nodal line segment appears, also shown in Fig. 3 (d) by plotting the zero-gap k -points in the whole BZ. The crossings along the Z-S 1 and Y 1 -Z directions are parts of the nodal line loops around the Z point on the (110) and ( 1 – 10 ) planes as protected by the diagonal mirror symmetries. With SOC, as plotted in Fig. 3 (b), the orbital degeneracy for the top two valence bands along the \(\:{\Gamma\:}\) -Z direction is lifted and the nodal loops are all gapped out, except for the crossing between the highest valence and lowest conduction band along the \(\:{\Gamma\:}\) -Z forming a BDP as protected by the four-fold rotational symmetry. Because of the time-reversal symmetry (TRS) and inversion symmetry, each band is still doubly degenerated. The BDP is zoomed in Fig. 3 (e) along the \(\:{\Gamma\:}\) -Z direction showing the zero gap and the switching between I p z and Pd d xz / d yz orbitals with the 2-dimensional irreducible representations of \(\:{\Gamma\:}\) 9 and \(\:{\Gamma\:}\) 6 . The BDPs are at the momentum energy of (0, 0, ± 0.1499 Å –1 ; E F +0.0236 eV), also shown as the red dots in Fig. 3 (c). The band structure of TiPd 5 I 2 along the Z-S 1 direction is zoomed in Fig. 3 (f) to show the small SOC-induced gap. Interestingly for the highest valence band (red), it is also gapped from below by the next valence band (blue). The lower branch of the orbital degenerated band N–2 along \(\:{\Gamma\:}\) -Z forms a band inversion region around the Z point with the top valence band N. Wilson loop calculations show this N–2 band manifold hosts a strong TI (STI) state with the Fu-Kane 41 topological index of (1;001). The Wilson loop with Wannier charge centers (WCC) on the k z =0.5 plane in Fig. 3 (g) shows the non-trivial Z 2 number with the odd number of crossings by the dashed line with WCC. Calculations with more recent r2SCAN + rVV10 42 XC functional show similar band features (see Fig.S3 in SM). For mBJ 43 functional, the BDP still remains, despite most of the valence bands being pushed lower and conduction bands higher in energy. But the band inversion at the Z point is lifted between band N–2 and N for mBJ functional giving no STI. The existence of this band inversion for STI or not in TiPd 5 I 2 will be the features need to be verified in experiment. To demonstrate the non-trivial band structure of TiPd 5 I 2 with a BDP above and a STI below the highest valence band, we have calculated the (001) surface spectral functions from the Wannier functions. On (001) surface, the projections of the BDP at ± k z onto the same \(\:{\Gamma\:}\) point are isolated in energy and have no overlap with other bulk band projection because of the clean FS. There are topological surface states (TSS) stemming from the BDP projection as seen in Fig. 3 (h) at E F +0.03 eV. Below that at E F –0.2 eV is the SDP from the STI of the N–2 band manifold also shown clearly even though on top of the other bulk band projections. The spin-texture of the surface Dirac cone is plotted at E F –0.185 eV in Fig. 3 (j) confirming the spin-momentum locking of the surface Dirac cone. The spin-momentum locking of the TSS stemming from the BDP projection is shown in Fig. 3 (i) at E F +0.045 eV. Thus, bulk TiPd 5 I 2 is a DSM with a clean FS surface and also possibly hosts a STI below the highest valence band. When the vdW layered TiPd 5 I 2 is exfoliated down to 1L, the band structure is plotted in Fig. 4 (a). A large band gap exists in most of the BZ, while a small gap appears along the \(\:{\Gamma\:}\) -X direction, which is projected from the Z-S 1 direction from the bulk band structure. Overall there is an indirect global band gap of 30 meV between the valence band maximum at X and conduction band minimum at \(\:{\Gamma\:}\) point. The Wilson loop calculation of the highest valence band manifold in Fig. 4 (b) indicates it is a QSH with an odd number of crossings of WCC. In contrast, for the N–2 band manifold (blue), the even number of crossings in the Wilson loop in Fig. 4 (c) shows it is topologically trivial. The edge spectral functions are plotted in Fig. 4 (d) and (e) for the different TiPd- and PdI-terminations, respectively. The topological edge states connect the gapped valence with conduction band projections and form TRS-protected edge Dirac points (EDP) at the \(\:\stackrel{-}{{\Gamma\:}}\) point. While the EDP on the TiPd-termination is inside the QSH gap, that on PdI-termination is merged into the valence band projection at E F –0.06 eV. With E F cutting through the QSH gap, the spin-momentum locked edge states are unavoidable from TRS topological protection. So 1L TiPd 5 I 2 is a tetragonal QSH insulator. Calculations with r2SCAN + rVV10 XC functional show similar band inversion feature at the \(\:{\Gamma\:}\) point for QSH (see Fig.S3 in SM). In contrast, HSE06 44 functional pushes the valence band lower and conduction bands higher in energy, and lift the band inversion and changes the indirect band gap to a direct one with 100 meV at \(\:{\Gamma\:}\) point (see Fig.S3(d)). Although not a QSH in HSE06, the small gap size can be potentially tuned to close and reopen by strain to induce the band inversion for a topological phase transition to realize a critical 2D Dirac point at the \(\:{\Gamma\:}\) point and then a QSH. Next for InPd 5 I 2 as an example from group III MPd 5 I 2 , its bulk band structure with SOC is plotted in Fig. 5 (a). Because of the TRS and inversion symmetry, each band is doubly degenerated. But because of the odd number of electrons, the highest valence band (red in Fig. 5 (a)) is only half-filled, indicated by E F sitting right in the middle of the band width. But it is still meaningful to discuss the topological features of the band manifolds below and above the half-filled top valence band, although the FS is finite. Between the highest valence and lowest conduction band, there is only one crossing along the \(\:{\Gamma\:}\) -Z direction as protected by the 4-fold rotational symmetry, similar to TiPd 5 I 2 . The BDP is zoomed in Fig. 5 (b) shown by the projection on I p z and Pd d xz and d yz orbitals with the 2-dimensional irreducible representations of \(\:{\Gamma\:}\) 9 and \(\:{\Gamma\:}\) 6 . The BDP are at the momentum energy of (0, 0, ± 0.0406 Å –1 ; E F +0.0955 eV). In contrast, between the highest and the next valence band (blue), there is no band crossing. For such gapped band manifolds, the Fu-Kane topological index has been calculated as (1;001) showing it hosts a STI state. The Wilson loop with WCC at the k z =0.5 plane is plotted in Fig. 5 (c). To confirm the STI with surface spectral function on (001), the surface Dirac cone is shown clearly in Fig. 5 (d) with the SDP right at the E F and inside the projected bulk gap. The spin-texture of the surface states at the E F is shown in Fig. 5 (e) confirming the spin-momentum locking topological feature without overlapping with bulk band projection. In contrast, the BDP projection at E F +0.10 eV on (001) surface in Fig. 5 (d) is buried inside the other bulk band projection and shows no TSS, unlike those in TiPd 5 I 2 with a clean FS. Thus, group III MPd 5 I 2 host both a BDP above and a STI below the half-filled highest valence band. For InPd 5 I 2 , both the SDP and BDP projection appear at the \(\:\stackrel{-}{{\Gamma\:}}\) point on (001), and they are also within an energy window of 0.1 eV with the SDP being right at the E F and BDP just above the E F . The band structure of 1L InPd 5 I 2 is plotted in Fig. 5 (f). Again, due to the odd number of electrons, the top valence band is half-filled with E F sitting in the middle of the band width. But the valence band is continuously gapped from both below and above with band inversion, so topological properties can be calculated. The Wilson loop calculation of the band manifolds in Fig. 5 (g) and (h) show the odd number of crossings of WCC confirming it hosts two QSH states. The edge spectral functions are plotted in Fig. 5 (i) and (j) for two different terminations, which are rather similar. The TRS-protected EDP at E F +0.3 eV is for the upper QSH and the EDP at E F is for the lower QSH. Calculations with r2SCAN + rVV10, mBJ and HSE06 XC functionals all show similar band inversion and topological features (see Fig.S4 in SM), which are much less affected than TiPd 5 I 2 , because InPd 5 I 2 bands are more metallic from the half-filled top valence band than TiPd 5 I 2 . So 1L InPd 5 I 2 hosts two QSH states in a tetragonal structure despite being a metal. Together with the QSH insulator with a small indirect band gap or a narrow-gap semiconductor in 1L TiPd 5 I 2 , the few layer tetragonal systems of these exfoliable 1-5-2 compounds will be an interesting playground for emergent quantum states in future studies. II-c. Magneto-anisotropy of CrPd 5 I 2 Among the magnetic 3 d TM MPd 5 I 2 compounds, the most interesting one is CrPd 5 I 2 with the largest MAE and easy-axis along the c -axis. First without SOC, the spin DOS of bulk and 1L CrPd 5 I 2 are plotted in Fig. 6 (a) and (b), respectively. While the spin down (majority) forms a pseudo gap near the E F , the spin up (minority) has a local DOS maximum at E F . via hybridization of Cr-3 d with Pd-4 d to form bonding and anti-bonding just above E F , the exchange splitting gives a sizable magnetic momentum of 2.8 \(\:{\mu\:}_{B}\) on Cr. The 1L spin DOS is similar and have narrower and sharper peaks due to the less band dispersion from the reduced interlayer interactions than bulk. To analyze the origin of the large MAE in CrPd 5 I 2 , we have calculated the k -point resolved MAE over the entire BZ by fixing the magnetic charge density but rotating the magnetic axis from [001] to [100] with SOC. As shown in Fig. 6 (c) and (d) for the \(\:\varDelta\:\) MAE = ± 0.03 meV/f.u, respectively, the positive MAE contribution (favoring the c -axis) in Fig. 6 (c) is mostly around the \(\:{\Gamma\:}\) and X points. In contrast, the negative MAE contribution (favoring in-plane) in Fig. 6 (d) is mostly from the Z, S point and also half way between \(\:{\Gamma\:}\) and X point. Going to the 1L CrPd 5 I 2 , the whole band width is reduced, but most of the hybridization peaks remain the same, which shows that the 1L can retain the chemical stability. The magnetic moment does not change much, the MAE is still quite high at 2.47 meV/f.u. With SOC, the band structures of FM bulk and 1L CrPd 5 I 2 are plotted in Fig. 6 (e) and (f), respectively. The band double degeneracies are all lifted. The top valence band is shown in red and there are many bands crossing the E F and a more complicated FS than the NM TiPd 5 I 2 and InPd 5 I 2 . These many crossings form 2-fold degenerated Weyl nodal lines as plotted in Fig. 6 (g) and (h). For the FM bulk CrPd 5 I 2 , besides the main Weyl nodal loops on the k z = ± 0.5 plane, there are also loops around the X points. For the FM 1L CrPd 5 I 2 , there are three Weyl nodal loops, one around the X point and two around the M points. These Weyl nodal lines are within E F ±0.2 eV. The high MAE in CrPd 5 I 2 reflects the unique structural motif of the -MPd 5 - slab, where each moment-bearing 3 d TM atom is surrounded by Pd with much larger SOC strength. The distance among the 3 d TM atoms is much larger than that in elemental solids. The magnetic coupling among the 3 d TM atoms are through Pd with a larger SOC and itself is near the Stoner magnetic instability. Such combination gives a range of magnetic configurations in MPd 5 I 2 . With the gradual filling of the 3 d orbitals. V, Cr and Mn prefer FM, while Fe, Co and Ni prefer AF. Importantly, both V and Cr prefer easy axis along the c -axis with Cr having the largest MAE of 2.88 meV/f.u. In contrast, FM Mn prefers the in-plane easy-axis, although with a larger moment. Then for AF, first Fe prefers in-plane and then Co and Ni prefer out-of-plane. With such a large MAE and easy-axis being out-of-plane, CrPd 5 I 2 can give a large coercivity field, which is attractive for developing rare-earth-free permanent magnets. III. Conclusions In conclusion, using high throughput density functional theory calculations, we have explored the phase stability, topological and magnetic properties of MPd 5 I 2 compounds (M = Ga, In and 3 d TM), a family of -MPd 5 - slabs separated by two anionic layers of I to design and predict new vdW-layered quantum materials with tetragonal structure. After confirming the existing AlPd 5 I 2 is on the ground state (GS) hull, we find non-magnetic (NM) compounds with M = Ga, In and Ti are also on the GS hull and thermodynamically stable. For the magnetic ones with 3 d TM, we find V, Cr, Mn and Fe are not far above the GS hull and metastable, given the existence of the binary structures with -MPd 5 - slab in the cubic MPd 3 structure. For Co and Ni, the hull energy is the largest and also these MPd 3 form random alloys. Using TiPd 5 I 2 and InPd 5 I 2 as examples, we show that the NM MPd 5 I 2 host a bulk Dirac point for the band manifolds just above the highest valence band and also possibly a strong topological insulator (TI) state from below, respectively. While TiPd 5 I 2 is a Dirac semimetal with a mostly clean Fermi surface, InPd 5 I 2 has a half-filled top valence band with the surface Dirac point from the strong TI appearing at the Fermi energy (E F ). This combination gives the (001) surface hosting both a surface Dirac point and a bulk Dirac projection just 0.1–0.2 eV separation at the \(\:\stackrel{-}{{\Gamma\:}}\) point. From different exchange-correlation functionals, the 1L TiPd 5 I 2 is either a quantum spin Hall (QSH) insulator with an indirect global band gap of 30 meV or a narrow-gap semiconductor with a direct gap of 100 meV, which can be tuned for a topological phase transition. In contrast, the 1L InPd 5 I 2 is always a metal from half band-filling and hosts two QSH states. For the magnetic MPd 5 I 2 with 3 d TMs, the preferred magnetic ground state changes with the gradual filling of the 3 d orbitals. V, Cr and Mn prefers an ferromagnetic (FM) ground states with less or at the half-filling, while Fe, Co and Ni prefers anti-ferromagnetic configuration with more than half-filling of 3 d orbitals. Interestingly both VPd 5 I 2 and CrPd 5 I 2 prefer their FM moment easy axis to be along the out-of-plane c -axis, a desirable feature to develop rare-earth-free permanent magnets. Our calculations predict that MPd 5 I 2 are synthesizable tetragonal vdW-layered quantum materials with non-trivial topological features or strong magnetic anisotropy. IV. Methods Density functional theory 36, 37 (DFT) calculations have been performed with different exchange-correlation (XC) functionals using a plane-wave basis set and projector augmented wave method 45 , as implemented in the Vienna Ab-initio Simulation Package 46, 47 (VASP). Besides PBEsol 39 , for van der Waals (vdW) interaction we have used vdW density functional (vdW-DF) of optB86b 40 and the most recent r2SCAN + rVV10 42 . Band structures have been calculated with spin-orbit coupling (SOC) and the results have also been checked with modified Becke-Johnson 43 (mBJ) and HSE06 44 exchange functional. We have used a kinetic energy cutoff of 400 eV, Γ -centered Monkhorst-Pack 48 with a k-point density of 0.025 1/Å and a Gaussian smearing of 0.05 eV. The ionic positions and unit cell vectors are fully relaxed with the remaining absolute force on each atom being less than 1×10 –2 eV/Å. For the single-layer (1L) structures, ionic relaxation is allowed in all the directions, while the lattice vectors are only relaxed along the in-plane directions ( x - y ) with a 20 Å vacuum inserted along the out-of-plane ( z ) direction. In magnetic systems, calculations are initialized with a magnetic moment of 5 µ B for transition metals and 0 µ B for other elements in both FM and AF configurations. Magnetic anisotropy energy (MAE) calculations are performed by changing the global spin quantization axis from the z to x direction. Phase stability analysis is conducted using the convex hull algorithm 49, 50 , which is implemented in the Pymatgen package 51, 52 . The high throughput calculations on electronic structure and thermodynamics have been carried out in the workflow of High throughput Electronic Structure Pakage (HTESP) 53 . To calculate Wilson loop and surface spectral functions, maximally localized Wannier functions (MLWF) 54, 55 and the tight-binding model have been constructed to reproduce closely the band structure within ± 1eV of the Fermi energy (E F ) by using Group III sp , TM sd and I p orbitals. The surface spectral functions have been calculated with the surface Green’s function methods 56, 57 as implemented in WannierTools 58 . Declarations Data Availability : The data that support the findings of this study are available from the corresponding authors upon reasonable request. Acknowledgements The topological band structure calculations and analysis were supported by the Center for the Advancement of Topological Semimetals, an Energy Frontier Research Center funded by the U.S. Department of Energy Office of Science, Office of Basic Energy Sciences through the Ames National Laboratory under its Contract No. DE-AC02-07CH11358. The phase stability and magneto-anisotropy calculations in this work at Ames National Laboratory were supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division. 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(a) Crystal structures of MPd\u003csub\u003e5\u003c/sub\u003e motif in the three-atomic-layer slab with increasing distance between slabs as in MPd\u003csub\u003e3\u003c/sub\u003e of \u003cem\u003ePm-3m\u003c/em\u003e (221) in Cu\u003csub\u003e3\u003c/sub\u003eAu-type, MPd\u003csub\u003e5\u003c/sub\u003eP of \u003cem\u003eP4/mmm\u003c/em\u003e (123) and MPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e of \u003cem\u003eI4/mmm\u003c/em\u003e (139). The atomic species are shown in different colors and labeled accordingly. (b) Projected density of states (PDOS) on atomic orbitals of non-magnetic InPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e, TiPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e and ferromagnetic (FM) CrPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e. (c) Convex hull energy (E\u003csub\u003eh\u003c/sub\u003e) of MPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e and MPd\u003csub\u003e5\u003c/sub\u003eI (M=Al, Ga, In, Ti, V, Cr, Mn, Fe, Co and Ni) calculated in density functional theory (DFT) with PBEsol and optB86b exchange-correlation functionals. The ground state magnetic configurations with easy axis are drawn with the listed moment size on the magnetic ions (from V to Ni) and magneto-anisotropy energy (MAE). FM and anti-ferromagnetic (AF) are shown in red and blue shaded squares, respectively.\u0026nbsp;\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-4830029/v1/0c6d5f92a5007fc55ef96de9.png"},{"id":66164619,"identity":"631a10de-3dc5-4ee3-a3fa-b41432a6138c","added_by":"auto","created_at":"2024-10-08 09:49:22","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":665123,"visible":true,"origin":"","legend":"\u003cp\u003ePhase stability and structural energies of MPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e. (a) Volume per atom of the fully relaxed elemental, binary and ternary compounds in PBEsol are compared to available experimental data with the mean absolute percentage errors (MAPE) listed. (b) Same comparison for optB86b. (c)-(l) The calculated phase stability and structural energies of MPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e (M=Al, Ga, In, Ti, V, Cr, Mn, Fe, Co and Ni) in optB86b. The compounds on the ground state hull are labeled as green dots. The MPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e are indicated with arrows and their respective hull energies are listed in parenthesis.\u0026nbsp;\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-4830029/v1/828af1b1f2af24ba5c72fe29.png"},{"id":66166566,"identity":"c8ceb8a3-3579-4be8-b34e-cca2efc432f1","added_by":"auto","created_at":"2024-10-08 09:57:22","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":2452197,"visible":true,"origin":"","legend":"\u003cp\u003eSee image above for figure legend.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-4830029/v1/34a275b6ef710ccd4edd58b6.png"},{"id":66164624,"identity":"cfa145c3-563c-4016-b015-22331941ebd1","added_by":"auto","created_at":"2024-10-08 09:49:22","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":1500294,"visible":true,"origin":"","legend":"\u003cp\u003eSee image above for figure legend.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-4830029/v1/badced54349b206823627e59.png"},{"id":66164623,"identity":"df8f2ce0-fb5f-4cef-a2eb-d8a1c02f28e5","added_by":"auto","created_at":"2024-10-08 09:49:22","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":2072804,"visible":true,"origin":"","legend":"\u003cp\u003eSee image above for figure legend.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-4830029/v1/c12d896927195fabd4dc338d.png"},{"id":66164622,"identity":"f9416c35-eedf-4e98-9adb-e77c19e6b212","added_by":"auto","created_at":"2024-10-08 09:49:22","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":1209236,"visible":true,"origin":"","legend":"\u003cp\u003eElectronic structures and crystalline magneto-anisotropy of bulk and single-layer (1L) CrPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e. (a-b) Up (minority) and down (majority) density of state (DOS) for bulk and 1L CrPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e without spin-orbit coupling (SOC) (c-d) k-point resolved magneto-anisotropy energy (MAE) isosurface at ±0.03 meV/f.u. for bulk CrPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e with switching the magnetic axis from [001] to [100] with SOC. (e-f) Band structure with SOC for bulk and 1L CrPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e with the highest valence band (N) shown in red. (g-h) Weyl nodal lines of bulk and 1L CrPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e between band N and N+1.\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-4830029/v1/afb1a4e44361a66cd91d48bd.png"},{"id":76740507,"identity":"61119717-b784-40e6-8b6f-7b5466da0b51","added_by":"auto","created_at":"2025-02-20 08:09:56","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":10509599,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4830029/v1/f46b4bb8-1d09-4c01-94b0-1cabd05abe82.pdf"},{"id":66166567,"identity":"7b67c2e1-7500-4316-9f3e-da636574a410","added_by":"auto","created_at":"2024-10-08 09:57:22","extension":"docx","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":3323626,"visible":true,"origin":"","legend":"","description":"","filename":"MPd5I2v5SM.docx","url":"https://assets-eu.researchsquare.com/files/rs-4830029/v1/ad4d4a759bd0a58c99399beb.docx"}],"financialInterests":"(Not answered)","formattedTitle":"Design and Predict Tetragonal van der Waals Layered Quantum Materials of MPd5I2 (M=Ga, In and 3d Transition Metals)","fulltext":[{"header":"I. Introduction","content":"\u003cp\u003eDesign and discovery of novel 2D van der Waals (vdW) layered topological and magnetic materials containing 3\u003cem\u003ed\u003c/em\u003e transition metals (TM) can be essential for advancing both fundamental science and applied technology. For example, understanding and manipulating itinerant 3\u003cem\u003ed\u003c/em\u003e TM magnetism in intermetallics are crucial to understand many emergent states including superconductivity\u003csup\u003e1\u0026ndash;5\u003c/sup\u003e. At the same time, rare-earth-free permanent magnets with 3\u003cem\u003ed\u003c/em\u003e TM having large coercivity and saturation moment are sought after for renewable energy technologies\u003csup\u003e6\u0026ndash;11\u003c/sup\u003e. When combining these two features in the same material, it is rare to find families of magnetic 2D vdW materials with only a handful examples such as CrX\u003csub\u003e3\u003c/sub\u003e (X\u0026thinsp;=\u0026thinsp;I, Br, Cl)\u003csup\u003e12\u0026ndash;17\u003c/sup\u003e, VI\u003csub\u003e3\u003c/sub\u003e\u003csup\u003e18\u003c/sup\u003e, Cr\u003csub\u003e2\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e6\u003c/sub\u003e\u003csup\u003e19\u003c/sup\u003e, Cr\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e6\u003c/sub\u003e\u003csup\u003e20, 21\u003c/sup\u003e, Fe\u003csub\u003e3\u003c/sub\u003eGeTe\u003csub\u003e2\u003c/sub\u003e\u003csup\u003e22\u003c/sup\u003e and MnBi\u003csub\u003e2n\u003c/sub\u003eTe\u003csub\u003e3n\u0026thinsp;+\u0026thinsp;1\u003c/sub\u003e(MBT)\u003csup\u003e23\u003c/sup\u003e. The MBT systems are particularly interesting because most of them are intrinsic antiferromagnetic (AF) topological insulator (TI) that can be exfoliated to a few layers. The discovery of these magnetic 2D vdW materials have galvanized extensive research activities to study their unique properties.\u003c/p\u003e \u003cp\u003eThe recent discovery\u003csup\u003e24\u0026ndash;29\u003c/sup\u003e of magnetic materials with the structural motif of -MPt\u003csub\u003e5\u003c/sub\u003e- and -MPd\u003csub\u003e5\u003c/sub\u003e- slabs in the tetragonal anti-CeCo\u003csub\u003e5\u003c/sub\u003eIn structure has attracted wide attention for incorporating 3\u003cem\u003ed\u003c/em\u003e TM magnetism of Cr, Mn and Fe into slabs of Pd and Pt with large spin-orbit coupling (SOC). Ferromagnetic (FM) CrPt\u003csub\u003e5\u003c/sub\u003eP\u003csup\u003e28\u003c/sup\u003e and MnPd\u003csub\u003e5\u003c/sub\u003eP\u003csup\u003e29\u003c/sup\u003e have shown large magneto-anisotropy energy (MAE) for possible rare-earth-free permanent magnet applications, however, the easy axis is in-plane. These 1-5-1 compounds with separation of -MPd\u003csub\u003e5\u003c/sub\u003e- and -MPt\u003csub\u003e5\u003c/sub\u003e- slabs by a single layer of P or As are not exfoliable due to the strong bonding of P or As to Pd or Pt on both sides. But it hints at a new way to design 2D vdW materials by inserting more anion layers to separate the well-structured atomic metal slabs. On the other hand, non-magnetic (NM) 2D vdW materials that can be exfoliated to a single layer are in high demand to realize a range of emergent quantum states from superconductivity\u003csup\u003e30\u003c/sup\u003e to fractional quantum Hall effect\u003csup\u003e31\u0026ndash;33\u003c/sup\u003e by twisting few-layer systems, as well as charge density wave (CDW) induced quantum spin Hall (QSH) effect\u003csup\u003e34\u003c/sup\u003e by gating. These new tetragonal vdW-layered materials predicted here can potentially provide a platform for the twisted few-layer systems with a tetragonal lattice\u003csup\u003e35\u003c/sup\u003e besides the twisted hexagonal and orthorhombic lattices.\u003c/p\u003e \u003cp\u003eHere we report the design and prediction of 2D vdW-layered I-separated -MPd\u003csub\u003e5\u003c/sub\u003e- slabs in the body-centered tetragonal crystal structure of MPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e with (M\u0026thinsp;=\u0026thinsp;Ga, In and 3d TMs) by first-principles calculations. The phase stability calculations based on density functional theory\u003csup\u003e36, 37\u003c/sup\u003e (DFT) show that the NM ones are on the ground state (GS) hull and thermodynamically stable, similar to the already existing AlPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e\u003csup\u003e38\u003c/sup\u003e, and a few magnetic ones are close to the GS hull and thus metastable. These materials have either topologically non-trivial band structures or interesting magnetic properties. In the two band manifolds near the Fermi energy (E\u003csub\u003eF\u003c/sub\u003e), the NM compounds host a pair of bulk Dirac points (BDPs) and a possible strong TI state just above and below the highest valence band, respectively. While TiPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e is a Dirac semimetal (DSM) with a relatively clean Fermi surface (FS), InPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e has a half-filled top valence band with the surface Dirac point (SDP) from the strong TI state appearing at the E\u003csub\u003eF\u003c/sub\u003e. This combined feature results in the surface states with both the BDP projection and SDP appearing at the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\Gamma\\:}\\)\u003c/span\u003e\u003c/span\u003e point in a narrow energy window of 0.1\u0026ndash;0.2 eV around the E\u003csub\u003eF\u003c/sub\u003e in TiPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e and InPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e. The single layer (1L) TiPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e is a QSH insulator with an indirect global band gap of 30 meV or a narrow-gap semiconductor with a small direct gap of 100 meV depending on the DFT exchange-correlation (XC) functional, while InPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e hosts two QSH states just above and below the half-filled top valence band. Among the magnetic ones, CrPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e stands out for having the highest MAE of 2.88 meV/f.u. with the FM easy axis along the \u003cem\u003ec\u003c/em\u003e-axis giving the desirable out-of-plane magnetic anisotropy needed for rare-earth-free permanent magnet. The large MAE remains for the 1L FM CrPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e. From the many band crossings around E\u003csub\u003eF\u003c/sub\u003e in both bulk and 1L CrPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e, there are Weyl nodal lines protected by the horizontal mirror plane as the FM magnetic moment is along the \u003cem\u003ec\u003c/em\u003e-axis.\u003c/p\u003e"},{"header":"II. Results and Discussion","content":"\u003cp\u003e \u003cb\u003eII-a. Structural motif and phase stability\u003c/b\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(a) summaries the design of layered compounds based on the -MPd\u003csub\u003e5\u003c/sub\u003e- slab. Without layer separation, the -MPd\u003csub\u003e5\u003c/sub\u003e- slab with shared plane boundary is in the Cu\u003csub\u003e3\u003c/sub\u003eAu-type structure in space group (SG) \u003cem\u003ePm-3m\u003c/em\u003e (221) with M being surrounded by 12 nearest-neighbor Pd in a local close-packed face-centered cubic (FCC) structure. As shown by the successful synthesis of MPd\u003csub\u003e5\u003c/sub\u003eP and MPd\u003csub\u003e5\u003c/sub\u003eAs compounds\u003csup\u003e27, 29\u003c/sup\u003e, an anionic layer can be inserted between the -MPd\u003csub\u003e5\u003c/sub\u003e- slabs to make new structures in the SG \u003cem\u003eP4/mmm\u003c/em\u003e (123). With P/As in the nominal valence of 3\u0026ndash;, it is possible to have two I to replace P and more importantly it becomes vdW layered, as shown by the existence of AlPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e\u003csup\u003e38\u003c/sup\u003e, the only reported compound in this structure so far. It replaces P with two I and shifts the -MPd\u003csub\u003e5\u003c/sub\u003e- slabs in-plane for every other layer, which results in a body-centered tetragonal (tI16) structure in SG \u003cem\u003eI4/mmm\u003c/em\u003e (139). Here we design and predict new vdW layered compounds in this structure by replacing Al with other group III elements and also 3\u003cem\u003ed\u003c/em\u003e TMs via high throughput DFT calculations.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAs plotted in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(b) for the projected density of states (PDOS) of NM InPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e, TiPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e and FM CrPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e, most of the I 5\u003cem\u003ep\u003c/em\u003e orbitals hybridize with the bottom of Pd 4\u003cem\u003ed\u003c/em\u003e orbitals from \u0026minus;\u0026thinsp;6 to \u0026minus;\u0026thinsp;4 eV to form the \u003cem\u003ep-d\u003c/em\u003e bonding states. The \u003cem\u003ep-d\u003c/em\u003e anti-bonding states are pushed to above 1 eV as empty states to gain more cohesion for the ternary compounds with additional bonding hybridization between Pd 5\u003cem\u003es\u003c/em\u003e (not shown) and I 5\u003cem\u003ep\u003c/em\u003e orbitals in the same low-energy range. In contrast to I 5\u003cem\u003ep\u003c/em\u003e, the \u003cem\u003ep\u003c/em\u003e orbitals of group III elements at M site, for example In, mostly hybridizes with Pd 4\u003cem\u003ed\u003c/em\u003e states at a higher energy range (\u0026ndash;4 to \u0026minus;\u0026thinsp;2 eV), reflecting their electron positive character. But the states near the E\u003csub\u003eF\u003c/sub\u003e in InPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e are dominated by Pd 4\u003cem\u003ed\u003c/em\u003e and I 5\u003cem\u003ep\u003c/em\u003e orbitals. Next moving to 3\u003cem\u003ed\u003c/em\u003e TM, Ti 3\u003cem\u003ed\u003c/em\u003e orbitals hybridize extensively with Pd 4\u003cem\u003ed\u003c/em\u003e orbitals giving the broader and lower Pd 4\u003cem\u003ed\u003c/em\u003e-derived bands than InPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e below the E\u003csub\u003eF\u003c/sub\u003e. There is also a large empty anti-bonding DOS peak just above the E\u003csub\u003eF\u003c/sub\u003e due to the 3\u003cem\u003ed\u003c/em\u003e-4\u003cem\u003ed\u003c/em\u003e hybridization. Then for Cr with two more 3\u003cem\u003ed\u003c/em\u003e electrons, these empty states get partially filled and induce a large exchange interaction shown as the two splitting DOS peaks at 0 and +\u0026thinsp;2 eV. This interaction gives a sizable magnetic moment on Cr of 2.80 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\mu\\:}_{B}\\)\u003c/span\u003e\u003c/span\u003e to prefer FM and importantly the easy axis is along the \u003cem\u003ec\u003c/em\u003e-axis with a large MAE of 2.88 meV/f.u. The PDOS for other magnetic 3\u003cem\u003ed\u003c/em\u003e TM MPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e are similar in terms of band hybridizations. The NM TiPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e is an interesting case with the right number of valence electrons that the anti-bonding states are almost completely empty giving a minimum DOS at E\u003csub\u003eF\u003c/sub\u003e to form a DSM, whose topological band structure will be detailed later.\u003c/p\u003e \u003cp\u003eThe GS convex hull energy (E\u003csub\u003eh\u003c/sub\u003e) for all the MPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e compounds studied are plotted in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(c) for PBEsol\u003csup\u003e39\u003c/sup\u003e and also with vdW exchange functional of optB86b\u003csup\u003e40\u003c/sup\u003e. To confirm that the introduction of I prefers two anion layers instead of one, besides the MPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e in the \u003cem\u003eI4/mmm\u003c/em\u003e structure, we have also calculated the hypothetical MPd\u003csub\u003e5\u003c/sub\u003eI in the \u003cem\u003eP4/mmm\u003c/em\u003e structure. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(c), E\u003csub\u003eh\u003c/sub\u003e for MPd\u003csub\u003e5\u003c/sub\u003eI are all above 0.10\u0026nbsp;eV/atom, much higher than MPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e, confirming the qualitative argument that the broken metallic interactions in separating -MPd\u003csub\u003e5\u003c/sub\u003e- slabs need to be compensated by a strong ionic interaction with enough anionic valence. For group III elements, Al, Ga and In, the E\u003csub\u003eh\u003c/sub\u003e of MPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e are all zero for PBEsol and slightly below 0.01\u0026nbsp;eV/atom for optB86b, which shows they are all thermodynamically stable as AlPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e has already been found in experiment\u003csup\u003e38\u003c/sup\u003e, although optB86b gives a small positive E\u003csub\u003eh\u003c/sub\u003e of 0.006\u0026nbsp;eV/atom. InPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e has the smallest E\u003csub\u003eh\u003c/sub\u003e, thus the most stable among the group III compounds. For the 3\u003cem\u003ed\u003c/em\u003e TMs, first TiPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e is quite stable on the GS hull even for optB86b and we found it is a DSM with a clean FS. Next for V and Cr, E\u003csub\u003eh\u003c/sub\u003e becomes positive, but smaller than 0.10\u0026nbsp;eV/atom. Then E\u003csub\u003eh\u003c/sub\u003e decreases for Mn and Fe at the middle of 3\u003cem\u003ed\u003c/em\u003e TM series, and increases again for the late 3\u003cem\u003ed\u003c/em\u003e Co and Ni, which are the least stable among the 3\u003cem\u003ed\u003c/em\u003e TM MPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e. Overall, optB86b gives a higher E\u003csub\u003eh\u003c/sub\u003e than PBEsol, showing a systematic shift between the different XC functionals. But the trends for the variation in E\u003csub\u003eh\u003c/sub\u003e across the whole series for both MPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e and MPd\u003csub\u003e5\u003c/sub\u003eI are the same for different XC functionals showing the results are well converged.\u003c/p\u003e \u003cp\u003eThe magnetic properties across the 3\u003cem\u003ed\u003c/em\u003e TM series for MPd5I2 are quite interesting and tabulated at the top of Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(c). Except for Ti being NM, the magnetic moment size increases first starting with V, reaching the maximum of 3.92 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\mu\\:}_{B}\\)\u003c/span\u003e\u003c/span\u003e for Mn before decreases at the end of the series for Co and Ni. With the gradual filling of the 3\u003cem\u003ed\u003c/em\u003e orbitals, V, Cr and Mn prefer FM, while Fe, Co and Ni prefer AF. Importantly, both V and Cr prefer easy axis along the \u003cem\u003ec\u003c/em\u003e-axis with Cr having the largest MAE of 2.88 meV/f.u., much higher than the 0.30 meV/f.u. for VPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e and the rest. In contrast, FM Mn prefers the in-plane easy-axis, although with the largest moment. Then for AF, first Fe moments prefers in-plane and then Co and Ni prefer out-of-plane directions.\u003c/p\u003e \u003cp\u003eTo study phase stability and construct GS hull, all the existing binary and ternary compounds together with the elemental ones in the ternary phase diagrams have been computed and their stability are calculated via different possible reaction paths. Although PBEsol gives AlPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e on the GS hull agreeing with experiment, Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(a) shows the calculated volume per atom is underestimated when compared to available experimental data. This underestimation of volume with PBEsol is improved by using optB86b exchange functional. Also, to explicitly include vdW interaction for the 1-5-2 compounds, we have chosen optB86b vdW exchange functional for the phase stability plots in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, as well as the band structure and magnetic property calculations. The GS hulls with PBEsol are similar and can be found in Fig.\u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e of SM.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAs shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, for Pd-I binary, there is only one stable line compound of PdI\u003csub\u003e2\u003c/sub\u003e. For M-I binaries, there are many stable line compounds for Ga, In, Ti and V. For the rest, there is only one stable binary M-I compound including CrI\u003csub\u003e3\u003c/sub\u003e for Cr-I. For M-Pd, Al, Ga, In, Ti, V and Mn have many stable line compounds. Interestingly, for the -MPd\u003csub\u003e5\u003c/sub\u003e- motif in MPd\u003csub\u003e3\u003c/sub\u003e or the Cu\u003csub\u003e3\u003c/sub\u003eAu-type, this binary line compound structure exists for In, Ti, V, Cr, Mn and Fe with Pd. But for Ni and Co, they form random alloy or solid solution with Pd. Because CoPd\u003csub\u003e3\u003c/sub\u003e and NiPd\u003csub\u003e3\u003c/sub\u003e both are only slightly above the GS hull at 0.06\u0026nbsp;eV/atom, they can be used as good representatives for the binary solid solution. We also include them in calculating the stability of the MPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e. Among the calculated MPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e, the NM compounds are more stable than the magnetic ones. Given AlPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e with the E\u003csub\u003eh\u003c/sub\u003e of 0.006\u0026nbsp;eV/atom in optB86b has already been synthesized, we predict the existence of GaPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e, InPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e and TiPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e because they are on the GS hull. For magnetic ones, Mn and Fe have the smallest E\u003csub\u003eh\u003c/sub\u003e above GS hull and then followed by V and Cr. Considering the approximations used in DFT calculations, we predict these four magnetic ternaries are metastable, also because the binary MPd\u003csub\u003e3\u003c/sub\u003e line compounds with the -MPd\u003csub\u003e5\u003c/sub\u003e- motif are stable and found in experiments. Lastly for Co and Ni, they have the largest E\u003csub\u003eh\u003c/sub\u003e above GS hull even with PBEsol and because the solid solution of MPd\u003csub\u003e3\u003c/sub\u003e, it is also possible to form solid solution for the ternary compounds. We predict these two are possible ternaries but with solid solution tendency, which needs to be further studied in the future. From an experimental viewpoint, these MPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e compounds are much more challenging to synthesize than MPd\u003csub\u003e5\u003c/sub\u003eP and MPd\u003csub\u003e5\u003c/sub\u003eAs because of the higher vapor pressure or lower sublimation temperature of I than P and As.\u003c/p\u003e \u003cp\u003e \u003cb\u003eII-b. Topological features of non-magnetic 1-5-2 compounds\u003c/b\u003e \u003c/p\u003e \u003cp\u003eFor the band structures of NM MPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e, we chose TiPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e and InPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e to present the topological band features of both the bulk and 1L structures. Bulk band structures of other MPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e can be found in Fig.S2 of SM. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(a) plots the band structure of bulk TiPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e without SOC with the body-centered tetragonal Brillouin zone (BZ) and high symmetry k-points shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(c). The highest valence band (N) and band below (N\u0026ndash;2) according to simple filling are shown in red and blue, respectively. Above the highest valence band, there is a sizable gap in most of the BZ, except for around the Z point in the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\Gamma\\:}\\)\u003c/span\u003e\u003c/span\u003e-Z, Z-S\u003csub\u003e1\u003c/sub\u003e and Y\u003csub\u003e1\u003c/sub\u003e-Z directions. Along the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\Gamma\\:}\\)\u003c/span\u003e\u003c/span\u003e-Z direction, band N and N\u0026ndash;2 are degenerate, giving triple degeneracy (or six-fold including spin) at the crossing point between the highest valence and lowest conduction band in the middle of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\Gamma\\:}\\)\u003c/span\u003e\u003c/span\u003e-Z. From the triple degeneracy point to the Z point, a doubly degenerated nodal line segment appears, also shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(d) by plotting the zero-gap \u003cem\u003ek\u003c/em\u003e-points in the whole BZ. The crossings along the Z-S\u003csub\u003e1\u003c/sub\u003e and Y\u003csub\u003e1\u003c/sub\u003e-Z directions are parts of the nodal line loops around the Z point on the (110) and (\u003cspan additionalcitationids=\"CR2 CR3 CR4 CR5 CR6 CR7 CR8 CR9\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e) planes as protected by the diagonal mirror symmetries.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eWith SOC, as plotted in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(b), the orbital degeneracy for the top two valence bands along the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\Gamma\\:}\\)\u003c/span\u003e\u003c/span\u003e-Z direction is lifted and the nodal loops are all gapped out, except for the crossing between the highest valence and lowest conduction band along the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\Gamma\\:}\\)\u003c/span\u003e\u003c/span\u003e-Z forming a BDP as protected by the four-fold rotational symmetry. Because of the time-reversal symmetry (TRS) and inversion symmetry, each band is still doubly degenerated. The BDP is zoomed in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(e) along the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\Gamma\\:}\\)\u003c/span\u003e\u003c/span\u003e-Z direction showing the zero gap and the switching between I \u003cem\u003ep\u003c/em\u003e\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e and Pd \u003cem\u003ed\u003c/em\u003e\u003csub\u003e\u003cem\u003exz\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003ed\u003c/em\u003e\u003csub\u003e\u003cem\u003eyz\u003c/em\u003e\u003c/sub\u003e orbitals with the 2-dimensional irreducible representations of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\Gamma\\:}\\)\u003c/span\u003e\u003c/span\u003e\u003csub\u003e9\u003c/sub\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\Gamma\\:}\\)\u003c/span\u003e\u003c/span\u003e\u003csub\u003e6\u003c/sub\u003e. The BDPs are at the momentum energy of (0, 0, \u0026plusmn;\u0026thinsp;0.1499 \u0026Aring;\u003csup\u003e\u0026ndash;1\u003c/sup\u003e; E\u003csub\u003eF\u003c/sub\u003e+0.0236 eV), also shown as the red dots in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(c). The band structure of TiPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e along the Z-S\u003csub\u003e1\u003c/sub\u003e direction is zoomed in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(f) to show the small SOC-induced gap.\u003c/p\u003e \u003cp\u003eInterestingly for the highest valence band (red), it is also gapped from below by the next valence band (blue). The lower branch of the orbital degenerated band N\u0026ndash;2 along \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\Gamma\\:}\\)\u003c/span\u003e\u003c/span\u003e-Z forms a band inversion region around the Z point with the top valence band N. Wilson loop calculations show this N\u0026ndash;2 band manifold hosts a strong TI (STI) state with the Fu-Kane\u003csup\u003e41\u003c/sup\u003e topological index of (1;001). The Wilson loop with Wannier charge centers (WCC) on the \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e=0.5 plane in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(g) shows the non-trivial Z\u003csub\u003e2\u003c/sub\u003e number with the odd number of crossings by the dashed line with WCC. Calculations with more recent r2SCAN\u0026thinsp;+\u0026thinsp;rVV10\u003csup\u003e42\u003c/sup\u003e XC functional show similar band features (see Fig.S3 in SM). For mBJ\u003csup\u003e43\u003c/sup\u003e functional, the BDP still remains, despite most of the valence bands being pushed lower and conduction bands higher in energy. But the band inversion at the Z point is lifted between band N\u0026ndash;2 and N for mBJ functional giving no STI. The existence of this band inversion for STI or not in TiPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e will be the features need to be verified in experiment.\u003c/p\u003e \u003cp\u003eTo demonstrate the non-trivial band structure of TiPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e with a BDP above and a STI below the highest valence band, we have calculated the (001) surface spectral functions from the Wannier functions. On (001) surface, the projections of the BDP at \u0026plusmn;\u0026thinsp;\u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e onto the same \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\Gamma\\:}\\)\u003c/span\u003e\u003c/span\u003e point are isolated in energy and have no overlap with other bulk band projection because of the clean FS. There are topological surface states (TSS) stemming from the BDP projection as seen in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(h) at E\u003csub\u003eF\u003c/sub\u003e+0.03 eV. Below that at E\u003csub\u003eF\u003c/sub\u003e\u0026ndash;0.2 eV is the SDP from the STI of the N\u0026ndash;2 band manifold also shown clearly even though on top of the other bulk band projections. The spin-texture of the surface Dirac cone is plotted at E\u003csub\u003eF\u003c/sub\u003e\u0026ndash;0.185 eV in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(j) confirming the spin-momentum locking of the surface Dirac cone. The spin-momentum locking of the TSS stemming from the BDP projection is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(i) at E\u003csub\u003eF\u003c/sub\u003e+0.045 eV. Thus, bulk TiPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e is a DSM with a clean FS surface and also possibly hosts a STI below the highest valence band.\u003c/p\u003e \u003cp\u003eWhen the vdW layered TiPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e is exfoliated down to 1L, the band structure is plotted in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e(a). A large band gap exists in most of the BZ, while a small gap appears along the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\Gamma\\:}\\)\u003c/span\u003e\u003c/span\u003e-X direction, which is projected from the Z-S\u003csub\u003e1\u003c/sub\u003e direction from the bulk band structure. Overall there is an indirect global band gap of 30 meV between the valence band maximum at X and conduction band minimum at \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\Gamma\\:}\\)\u003c/span\u003e\u003c/span\u003e point. The Wilson loop calculation of the highest valence band manifold in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e(b) indicates it is a QSH with an odd number of crossings of WCC. In contrast, for the N\u0026ndash;2 band manifold (blue), the even number of crossings in the Wilson loop in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e(c) shows it is topologically trivial. The edge spectral functions are plotted in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e(d) and (e) for the different TiPd- and PdI-terminations, respectively. The topological edge states connect the gapped valence with conduction band projections and form TRS-protected edge Dirac points (EDP) at the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\stackrel{-}{{\\Gamma\\:}}\\)\u003c/span\u003e\u003c/span\u003e point. While the EDP on the TiPd-termination is inside the QSH gap, that on PdI-termination is merged into the valence band projection at E\u003csub\u003eF\u003c/sub\u003e\u0026ndash;0.06 eV. With E\u003csub\u003eF\u003c/sub\u003e cutting through the QSH gap, the spin-momentum locked edge states are unavoidable from TRS topological protection. So 1L TiPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e is a tetragonal QSH insulator. Calculations with r2SCAN\u0026thinsp;+\u0026thinsp;rVV10 XC functional show similar band inversion feature at the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\Gamma\\:}\\)\u003c/span\u003e\u003c/span\u003e point for QSH (see Fig.S3 in SM). In contrast, HSE06\u003csup\u003e44\u003c/sup\u003e functional pushes the valence band lower and conduction bands higher in energy, and lift the band inversion and changes the indirect band gap to a direct one with 100 meV at \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\Gamma\\:}\\)\u003c/span\u003e\u003c/span\u003e point (see Fig.S3(d)). Although not a QSH in HSE06, the small gap size can be potentially tuned to close and reopen by strain to induce the band inversion for a topological phase transition to realize a critical 2D Dirac point at the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\Gamma\\:}\\)\u003c/span\u003e\u003c/span\u003e point and then a QSH.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eNext for InPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e as an example from group III MPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e, its bulk band structure with SOC is plotted in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(a). Because of the TRS and inversion symmetry, each band is doubly degenerated. But because of the odd number of electrons, the highest valence band (red in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(a)) is only half-filled, indicated by E\u003csub\u003eF\u003c/sub\u003e sitting right in the middle of the band width. But it is still meaningful to discuss the topological features of the band manifolds below and above the half-filled top valence band, although the FS is finite. Between the highest valence and lowest conduction band, there is only one crossing along the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\Gamma\\:}\\)\u003c/span\u003e\u003c/span\u003e-Z direction as protected by the 4-fold rotational symmetry, similar to TiPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e. The BDP is zoomed in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(b) shown by the projection on I \u003cem\u003ep\u003c/em\u003e\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e and Pd \u003cem\u003ed\u003c/em\u003e\u003csub\u003e\u003cem\u003exz\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003ed\u003c/em\u003e\u003csub\u003e\u003cem\u003eyz\u003c/em\u003e\u003c/sub\u003e orbitals with the 2-dimensional irreducible representations of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\Gamma\\:}\\)\u003c/span\u003e\u003c/span\u003e\u003csub\u003e9\u003c/sub\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\Gamma\\:}\\)\u003c/span\u003e\u003c/span\u003e\u003csub\u003e6\u003c/sub\u003e. The BDP are at the momentum energy of (0, 0, \u0026plusmn;\u0026thinsp;0.0406 \u0026Aring;\u003csup\u003e\u0026ndash;1\u003c/sup\u003e; E\u003csub\u003eF\u003c/sub\u003e+0.0955 eV). In contrast, between the highest and the next valence band (blue), there is no band crossing. For such gapped band manifolds, the Fu-Kane topological index has been calculated as (1;001) showing it hosts a STI state. The Wilson loop with WCC at the \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e=0.5 plane is plotted in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(c). To confirm the STI with surface spectral function on (001), the surface Dirac cone is shown clearly in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(d) with the SDP right at the E\u003csub\u003eF\u003c/sub\u003e and inside the projected bulk gap. The spin-texture of the surface states at the E\u003csub\u003eF\u003c/sub\u003e is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(e) confirming the spin-momentum locking topological feature without overlapping with bulk band projection. In contrast, the BDP projection at E\u003csub\u003eF\u003c/sub\u003e+0.10 eV on (001) surface in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(d) is buried inside the other bulk band projection and shows no TSS, unlike those in TiPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e with a clean FS. Thus, group III MPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e host both a BDP above and a STI below the half-filled highest valence band. For InPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e, both the SDP and BDP projection appear at the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\stackrel{-}{{\\Gamma\\:}}\\)\u003c/span\u003e\u003c/span\u003e point on (001), and they are also within an energy window of 0.1 eV with the SDP being right at the E\u003csub\u003eF\u003c/sub\u003e and BDP just above the E\u003csub\u003eF\u003c/sub\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe band structure of 1L InPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e is plotted in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(f). Again, due to the odd number of electrons, the top valence band is half-filled with E\u003csub\u003eF\u003c/sub\u003e sitting in the middle of the band width. But the valence band is continuously gapped from both below and above with band inversion, so topological properties can be calculated. The Wilson loop calculation of the band manifolds in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(g) and (h) show the odd number of crossings of WCC confirming it hosts two QSH states. The edge spectral functions are plotted in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(i) and (j) for two different terminations, which are rather similar. The TRS-protected EDP at E\u003csub\u003eF\u003c/sub\u003e+0.3 eV is for the upper QSH and the EDP at E\u003csub\u003eF\u003c/sub\u003e is for the lower QSH. Calculations with r2SCAN\u0026thinsp;+\u0026thinsp;rVV10, mBJ and HSE06 XC functionals all show similar band inversion and topological features (see Fig.S4 in SM), which are much less affected than TiPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e, because InPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e bands are more metallic from the half-filled top valence band than TiPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e. So 1L InPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e hosts two QSH states in a tetragonal structure despite being a metal. Together with the QSH insulator with a small indirect band gap or a narrow-gap semiconductor in 1L TiPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e, the few layer tetragonal systems of these exfoliable 1-5-2 compounds will be an interesting playground for emergent quantum states in future studies.\u003c/p\u003e \u003cp\u003e \u003cb\u003eII-c. Magneto-anisotropy of CrPd\u003c/b\u003e \u003csub\u003e \u003cb\u003e5\u003c/b\u003e \u003c/sub\u003e \u003cb\u003eI\u003c/b\u003e \u003csub\u003e \u003cb\u003e2\u003c/b\u003e \u003c/sub\u003e \u003c/p\u003e \u003cp\u003eAmong the magnetic 3\u003cem\u003ed\u003c/em\u003e TM MPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e compounds, the most interesting one is CrPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e with the largest MAE and easy-axis along the \u003cem\u003ec\u003c/em\u003e-axis. First without SOC, the spin DOS of bulk and 1L CrPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e are plotted in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e(a) and (b), respectively. While the spin down (majority) forms a pseudo gap near the E\u003csub\u003eF\u003c/sub\u003e, the spin up (minority) has a local DOS maximum at E\u003csub\u003eF\u003c/sub\u003e. via hybridization of Cr-3\u003cem\u003ed\u003c/em\u003e with Pd-4\u003cem\u003ed\u003c/em\u003e to form bonding and anti-bonding just above E\u003csub\u003eF\u003c/sub\u003e, the exchange splitting gives a sizable magnetic momentum of 2.8 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\mu\\:}_{B}\\)\u003c/span\u003e\u003c/span\u003e on Cr. The 1L spin DOS is similar and have narrower and sharper peaks due to the less band dispersion from the reduced interlayer interactions than bulk. To analyze the origin of the large MAE in CrPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e, we have calculated the \u003cem\u003ek\u003c/em\u003e-point resolved MAE over the entire BZ by fixing the magnetic charge density but rotating the magnetic axis from [001] to [100] with SOC. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e(c) and (d) for the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varDelta\\:\\)\u003c/span\u003e\u003c/span\u003eMAE\u0026thinsp;=\u0026thinsp;\u0026plusmn;\u0026thinsp;0.03 meV/f.u, respectively, the positive MAE contribution (favoring the \u003cem\u003ec\u003c/em\u003e-axis) in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e(c) is mostly around the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\Gamma\\:}\\)\u003c/span\u003e\u003c/span\u003e and X points. In contrast, the negative MAE contribution (favoring in-plane) in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e(d) is mostly from the Z, S point and also half way between \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\Gamma\\:}\\)\u003c/span\u003e\u003c/span\u003e and X point. Going to the 1L CrPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e, the whole band width is reduced, but most of the hybridization peaks remain the same, which shows that the 1L can retain the chemical stability. The magnetic moment does not change much, the MAE is still quite high at 2.47 meV/f.u.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eWith SOC, the band structures of FM bulk and 1L CrPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e are plotted in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e(e) and (f), respectively. The band double degeneracies are all lifted. The top valence band is shown in red and there are many bands crossing the E\u003csub\u003eF\u003c/sub\u003e and a more complicated FS than the NM TiPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e and InPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e. These many crossings form 2-fold degenerated Weyl nodal lines as plotted in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e(g) and (h). For the FM bulk CrPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e, besides the main Weyl nodal loops on the \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;\u0026plusmn;\u0026thinsp;0.5 plane, there are also loops around the X points. For the FM 1L CrPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e, there are three Weyl nodal loops, one around the X point and two around the M points. These Weyl nodal lines are within E\u003csub\u003eF\u003c/sub\u003e\u0026plusmn;0.2 eV.\u003c/p\u003e \u003cp\u003eThe high MAE in CrPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e reflects the unique structural motif of the -MPd\u003csub\u003e5\u003c/sub\u003e- slab, where each moment-bearing 3\u003cem\u003ed\u003c/em\u003e TM atom is surrounded by Pd with much larger SOC strength. The distance among the 3\u003cem\u003ed\u003c/em\u003e TM atoms is much larger than that in elemental solids. The magnetic coupling among the 3\u003cem\u003ed\u003c/em\u003e TM atoms are through Pd with a larger SOC and itself is near the Stoner magnetic instability. Such combination gives a range of magnetic configurations in MPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e. With the gradual filling of the 3\u003cem\u003ed\u003c/em\u003e orbitals. V, Cr and Mn prefer FM, while Fe, Co and Ni prefer AF. Importantly, both V and Cr prefer easy axis along the \u003cem\u003ec\u003c/em\u003e-axis with Cr having the largest MAE of 2.88 meV/f.u. In contrast, FM Mn prefers the in-plane easy-axis, although with a larger moment. Then for AF, first Fe prefers in-plane and then Co and Ni prefer out-of-plane. With such a large MAE and easy-axis being out-of-plane, CrPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e can give a large coercivity field, which is attractive for developing rare-earth-free permanent magnets.\u003c/p\u003e"},{"header":"III. Conclusions","content":"\u003cp\u003eIn conclusion, using high throughput density functional theory calculations, we have explored the phase stability, topological and magnetic properties of MPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e compounds (M\u0026thinsp;=\u0026thinsp;Ga, In and 3\u003cem\u003ed\u003c/em\u003e TM), a family of -MPd\u003csub\u003e5\u003c/sub\u003e- slabs separated by two anionic layers of I to design and predict new vdW-layered quantum materials with tetragonal structure. After confirming the existing AlPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e is on the ground state (GS) hull, we find non-magnetic (NM) compounds with M\u0026thinsp;=\u0026thinsp;Ga, In and Ti are also on the GS hull and thermodynamically stable. For the magnetic ones with 3\u003cem\u003ed\u003c/em\u003e TM, we find V, Cr, Mn and Fe are not far above the GS hull and metastable, given the existence of the binary structures with -MPd\u003csub\u003e5\u003c/sub\u003e- slab in the cubic MPd\u003csub\u003e3\u003c/sub\u003e structure. For Co and Ni, the hull energy is the largest and also these MPd\u003csub\u003e3\u003c/sub\u003e form random alloys. Using TiPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e and InPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e as examples, we show that the NM MPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e host a bulk Dirac point for the band manifolds just above the highest valence band and also possibly a strong topological insulator (TI) state from below, respectively. While TiPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e is a Dirac semimetal with a mostly clean Fermi surface, InPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e has a half-filled top valence band with the surface Dirac point from the strong TI appearing at the Fermi energy (E\u003csub\u003eF\u003c/sub\u003e). This combination gives the (001) surface hosting both a surface Dirac point and a bulk Dirac projection just 0.1\u0026ndash;0.2 eV separation at the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\stackrel{-}{{\\Gamma\\:}}\\)\u003c/span\u003e\u003c/span\u003e point. From different exchange-correlation functionals, the 1L TiPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e is either a quantum spin Hall (QSH) insulator with an indirect global band gap of 30 meV or a narrow-gap semiconductor with a direct gap of 100 meV, which can be tuned for a topological phase transition. In contrast, the 1L InPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e is always a metal from half band-filling and hosts two QSH states. For the magnetic MPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e with 3\u003cem\u003ed\u003c/em\u003e TMs, the preferred magnetic ground state changes with the gradual filling of the 3\u003cem\u003ed\u003c/em\u003e orbitals. V, Cr and Mn prefers an ferromagnetic (FM) ground states with less or at the half-filling, while Fe, Co and Ni prefers anti-ferromagnetic configuration with more than half-filling of 3\u003cem\u003ed\u003c/em\u003e orbitals. Interestingly both VPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e and CrPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e prefer their FM moment easy axis to be along the out-of-plane \u003cem\u003ec\u003c/em\u003e-axis, a desirable feature to develop rare-earth-free permanent magnets. Our calculations predict that MPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e are synthesizable tetragonal vdW-layered quantum materials with non-trivial topological features or strong magnetic anisotropy.\u003c/p\u003e"},{"header":"IV. Methods","content":"\u003cp\u003eDensity functional theory\u003csup\u003e36, 37\u003c/sup\u003e (DFT) calculations have been performed with different exchange-correlation (XC) functionals using a plane-wave basis set and projector augmented wave method\u003csup\u003e45\u003c/sup\u003e, as implemented in the Vienna Ab-initio Simulation Package\u003csup\u003e46, 47\u003c/sup\u003e (VASP). Besides PBEsol\u003csup\u003e39\u003c/sup\u003e, for van der Waals (vdW) interaction we have used vdW density functional (vdW-DF) of optB86b\u003csup\u003e40\u003c/sup\u003e and the most recent r2SCAN\u0026thinsp;+\u0026thinsp;rVV10\u003csup\u003e42\u003c/sup\u003e. Band structures have been calculated with spin-orbit coupling (SOC) and the results have also been checked with modified Becke-Johnson\u003csup\u003e43\u003c/sup\u003e (mBJ) and HSE06\u003csup\u003e44\u003c/sup\u003e exchange functional. We have used a kinetic energy cutoff of 400 eV, \u003cem\u003eΓ\u003c/em\u003e-centered Monkhorst-Pack\u003csup\u003e48\u003c/sup\u003e with a k-point density of 0.025 1/\u0026Aring; and a Gaussian smearing of 0.05 eV. The ionic positions and unit cell vectors are fully relaxed with the remaining absolute force on each atom being less than 1\u0026times;10\u003csup\u003e\u0026ndash;2\u003c/sup\u003e eV/\u0026Aring;. For the single-layer (1L) structures, ionic relaxation is allowed in all the directions, while the lattice vectors are only relaxed along the in-plane directions (\u003cem\u003ex\u003c/em\u003e-\u003cem\u003ey\u003c/em\u003e) with a 20 \u0026Aring; vacuum inserted along the out-of-plane (\u003cem\u003ez\u003c/em\u003e) direction. In magnetic systems, calculations are initialized with a magnetic moment of 5 \u0026micro;\u003csub\u003eB\u003c/sub\u003e for transition metals and 0 \u0026micro;\u003csub\u003eB\u003c/sub\u003e for other elements in both FM and AF configurations. Magnetic anisotropy energy (MAE) calculations are performed by changing the global spin quantization axis from the \u003cem\u003ez\u003c/em\u003e to \u003cem\u003ex\u003c/em\u003e direction. Phase stability analysis is conducted using the convex hull algorithm\u003csup\u003e49, 50\u003c/sup\u003e, which is implemented in the Pymatgen package\u003csup\u003e51, 52\u003c/sup\u003e. The high throughput calculations on electronic structure and thermodynamics have been carried out in the workflow of High throughput Electronic Structure Pakage (HTESP)\u003csup\u003e53\u003c/sup\u003e. To calculate Wilson loop and surface spectral functions, maximally localized Wannier functions (MLWF)\u003csup\u003e54, 55\u003c/sup\u003e and the tight-binding model have been constructed to reproduce closely the band structure within \u0026plusmn;\u0026thinsp;1eV of the Fermi energy (E\u003csub\u003eF\u003c/sub\u003e) by using Group III \u003cem\u003esp\u003c/em\u003e, TM \u003cem\u003esd\u003c/em\u003e and I \u003cem\u003ep\u003c/em\u003e orbitals. The surface spectral functions have been calculated with the surface Green\u0026rsquo;s function methods\u003csup\u003e56, 57\u003c/sup\u003e as implemented in WannierTools\u003csup\u003e58\u003c/sup\u003e.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eData Availability\u003c/strong\u003e: The data that support the findings of this study are available from the corresponding authors upon reasonable request.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe topological band structure calculations and analysis were supported by\u0026nbsp;the Center for the Advancement of Topological Semimetals, an Energy Frontier Research Center funded by the U.S. Department of Energy Office of Science, Office of Basic Energy Sciences through the Ames\u0026nbsp;National\u0026nbsp;Laboratory under its Contract No. DE-AC02-07CH11358.\u0026nbsp;The phase stability and magneto-anisotropy calculations in this work at Ames National Laboratory were supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division. The Ames National Laboratory is operated for the U.S. Department of Energy by Iowa State University under Contract No. DE-AC02-07CH11358.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003cstrong\u003eAuthor Contributions\u003c/strong\u003e: L.-L.W. and P.C.C.\u0026nbsp;conceived and designed the work with inputs from T.J.S. and N.K.N.\u0026nbsp;N.K.N.\u0026nbsp;and\u0026nbsp;L.-L.W. performed the ab initio calculations on phase stability, topological band structure analysis and magneto-anisotropy. All authors discussed the results and contributed to the final manuscript.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003cstrong\u003eCompeting Interests\u003c/strong\u003e: The authors declare no competing interests.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003e\u003cstrong\u003e\u003c/strong\u003e1. M. Brando, D. Belitz, F. M. Grosche, T. R. 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Soluyanov, WannierTools: An open-source software package for novel topological materials. \u003cem\u003eComputer Physics Communications\u003c/em\u003e \u003cstrong\u003e224\u003c/strong\u003e, 405-416 (2018).\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-2d-materials-and-applications","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"npj2dmaterials","sideBox":"Learn more about [npj 2D Materials and Applications](http://www.nature.com/npj2dmaterials/)","snPcode":"41699","submissionUrl":"https://submission.springernature.com/new-submission/41699/3","title":"npj 2D Materials and Applications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"NPJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-4830029/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4830029/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eQuantum materials with stacking van der Waals (vdW) layers that can host non-trivial band structure topology and magnetism have shown many interesting properties. Here using high-throughput density functional theory calculations, we design and predict tetragonal vdW-layered quantum materials in the MPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e structure (M\u0026thinsp;=\u0026thinsp;Ga, In and 3\u003cem\u003ed\u003c/em\u003e transition metals). Our study shows that besides the known AlPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e, the -MPd\u003csub\u003e5\u003c/sub\u003e- structural motif of three-layer slabs separated by two I layers can host a variety of metal elements giving arise to topological interesting features and highly tunable magnetic properties in both bulk and single layer 2D structures. Among them, TiPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e and InPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e host a pair of Dirac points and a likely strong topological insulator state for the band manifolds just above and below the top valence band, respectively, with their single layers possibly hosting quantum spin Hall states. CrPd\u003csub\u003e5\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e is a ferromagnet with a large out-of-plane magneto-anisotropy energy, desirable for rare-earth-free permanent magnets.\u003c/p\u003e","manuscriptTitle":"Design and Predict Tetragonal van der Waals Layered Quantum Materials of MPd5I2 (M=Ga, In and 3d Transition Metals)","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-10-08 09:49:17","doi":"10.21203/rs.3.rs-4830029/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Reject after peer review","date":"2024-10-29T07:36:39+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"This content is not available.","date":"2024-10-20T20:30:56+00:00","index":3,"fulltext":"This content is not available."},{"type":"reviewerAgreed","content":"This content is not available.","date":"2024-10-15T12:35:35+00:00","index":3,"fulltext":"This content is not available."},{"type":"editorInvitedReview","content":"This content is not available.","date":"2024-10-08T01:07:34+00:00","index":2,"fulltext":"This content is not available."},{"type":"editorInvitedReview","content":"This content is not available.","date":"2024-09-30T03:53:06+00:00","index":1,"fulltext":"This content is not available."},{"type":"reviewerAgreed","content":"This content is not available.","date":"2024-09-18T05:36:02+00:00","index":2,"fulltext":"This content is not available."},{"type":"reviewerAgreed","content":"This content is not available.","date":"2024-09-11T10:33:17+00:00","index":1,"fulltext":"This content is not available."},{"type":"reviewersInvited","content":"","date":"2024-09-05T14:29:43+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-08-05T19:01:43+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-07-30T15:50:30+00:00","index":"","fulltext":""},{"type":"submitted","content":"npj 2D Materials and Applications","date":"2024-07-30T15:50:29+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"npj-2d-materials-and-applications","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"npj2dmaterials","sideBox":"Learn more about [npj 2D Materials and Applications](http://www.nature.com/npj2dmaterials/)","snPcode":"41699","submissionUrl":"https://submission.springernature.com/new-submission/41699/3","title":"npj 2D Materials and Applications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"NPJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"46047eed-0b36-4d7f-b9d5-892c1661b329","owner":[],"postedDate":"October 8th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-02-20T08:09:46+00:00","versionOfRecord":{"articleIdentity":"rs-4830029","link":"https://doi.org/10.1038/s41699-025-00536-6","journal":{"identity":"npj-2d-materials-and-applications","isVorOnly":false,"title":"npj 2D Materials and Applications"},"publishedOn":"2025-02-19 05:00:00","publishedOnDateReadable":"February 19th, 2025"},"versionCreatedAt":"2024-10-08 09:49:17","video":"","vorDoi":"10.1038/s41699-025-00536-6","vorDoiUrl":"https://doi.org/10.1038/s41699-025-00536-6","workflowStages":[]},"version":"v1","identity":"rs-4830029","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4830029","identity":"rs-4830029","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}