An energy efficient way for quantitative magnetization switching

An energy efficient way for quantitative magnetization switching | 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 An energy efficient way for quantitative magnetization switching Jeongmin Hong, Xin Li, Hanuman Bana, Jie Lin, Shuai Zhang, Bao Yi, and 7 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3951579/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 7 You are reading this latest preprint version Abstract When controlling ferroelectric (FE) and ferromagnetic (FM) properties together, this multiferroic system offers many opportunities for energy-efficient electronics such as memories, logic and other novel spintronic devices. Recent progress of electrically controlled spin devices blazes a trail to develop energy efficient devices by controlling magnetization switching. Here, we integrate spin orbit torque (SOT) devices in multiferroics and systematically study the angle dependency of SOT effects on a piezoelectric substrate to control localized in-plane strain using the electric field across the substrate. The controlled strain modulates the magnetization switching quantitatively through SOT in the multiferroic heterostructures. Besides, the strain shows distinguished modulation capability with the different orientations, which can immediately be used in logic arrays. The controllability of electric field on the magnetization switching behavior was revealed by harmonic Hall measurement, X-ray magnetic circular dichroism-photoemission electron microscopy (PEEM), X-ray diffraction, and magnetic force microscopy (MFM) as well as micromagnetic simulation. In virtue of electric-field-induced strain, the result finds the way for controlling SOT-induced magnetization switching with ultralow energy consumption, which will be applicable to the next generation spin-based logic devices. Physical sciences/Nanoscience and technology/Nanoscale devices/Magnetic devices Physical sciences/Nanoscience and technology/Nanoscale materials/Magnetic properties and materials spintronics spin orbit torque strain-mediated magnetization quantitative magnetization switching Figures Figure 1 Figure 2 Figure 3 Figure 4 Introduction Spintronics employing a spin quantum number could be used to many applications including memory, sensors, processing in-memory, neuromorphic computing, quantum/probabilistic computing, flexible spintronic devices, and radiation-tolerant devices. [ 1 – 9 ] To achieve the capability, surface and interface roughness strongly influences the electron transport properties in the systems. [ 10 – 11 ] Multiferroic materials and structures have attracted attention due to their potential in energy conversion and novel spintronic devices. [ 12 – 16 ] Nevertheless, single-phase multiferroic materials, such as BFO, remains limited. In traditional ferroelectrics materials, its polarization originates from the off-centered ions, which are capable of maintaining stable states with full or empty orbitals, whereas magnetic order is usually fulfilled by ordered electron spins with partially filled orbitals. [ 17 ] In this way, multiferroic heterostructure, which is also called artificial multiferroics, was emerged to implement this energy conversion in room temperature. [ 18 , 19 ] In parallel, spin-orbit torque (SOT) has gained considerable attention due to its superior performance. [ 20 , 21 ] SOT-based magnetization switching has been proven to be an efficient and faster device in the aspects of write/read time and write/read energy [ 22 ] with nonvolatility, reversibility, high speed, low power dissipation and good compatibility with the well-developed semiconductor devices. [ 23 , 24 ] Two mechanisms of SOT are known as Rashba effect and spin hall effect (SHE), which are generated at the interface of magnetic heterostructures with broken inversion symmetry and from the bulk spin orbit coupling of heavy metal (HM) layer, respectively. [ 25 ] Pioneering experimental studies have proposed the existence of sizeable damping-like (or Slonczewski) torque (DLT) [ 26 , 27 ], with the form of \(\overrightarrow{m}\times \left(\overrightarrow{m}\times \overrightarrow{p}\right)\) , and field-like torque (FLT) [ 28 ], with the form of \(\overrightarrow{m}\times \overrightarrow{p}\) in ferromagnet/heavy metal (FM/HM) bilayers, in which \(\overrightarrow{m}\) and \(\overrightarrow{p}\) represent the directions of the magnetization and polarization of the spin current, respectively. DLT and FLT are the most significant torques for magnetization switching, nevertheless, the relative contribution of these two kinds of SOTs in a variety of device structures are still under sufficient discussion. The role of DLT and FLT has been extensively explored in HM [ 29 – 31 ]. Ta-based SOT device was fabricated in this work because the magnitudes of DLT and FLT are comparable with each other [ 31 ]. Manipulation of SOTs could help controlling the magnetic transport behaviors in FM/HM heterostructure [ 32 – 33 ]. Apart from current induced magnetization switching, multiferroic heterostructure [ 34 – 36 ] provides more efficient way by utilizing electric field induced strain to control magnetization switching, specifically, to dynamically tune the amplitude of SOTs effective field [ 37 ], in the FM layer. Locally generated strains in simplified device architectures allow an additional degree to control magnetization switching [ 38 – 39 ], which makes spin orbit-based devices a competitive technology in the next generation information devices. In this work, we fabricated in-plane magnetized Ta/CoFeB multilayers on a PMN-PT substrate. Tuning of SOTs by in-plane strain, which is induced by a perpendicular electric field on piezoelectric substrate, is investigated by the harmonic hall voltage measurements. Angle dependency of the SOT effective field on the piezoelectric substrate has also been systematically studied. Effective field of DLT is found to be linearly manipulated by in-plane strain. In-plane strain assisted magnetization switching has been corroborated by PEEM, X-ray microdiffraction, MFM and micromagnetic simulation. Spintronics logic device architecture based on SOT and piezoelectric regulation could help implement complete Boolean logic functions and it has also been proposed with ultralow energy consumption. Results Figure | 1 (a) Schematic of Ta/CoFeB/Pt/PMN-PT heterostructure and the harmonic hall voltage testing method. (b) Devices are structured with the orientations of 0°, 45°, 90° and 135° to measure angular dependence. (c) Magnetic moment measurement of the device under in-plane magnetic field, insert shows the M-H loop with external field varying from − 30 ~ 30 mT. (d) Typical AHE curve of the device under out-of-plane magnetic field. As shown in Fig. 1a, (011) oriented single crystal PMN-PT substrate, with thickness of 500 µm, is double side polished and with both top and bottom surfaces covered by Pt electrodes. Before depositing the magnetic layers on top of the substrate, PMN-PT is electrically pre-poled in (011) direction, with the polarization pointing “up”. Under a vertical upward electric field, the PMN-PT substrate produces an anisotropic in-plane piezoelectric response, generated compressive strain in the [ \(100\) ] direction and tensile strain in the [ \(0\stackrel{-}{1}1\) ] direction. The SOT devices are fabricated into Hall bar by lithography. Devices with different orientations are designed to verify the angle dependance of SOT efficiency manipulation, as shown in the sample picture in Fig. 1b. External magnetic field response of the CoFeB/PMN − PT heterostructure device has been characterized in Fig. 1c and 1d, which indicates that the system is in-plane magnetized. Several methods including Spin Transfer Torque-Ferromagnetic Resonance (ST-FMR), Magneto-optic Kerr effect (MOKE) and Second harmonic spin-torque magnetometry have been put forward for the quantitative characterization of current-induced torques. Among them, the harmonic hall measurements [ 40 – 42 ] injected an alternating current (AC) with specific frequency to induce alternating torque, which drives the magnetization of FM layer tilts periodically around the homeostatic states. DLT and FLT can be separated according to the different dependencies on variational magnetic field angle or magnitude. Among these, the method of varying in-plane magnetic field angle is appropriate to the devices which are in-plane magnetized or with weak perpendicular magnetic anisotropy (PMA). In the structure shown in Fig. 1(a), a constant sinusoidal current \(I\left(t\right)={I}_{0}\text{sin}\omega t\) with frequency of \(f=\left(\omega /2\pi \right)=133 Hz\) is applied to the Hall bar through bias tee while orthogonal voltage \({V}_{xy}={R}_{xy}\bullet {I}_{0}\text{sin}\omega t\) was measured by a lock-in amplifier (LIA), where the hall resistance is mainly contributed by anomalous hall Effect (AHE) and planar hall effect(PHE). Hall voltage signal can be expressed as: $${V}_{xy}={I}_{0}\text{sin}\omega t\times \left[\begin{array}{c}{R}_{A}\left(\text{cos}\theta -\text{sin}\theta \bullet \varDelta \theta \right)+\\ {R}_{P}({sin}^{2}\theta +\text{sin}2\theta \bullet \varDelta \theta )(\text{sin}2\phi +2\text{cos}2\phi \bullet \varDelta \phi )\end{array}\right]$$ Assuming that the external field rotates in XOY plane, which means angle \(\phi\) varies, and the direction of spin polarized current is along (0,1,0) direction, the hall voltage signal can be simplified as: $${V}_{xy}={I}_{0}\text{sin}\omega t\times \left[\begin{array}{c}{R}_{P}\text{sin}2\phi -\\ {R}_{A}\left(-\frac{{H}_{DL}}{-{H}_{K}+H}\right)\text{sin}\omega t+2{R}_{P}\frac{{H}_{FL}}{H}\text{cos}2\phi \text{cos}\phi \text{sin}\omega t\end{array}\right]$$ Among these, $${V}_{xy}^{1\omega }={I}_{0}\text{sin}\omega t\times {R}_{P}\text{sin}2\phi$$ $${V}_{xy}^{2\omega }={I}_{0}\text{sin}\omega t\times \left({R}_{A}\bullet \frac{{H}_{DL}}{-{H}_{K}+H}\text{cos}\phi +2{R}_{P}\frac{{H}_{FL}}{H}\text{cos}2\phi \text{cos}\phi \right)$$ Where \({R}_{P}\) , \({R}_{A}\) represents the planar hall resistance and anomalous hall resistances respectively, \({H}_{FL}\) , \({H}_{DL}\) , \({H}_{K}\) , \(H\) represent the current induced effective field of FLT and DLT, effective perpendicular anisotropy field and external field respectively. First and second harmonic hall voltage curves under increasing magnetic field are shown in Fig. 1(e) & (f). The magnitude of FLT and DLT effective field can be calculated through the coefficient, which are derived by fitting the measured curves with the aforementioned functions. As shown in Fig. 1(b), four different orientation, described as 0-, 45-, 90- and 135-degree devices according to their current direction, are designed to experience different strain distribution from the piezoelectric substrate. Vertical electric field is applied on the piezoelectric substrates with the top electrode grounded and bottom electrode connected to positive high voltage, which varies from 0V to 400V and supplies the electric field varies from 0-800 kV/m. As shown in Fig. 2 (a), effective field of DLT and FLT at zero electric field is setting as the base, and variation of it from the base under increased electric field are listed. Due to the electric field polarity and the substrate orientation, compressive strain acts on 0-drgree device and tensile strain acts on 90-degree device. It’s not hard to find that compressive strain decreases the effective field of DLT while tensile strain increases the effective field of it. For 45- and 135-degree devices, the effective field of DLT still increases, which indicates that tensile strain dominates the stain distribution on them. As for the effective field of FLT, it almost remains unchanged for various device direction as shown in the dashed line in Fig. 2 (a). Micromagnetic simulation was also performed to confirm and further analysis the measurement results. The multiferroic heterostructure is built in COMSOL Multiphysics to get the strain distribution in FM layer under electric field. After that it is modeled in Object oriented micromagnetic framework (OOMMF) [ 43 ] to demonstrate the magnetization dynamics under the aforementioned strain. More settings are described in Methods. As shown in Fig. 2 (b), the device is simplified as a current path with two electrodes in simulation. We can qualitatively find that tensile and compressive strain acts on 0- and 90-degree device respectively, as shown in the inserts of Fig. 2 (b). For 45- and 135-degree device, there is mainly tensile strain on it, which is consistent with test results. As shown in Fig. 2 (b), magnetization precession of FM layer under two cases were compared, which are called “without strain” and “on [011] PMN-PT”. No strain and electric field on [011] PMN-PT induced strain acts on the FM layer during the magnetization precession under these two cases, in respectively. Three stages are observed, which are ①initial state, ②middle state after the action of SOT current and magnetoelastic energy and ③final state after relaxation, respectively. Snapshots of in-plane magnetization on each stage are shown in Fig. 2 (b). Magnetization direction of FM layer \(\left(\overrightarrow{M}\right)\) along + x/-x are represented by red and blue color, average \(\overrightarrow{M}\) of the device is shown by black arrow in the middle of the bar. As a secondary proof, magnetization dynamics of the FM layer in X-axis and Y-axis are shown in Fig. 2 (c). Spin direction of initial and final states is indicated in the picture. Under the aforementioned two cases, we used the same current density of 5×10 − 11 A/cm 2 . Compare these two cases of with/without strain, it’s not hard to find that the magneto-elastic energy couldn’t help implement magnetization switching at final state in 0-degree case. Nevertheless, in 45-, 90- and 135-degree cases, the magneto-elastic energy facilitates the magnetization switching. It illustrates that under this current density, in-plane strain helped the FM layer implement determined magnetization switching rather than random magnetization switching. The electric field induced in-plane strain makes it possible to switch the magnetization with much lower energy consumption, which is around 200 fJ in one operation through estimation, and it can help implement deterministic switching without external magnetic field to break the symmetry. Also, in straintronic logic devices, locally generated strain also provides a way to write information to logic bits in selected area, which helps implement specific logic functions. The scenario of SOT operation in our device is shown in Fig. 3 (a). \({H}_{DL}\text{’}\) and \({\tau }_{DL}\text{’}\) are effective field and torque of DLT, which is compared to normal cases ( \({H}_{DL}\) and \({\tau }_{DL}\) ), after electric field applied on the substrate. Black arrow in top layer and bottom layer represents \(\overrightarrow{M}\) and injected electron current, in respectively. MFM, X-ray microdiffraction and PEEM were also adapted to help verify the electric field-assisted magnetization switching. More experimental details are described in Methods part. Figure 3 (b) shows MFM results of the magnetization switching process of the CoFeB magnetic dot under four different excitation conditions. The magnetic dot with diameter of 20um was fabricated here for better observation of magnetization switching. From the MFM pictures, it’s not hard to find that, with strain only, partial magnetization reversal occurs while with both strain and current applied on the dot, it was fully magnetized. After that, in stage 4, with reverse strain and current direction, magnetization was switched back to the initial state. It can be observed that from stage 1 to 2, the strain applied help implement partial magnetization switching; from stage 2 to 3, current along with strain can help implement full magnetization switching. The MFM results verified that not only strain could help implement full magnetization switching, but also opposite current direction could help rewrite \(\overrightarrow{M}\) , which is essential to the information writing in storage technology. As shown in Fig. 3 (c), effective field of FLT and DLT under different substrate voltage was tested, it’s not hard to find that the effective field of DLT keeps increasing but that of FLT remain unchanged. Laue X-ray microdiffraction was carried out to investigate the elastic strain distribution on the heterojunction device. As shown in Fig. 3 (c), the X-ray microdiffraction results demonstrated that the strain increased (red region expanded) in the middle of the bar as the applied voltage rises. PEEM results also demonstrated the magnetization switching on the magnetic dot when the substrate voltage rising from 0V to 400V. It can be confirmed that the increasing effective field of DLT, which is caused by the electric field induced in-plane strain, assisted the magnetization switching. Combine the above effective field data, PEEM, MFM and X-ray microdiffraction test results together, we can draw the conclusion, with sufficient data support, that increasing in-plane strain induced by the increased substrate voltage is transferred to the FM layer, contributed to the rising of DLT effective field, which has an auxiliary role to the full magnetization switching on the FM layer. Also, these characterization results are consistent with the aforementioned experimental and micromagnetic simulation results shown in Fig. 2 . Logic applications (Fig. 4 ) As shown in Fig. 4 (a), Three inputs (ends of arms) and three control parts (arms), as well as one output (connection) are integrated in single logic device. While in buffer device and negation device shown in Fig. 4 (b) and (c), an extra arm was designed to implement the function of buffer and negation. The original output is then called middle to storage intermediate state of the FM layer. MTJ stacks are designed at each input, middle and output ends to readout the magnetization state of FM layer. Logic state of each end is represented by the resistance state of the readout MTJ stack, which can be rewritten by the polarity of SOT current according to aforementioned method. Logic state of “0”/ “1” represents low/high resistance state of the MTJ stack, respectively. Piezoelectric substrate PMN-PT [011] is designed under each arm of the logic unit for utilizing the strain to assist the magnetization switching. In controlling parts, as well as buffer and negation control arms, strain is delivered to the FM layer through the protruding yellow part. While in other region, strain is impeded by the oxide material (represent by dark grey) to prevent effect on logic state of inputs/output MTJs. In this way, for the control and buffer/negation arms, its logic states of “0”/ “1” represent the existence of strain, namely power on/power off of the electric field under this FM arm, respectively. In single logic unit shown in Fig. 4 (a), with three control ends setting as “1”, “AND” and” OR” logic functions can be toggled in a reconfigurable way in the majority gate, as listed in the top half part of the truth table in Fig. 4 (d). Any two of the inputs can be selected to perform “AND” and” OR” operations. For the logic function of selector shown in the bottom half, the result of “AND” operation of the two inputs, which are setting as “1” and the remaining one setting as “0”, will be shown in the output. In this way, control ends own the ability to select inputs for logic operations. Beyond that, data buffering and negation can be implemented in structures shown in Figs. 4 (b) and (c). According to the angle dependence of the magnetization switching, which has been descripted in micromagnetic simulation section, with the same magnitude of current density as well as electric field applied on the logic device, magnetization state of the middle end will be buffered/negated to the output end while in the “BUFFER” / “NOT” structure, in respectively. In this way, BUFFER and NOT logic functions can be easily implemented. Corresponding logic settings of input/output and control arms (buffer/negation) are listed in the truth table shown in Fig. 4 (e). Cascading ability is also possessed in this logic device. Benefit from the control arms, only when the electric field is power on, the magnetization state transferring is able to carried out. Magnetic states of the output-MTJ can be only transferred to the post unit without any influence on the inputs of the prior unit to achieve good nonreciprocity. Parts of the device region can be altered customizable by utilizing a different configuration of the electric fields to produce correspondingly strain in demand, which allows for an additional level of control. With this extra controlling approach, abundant logic functions, such as “AND”, “OR” and selector, can be implemented in single logic device. With buffer and not, cascading between logic units can be achieved, therefore, complicated logic functions can be implemented. With the assistance of electric field produced strain, the magnetization switching happened at lower current density through SOT, which can largely reduce the power consumption. In the meantime, application of the electric field generates negligible power consumption. The electric-field assisted SOT device we proposed is able to implement full Boole logic with extremely low power assumption and easy, reconfigurable structure, and is highly competitive in energy consumption compared with traditional SOT-based logic devices. Conclusion We demonstrate the quantitative control of magnetization switching through the FM/HM/PMN-PT heterostructure by systematically studying the angle dependence of the SOT effect. Localized in-plane strain on a piezoelectric substrate is controlled by applying vertical DC electric field across the substrate. (011 direction strain / depending on tensile and compressive damping like field and field like torque) damping like effective field / field like effective field (torque is final product) We found that the controlled strain makes it possible to quantitatively modulate the magnetization switching of SOT devices. According to the device setting, effective field of DLT decreased on 0-degree device (compressive strain) and increased on 45-, 90-, and 135-degree (tensile strain) devices, which could hinder or facilitate the magnetization switching, respectively. This phenomenon is subsequently verified by MFM, XMCD-PEEM, as well as micromagnetic simulation. It can be utilized in multiferroic logic devices to supply low-power consumption performance. Methods Summary Device fabrication The hall bar with length = 90 um and width = 15 um were patterned through electron beam lithography and lift-off processes. VSM A VSM 7400 from Lake Shore Cryotronics Inc. was used to perform conventional volume averaging magnetometry measurements. The sample was mounted on a quartz holder and its magnetic moment was measured and averaged with the magnetic field sweeping from − 1T ~ 1T. MFM MFM measurements were conducted in a dynamic lift mode with a lift distance of 30 nm. The dynamics were measured by sweeping the field range in the presence of a magnetic field. PEEM XMCD-PEEM was used to image the magnetic state. The magnetic state in each magnetic layer was separately imaged by exploiting the probe depth of approximately 5 nm and the elemental sensitivity of X-ray absorption at the Co L3-edges. X-ray diffraction Microdiffraction scanning collects individual diffraction patterns step by step from grid points to provide information on lattice strain and crystal orientation. The electrically induced deviatoric strain is calculated for each step by taking the difference between the extracted strain at a non-zero voltage and at a zero voltage. The 2D strain maps are constructed with 10 x 10 um 2 pixels. Simulation COMSOL and OOMMF were used for simulation in this work. The Structural Mechanics Module, Piezoelectric Module, and Magnetostrictive Module were added in COMSOL Multiphysics to analyze the strain and coupling between the piezoelectric substrate and FM thin film in the multiferroic heterostructure. The strain distribution on the FM layer was then induced to the micromagnetic simulation toolkit OOMMF. The YY_FixedMEL: magnetoelastic [ 44 ] term was used to calculate magnetoelastic energy based on the displacement field, in the form of Oxs_VectorField. The strain distribution obtained from COMSOL was converted by the magnetoelastic coupling constant to a spatially correlated uniaxial anisotropy-like magnetoelastic energy with the magnetoelastic coupling constant consistent with the corresponding constant in thin film CoFeB. Other key contributing terms of effective magnetic field are uniaxial anisotropy, exchange coupling, and demagnetization. The FM layer (300×300×1 nm 3 ) is divided by the finite element method (FEM) with a mesh size of 3×3×1 nm 3 . Areas other than the FM bar and electrodes are vacuum by setting Ms = 0. The saturation magnetization (Ms), exchange constant (Aex), magnetic anisotropy energy density (Ku), spin polarization (p), and Gilbert damping constant (α) values used in this paper are 0.86×10 6 A/m, 30×10 − 12 J/m, 0.84 MJ/m 3 , 0.6, and 0.014, respectively, for the FM layer, consistent with CoFeB-based FM material properties. Uniaxial anisotropy direction and initial magnetization direction are setting along the longitudinal direction of the bar due to the shape anisotropy of in-plane magnetized film and demagnetization. Polarization direction of the spin current is perpendicular to the bar due to the spin hall effect. Declarations Data Availability The data that support the findings of this study are available from the corresponding author upon reasonable request. Competing interests: Authors declare that they have no competing interests. Data and materials availability All data are available upon request Author Contribution J.H. and L.X. wrote the main manuscript text and L.X. and H.S. prepared figures 1-4. All authors reviewed the manuscript. Acknowledgments: We acknowledge HBUT starting funding and the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Contract No. DE-AC02-05CH11231. This work also was supported by the Director, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division, of the U.S. Department of Energy under Contract No. DE-AC02-05-CH11231 within the Nonequilibrium Magnetic Materials Program (MSMAG) (sample fabrication and characterization); and the Berkeley Emerging Technology Research (BETR) Center. References Audia, P. G., & Goncalo, J. A. 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Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 21 Mar, 2024 Reviews received at journal 01 Mar, 2024 Reviewers agreed at journal 14 Feb, 2024 Reviewers invited by journal 14 Feb, 2024 Editor assigned by journal 13 Feb, 2024 Submission checks completed at journal 13 Feb, 2024 First submitted to journal 12 Feb, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3951579","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":272921402,"identity":"65be8ef2-c483-4302-8749-b99e58e5b1e9","order_by":0,"name":"Jeongmin Hong","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAq0lEQVRIiWNgGAWjYBACxgYeEGUjY8BOopY0HgNm4u0BazlMghbmaWcPPi74dZ7HnJmB+cXHNmIcNjsv2Xhm320ey2YGNsuZxGnJMZPm7bnNY3CYgc2Y5wzxWs6RqoXnxwGQFubHPBXEaTE25m1IBvqFsY1xBjFaDGfnGD7m+WMnZ87efPjDBwNitDSArAIHFGObBBEaGBjkweQfMMn8gSgto2AUjIJRMOIAAELHMCpgk7ThAAAAAElFTkSuQmCC","orcid":"","institution":"University of California Berkeley","correspondingAuthor":true,"prefix":"","firstName":"Jeongmin","middleName":"","lastName":"Hong","suffix":""},{"id":272921403,"identity":"b1e94b7e-4660-43cd-b39d-fa3964cd9e24","order_by":1,"name":"Xin Li","email":"","orcid":"","institution":"HUST","correspondingAuthor":false,"prefix":"","firstName":"Xin","middleName":"","lastName":"Li","suffix":""},{"id":272921404,"identity":"089117a4-b9e9-4d3f-940f-3f395665273f","order_by":2,"name":"Hanuman Bana","email":"","orcid":"","institution":"Indian Institute of Technology Bombay","correspondingAuthor":false,"prefix":"","firstName":"Hanuman","middleName":"","lastName":"Bana","suffix":""},{"id":272921405,"identity":"4b44c894-6553-4f91-8987-98db0b353187","order_by":3,"name":"Jie Lin","email":"","orcid":"","institution":"Huazhong University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Jie","middleName":"","lastName":"Lin","suffix":""},{"id":272921406,"identity":"b1d576b2-37f1-4fa1-869a-d1bd2636843b","order_by":4,"name":"Shuai Zhang","email":"","orcid":"","institution":"School of Optical and Electronics Information, Huazhong University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Shuai","middleName":"","lastName":"Zhang","suffix":""},{"id":272921407,"identity":"b307693a-8573-45cb-bbc4-f57216114953","order_by":5,"name":"Bao Yi","email":"","orcid":"","institution":"Huazhong University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Bao","middleName":"","lastName":"Yi","suffix":""},{"id":272921408,"identity":"90ad9f4e-aead-4433-b53e-ee2eabcb9ed9","order_by":6,"name":"Jyotirmoy Chatterjee","email":"","orcid":"","institution":"iMec","correspondingAuthor":false,"prefix":"","firstName":"Jyotirmoy","middleName":"","lastName":"Chatterjee","suffix":""},{"id":272921409,"identity":"95552df1-6837-4225-b458-f7a37542d7a3","order_by":7,"name":"Zhuyun Xiao","email":"","orcid":"","institution":"University of California, Los Angeles","correspondingAuthor":false,"prefix":"","firstName":"Zhuyun","middleName":"","lastName":"Xiao","suffix":""},{"id":272921410,"identity":"4f4188f0-84b9-47cd-8ca2-756b3f6d9aa7","order_by":8,"name":"Sucheta Mondal","email":"","orcid":"","institution":"UC Berkeley","correspondingAuthor":false,"prefix":"","firstName":"Sucheta","middleName":"","lastName":"Mondal","suffix":""},{"id":272921411,"identity":"fb779c58-cb41-40e2-8992-04dc1b7b4081","order_by":9,"name":"Nobumichi Tamura","email":"","orcid":"","institution":"Lawrence Berkeley National Laboratory","correspondingAuthor":false,"prefix":"","firstName":"Nobumichi","middleName":"","lastName":"Tamura","suffix":""},{"id":272921412,"identity":"529cd202-334d-4573-9610-8544e2fd8852","order_by":10,"name":"Rob N. Candler","email":"","orcid":"","institution":"University of California, Los Angeles","correspondingAuthor":false,"prefix":"","firstName":"Rob","middleName":"N.","lastName":"Candler","suffix":""},{"id":272921413,"identity":"c989a2d3-7cae-4987-8db3-cc2047ba3455","order_by":11,"name":"Long You","email":"","orcid":"","institution":"Huazhong University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Long","middleName":"","lastName":"You","suffix":""},{"id":272921414,"identity":"eb3527fe-1ed0-4ecb-bbe2-232b6e942616","order_by":12,"name":"Jeffrey Bokor","email":"","orcid":"","institution":"UC Berkeley","correspondingAuthor":false,"prefix":"","firstName":"Jeffrey","middleName":"","lastName":"Bokor","suffix":""}],"badges":[],"createdAt":"2024-02-12 17:45:01","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3951579/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3951579/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":51189420,"identity":"b86d9784-ca6e-4bc9-9de5-fc734508aab0","added_by":"auto","created_at":"2024-02-15 16:50:44","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":509368,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Schematic of Ta/CoFeB/Pt/PMN-PT heterostructure and the harmonic hall voltage testing method. (b) Devices are structured with the orientations of 0°, 45°, 90° and 135° to measure angular dependence. (c) Magnetic moment measurement of the device under in-plane magnetic field, insert shows the M-H loop with external field varying from -30~30 mT. (d) Typical AHE curve of the device under out-of-plane magnetic field.\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-3951579/v1/a385943b20a7211b317bd891.png"},{"id":51189417,"identity":"4b828290-5a89-46ea-a6b6-9923b9404b98","added_by":"auto","created_at":"2024-02-15 16:50:43","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":398655,"visible":true,"origin":"","legend":"\u003cp\u003eHarmonic hall measurement results and micromagnetic simulation results of devices aligned with the angle of 0, 45, 90 and 135 degrees, respectively. (a) Effective field of damping like torque and field like torque varied with the substrate voltage in devices with different orientations. (b \u0026amp; c) Strain distribution and magnetization switching process in FM layer of devices with four orientations. Two cases: without strain and on [011] PMN-PT (with strain) are compared. We demonstrated different switching scenarios by two ways, which are the screenshot of in-plane magnetization and mx, my varied with time, in respectively.\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-3951579/v1/dc0d03b75c367df2fddd2953.png"},{"id":51189416,"identity":"d29f3bc8-0882-4073-acff-53ff728ec493","added_by":"auto","created_at":"2024-02-15 16:50:43","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":667853,"visible":true,"origin":"","legend":"\u003cp\u003e(a) SOT operation scenario of the FM/HM/FE heterostructure. (b) MFM results of the magnetization switching process of the CoFeB magnetic dot. Four pictures indicate different stages, which are 1. with no current, no strain; 2. with strain only; 3. with strain and current; 4. strain with reverse current direction. (c) With the applied voltage increased, changing trend of the effective field of FLT and DLT, PEEM pictures of the magnetic dot as well as X-ray microdiffraction result of the device.\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-3951579/v1/c3fce3eeb17fa8a6eb07cf0e.png"},{"id":51189419,"identity":"9cd7475d-cf71-49b2-8b62-d07d6d2e5a15","added_by":"auto","created_at":"2024-02-15 16:50:43","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":393046,"visible":true,"origin":"","legend":"\u003cp\u003eDesign of logic device structure. (a). Single unit of majority gate device to implement and/or/selector logic functions. (b) and (c) Implementation of data buffering/negation logic functions.\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-3951579/v1/61b0059adc9e751ab924c00a.png"},{"id":51190912,"identity":"36815cae-8850-4ecf-a5d9-0e6d64365736","added_by":"auto","created_at":"2024-02-15 16:58:44","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2366127,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3951579/v1/a5daa4e7-bde5-4f40-a886-364a7f9d6616.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"An energy efficient way for quantitative magnetization switching","fulltext":[{"header":"Introduction","content":"\u003cp\u003eSpintronics employing a spin quantum number could be used to many applications including memory, sensors, processing in-memory, neuromorphic computing, quantum/probabilistic computing, flexible spintronic devices, and radiation-tolerant devices. [\u003cspan additionalcitationids=\"CR2 CR3 CR4 CR5 CR6 CR7 CR8\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e] To achieve the capability, surface and interface roughness strongly influences the electron transport properties in the systems. [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e] Multiferroic materials and structures have attracted attention due to their potential in energy conversion and novel spintronic devices. [\u003cspan additionalcitationids=\"CR13 CR14 CR15\" citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e] Nevertheless, single-phase multiferroic materials, such as BFO, remains limited. In traditional ferroelectrics materials, its polarization originates from the off-centered ions, which are capable of maintaining stable states with full or empty orbitals, whereas magnetic order is usually fulfilled by ordered electron spins with partially filled orbitals. [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e] In this way, multiferroic heterostructure, which is also called artificial multiferroics, was emerged to implement this energy conversion in room temperature. [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]\u003c/p\u003e \u003cp\u003eIn parallel, spin-orbit torque (SOT) has gained considerable attention due to its superior performance. [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e] SOT-based magnetization switching has been proven to be an efficient and faster device in the aspects of write/read time and write/read energy [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e] with nonvolatility, reversibility, high speed, low power dissipation and good compatibility with the well-developed semiconductor devices. [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e] Two mechanisms of SOT are known as Rashba effect and spin hall effect (SHE), which are generated at the interface of magnetic heterostructures with broken inversion symmetry and from the bulk spin orbit coupling of heavy metal (HM) layer, respectively. [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]\u003c/p\u003e \u003cp\u003ePioneering experimental studies have proposed the existence of sizeable damping-like (or Slonczewski) torque (DLT) [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e], with the form of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\overrightarrow{m}\\times \\left(\\overrightarrow{m}\\times \\overrightarrow{p}\\right)\\)\u003c/span\u003e\u003c/span\u003e, and field-like torque (FLT) [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e], with the form of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\overrightarrow{m}\\times \\overrightarrow{p}\\)\u003c/span\u003e\u003c/span\u003e in ferromagnet/heavy metal (FM/HM) bilayers, in which \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\overrightarrow{m}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\overrightarrow{p}\\)\u003c/span\u003e\u003c/span\u003e represent the directions of the magnetization and polarization of the spin current, respectively. DLT and FLT are the most significant torques for magnetization switching, nevertheless, the relative contribution of these two kinds of SOTs in a variety of device structures are still under sufficient discussion. The role of DLT and FLT has been extensively explored in HM [\u003cspan additionalcitationids=\"CR30\" citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]. Ta-based SOT device was fabricated in this work because the magnitudes of DLT and FLT are comparable with each other [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eManipulation of SOTs could help controlling the magnetic transport behaviors in FM/HM heterostructure [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e]. Apart from current induced magnetization switching, multiferroic heterostructure [\u003cspan additionalcitationids=\"CR35\" citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e] provides more efficient way by utilizing electric field induced strain to control magnetization switching, specifically, to dynamically tune the amplitude of SOTs effective field [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e], in the FM layer. Locally generated strains in simplified device architectures allow an additional degree to control magnetization switching [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e], which makes spin orbit-based devices a competitive technology in the next generation information devices.\u003c/p\u003e \u003cp\u003eIn this work, we fabricated in-plane magnetized Ta/CoFeB multilayers on a PMN-PT substrate. Tuning of SOTs by in-plane strain, which is induced by a perpendicular electric field on piezoelectric substrate, is investigated by the harmonic hall voltage measurements. Angle dependency of the SOT effective field on the piezoelectric substrate has also been systematically studied. Effective field of DLT is found to be linearly manipulated by in-plane strain. In-plane strain assisted magnetization switching has been corroborated by PEEM, X-ray microdiffraction, MFM and micromagnetic simulation. Spintronics logic device architecture based on SOT and piezoelectric regulation could help implement complete Boolean logic functions and it has also been proposed with ultralow energy consumption.\u003c/p\u003e"},{"header":"Results","content":"\u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure | 1 (a) Schematic of Ta/CoFeB/Pt/PMN-PT heterostructure and the harmonic hall voltage testing method. (b) Devices are structured with the orientations of 0\u0026deg;, 45\u0026deg;, 90\u0026deg; and 135\u0026deg; to measure angular dependence. (c) Magnetic moment measurement of the device under in-plane magnetic field, insert shows the M-H loop with external field varying from \u0026minus;\u0026thinsp;30\u0026thinsp;~\u0026thinsp;30 mT. (d) Typical AHE curve of the device under out-of-plane magnetic field.\u003c/p\u003e \u003cp\u003eAs shown in Fig.\u0026nbsp;1a, (011) oriented single crystal PMN-PT substrate, with thickness of 500 \u0026micro;m, is double side polished and with both top and bottom surfaces covered by Pt electrodes. Before depositing the magnetic layers on top of the substrate, PMN-PT is electrically pre-poled in (011) direction, with the polarization pointing \u0026ldquo;up\u0026rdquo;. Under a vertical upward electric field, the PMN-PT substrate produces an anisotropic in-plane piezoelectric response, generated compressive strain in the [\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(100\\)\u003c/span\u003e\u003c/span\u003e] direction and tensile strain in the [\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(0\\stackrel{-}{1}1\\)\u003c/span\u003e\u003c/span\u003e] direction. The SOT devices are fabricated into Hall bar by lithography. Devices with different orientations are designed to verify the angle dependance of SOT efficiency manipulation, as shown in the sample picture in Fig.\u0026nbsp;1b. External magnetic field response of the CoFeB/PMN\u0026thinsp;\u0026minus;\u0026thinsp;PT heterostructure device has been characterized in Fig.\u0026nbsp;1c and 1d, which indicates that the system is in-plane magnetized.\u003c/p\u003e \u003cp\u003eSeveral methods including Spin Transfer Torque-Ferromagnetic Resonance (ST-FMR), Magneto-optic Kerr effect (MOKE) and Second harmonic spin-torque magnetometry have been put forward for the quantitative characterization of current-induced torques. Among them, the harmonic hall measurements [\u003cspan additionalcitationids=\"CR41\" citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e] injected an alternating current (AC) with specific frequency to induce alternating torque, which drives the magnetization of FM layer tilts periodically around the homeostatic states. DLT and FLT can be separated according to the different dependencies on variational magnetic field angle or magnitude. Among these, the method of varying in-plane magnetic field angle is appropriate to the devices which are in-plane magnetized or with weak perpendicular magnetic anisotropy (PMA).\u003c/p\u003e \u003cp\u003eIn the structure shown in Fig.\u0026nbsp;1(a), a constant sinusoidal current \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(I\\left(t\\right)={I}_{0}\\text{sin}\\omega t\\)\u003c/span\u003e\u003c/span\u003e with frequency of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(f=\\left(\\omega /2\\pi \\right)=133 Hz\\)\u003c/span\u003e\u003c/span\u003e is applied to the Hall bar through bias tee while orthogonal voltage \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({V}_{xy}={R}_{xy}\\bullet {I}_{0}\\text{sin}\\omega t\\)\u003c/span\u003e\u003c/span\u003e was measured by a lock-in amplifier (LIA), where the hall resistance is mainly contributed by anomalous hall Effect (AHE) and planar hall effect(PHE). Hall voltage signal can be expressed as:\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$${V}_{xy}={I}_{0}\\text{sin}\\omega t\\times \\left[\\begin{array}{c}{R}_{A}\\left(\\text{cos}\\theta -\\text{sin}\\theta \\bullet \\varDelta \\theta \\right)+\\\\ {R}_{P}({sin}^{2}\\theta +\\text{sin}2\\theta \\bullet \\varDelta \\theta )(\\text{sin}2\\phi +2\\text{cos}2\\phi \\bullet \\varDelta \\phi )\\end{array}\\right]$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eAssuming that the external field rotates in XOY plane, which means angle \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\phi\\)\u003c/span\u003e\u003c/span\u003e varies, and the direction of spin polarized current is along (0,1,0) direction, the hall voltage signal can be simplified as:\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e\n$${V}_{xy}={I}_{0}\\text{sin}\\omega t\\times \\left[\\begin{array}{c}{R}_{P}\\text{sin}2\\phi -\\\\ {R}_{A}\\left(-\\frac{{H}_{DL}}{-{H}_{K}+H}\\right)\\text{sin}\\omega t+2{R}_{P}\\frac{{H}_{FL}}{H}\\text{cos}2\\phi \\text{cos}\\phi \\text{sin}\\omega t\\end{array}\\right]$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eAmong these,\u003cdiv id=\"Equc\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equc\" name=\"EquationSource\"\u003e\n$${V}_{xy}^{1\\omega }={I}_{0}\\text{sin}\\omega t\\times {R}_{P}\\text{sin}2\\phi$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equd\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equd\" name=\"EquationSource\"\u003e\n$${V}_{xy}^{2\\omega }={I}_{0}\\text{sin}\\omega t\\times \\left({R}_{A}\\bullet \\frac{{H}_{DL}}{-{H}_{K}+H}\\text{cos}\\phi +2{R}_{P}\\frac{{H}_{FL}}{H}\\text{cos}2\\phi \\text{cos}\\phi \\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({R}_{P}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({R}_{A}\\)\u003c/span\u003e\u003c/span\u003e represents the planar hall resistance and anomalous hall resistances respectively, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({H}_{FL}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({H}_{DL}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({H}_{K}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(H\\)\u003c/span\u003e\u003c/span\u003e represent the current induced effective field of FLT and DLT, effective perpendicular anisotropy field and external field respectively. First and second harmonic hall voltage curves under increasing magnetic field are shown in Fig.\u0026nbsp;1(e) \u0026amp; (f).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe magnitude of FLT and DLT effective field can be calculated through the coefficient, which are derived by fitting the measured curves with the aforementioned functions. As shown in Fig.\u0026nbsp;1(b), four different orientation, described as 0-, 45-, 90- and 135-degree devices according to their current direction, are designed to experience different strain distribution from the piezoelectric substrate. Vertical electric field is applied on the piezoelectric substrates with the top electrode grounded and bottom electrode connected to positive high voltage, which varies from 0V to 400V and supplies the electric field varies from 0-800 kV/m.\u003c/p\u003e \u003cp\u003eAs shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e2\u003c/span\u003e(a), effective field of DLT and FLT at zero electric field is setting as the base, and variation of it from the base under increased electric field are listed. Due to the electric field polarity and the substrate orientation, compressive strain acts on 0-drgree device and tensile strain acts on 90-degree device. It\u0026rsquo;s not hard to find that compressive strain decreases the effective field of DLT while tensile strain increases the effective field of it. For 45- and 135-degree devices, the effective field of DLT still increases, which indicates that tensile strain dominates the stain distribution on them. As for the effective field of FLT, it almost remains unchanged for various device direction as shown in the dashed line in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e2\u003c/span\u003e(a).\u003c/p\u003e \u003cp\u003eMicromagnetic simulation was also performed to confirm and further analysis the measurement results. The multiferroic heterostructure is built in COMSOL Multiphysics to get the strain distribution in FM layer under electric field. After that it is modeled in Object oriented micromagnetic framework (OOMMF) [\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e] to demonstrate the magnetization dynamics under the aforementioned strain. More settings are described in Methods. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e2\u003c/span\u003e(b), the device is simplified as a current path with two electrodes in simulation. We can qualitatively find that tensile and compressive strain acts on 0- and 90-degree device respectively, as shown in the inserts of Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e2\u003c/span\u003e(b). For 45- and 135-degree device, there is mainly tensile strain on it, which is consistent with test results.\u003c/p\u003e \u003cp\u003eAs shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e2\u003c/span\u003e(b), magnetization precession of FM layer under two cases were compared, which are called \u0026ldquo;without strain\u0026rdquo; and \u0026ldquo;on [011] PMN-PT\u0026rdquo;. No strain and electric field on [011] PMN-PT induced strain acts on the FM layer during the magnetization precession under these two cases, in respectively. Three stages are observed, which are ①initial state, ②middle state after the action of SOT current and magnetoelastic energy and ③final state after relaxation, respectively. Snapshots of in-plane magnetization on each stage are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e2\u003c/span\u003e(b). Magnetization direction of FM layer\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left(\\overrightarrow{M}\\right)\\)\u003c/span\u003e\u003c/span\u003e along +\u0026thinsp;x/-x are represented by red and blue color, average \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\overrightarrow{M}\\)\u003c/span\u003e\u003c/span\u003e of the device is shown by black arrow in the middle of the bar. As a secondary proof, magnetization dynamics of the FM layer in X-axis and Y-axis are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e2\u003c/span\u003e(c). Spin direction of initial and final states is indicated in the picture.\u003c/p\u003e \u003cp\u003eUnder the aforementioned two cases, we used the same current density of 5\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;11\u003c/sup\u003eA/cm\u003csup\u003e2\u003c/sup\u003e. Compare these two cases of with/without strain, it\u0026rsquo;s not hard to find that the magneto-elastic energy couldn\u0026rsquo;t help implement magnetization switching at final state in 0-degree case. Nevertheless, in 45-, 90- and 135-degree cases, the magneto-elastic energy facilitates the magnetization switching. It illustrates that under this current density, in-plane strain helped the FM layer implement determined magnetization switching rather than random magnetization switching.\u003c/p\u003e \u003cp\u003eThe electric field induced in-plane strain makes it possible to switch the magnetization with much lower energy consumption, which is around 200 fJ in one operation through estimation, and it can help implement deterministic switching without external magnetic field to break the symmetry. Also, in straintronic logic devices, locally generated strain also provides a way to write information to logic bits in selected area, which helps implement specific logic functions.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe scenario of SOT operation in our device is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e3\u003c/span\u003e(a). \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({H}_{DL}\\text{\u0026rsquo;}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\tau }_{DL}\\text{\u0026rsquo;}\\)\u003c/span\u003e\u003c/span\u003e are effective field and torque of DLT, which is compared to normal cases (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({H}_{DL}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\tau }_{DL}\\)\u003c/span\u003e\u003c/span\u003e), after electric field applied on the substrate. Black arrow in top layer and bottom layer represents \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\overrightarrow{M}\\)\u003c/span\u003e\u003c/span\u003e and injected electron current, in respectively.\u003c/p\u003e \u003cp\u003eMFM, X-ray microdiffraction and PEEM were also adapted to help verify the electric field-assisted magnetization switching. More experimental details are described in Methods part. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e3\u003c/span\u003e(b) shows MFM results of the magnetization switching process of the CoFeB magnetic dot under four different excitation conditions. The magnetic dot with diameter of 20um was fabricated here for better observation of magnetization switching. From the MFM pictures, it\u0026rsquo;s not hard to find that, with strain only, partial magnetization reversal occurs while with both strain and current applied on the dot, it was fully magnetized. After that, in stage 4, with reverse strain and current direction, magnetization was switched back to the initial state. It can be observed that from stage 1 to 2, the strain applied help implement partial magnetization switching; from stage 2 to 3, current along with strain can help implement full magnetization switching. The MFM results verified that not only strain could help implement full magnetization switching, but also opposite current direction could help rewrite \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\overrightarrow{M}\\)\u003c/span\u003e\u003c/span\u003e, which is essential to the information writing in storage technology.\u003c/p\u003e \u003cp\u003eAs shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e3\u003c/span\u003e(c), effective field of FLT and DLT under different substrate voltage was tested, it\u0026rsquo;s not hard to find that the effective field of DLT keeps increasing but that of FLT remain unchanged. Laue X-ray microdiffraction was carried out to investigate the elastic strain distribution on the heterojunction device. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e3\u003c/span\u003e(c), the X-ray microdiffraction results demonstrated that the strain increased (red region expanded) in the middle of the bar as the applied voltage rises. PEEM results also demonstrated the magnetization switching on the magnetic dot when the substrate voltage rising from 0V to 400V. It can be confirmed that the increasing effective field of DLT, which is caused by the electric field induced in-plane strain, assisted the magnetization switching.\u003c/p\u003e \u003cp\u003eCombine the above effective field data, PEEM, MFM and X-ray microdiffraction test results together, we can draw the conclusion, with sufficient data support, that increasing in-plane strain induced by the increased substrate voltage is transferred to the FM layer, contributed to the rising of DLT effective field, which has an auxiliary role to the full magnetization switching on the FM layer. Also, these characterization results are consistent with the aforementioned experimental and micromagnetic simulation results shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eLogic applications (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e4\u003c/span\u003e)\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAs shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e4\u003c/span\u003e(a), Three inputs (ends of arms) and three control parts (arms), as well as one output (connection) are integrated in single logic device. While in buffer device and negation device shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e4\u003c/span\u003e(b) and (c), an extra arm was designed to implement the function of buffer and negation. The original output is then called middle to storage intermediate state of the FM layer. MTJ stacks are designed at each input, middle and output ends to readout the magnetization state of FM layer. Logic state of each end is represented by the resistance state of the readout MTJ stack, which can be rewritten by the polarity of SOT current according to aforementioned method. Logic state of \u0026ldquo;0\u0026rdquo;/ \u0026ldquo;1\u0026rdquo; represents low/high resistance state of the MTJ stack, respectively. Piezoelectric substrate PMN-PT [011] is designed under each arm of the logic unit for utilizing the strain to assist the magnetization switching. In controlling parts, as well as buffer and negation control arms, strain is delivered to the FM layer through the protruding yellow part. While in other region, strain is impeded by the oxide material (represent by dark grey) to prevent effect on logic state of inputs/output MTJs. In this way, for the control and buffer/negation arms, its logic states of \u0026ldquo;0\u0026rdquo;/ \u0026ldquo;1\u0026rdquo; represent the existence of strain, namely power on/power off of the electric field under this FM arm, respectively.\u003c/p\u003e \u003cp\u003eIn single logic unit shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e4\u003c/span\u003e(a), with three control ends setting as \u0026ldquo;1\u0026rdquo;, \u0026ldquo;AND\u0026rdquo; and\u0026rdquo; OR\u0026rdquo; logic functions can be toggled in a reconfigurable way in the majority gate, as listed in the top half part of the truth table in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e4\u003c/span\u003e(d). Any two of the inputs can be selected to perform \u0026ldquo;AND\u0026rdquo; and\u0026rdquo; OR\u0026rdquo; operations. For the logic function of selector shown in the bottom half, the result of \u0026ldquo;AND\u0026rdquo; operation of the two inputs, which are setting as \u0026ldquo;1\u0026rdquo; and the remaining one setting as \u0026ldquo;0\u0026rdquo;, will be shown in the output. In this way, control ends own the ability to select inputs for logic operations.\u003c/p\u003e \u003cp\u003eBeyond that, data buffering and negation can be implemented in structures shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e4\u003c/span\u003e (b) and (c). According to the angle dependence of the magnetization switching, which has been descripted in micromagnetic \u003cspan refid=\"Sec12\" class=\"InternalRef\"\u003esimulation\u003c/span\u003e section, with the same magnitude of current density as well as electric field applied on the logic device, magnetization state of the middle end will be buffered/negated to the output end while in the \u0026ldquo;BUFFER\u0026rdquo; / \u0026ldquo;NOT\u0026rdquo; structure, in respectively. In this way, BUFFER and NOT logic functions can be easily implemented. Corresponding logic settings of input/output and control arms (buffer/negation) are listed in the truth table shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e4\u003c/span\u003e(e). Cascading ability is also possessed in this logic device. Benefit from the control arms, only when the electric field is power on, the magnetization state transferring is able to carried out. Magnetic states of the output-MTJ can be only transferred to the post unit without any influence on the inputs of the prior unit to achieve good nonreciprocity.\u003c/p\u003e \u003cp\u003eParts of the device region can be altered customizable by utilizing a different configuration of the electric fields to produce correspondingly strain in demand, which allows for an additional level of control. With this extra controlling approach, abundant logic functions, such as \u0026ldquo;AND\u0026rdquo;, \u0026ldquo;OR\u0026rdquo; and selector, can be implemented in single logic device. With buffer and not, cascading between logic units can be achieved, therefore, complicated logic functions can be implemented. With the assistance of electric field produced strain, the magnetization switching happened at lower current density through SOT, which can largely reduce the power consumption. In the meantime, application of the electric field generates negligible power consumption. The electric-field assisted SOT device we proposed is able to implement full Boole logic with extremely low power assumption and easy, reconfigurable structure, and is highly competitive in energy consumption compared with traditional SOT-based logic devices.\u003c/p\u003e \u003c/div\u003e"},{"header":"Conclusion","content":"\u003cp\u003eWe demonstrate the quantitative control of magnetization switching through the FM/HM/PMN-PT heterostructure by systematically studying the angle dependence of the SOT effect. Localized in-plane strain on a piezoelectric substrate is controlled by applying vertical DC electric field across the substrate.\u003c/p\u003e \u003cp\u003e(011 direction strain / depending on tensile and compressive damping like field and field like torque) damping like effective field / field like effective field (torque is final product)\u003c/p\u003e \u003cp\u003eWe found that the controlled strain makes it possible to quantitatively modulate the magnetization switching of SOT devices. According to the device setting, effective field of DLT decreased on 0-degree device (compressive strain) and increased on 45-, 90-, and 135-degree (tensile strain) devices, which could hinder or facilitate the magnetization switching, respectively. This phenomenon is subsequently verified by MFM, XMCD-PEEM, as well as micromagnetic simulation. It can be utilized in multiferroic logic devices to supply low-power consumption performance.\u003c/p\u003e"},{"header":"Methods Summary","content":"\u003cdiv id=\"Sec7\" class=\"Section3\"\u003e \u003ch2\u003eDevice fabrication\u003c/h2\u003e \u003cp\u003eThe hall bar with length\u0026thinsp;=\u0026thinsp;90 um and width\u0026thinsp;=\u0026thinsp;15 um were patterned through electron beam lithography and lift-off processes.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003eVSM\u003c/h2\u003e \u003cp\u003eA VSM 7400 from Lake Shore Cryotronics Inc. was used to perform conventional volume averaging magnetometry measurements. The sample was mounted on a quartz holder and its magnetic moment was measured and averaged with the magnetic field sweeping from \u0026minus;\u0026thinsp;1T\u0026thinsp;~\u0026thinsp;1T.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003eMFM\u003c/h2\u003e \u003cp\u003eMFM measurements were conducted in a dynamic lift mode with a lift distance of 30 nm. The dynamics were measured by sweeping the field range in the presence of a magnetic field.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003ePEEM\u003c/h2\u003e \u003cp\u003eXMCD-PEEM was used to image the magnetic state. The magnetic state in each magnetic layer was separately imaged by exploiting the probe depth of approximately 5 nm and the elemental sensitivity of X-ray absorption at the Co L3-edges.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003eX-ray diffraction\u003c/h2\u003e \u003cp\u003eMicrodiffraction scanning collects individual diffraction patterns step by step from grid points to provide information on lattice strain and crystal orientation. The electrically induced deviatoric strain is calculated for each step by taking the difference between the extracted strain at a non-zero voltage and at a zero voltage. The 2D strain maps are constructed with 10 x 10 um\u003csup\u003e2\u003c/sup\u003e pixels.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003eSimulation\u003c/h2\u003e \u003cp\u003eCOMSOL and OOMMF were used for simulation in this work. The Structural Mechanics Module, Piezoelectric Module, and Magnetostrictive Module were added in COMSOL Multiphysics to analyze the strain and coupling between the piezoelectric substrate and FM thin film in the multiferroic heterostructure. The strain distribution on the FM layer was then induced to the micromagnetic simulation toolkit OOMMF. The YY_FixedMEL: magnetoelastic [\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e] term was used to calculate magnetoelastic energy based on the displacement field, in the form of Oxs_VectorField. The strain distribution obtained from COMSOL was converted by the magnetoelastic coupling constant to a spatially correlated uniaxial anisotropy-like magnetoelastic energy with the magnetoelastic coupling constant consistent with the corresponding constant in thin film CoFeB. Other key contributing terms of effective magnetic field are uniaxial anisotropy, exchange coupling, and demagnetization. The FM layer (300\u0026times;300\u0026times;1 nm\u003csup\u003e3\u003c/sup\u003e) is divided by the finite element method (FEM) with a mesh size of 3\u0026times;3\u0026times;1 nm\u003csup\u003e3\u003c/sup\u003e. Areas other than the FM bar and electrodes are vacuum by setting Ms\u0026thinsp;=\u0026thinsp;0. The saturation magnetization (Ms), exchange constant (Aex), magnetic anisotropy energy density (Ku), spin polarization (p), and Gilbert damping constant (α) values used in this paper are 0.86\u0026times;10\u003csup\u003e6\u003c/sup\u003e A/m, 30\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;12\u003c/sup\u003e J/m, 0.84 MJ/m\u003csup\u003e3\u003c/sup\u003e, 0.6, and 0.014, respectively, for the FM layer, consistent with CoFeB-based FM material properties. Uniaxial anisotropy direction and initial magnetization direction are setting along the longitudinal direction of the bar due to the shape anisotropy of in-plane magnetized film and demagnetization. Polarization direction of the spin current is perpendicular to the bar due to the spin hall effect.\u003c/p\u003e \u003c/div\u003e"},{"header":"Declarations","content":"\u003ch2\u003eData Availability \u003c/h2\u003e\n\u003cp\u003eThe data that support the findings of this study are available from the corresponding author upon reasonable request.\u0026nbsp;\u003c/p\u003e\u003cp\u003e \u003ch2\u003eCompeting interests:\u003c/h2\u003e \u003cp\u003eAuthors declare that they have no competing interests.\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eData and materials availability\u003c/strong\u003e \u003cp\u003eAll data are available upon request\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eJ.H. and L.X. wrote the main manuscript text and L.X. and H.S. prepared figures 1-4. All authors reviewed the manuscript.\u003c/p\u003e\u003ch2\u003eAcknowledgments:\u003c/h2\u003e \u003cp\u003eWe acknowledge HBUT starting funding and the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Contract No. DE-AC02-05CH11231. This work also was supported by the Director, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division, of the U.S. Department of Energy under Contract No. DE-AC02-05-CH11231 within the Nonequilibrium Magnetic Materials Program (MSMAG) (sample fabrication and characterization); and the Berkeley Emerging Technology Research (BETR) Center.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAudia, P. G., \u0026amp; Goncalo, J. A. Past success and creativity over time: A study of inventors in the hard disk drive industry. 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Physical Review B. 90, 140405 (2014).\u003c/span\u003e\u003c/li\u003e\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-spintronics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [npj Spintronics](https://www.nature.com/npjspintronics/)","snPcode":"44306","submissionUrl":"https://submission.springernature.com/new-submission/44306/3","title":"npj Spintronics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"NPJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"spintronics, spin orbit torque, strain-mediated magnetization, quantitative magnetization switching","lastPublishedDoi":"10.21203/rs.3.rs-3951579/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3951579/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWhen controlling ferroelectric (FE) and ferromagnetic (FM) properties together, this multiferroic system offers many opportunities for energy-efficient electronics such as memories, logic and other novel spintronic devices. Recent progress of electrically controlled spin devices blazes a trail to develop energy efficient devices by controlling magnetization switching. Here, we integrate spin orbit torque (SOT) devices in multiferroics and systematically study the angle dependency of SOT effects on a piezoelectric substrate to control localized in-plane strain using the electric field across the substrate. The controlled strain modulates the magnetization switching quantitatively through SOT in the multiferroic heterostructures. Besides, the strain shows distinguished modulation capability with the different orientations, which can immediately be used in logic arrays. The controllability of electric field on the magnetization switching behavior was revealed by harmonic Hall measurement, X-ray magnetic circular dichroism-photoemission electron microscopy (PEEM), X-ray diffraction, and magnetic force microscopy (MFM) as well as micromagnetic simulation. In virtue of electric-field-induced strain, the result finds the way for controlling SOT-induced magnetization switching with ultralow energy consumption, which will be applicable to the next generation spin-based logic devices.\u003c/p\u003e","manuscriptTitle":"An energy efficient way for quantitative magnetization switching","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-02-15 16:50:32","doi":"10.21203/rs.3.rs-3951579/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-03-21T23:32:34+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-03-01T17:50:09+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"deade955-bc91-4cde-b510-2e80e6e56b8e","date":"2024-02-14T06:55:39+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-02-14T06:45:39+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-02-13T16:22:42+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-02-13T13:21:49+00:00","index":"","fulltext":""},{"type":"submitted","content":"npj Spintronics","date":"2024-02-12T17:42:24+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"npj-spintronics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [npj Spintronics](https://www.nature.com/npjspintronics/)","snPcode":"44306","submissionUrl":"https://submission.springernature.com/new-submission/44306/3","title":"npj Spintronics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"NPJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"a30841cd-0e69-4c36-97f6-aed572b39db1","owner":[],"postedDate":"February 15th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":28769225,"name":"Physical sciences/Nanoscience and technology/Nanoscale devices/Magnetic devices"},{"id":28769226,"name":"Physical sciences/Nanoscience and technology/Nanoscale materials/Magnetic properties and materials"}],"tags":[],"updatedAt":"2024-06-10T14:33:43+00:00","versionOfRecord":[],"versionCreatedAt":"2024-02-15 16:50:32","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-3951579","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3951579","identity":"rs-3951579","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}