Confined antiferromagnetic magnons for efficient spin-charge conversion via the spin hall and inverse spin hall effect

Abstract

A magnetoelectric spin-orbit (MESO) memory device comprises a substrate; an antiferromagnetic (AFM) magnon heterostructure above the substrate comprising: a first AFM layer; a multiferroic layer positioned above the first AFM layer; and a second AFM layer above the multiferroic layer; and a spin-orbit (S-O) metal layer above the AFM magnon heterostructure. Related methods and devices are also disclosed.

Description

CONFINED ANTIFERROMAGNETIC MAGNONS FOR EFFICIENT SPIN-CHARGE CONVERSION VIA THE SPIN HALL AND INVERSE SPIN HALL EFFECTCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to U. S. provisional application No. 63 / 727,446 filed December 3, 2024, incorporated herein by reference in its entirety.STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

[0002] This invention was made with government support under Contract No. DE-AC02-05CH11231 awarded by the U. S. Department of Energy, Grant No. W911NF1920119 and Grant No. W911NF2420100 awarded by the U. S. Department of Defense, Army Research Laboratory. The government has certain rights in the invention.BACKGROUND OF THE INVENTION

[0003] Spin-based devices such as spin transfer torque (STT) or spin-orbit torque (SOT) driven magnetic random-access memories (MRAMs) are examples of non-volatile memories (see Saha, et al., J Magn Mater, 2022; EE Times Europe; Samsung Semiconductor Global; and SOT-MRAM To Challenge SRAM), where the information can be stored for years without requiring power to refresh. In contrast, charge-based static or dynamic random-access memories (SRAM or DRAM) must remain powered on at all times (Lee, et al., CCS CONCEPTS), consuming significant amounts of energy (around 70% of its total energy). However, these charge-based memories are still popular due to their compatibility with today's electronics and the perception that they have no viable alternatives. MRAMs, though non-volatile, still fall short in terms of energy consumption (SOT-MRAM To Challenge SRAM) and information transfer speed compared to charge-based memories. To address these issues, a recently proposed device architecture known as magnetoelectric spin-orbit (MESO) logic based on magnetoelectric materials such asBiFeO₃, has shown significant potential for energy-efficient logic computation (see Manipatruni, et al., Nature, 2019; Manipatruni, et al., W02019005175A1, 2019). However, the complicated design, which includes ferromagnetic elements (limited by the spin polarization, leading to a 30-40% spin or energy loss at the input current), and high error rate due to weak antiferromagnetic exchange coupling between ferromagnet and antiferromagnetic BiFeO₃ (see Vaz et al., Nature Communications 2024) limit its efficiency for future integration into nonvolatile memory.

[0004] Thus, there is a need in the art for improved magneto-electric spin-orbit memory devices, systems, and methods.SUMMARY OF THE INVENTION

[0005] Some embodiments of the invention disclosed herein are set forth below, and any combination of these embodiments (or portions thereof) may be made to define another embodiment.

[0006] In one aspect a magnetoelectric spin-orbit (MESO) memory device comprises a substrate, an antiferromagnetic (AFM) magnon heterostructure above the substrate comprising a first AFM layer, a multiferroic layer positioned above the first AFM layer, and a second AFM layer above the multiferroic layer, and first and second terminals positioned in contact with the AFM magnon heterostructure.

[0007] In one embodiment, the first and second terminals comprise a spin-orbit coupled metal or an orbital metal.

[0008] In one embodiment, the first and second terminals are positioned over the second AFM layer.

[0009] In one embodiment, the first terminal is positioned below the first AFM layer and the second terminal is positioned above the second AFM layer.

[0010] In one embodiment, the first and second AFM layers each have a thickness between 5 nm and 10 nm.

[0011] In one embodiment, the multiferroic layer has a thickness between 5 nm and 7 nm.

[0012] In one embodiment, the device is configured to encode information in a non-volatile manner via magnons.

[0013] In one embodiment, the multiferroic layer comprises a perovskite structure multiferroic of L-BiFeO₃, where L is a rare earth ion comprising at least one of La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, or Y.

[0014] In one embodiment, at least one of the first AFM layer and second AFM layer comprises a perovskite structured AFM oxide.

[0015] In one embodiment, the AFM oxide comprises REFeO₃, where RE comprises a rare earth element.

[0016] In one embodiment, the rare earth element comprises at least one of Y, La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu.

[0017] In one embodiment, the first and second terminals comprise a topological insulator.

[0018] In one embodiment, the first and second terminals comprise at least one of SrIrO₃, Bi₂Se₃, BiSb, α-Sn, Bi₂Te₃, or BiSbTe₃.

[0019] In one embodiment, at least one of the first and second terminals has a resistivity of 50 micro Ohms-cm to 100 milli Ohms-cm.

[0020] In one embodiment, a lattice parameter of the multiferroic layer is matched to a lattice parameter of at least one of the first AFM layer and the second AFM layer.

[0021] In another aspect, an information storage element comprises the MESO memory device as described above, wherein the information storage element is configured as a nondestructive read out non-volatile memory element.206595-0002-00WO

[0022] In another aspect, a method for fabricating a magnetoelectric spin-orbit (MESO) memory device comprises depositing a first AFM layer on a substrate, depositing a multiferroic layer on the first AFM layer, depositing a second AFM layer on the multiferroic layer, and depositing a spin-orbit (S-O) metal layer on the second AFM layer.

[0023] In one embodiment, the layers are deposited via sputtering, pulsed laser deposition, molecular beam epitaxy, atomic layer deposition, or metal-organic chemical vapor deposition.

[0024] In another aspect, an information storage method comprises providing the MESO memory device as described above and writing information to the MESO memory device via the steps of applying an electric field to the AFM magnon heterostructure via a differential voltage between the first and second terminals and storing a data bit as a confined magnon in the multiferroic layer via the spin Hall effect.

[0025] In one embodiment, the method further comprises reading information from the MESO memory device via the steps of applying an electrical current to the first terminal, transferring the momentum to the confined magnon in the multiferroic layer, creating an output voltage via inverse spin Hall effect in the second terminal, and measuring the output voltage, wherein the confined magnon generates the output voltage via the AFM magnon heterostructure.BRIEF DESCRIPTION OF THE DRAWINGS

[0026] The foregoing purposes and features, as well as other purposes and features, will become apparent with reference to the description and accompanying figures below, which are included to provide an understanding of the invention and constitute a part of the specification, in which like numerals represent like elements, and in which:

[0027] Figs. 1A-1B show the inverse spin Hall voltage measured in the exemplary SIO / BLFO / SIO-based MESO device. Fig. 1A shows ISHE voltage as a function of an applied electrical voltage pulse across the BLFO. Fig. IB shows the non-volatile response of the device in two P states.

[0028] Figs. 1C-D illustrate details of an exemplary epitaxial LFO / BFO / LFO heterostructure. Fig. 1C shows a schematic view of the atomic structures of the LaFeO3 and BiFeO3. Fig. ID shows HAADF Scanning transmission electron microscopy of the LFO / BFO / LFO heterostructure, and the inset shows a false color contrast for elemental mapping measured by energy dispersive X-ray spectroscopy. Elemental diffusion at the interface appears to be negligible.

[0029] Fig. IE shows a phase image of the BFO layer within the heterostructure reconstructed by electron ptychography along the

[0100] zone axes, scale bar is 5 A. The vector map shows the unit cell doubling represents the antipolar phase of BFO.

[0030] Fig. IF shows a phase image of the BFO unit cell, scale bar is 2 A.

[0031] Fig. 1G shows a switchable polarization measure by PUND (Positive-Up Negative- Down) experiment at 5 us and 50 [is voltage pulses. It shows the material undergoes antipolar to polar transition after an application of external electric field.

[0032] Figs. 2A-2B show exemplary magneto-electric spin-orbit memory devices geometry and exemplary magnon confinement in the devices circuit design.

[0033] Figs. 2C-2E illustrate symmetry breaking and spin transmission. Fig. 20 shows a schematic of the non-local magnon transport in the LaFeO3 / BiFeO3 / LaFeO3 with Pt as spin Hall source / detector, where Jc and Jsare the injected charge current and detected spin current densities, respectively. VISHE is the measured non-local inverse spin Hall voltage. The bottom panel in Fig. 2C represents the measurement geometry for non-reciprocal spin transport by swapping the source / detector, named as current-left voltage right (cLvR) and current-right voltage-left (cRvL) designated as 1 and 2, respectively. The spin wave drawing represents the right and left propagating magnons in 1 and 2, respectively.

[0034] Fig. 2D shows non-local VISHE measured in the pristine state of the device (when no electric field was applied) and poled state (after electric field applied) enabled magnon transport. The circled number corresponds to the data measured in the cLvR and cRvL geometry. Both data sets in Fig. 2D are recorded in the absence of an electric field. The spin texture drawing (top panel) only in the BFO is the representation of the electric field controlled206595-0002-00WOregion. LFO is transparent to the electric field response as discussed below. Lines are guided to the eye. The two measured states (blue and pink) corresponds to the two symmetry states of crystal structure of the BFO shown in Fig. 2E corresponding to structural transformation under electrical excitation. Symmetric (Pnma-antiferroelectric 'AFE') to non-centrosymmetric (R3c) like phase emerges after applying electrical pulses.

[0035] Figs. 2F-2G show exemplary magnon confinement in the devices.

[0036] Figs. 3A-3C illustrate the efficacy of magnon confinement.

[0037] Figs. 3D shows non-volatile magnon Hall voltage retention measured in the two opposite poled states (using the electric field ~300kV / cm) representing the deterministic switching of the antiferromagnetic and polar order of the BFO and the corresponding magnon transport.

[0038] Fig. 3E shows the differential of the retention fit to the stretched exponential fit (equation is the inset). The slow-relaxation describes the ferroelectric to antiferroelectric phase transition over a time scale of days. It can switch back to the ferroelectric state repeatedly using an electric field. The bottom data corresponds to the LFO(5nm) / BFO(20nm) / LFO(5nm) and does not show any decay within the same time scale.

[0039] Figs. 4A shows the thickness dependence of magnon transport in the LFO / BFO / LFO trilayer, and a comparison of the effect of magnon confinement on the inverse spin Hall readout voltage differential ( VISHE) for pure BFO with conventional metals. Figure shows nonlocal ISHE (differential) voltage as a function of BFO thickness (trilayer and the single layer BFO comparison). The data measured in the trilayer is recorded both in the nonpolar (square data) and polar states (filled circles).

[0040] Figs. 4B illustrate magnon confinement in BFO and ISHE voltage benchmarking to enable a new MESO device discovered here. The dotted line is a guide to the eye. Y-axis shows Spin Hall resistance calculated from ISHE voltage and scaled with the length of the wire as a function of the SO metal spacing. The benchmarking of the output voltage measured in nonlocal spin transport in the range of material systems including the ferrimagnets 'i,ii', hematite206595-0002-00WO'iii,v', van der Walls antiferromagnet 'vi', MESO with a FM 'vii', and multiferroic correlated oxide with SO metals such as Pt, W and SIO 'viii'. Data in filled circles big (Pt), big triangle (W) and star (SIO) belong to this work with confined magnon heterostructure. Lines are the extrapolation of the data for three SO metals. The difference between the BFO / Pt, [BFO / LFO / BFO] / (Pt, W), and BFO / SIO provides the possible pathway to achieve 100 mV with further device lateral or vertical scaling scattering.

[0041] Fig. 5 shows an exemplary computing environment in which aspects of the invention may be practiced.DETAILED DESCRIPTION OF THE INVENTION

[0042] It is to be understood that the figures and descriptions of the present invention have been simplified to illustrate elements that are relevant for a clearer comprehension of the present invention, while eliminating, for the purpose of clarity, many other elements found in systems and methods of confined antiferromagnetic magnons for efficient spin-charge conversion via the spin Hall and inverse spin Hall effect. Those of ordinary skill in the art may recognize that other elements and / or steps are desirable and / or required in implementing the present invention. However, because such elements and steps are well known in the art, and because they do not facilitate a better understanding of the present invention, a discussion of such elements and steps is not provided herein. The disclosure herein is directed to all such variations and modifications to such elements and methods known to those skilled in the art.

[0043] Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. Although any methods and materials similar or equivalent to those described herein can be used in the practice or testing of the present invention, exemplary methods and materials are described.

[0044] As used herein, each of the following terms has the meaning associated with it in this section.

[0045] The articles "a" and "an" are used herein to refer to one or to more than one ( / .e., to at least one) of the grammatical object of the article. By way of example, "an element" means one element or more than one element.

[0046] " About" as used herein when referring to a measurable value such as an amount, a temporal duration, and the like, is meant to encompass variations of ±20%, ±10%, ±5%, ±1%, and ±0.1% from the specified value, as such variations are appropriate.

[0047] Ranges: throughout this disclosure, various aspects of the invention can be presented in a range format. It should be understood that the description in range format is merely for convenience and brevity and should not be construed as an inflexible limitation on the scope of the invention. Where appropriate, the description of a range should be considered to have specifically disclosed all the possible subranges as well as individual numerical values within that range. For example, description of a range such as from 1 to 6 should be considered to have specifically disclosed subranges such as from 1 to 3, from 1 to 4, from 1 to 5, from 2 to 4, from 2 to 6, from 3 to 6 etc., as well as individual numbers within that range, for example, 1, 2, 2.7, 3, 4, 5, 5.3, and 6. This applies regardless of the breadth of the range.

[0048] Referring now in detail to the drawings, in which like reference numerals indicate like parts or elements throughout the several views, in various embodiments, presented herein are systems and methods of confined antiferromagnetic magnons for efficient spin-charge conversion via the spin Hall and inverse spin Hall effect.

[0049] More than 50 years after the famous comment by Louis N'eel in his Nobel lecture that antiferromagnets are "interesting but useless", an exciting era of antiferromagnetic spintronics is rapidly emerging (see V. Baltz, et al., Antiferromagnetic spintronics. Rev. Mod. Phys. 90 (1), 015005 (2018)). Although it is true that controlling antiferromagnets with tools commonly used for ferromagnets, such as a magnetic field, is theoretically possible, it requires impractically large magnetic fields. However, the emergence of spin-transport physics has completely transformed this perspective by enabling electrical manipulation (see T. Jungwirth, X. Marti, P. Wadley, J. Wunderlich, Antiferromagnetic spintronics. Nature nanotechnology 11(3), 231-241 (2016)). Modern control of antiferromagnets takes advantage of a variety of approaches such as electromagnetic radiation (see P. Němec, M. Fiebig, T. Kampfrath, A. V. Kimel, Antiferromagnetic opto-spintronics. Nat. Phys. 14 (3), 229-241 (2018)), relativistic current-induced fields in broken inversion-symmetry antiferromagnets through the inverse spin-galvanic effect / Rashba-Edelstein effect (see P. Wadley, et aL, Electrical switching of an antiferromagnet. Science 351 (6273), 587-590 (2016))(see J. Zelezny, et al., Relativistic N'eel-order fields induced by electrical current in antiferromagnets. Phys. Rev. Lett. 113 (15), 157201 (2014))(see S. Bhattacharjee, S. Singh, D. Wang, M. Viret, L. Bellaiche, Prediction of novel interface-driven spintronic effects. Journal of Physics: Condensed Matter 26 (31), 315008 (2014)), as well as the spin-Hall effect (see S. DuttaGupta, et al., Spin-orbit torque switching of an antiferromagnetic metallic heterostructure. Nat. Comm. 11 (1), 5715 (2020)). The classical model systems for such demonstration are canted antiferromagnets such as a-Fe2C>3 (see R. Lebrun, et al., Tunable long-distance spin transport in a crystalline antiferromagnetic iron oxide. Nature 561 (7722), 222-225 (2018)), or ferrimagnetic insulators such as yttrium-iron garnet (see X.-Y. Wei, et al., Giant magnon spin conductivity in ultrathin yttrium iron garnet films. Nat. Mat. 21 (12), 1352-1356 (2022)), and many more (see J. Han, R. Cheng, L. Liu, H. Ohno, S.Fukami, Coherent antiferromagnetic spintronics. Nat. Mat. 22 (6), 684-695 (2023)) wherein studies have led to some striking discoveries (see E. Parsonnet, et al., Nonvolatile electric field control of thermal magnons in the absence of an applied magnetic field. Phys. Rev. Lett. 129 (8), 087601 (2022)), such as a strong enhancement in the inverse spin-Hall voltage with material and device dimensions (see X.-Y. Wei, et al., Giant magnon spin conductivity in ultrathin yttrium iron garnet films. Nat. Mat. 21 (12), 1352-1356 (2022))(see X. Huang, et al., Manipulating chiral spin transport with ferroelectric polarization. Nat. Mat. p. 898-904 (2024)). Antiferromagnets present several advantages as compared to ferromagnets such as a larger magnon-group velocity (see M. Hamdi, F. Posva, D. Grundler, Spin wave dispersion of ultra-low damping hematite (a -Fe2O3) at GHz frequencies. Phys. Rev. Mat. 7 (5), 054407 (2023)), a significantly higher antiferromagnetic resonance frequency ranging from several hundred GHz to THz (which is compatible with the frequency ranges for future telecommunications such as 6G and beyond), and insensitivity to external magnetic fields (avoiding cross-talk between theinformation bits). Most importantly, a wide range of antiferromagnets are insulators, and thus there is a strong potential to reduce Joule energy losses during transmission which improves the overall energy efficiency.

[0050] From a macroscopic perspective, energy efficiency in computing has become an increasingly pervasive global challenge, triggering numerous parallel pathways aimed at addressing it (see A. Fert, R. Ramesh, V. Garcia, F. Casanova, M. Bibes, Electrical control of magnetism by electric field and current-induced torques. Rev. Mod. Phys. 96, 015005 (2024))(see 5. Salahuddin, K. Ni, 5. Datta, The era of hyper-scaling in electronics. Nat. Elect. 1 (8), 442-450 (2018)). Among those are intriguing ideas that involve creating an in-memory compute element using the bistable ferroelectric state of a multiferroic for non-volatile storage and the spin component to carry out logic operations in a so-called magnetoelectric spin-orbit (MESO) logic (see S. Manipatruni, et al., Scalable energy-efficient magnetoelectric spin-orbit logic. Nature 565 (7737), 35-42 (2019)). A key recognition was that the operating voltage translates to the energy consumed in the logic / memory element - a requirement that drives the need to achieve sub-100 mV operation to reach the desired attoJoule / operation computing element scale. Such devices work with a voltage input which is converted by the ME multiferroic into a spin signal through a ferromagnet which is used to carry out the logic operations. Reading out the spin state is accomplished through spin-charge conversion, e.g., by the inverse-spin-Hall effect (ISHE) (see D. C. Vaz, et al., Voltage-based magnetization switching and reading in magnetoelectric spin-orbit nanodevices. Nat. Comm. 15 (1), 1902 (2024)). The original MESO concept (see S. Manipatruni, et al., Scalable energy-efficient magnetoelectric spin-orbit logic. Nature 565 (7737), 35-42 (2019)) used a ferromagnetic layer in contact with the multiferroic to help read the magnetic state. However, recent works (see X. Huang, et al., Manipulating chiral spin transport with ferroelectric polarization. Nat. Mat. p. 898-904 (2024)^ see Y. Chai, et al., Voltage control of multiferroic magnon torque for reconfigurable logic-in-memory. Nat. Comm. 15 (1), 5975 (2024)) have demonstrated that the antiferromagnetic state in bismuth ferrite 'BiFeO₃' (BFO) can be manipulated with an electric field (for writing) (see R. Cherifi, et al., Electric-field control of magnetic order above room temperature. Nat. Mat. 13 (4), 345-351 (2014))(see Y.-H. Chu, et al., Electric-field control oflocal ferromagnetism using a magnetoelectric multiferroic. Nat. Mat. 7 (6), 478-482 (2008)) and sensed by the ISHE through a SO metal (for reading) (see E. Parsonnet, et al., Nonvolatile electric field control of thermal magnons in the absence of an applied magnetic field. Phys. Rev. Lett. 129 (8), 087601 (2022)). The requirement of obtaining greater than 100 mV output through the spin-to-charge conversion (VISHE) has been identified as a materials physics "grand challenge". Indeed, until recently, the magnitude of the VISHE (with Pt) was typically about 100 nV in BFO (see E. Parsonnet, et al., Nonvolatile electric field control of thermal magnons in the absence of an applied magnetic field. Phys. Rev. Lett. 129 (8), 087601 (2022)) and about 4x larger in lanthanum-substituted BFO (see S. Husain, et al., Non-volatile magnon transport in a single domain multiferroic. Nat. Comm. 15 (1), 5966 (2024)). The VISHE further goes up by order of magnitude with a large spin-charge conversion efficiency of a metal oxide such as SrIrO3(see X. Huang, et al., Manipulating chiral spin transport with ferroelectric polarization. Nat. Mat. p.898-904 (2024)). This indicates the critical role of the spin-charge conversion efficiency of the SO metal and magnon-spin-transmission channels such as BFO. Disclosed herein is an unexplored pathway to exploit both the SO metal and the magnon channel spin transmission efficiency. In the latter, magnons can carry the spins efficiently without loss of information over a long distance by utilizing the dynamics of antiferromagnets order (see R. Lebrun, et al., Tunable long-distance spin transport in a crystalline antiferromagnetic iron oxide. Nature 561 (7722), 222-225 (2018))(see J. Han, R. Cheng, L. Liu, H. Ohno, S. Fukami, Coherent antiferromagnetic spintronics. Nat. Mat. 22 (6), 684-695 (2023)) and two-dimensional confinement effects (see X.-Y. Wei, et al., Giant magnon spin conductivity in ultrathin yttrium iron garnet films. Nat. Mat. 21 (12), 1352-1356 (2022)). As an efficient approach to two-dimensional magnon confinement in multiferroics, antiferromagnets can provide the additional degree of freedom to control the magnon flow electrically - effects which have been modeled (see S. Beairsto, M. Cazayous, R. S. Fishman, R. de Sousa, Confined magnons. Phys. Rev. B 104 (13), 134415 (2021)).

[0051] Since Felix Bloch's introduction of the concept of spin waves in 1930, magnons (the quanta of spin waves) have been extensively studied in a range of materials for spintronics, particularly for non-volatile logic-in-memory devices. Controlling magnons in conventional206595-0002-00WOantiferromagnets and harnessing them in practical applications, however, remains a challenge. Demonstrate herein is highly efficient magnon transport in an LaFeO3 / BiFeO3 / LaFeO3 all-antiferromagnetic system which can be controlled electrically, making it highly desirable for energy-efficient computation. Leveraging spin-orbit-driven spin-charge transduction permits this material architecture to utilize magnon confinement in ultrathin antiferromagnets, enhancing the output voltage generated by magnon transport by several orders of magnitude, which provides a pathway to enable magnetoelectric memory and logic functionalities.Additionally, its non-volatility enables ultralow-power logic-in-memory processing, where magnonic devices can be efficiently reconfigured via electrically controlled magnon spin currents within magnetoelectric channels.

[0052] Magnon-based memory computing has the potential to be highly energy-efficient, as it reduces or avoids Joule heating during information transfer. Additionally, magnons in magnetoelectric materials offer an extra degree of freedom by allowing magnetization control through an electric field. Magnetoelectric spin-orbit (MESO) logic-in-memory has been proposed as a low-energy alternative to modern magnetic and static random-access memories. However, the conventional MESO design, with its complex structures and additional ferromagnetic elements, limits its performance. Disclosed herein is an antiferromagnetic heterostructure design to lead to a roughly 100X enhancement in confined magnon transport, and thus a corresponding enhancement of the inverse spin Hall output voltages through spincharge conversion.

[0053] In these embodiments, the need for ferromagnetic elements is eliminated and the magnetic quasiparticle (magnon) is used to encode the information in a non-volatile manner with an improved read / write process. Further disclosed is the confinement of the magnons in the antiferromagnetic (AFM) multiferroic BiFeO3(or derivatives from it) by creating a magnonic heterostructure comprised of the AFM multiferroic that is sandwiched between two layers of an AFM that is structurally related to the multiferroic, but has a difference in the magnetic anisotropy, and thus a difference in the antiferromagnetic resonance frequency and the spin wave group velocity (see Park et al., Journal of Physics Condensed Matter, 2018 and Rovillain,206595-0002-00WOet al., Nat Mater, 2010). In some embodiments, leveraging the confinement of magnons can further magnify the output by one or more orders of magnitude due to minimal loss and scattering (Beairsto, et aL, Phys Rev B, 2021). In some embodiments, the writing pathway is a single step process via inherent magnetoelectric coupling. In some embodiments, the absence of ferromagnetic elements suppresses stray-field-induced errors, making the writing process dependent solely on the ferroelectric order parameter, which allows for faster switching, up to the 100ps scale (see Parsonnet, et aL, Phys Rev Lett, 2020). This also offers the flexibility to further optimize switching energy by manipulating the ferroelectric energy landscape. In some embodiments, by introducing elements such as lanthanum (La) into the BiFeO3lattice, switching energy can be reduced to below 200mV (Prasad et aL, Adv. Mater., 2020). In some embodiments, the BiFeO3lattice is substituted with any rare-earth element, including, but not limited to La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, Y, and mixtures thereof. Such embodiments work to destabilize the ferroelectric phase and reduce the switching energy. This has been explicitly shown for doping BiFeO3with Sm, Gd, and Dy by Kan, et aL, Adv. Funct. Mater., 2010, and for mixtures that involve La and Lu by Chen, et al., Appl. Phys. Lett., 2021. First-principles theory calculations also expect it to hold for Y-doped BiFeO3(see Graf, et al., J. Phys.: Condens. Matter, 2018).

[0054] Understanding the magnetic texture of BiFeO3and doped BiFeO3enables one to design magnonic quasiparticle interactions for reading the memory state via spin-charge interconversion (see Meisenheimer et al., Advanced Materials, 2404639 (2024); Husain et al., Nature Communications 15 (1), 5966(2024); and Huang et aL, Nature Materials 23, 898-904, 2024, Harris, Husain et al arXiv:2411.10903 (2024)). In some embodiments, the output voltage can be further optimized by utilizing different spin-orbit coupling materials such as correlated oxides, topological insulators as well as orbital current materials and protocols in non-local devices (see Meisenheimer et aL, ArXiv, 2023; Husain et aL, ArXiv:2404.04746, 2024; and Huang et aL, Nature Materials, 2024) advancing the fundamental understanding of various magnetic and ferroelectric domain structures. In some embodiments, magnon confinement is used to enhance spin transport for memory and logic.206595-0002-00WO

[0055] In this work, the fundamental hypothesis is that one can confine magnon transport in the BFO system by sandwiching it between layers of non-polar antiferromagnets such as LaFeO3(LFO) to induce, in a simplistic picture, confinement of magnon modes in the plane. This, in turn, would lead to a more efficient transport of spins in the BFO and, consequently, a higher VISHE at the SO metal could be achieved and controlled by an electric field. This was determined to be the case for a model, epitaxial LFO / BFO / LFO trilayer heterostructure, leading to several orders of magnitude enhancement in the VISHE as compared to a single BFO layer of commensurate thickness. Disclosed herein are these observations and their implications for electric-field-controlled spin-based memory and logic elements (see S. Manipatruni, et al., Scalable energy-efficient magnetoelectric spin-orbit logic. Nature 565 (7737), 35-42 (2019)).

[0056] In some embodiments, with reference to Figs. 2A-2B, a magnetoelectric spin-orbit (MESO) memory device 100 includes a substrate 102, an antiferromagnetic (AFM) magnon heterostructure 101 above the substrate 102, and a spin-orbit (S-O) metal layer 106 above the AFM magnon heterostructure 101. In some embodiments, the antiferromagnetic (AFM) magnon heterostructure 101 comprises a first AFM layer 103, a multiferroic layer 104 positioned above the first AFM layer 103, and a second AFM layer 105 above the multiferroic layer 104. In some embodiments, the device 100 does not include a ferromagnetic element. In some embodiments, the device 100 is configured to encode information in a non-volatile manner via magnons. In some embodiments, the multiferroic layer 104 is configured to confine the magnons.

[0057] In some embodiments, the S-0 metal layer 106 includes a first terminal or electrode 106A and a second terminal or electrode 106B. In some embodiments, the first and second terminals (106A, 106B) are separated physically and / or electrically.

[0058] With reference to Fig. 4B, a graph showing device performance is shown, with R1ωof different material and device configurations with contact spacing in pm on the x-axis. Contact spacing in the graph of Fig. 4B is the distance between the inner edges of S-0 metal contacts 106A and 106B as shown in Fig. 2A. As depicted in the graph, devices contemplated in thepresent disclosure use a range of contact spacing depending on the underlying materials in order to achieve an inverse spin Hall voltage of lOOmV.

[0059] In some embodiments, the substrate 102 comprises a Si substrate which may include a film deposited over the Si substrate, the film for example comprising SrTiO3(STO) thin layer, (see McKee, et al., Phys Rev Lett, 1998; and Warusawithana, et al., Science, 2009)

[0060] In some embodiments, the multiferroic layer 104 comprises a perovskite structure multiferroic of L-BiFeO₃, where L is a rare earth ion. In some embodiments, the rare earth ion comprises at least one of La, Sm, and Nd substitutions at the Bi-site up to 20 at %. In some embodiments, the rare earth ion comprises an ion of one or more of La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, or Y.

[0061] In some embodiments, at least one of the first AFM layer 103 and second AFM layer 105 comprises a perovskite structured AFM oxide. In some embodiments, the AFM oxide comprises REFeO3, where RE comprises a rare-earth element or a mixture of rare-earth elements. In some embodiments, the rare earth element comprises at least one of Y, La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu. In some embodiments, at least one of the first AFM layer 103 and second AFM layer 105 comprises perovskite oxides LaCrO3, LaCoO3, SrIrO3or topological insulator Bi2Se3.

[0062] In some embodiments, the multiferroic layer 104 has a thickness of 1-100 nm, 2-100 nm, 5-100 nm, 1-50 nm, 1-40 nm, 1-20 nm, 1-10 nm, 2-7 nm, 4-6 nm, 5-10 nm, or about 5 nm. In some embodiments, the first AFM layer 103 has a thickness of 1-100 nm, 2-100 nm, 5-100 nm, 1-50 nm, 1-40 nm, 1-20 nm, 1-10 nm, 2-7 nm, 4-6 nm, 5-10 nm, or about 5 nm, and / or the second AFM layer 105 has a thickness of 1-100 nm, 2-100 nm, 5-100 nm, 1-50 nm, 1-40 nm, 1-20 nm, 1-10 nm, 2-7 nm, 4-6 nm, 5-10 nm, or about 5 nm. In one embodiment, the multiferroic layer 104 and the first AFM layers 103 and 105 each have a thickness of about 5 nm or between 5-10 nm, or between 4-6 nm. In some embodiments, at least one of the first AFM layer 103 and second AFM layer 105 has a resistivity of 50 micro Ohms-cm to 100 milli Ohms-cm. In some embodiments, a lattice parameter of the multiferroic layer 104 is matched to a lattice parameter of at least one of the first AFM layer 103 and the second AFM layer 105.

[0063] In some embodiments, an information storage element comprises the AFM magnon heterostructure 101. In some embodiments, the information storage element comprises a nondestructive read out non-volatile memory element.

[0064] In some embodiments, a method for fabricating the magnetoelectric spin-orbit (MESO) memory device 100 comprises depositing a first AFM layer 103 on a substrate 102, depositing a multiferroic layer 104 on the first AFM layer 103, depositing a second AFM layer 105 on the multiferroic layer 104, and depositing a spin-orbit (S-O) metal layer 106 on the second AFM layer. In some embodiments, the layers are deposited via at least one of a physical vapor deposition process comprising at least one of sputtering, pulsed-laser deposition, reactive evaporation, molecular-beam epitaxy, and atomic layer deposition.

[0065] In some embodiments, an information storage method comprises providing the MESO memory device 100 or 200 and writing information to the MESO memory device 100 or 200 via application of an electric field to the AFM magnon heterostructure 101. In one embodiment, writing information to the MESO memory device comprises applying a differential voltage across the first and second S-0 layers or terminals 106A / 106B or 206A / 206B. The differential voltage, if above a certain threshold dictated by the materials and thicknesses of layers in the AFM magnon heterostructure 101, creates an electric field within the AFM magnon heterostructure 101 or 201, which stores data within the multiferroic layer 104 or 204 as a confined magnon.

[0066] In some embodiments, the method further comprises reading the written information from the AFM magnon heterostructure 101. In one embodiment, information is read from the AFM magnon heterostructure 101 by applying an electric current to the first S-0 layer or terminal 106A or 206A, and thereby transferring momentum to the confined magnon within the multiferroic layer 104 or 204. This then generates an output voltage in the second S-O layer or terminal 106B or 206B, which can then be measured in order to read the data non-destructively from the AFM magnon heterostructure. As would be understood by one skilled in the art, the read operation also operates in the reverse direction, i.e. in some embodiments the current may be induced in the second S-0 layer or terminal 106B or 206B, which may thengenerate the output voltage via the inverse spin Hall effect, to be read from the first S-0 layer or terminal 106A or 206A.Device Structure and Measurements Strategy:

[0067] The voltage response as a function of electrical pulses of BFO is shown in Figs. 1A-B. In some embodiments, the output voltage (about lmV) is generated via the inverse spin Hall effect (ISHE) from the SIO metal, which gives the access of reading the memory state. In some embodiments, the nonvolatile response is recorded for about 200s in the up and down state of P, which is indicative of the non-destructive readout of the non-volatile memory. This gives one the freedom to design a new kind of memory using a magnetoelectric compound. In this way, one can control the memory state electrically and a magnon current can be used to read it.

[0068] With reference to Fig. 2A, in some embodiments, such as in the disclosed MESO device 101, a BLFO multiferroic 104 is sandwiched between the AFM layers (103, 105) (Fig. 2A). Further, in some embodiments, a S-0 metal 106 is electrically connected to the heterostructure 101 defined by the sandwiched layers (103, 104, 105). In some embodiments, the S-0 metal 106 comprises SIO (SrIrO3), which is known for its high spin torque efficiency (Huang et al., Advanced Materials, 2021), where the charge-to-spin current conversion (known as spin Hall effect) is significantly greater than that of conventional heavy metals such as Pt and W (see Husain, et al., Appl Phys Lett, 2023). Thus, in some embodiments, SIO is expected to generate a larger voltage via the inverse spin Hall effect (ISHE) in such a heterostructure. In the spin Hall effect (SHE), electrical current, carrying equal spin up / down electrons, is converted into a spin current (with only one direction of the spin) at the surface of the metal wire. Conversely, excited magnetization at the interface can produce a similar voltage via ISHE.

[0069] In some embodiments, both SHE and ISHE processes are used in the exemplary SIO / AFM / BLFO / AFM / SIO device 100. In this geometry the inverse spin Hall voltage has increased up to about 100 pV (Fig. 3A). This is possible due to the confinement of the magnons within the BLFO. In some embodiments, an electric-field-driven magnon confinement ispossible only within the BFO in response to electric field dependence due to ME coupling, meaning that the LFO layers progressively assist in squeezing the magnon path in the form of waveguide cavity.

[0070] In some embodiments, in the trilayer heterostructure 101, the LFO interface impacts the structural, polar, and / or magnetic response of the BFO. To further detail, for example, in Fig. 4A the thickness of BFO is varied keeping the LFO (5nm) fixed, and surprisingly the magnon output decreases in thicker BFO samples towards the bulk value. Below 5nm BFO thickness, a decrease was observed in the V(ISHE), which is attributed to more scattering from the interfaces. Nevertheless, it is switchable by electric field. The thickness dependence provides a pathway to increase the confinement of magnons, which shows a potential to reach 100meV.

[0071] In the magnon confinement model (see Beairsto, et al., Phys Rev B, 2021), the magnon modes are dependent on the relative magnetic anisotropy in the two layers (which is related to the antiferromagnetic resonance frequency). In a classical easy plane AFM, the magnetic anisotropy proportional to ω2, where w is the antiferromagnetic resonance frequency. The confinement of magnons is related to the difference in anisotropy, K, between the BFO and LFO layers. Fig. 4A schematically illustrates the magnon modes excitation as a function of BFO layer thickness. Based on the reported values of KBFO and KLFO, a critical range of BFO thickness for increased confinement is calculated to be 5-7nm.

[0072] In some embodiments, a magneto-electric spin-orbit memory device includes an antiferromagnetic heterostructure 101 comprising a perovskite structure multiferroic L-BiFeO3. In some embodiments, L is a rare earth ion such as Y, La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu. In some embodiments, the device comprises substitutions at the Bi-site of up to 20% of the heterostructure with a perovskite structured antiferromagnetic oxide, such as REFeO3, where RE is any element in the family of rare earth elements, such as Y, La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu.

[0073] In some embodiments, a magneto-electric spin-orbit memory device 100 comprises a heterostructure 101 which includes an LBFO layer, said heterostructure 101 being deposited onto a STO / Si substrate 102 to enable the synthesis of phase pure, highly textured or epitaxialheterostructure 101 described above. In some embodiments, the LBFO has a thickness spanning 2nm-100nm. In some embodiments, the REFeO3layers each have a thickness of 2-lOOnm.

[0074] Another exemplary device with a vertical configuration is shown in Fig. 2B. With reference to Fig. 2B, the device 200 comprises a similar LFO / BFO / LFO heterostructure 201 to the device 100, but instead of arranging the S-0 or Pt contacts horizontally on top of the top LFO layer 205 in the heterostructure 201, the contacts 206A and 206B are instead arranged vertically, with the first contact 206A positioned over a portion of the heterostructure 201, and the second contact 206B positioned between the bottom LFO layer 203 of the heterostructure 201 and the substrate 202. The depicted substrate 202 comprises a main substrate 212, which may comprise Si, and a thin layer 211 which may comprise SrTiOs (STO). In some embodiments, the vertical configuration of Fig. 2B increases the output voltage during a read operation, due to the smaller distance between the two contacts 206A and 206B. In some embodiments, in the vertical configuration, a distance between the two contacts 206A and 206B may be 5-20 nm, or 5-10 nm, or 10-20 nm.

[0075] In some embodiments, a method to make contact with a metal with a large spinorbit coupling comprises depositing the metal on top of the layer 105 by sputtering, evaporation, pulsed-laser deposition, or molecular-beam epitaxy, and patterning the deposited layer to produce contacts 106A and 106B. Such patterning could be achieved by deposition through a shadow mask, etching, or liftoff. Typical metals for use with the method are heavy elements such as Pt, W, Ta, all of which have large spin orbit coupling.

[0076] In some embodiments, a method to make contact with a metallic perovskite oxide with a lattice parameter that is matched to the antiferromagnetic perovskites comprises depositing the metallic oxide perovskite on top of the layer 105. To improve performance, epitaxial deposition may be used and can be achieved for the desired metallic oxide perovskite by heating the substrate containing layer 105 to a sufficiently high substrate temperature during deposition (or subsequent to deposition) that epitaxial growth of layer 106 occurs on layer 105. Suitable techniques to deposit the metallic oxide perovskite layer 106 includingsputtering, reactive evaporation, chemical vapor deposition, pulsed-laser deposition, atomic layer epitaxy, or molecular-beam epitaxy. An alternative would be first depositing the metallic oxide perovskite in amorphous or polycrystalline form and then using a form of energy (e.g., laser flash annealing) to transform the deposited layer into an epitaxial layer using solid-phase epitaxy. To complete the structure, deposited layer 106 may be patterned to produce contacts 106A and 106B. Such patterning could be achieved by deposition through a shadow mask, etching, or liftoff. In some embodiments, the metallic oxide has a resistivity that is tuned between 50 micro Ohms-cm to 100milli Ohms-cm through chemical substitutions or thickness. In some embodiments, the terminal or contact 106A or 106B, which may comprise a metal, metal oxide, or S-0 coupled metal oxide, has a thickness of 3-30nm. In one embodiment, an exemplary metallic oxide comprises the perovskite oxide SrIrO3.

[0077] In some embodiments, the disclosure includes a method to make a contact with a Topological Insulator (Tl) such as Bi2Se3, which may be used for the controlling the ISHE nonvolatile output voltage. In some embodiments, the Tl has a resistivity between 50 micro Ohms-cm to 100milli Ohms-cm which may be adjusted through chemical substitutions or thickness, the thickness of which may be between 3-30nm.

[0078] In some embodiments, synthesis of the above heterostructure 101 is performed using physical vapor deposition (sputtering, pulsed laser deposition, molecular beam epitaxy) or chemical vapor deposition (atomic layer deposition or metal-organic chemical vapor deposition).

[0079] In some embodiments, a memory device 100 includes a heterostructure 101 with an antiferromagnetic heterostructure sandwiched between large spin orbit coupled metal for large spin-charge interconversion through confined magnons in L-BiFeO3.

[0080] In some embodiments, an information storage element includes the above heterostructure 101 and functions as a non-destructively read out non-volatile memory element.

[0081] Exemplary materials and related methods are further detailed in Table 1 below:206595-0002-00WOActive Multiferroic Layer Magnon Confinement Layer Spin-Orbit Read-Out Metal BiFeO3REFeO3Orthoferrites where Heavy metals: Pt, Ir, Ta, W, Pd, RE: rare earths (Y, La, Ce, Pr, WxTa1-x, Pt75Pd25, PtxW1-x, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Pt3(MgO)3, Ta10Au90, WTe2, WOXHo, Er, Tm, Yb, and Lu) Oxide SO-metal:Example: LaFeO3; SrIrO3, lrO2, SrRuO3, Sr2IrO4, LaCrO3, LaCoO3Topological insulators:Bi2Se3, BiSb, Ru2Sn3, a-Sn, BiSbTe3, Bi2Te3.RE-BiFeO3where RE: NiO, MnO, CoO, FeO, α-Fe2O3, Correlated Oxides: SrIrO3, Rare Earths, such as La, α-Cr2O3CaIrO3, CaRuO3, SrRuO3,Ce, Pr, Nd, Pm, Sm, Eu, BaRuO3, SrRhO3, SrMoO3, Gd, Tb, Dy, Ho, Er, Tm, CaVO3, SrVO3, YBa2Cu3O7, Yb, Lu, and Y (Example: PrBa2Cu3O7, La2-xMxCuO4, IrO2, (La, Bi)FeO3) Bi2Ru2O7, Bi2Pt2O7, Bi2Ir2O7,Pb2Ru2O6.5, Pb2Ir2O6.5, RE2Ir2O7whereRE: rare earths (Y, La, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu)Altermagnets: La2NiO4; Orbital Metals: Ba(Pb, Bi)O3; La3Ni2O7; La2CoO4; Sr2MnO4; Ba(Pb, Sb)O3, (Ba, K)BiO3, BiNiO3; PbNiO3; RuO2(Ba, Rb)BiO3, RuO2, Cr, Cr / NiFe,VTable 1206595-0002-00WOColossal enhancement of spin transmission through magnon confinement in an antiferromagnet:

[0082] Cross-sectional high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) images reveal the atomically precise nature of the STO / LFO (5nm) / BFO (5nm) / LFO (5nm) interfaces (Figs. 1C-1D). The inset in Fig. 1D is an atomic-scale resolved energy dispersive X-ray map of the lanthanum and bismuth which authenticates the atomically abrupt interfaces, with negligible inter-diffusion between the layers due to the atomic layer-by-layer growth. Vector mapping reveals that portions of the BFO layer exhibit a distorted BFO, reminiscent of the Pnma-antiferroelectric phase (see J. A. Mundy, et al., Liberating a hidden antiferroelectric phase with interfacial electrostatic engineering. Science Advances 8 (5), eabg5860 (2022))(see L. Caretta, et al., Non-volatile electric-field control of inversion symmetry. Nat. Mat. 22 (2), 207-215 (2023)). It has been shown that the interfacial electrostatic boundary conditions (from dielectric layers) imposed on a confined BFO layer, leads to the antipolar phase, which is manifested in the doubling of the unit cell (opposite vector mapping (Fig. IE) and BFO unit cell (Fig. IF)). This can be switched into a polar ferroelectric state with an applied electric bias (see J. A. Mundy, et al., Liberating a hidden antiferroelectric phase with interfacial electrostatic engineering. Science Advances 8 (5), eabg5850 (2022))(see L. Caretta, et al., Non-volatile electric-field control of inversion symmetry. Nat. Mat. 22 (2), 207-215 (2023))(see A. Y. Borisevich, et al., Suppression of Octahedral Tilts and Associated Changes in Electronic Properties at Epitaxial Oxide Heterostructure Interfaces. Phys. Rev. Lett. 105, 087204 (2010)) as shown by the ferroelectric polarization (Polarization, P electric field, E) (Fig. IF) using PUND (positive-up negative-down) measurements were performed under short electrical pulses. The voltage-induced switching at fixed pulse widths (5 ps and 50 / zs) represents the switchable polarization AP, confirming the ferroelectric nature of the BFO(5nm) sandwiched between the LFO layers after electrical switching.

[0083] Non-local spin transport measurements (first (ω) and second harmonic (2ω)) were designed as illustrated in Fig. 2C. In these heterostructures, both the antiferromagnetic compounds (LFO and BFO) intrinsically show antiferrodistortive distortions (see C. Weingart, N.Spaldin, E. Bousquet, Noncollinear magnetism and single-ion anisotropy in multiferroic perovskites. Phys. Rev. B 86 (9), 094413 (2012)) (responsible for nonpolar oxygen octahedra rotations), while BFO has the additional feature of having a ferroelectric order parameter that gives the electric-field controllability, whereas LFO does not. Importantly, both are canted antiferromagnets due to a large Dzyaloshinskii-Moriya interaction (DMI) which is susceptible to the non-reciprocity in magnon dispersion (see S.-W. Cheong, D. Talbayev, V. Kiryukhin, A.Saxena, Broken symmetries, non-reciprocity, and multiferroicity. npj Quantum Mat. 3 (1), 19 (2018))(see D. Albrecht, et al., Ferromagnetism in multiferroic BiFeO3 films: a first-principles-based study. Physical Review B— Condensed Matter and Materials Physics 81 (14), 140401 (2010)). Additionally, the polar order, which is the highest-energy order parameter in multiferroics, imposes further symmetry constraints (see S. Dong, H. Xiang, E. Dagotto, Magnetoelectricity in multiferroics: a theoretical perspective. Nat. Sci. Rev. 6 (4), 629-641 (2019)). As discussed in Figs. 1C-1F, the as-grown state is mainly in the antipolar phase, in which the DMI-based canting is minimal due to symmetry considerations (see E. Bertaut, Representation analysis of magnetic structures. Acta Crystallographica Section A: Crystal Physics, Diffraction, Theoretical and General Crystallography 24 (1), 217-231 (1968)). Thus, before the application of an electric field (in the pristine state), the VISHE — 100 nV is insignificant as illustrated. The two schematics (Current-Left, Voltage-Right 'cLvR' schematic 1 and Current-Right, Voltage-Left 'cRvL' schematic 2, Fig. 2C) illustrate the two measurement cases with the source and detector swapped using a switch box. Hereinafter, the spin transport process is called non-reciprocal if the non-local signal in cLvR and cRvL configurations does not have the same magnitude.

[0084] In contrast, after the device is subjected to an electric field of about 300 kV / cm, a strikingly large inverse-spin-Hall response was observed (bottom (red) data, Fig. 2D). No change in physical parameters such as resistance (of the Pt or BFO) was observed. The output voltage signal has increased to —10 / / V (differential voltage, / VISHE). The data recorded for about 50 sec in each (cLvR / cRvL) configuration with no applied electric field during the measurement is indicative of the non-volatile nature of the magnon propagation, consistent with previous observations (see E. Parsonnet, et al., Nonvolatile electric field control of thermal magnons inthe absence of an applied magnetic field. Phys. Rev. Lett. 129 (8), 087601 (2022)(see S. Husain, et al., Non-volatile magnon transport in a single domain multiferroic. Nat. Comm. 15 (1), 5966 (2024)). It is hypothesized that the significantly larger output voltage (compared to the pristine state) is a consequence of the structural phase transition of the antipolar Pnma phase to a polar R3c-\ ike state in BFO after the application of an electric field as depicted in Fig. 2E. Due to the symmetric nature of the antipolar phase in the multiferroic, it should not produce a sizable DMI and therefore non-reciprocal effects are not expected as evidenced by the very small nonlocal voltage measured in the pristine state. The large ISHE voltage emerges in the poled state. It is particularly noteworthy that the BFO single layer does not show a measurable spin-Hall effect with Pt (see E. Parsonnet, et al., Nonvolatile electric field control of thermal magnons in the absence of an applied magnetic field. Phys. Rev. Lett. 129 (8), 087601 (2022)(see S. Husain, et al., Non-volatile magnon transport in a single domain multiferroic. Nat. Comm. 15 (1), 5966 (2024)) and the spin-Seebeck effect for a 100-nm-thick BFO layer is VISHE ~ 100 nV. Thus, the observation of a about 100X larger spin-Hall voltage response of about 10 μV is exciting.Possible origins for such a "colossal" enhancement in VISHE are further detailed below.

[0085] Armed with this emergent large voltage signal from the magnon transport, VISHE was then mapped as a function of applied electric field for the LFO / BFO / LFO trilayer heterostructures and compare it with that from a single LFO and BFO layer and other control samples. This is captured in Fig. 3A.

[0086] The electric field drives a change in the polar state, and by extension, sets the particular antiferromagnetic state (L) (Fig. 2F) due to the strong magnetoelectric coupling (see J. Heron, et al., Deterministic switching of ferromagnetism at room temperature using an electric field. Nature 516 (7531), 370-373 (2014)), 8(M, L) / 8E determines the magnetic signal driven by the ISHE-conversion process in the Pt, W, or SIO interface. This is enabled by the direction of the electric field controlled polarization. The corresponding evolution of the charge current magnitude dependence shows a linear change of the magnon output voltage due to the spin-Hall / Seebeck effect. The red (blue) U-shaped arrow indicates the low (high) state of the output voltage governed by the L order parameter (Fig. 2F). Since only the BFO responds to theelectric field, the hysteretic behavior of the magnons is depicted to be confined within the BFO layer. Strikingly, the effects also disappear when the LFO antiferromagnetic layer is replaced by dielectric layers such as SrTiO3 or TbScOS. Due to the negligible spin-orbit coupling in copper (Cu), the spin transport is also suppressed when Pt wires are replaced by Cu wires. Most importantly, the non-local voltage is stable over at least 40 hours and found to slowly decay (Fig. 3D-3E). The differential voltage WISHE) follows a stretched-exponential (see R.Kohlrausch, Theorie des elektrischen R"uckstandes in der Leidener Flasche. Annalen der Physik 167 (2), 179-214 (1854)) (Fig. 3E), & VISHE= Voe^-^0), where t is the time and to=7.65±O. OlxlO4sec, 7o=5.58±O. Ol M, and the exponent, n = 0.27±0.02, represents the relaxation behavior of the ferroelectric back to the antiferroelectric state (see H. He, X. Tan, Raman spectroscopy study of the phase transitions inPb0.99Nb0.02[(Zr0.57Sn0.43)l-yTiy]0.9803 ceramics. Journal of Physics: Condensed Matter 19 (13), 136003 (2007)(see X. Tan, et al., Transformation toughening in an antiferroelectric ceramic. Acta materialia 62, 114-121 (2014)(see V. Ishchuk, 0. Belichenko, 0. Nikolov, V.Sobolev, Peculiarities of ferro-antiferroelectric phase transitions. 6. Experiments on low-frequency dynamics of interphase domain walls. Ferroelectrics 248 (1), 107-122 (2000)). The relaxation process may vary from hours to days depending on the material system (see J. A. Mundy, et aL, Liberating a hidden antiferroelectric phase with interfacial electrostatic engineering. Science Advances 8 (5), eabg5860 (2022)(see L. Caretta, et al., Non-volatile electric-field control of inversion symmetry. Nat. Mat. 22 (2), 207-215 (2023)(see K. Nadaud, et al., Study of the long time relaxation of the weak ferroelectricity in PbZrO3. Thin Solid Films 773, 139817 (2023)(see R. Faye, H. Liu, J.-M. Kiat, B. Dkhil, P.-E. Janolin, Non-ergodicity and polar features of the transitional phase in lead zirconate. Applied Physics Letters 105 (16) (2014)). When the BFO thickness in the LFO / BFO / LFO trilayer is increased to 20nm keeping the LFO thickness at 5nm, a primarily polar state was observed in the BFO. Correspondingly, a retention time-independent ISHE voltage of about 0.6 / / was observed in the as-grown state (Fig. 3E, bottom data), and is only weakly enhanced when poled with an electric field. It is noteworthy that the spin Hall voltage magnitude is still about SOX higher compared to a singleBFO layer of commensurate thickness, indicating the role of magnon confinement, albeit weaker.

[0087] In the trilayer heterostructures, the LFO layers impart boundary conditions that impact the structural / polar (Figs. 1C-1F) and magnetic response of the BFO (see C. Weingart, N. Spaldin, E. Bousquet, Noncollinear magnetism and single-ion anisotropy in multiferroic perovskites. Phys. Rev. B 86 (9), 094413 (2012)(see B. Carcan, et al., Phase diagram of Bi'FeO3 / LaFeO3 superlattices: antiferroelectric-like state stability arising from strain effects and symmetry Mismatch at Heterointerfaces. Adv. Mat. Int. 4 (11), 1601036 (2017)). In Fig. 4A, the thickness of BFO was varied keeping the LFO thickness fixed (5 nm for both layers). The inverse spin Hall voltage asymptotes towards the bulk value (see E. Parsonnet, et al., Nonvolatile electric field control of thermal magnons in the absence of an applied magnetic field. Phys. Rev. Lett. 129 (8), 087601 (2022))(see X. Huang, et al., Manipulating chiral spin transport with ferroelectric polarization. Nat. Mat. p. 898-904 (2024)(see S. Husain, et al., Non-volatile magnon transport in a single domain multiferroic. Nat. Comm. 15 (1), 5966 (2024)). Below approximately 5 nm, a decrease was observed in the VISHE, which can be attributed to a stronger interfacial scattering. Such a thickness dependence of the magnon transport points to the essential role of the two-dimensional confinement of magnons in the BFO channel.

[0088] Fig. 2G shows the spin wave propagating (localized) along x

[0100] (Z

[0001] ). The magnons with non-zero out-of-plane momentum are scattered at the LFO / BFO interface experiencing an almost total internal reflection. In turn, the interference of incident and reflected spin excitations gives rise to standing wave-like magnons (Fig. 2G) in the z-direction. While the confined magnons do not transfer energy in the out-of-plane direction, they do propagate in-plane. For the polar BFO case, the in-plane group velocity of such excitations remains high, thereby providing additional spin current channels. It was also found that the trilayer with switched BFO features a higher spin pumping current at the top electrode / LFO interface. The efficiency of the de spin current Js strongly depends on the magnon polarization and in the case of antiferromagnets, is proportional to the sum of the N'eel vector L and magnetization M contributions Js~MxdM / dt+L*dL / dt (see R. Cheng, J. Xiao, Q. Niu, A. Brataas,Spin Pumping and Spin-Transfer Torques in Antiferromagnets. Phys. Rev. Lett. 113, 057601 (2014)). The estimated efficiency of spin pumping for the cases of polar and non-polar trilayers as well as the R3c phase of bulk BFO (Fig. 3C) shows a significant enhancement of spin pumping in the case of trilayer system with the polar BFO. This enhancement is attributed to the long-wavelength confined magnons that exhibit high amplitude of spin and magnetization precession at the surface of the top LFO layer. In addition, it can also be shown theoretically that a model of spin transport based on both interface-confined and BFO-confined magnons supports a dramatic enhancement of spin conductivity as the BFO layer thickness tBFO decreases. As tero decreases, the BFO-confined sub-bands are depopulated, leading to reduction in magnon-magnon interaction.

[0089] In conclusion, disclosed herein is a pathway by which there is an approximate 100X enhancement in the spin transmission, leading to a corresponding enhancement in the VISHE, and its manipulation by an electric field in a perfectly epitaxial LFO / BFO / LFO all antiferromagnet heterostructure. The stark differences between a single BFO layer and the trilayer heterostructure (Fig. 3A, and Fig. 4A) point to the key role of the LFO layers in confining the magnons within the BFO substantiated with the fundamental understanding of the origin of such an enhancement using the model Hamiltonian. A comparative benchmarking of the spin-Hall data reported in conventional ferrimagnetic insulators, hematite, orthoferrites, and correlated oxides is presented (Fig. 4B). The voltage is normalized with the supply current (lac) and the length of the wire (L) as R1ωVio / ac'x-L) for comparison. The overall magnitude of the output voltage has been shown to depend on the spacing between the spin orbit metal wires and the spin-Hall angle (for platinum, tungsten and SrIrO3). An order of magnitude enhancement has been observed going from platinumSrIrO3(from circle to star symbols Fig.4B), due to the difference in the intrinsic spin-Hall angle between Pt and SrIrO3. From a practical perspective, this discovery, in conjunction with the significant enhancements (-10-30X) in the spin-to-charge conversion using epitaxial complex oxides opens up a wide spectrum of opportunities for both fundamental science of magnon confinement in such epitaxial heterostructures as well as enhancing the VISHE towards 100 mV to enable low-voltage, logic-in memory functionalities. See Sajid Husain et al., " Colossal enhancement of spin transmission206595-0002-00WOthrough magnon confinement in an antiferromagnet", 2025, 2503.23724, arXiv, which is incorporated herein by reference in its entirety.COMPUTING ENVIRONMENT

[0090] In some aspects of the present invention, software executing the instructions provided herein may be stored on a non-transitory computer-readable medium, wherein the software performs some or all of the steps of the present invention when executed on a processor.

[0091] Aspects of the invention relate to algorithms executed in computer software.Though certain embodiments may be described as written in particular programming languages, or executed on particular operating systems or computing platforms, it is understood that the system and method of the present invention is not limited to any particular computing language, platform, or combination thereof. Software executing the algorithms described herein may be written in any programming language known in the art, compiled or interpreted, including but not limited to C, C++, C#, Objective-C, Java, JavaScript, MATLAB, Python, PHP, Perl, Ruby, or Visual Basic. It is further understood that elements of the present invention may be executed on any acceptable computing platform, including but not limited to a server, a cloud instance, a workstation, a thin client, a mobile device, an embedded microcontroller, a television, or any other suitable computing device known in the art.

[0092] Parts of this invention are described as software running on a computing device. Though software described herein may be disclosed as operating on one particular computing device (e.g. a dedicated server or a workstation), it is understood in the art that software is intrinsically portable and that most software running on a dedicated server may also be run, for the purposes of the present invention, on any of a wide range of devices including desktop or mobile devices, laptops, tablets, smartphones, watches, wearable electronics or other wireless digital / cellular phones, televisions, cloud instances, embedded microcontrollers, thin client devices, or any other suitable computing device known in the art.

[0093] Similarly, parts of this invention are described as communicating over a variety of wireless or wired computer networks. For the purposes of this invention, the words "network", "networked", and "networking" are understood to encompass wired Ethernet, fiber optic connections, wireless connections including any of the various 802.11 standards, cellular WAN infrastructures such as 3G, 4G / LTE, or 5G networks, Bluetooth®, Bluetooth® Low Energy (BLE) or Zigbee® communication links, or any other method by which one electronic device is capable of communicating with another. In some embodiments, elements of the networked portion of the invention may be implemented over a Virtual Private Network (VPN).

[0094] Fig. 5 and the following discussion are intended to provide a brief, general description of a suitable computing environment in which the invention may be implemented. While the invention is described above in the general context of program modules that execute in conjunction with an application program that runs on an operating system on a computer, those skilled in the art will recognize that the invention may also be implemented in combination with other program modules.

[0095] Generally, program modules include routines, programs, components, data structures, and other types of structures that perform particular tasks or implement particular abstract data types. Moreover, those skilled in the art will appreciate that the invention may be practiced with other computer system configurations, including hand-held devices, multiprocessor systems, microprocessor-based or programmable consumer electronics, minicomputers, mainframe computers, and the like. The invention may also be practiced in distributed computing environments where tasks are performed by remote processing devices that are linked through a communications network. In a distributed computing environment, program modules may be located in both local and remote memory storage devices.

[0096] Fig. 5 depicts an illustrative computer architecture for a computer 1000 for practicing the various embodiments of the invention. The computer architecture shown in Fig.5 illustrates a conventional personal computer, including a central processing unit 1050 (" CPU"), a system memory 1005, including a random-access memory 1010 (" RAM") and a readonly memory (" ROM") 1015, and a system bus 1035 that couples the system memory 1005 tothe CPU 1050. A basic input / output system containing the basic routines that help to transfer information between elements within the computer, such as during startup, is stored in the ROM 1015. The computer 1000 further includes a storage device 1020 for storing an operating system 1025, application / program 1030, and data.

[0097] The storage device 1020 is connected to the CPU 1050 through a storage controller (not shown) connected to the bus 1035. The storage device 1020 and its associated computer-readable media, provide non-volatile storage for the computer 1000. Although the description of computer-readable media contained herein refers to a storage device, such as a hard disk or CD-ROM drive, it should be appreciated by those skilled in the art that computer-readable media can be any available media that can be accessed by the computer 1000.

[0098] By way of example, and not to be limiting, computer-readable media may comprise computer storage media. Computer storage media includes volatile and non-volatile, removable and non-removable media implemented in any method or technology for storage of information such as computer-readable instructions, data structures, program modules or other data. Computer storage media includes, but is not limited to, RAM, ROM, EPROM, EEPROM, flash memory or other solid state memory technology, CD-ROM, DVD, or other optical storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to store the desired information and which can be accessed by the computer.

[0099] According to various embodiments of the invention, the computer 1000 may operate in a networked environment using logical connections to remote computers through a network 1040, such as TCP / IP network such as the Internet or an intranet. The computer 1000 may connect to the network 1040 through a network interface unit 1045 connected to the bus 1035. It should be appreciated that the network interface unit 1045 may also be utilized to connect to other types of networks and remote computer systems.

[0100] The computer 1000 may also include an input / output controller 1055 for receiving and processing input from a number of input / output devices 1060, including a keyboard, a mouse, a touchscreen, a camera, a microphone, a controller, a joystick, or other type of inputdevice. Similarly, the input / output controller 1055 may provide output to a display screen, a printer, a speaker, or other type of output device. The computer 1000 can connect to the input / output device 1060 via a wired connection including, but not limited to, fiber optic, ethernet, or copper wire or wireless means including, but not limited to, Bluetooth, Near-Field Communication (NFC), infrared, or other suitable wired or wireless connections.

[0101] As mentioned briefly above, a number of program modules and data files may be stored in the storage device 1020 and RAM 1010 of the computer 1000, including an operating system 1025 suitable for controlling the operation of a networked computer. The storage device 1020 and RAM 1010 may also store one or more applications / programs 1030. In particular, the storage device 1020 and RAM 1010 may store an application / program 1030 for providing a variety of functionalities to a user. For instance, the application / program 1030 may comprise many types of programs such as a word processing application, a spreadsheet application, a desktop publishing application, a database application, a gaming application, internet browsing application, electronic mail application, messaging application, and the like. According to an embodiment of the present invention, the application / program 1030 comprises a multiple functionality software application for providing word processing functionality, slide presentation functionality, spreadsheet functionality, database functionality and the like.

[0102] The computer 1000 in some embodiments can include a variety of sensors 1065 for monitoring the environment surrounding and the environment internal to the computer 1000. These sensors 1065 can include a Global Positioning System (GPS) sensor, a photosensitive sensor, a gyroscope, a magnetometer, thermometer, a proximity sensor, an accelerometer, a microphone, biometric sensor, barometer, humidity sensor, radiation sensor, or any other suitable sensor.REFERENCES

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[0172] The disclosures of each and every patent, patent application, and publication cited herein are hereby incorporated herein by reference in their entirety. While this invention has been disclosed with reference to specific embodiments, it is apparent that other embodiments and variations of this invention may be devised by others skilled in the art without departing from the true spirit and scope of the invention.

Claims

CLAIMSWhat is claimed is:

1. A magnetoelectric spin-orbit (MESO) memory device, comprising:a substrate;an antiferromagnetic (AFM) magnon heterostructure above the substrate comprising:a first AFM layer;a multiferroic layer positioned above the first AFM layer; anda second AFM layer above the multiferroic layer; andfirst and second terminals positioned in contact with the AFM magnon heterostructure.

2. The device of claim 1, wherein the first and second terminals comprise a spin-orbit coupled metal or an orbital metal.

3. The device of claim 1, wherein the first and second terminals are positioned over the second AFM layer.

4. The device of claim 1, wherein the first terminal is positioned below the first AFM layer and the second terminal is positioned above the second AFM layer.

5. The device of claim 1, wherein the first and second AFM layers each have a thickness between 2 nm and 100 nm.

6. The device of claim 1, wherein the multiferroic layer has a thickness between 5 nm and 7 nm.

7. The device of claim 1, wherein the device is configured to encode information in a nonvolatile manner via magnons.206595-0002-00WO8. The device of claim 1, wherein the multiferroic layer comprises a perovskite structure multiferroic of L-BiFeO3, where L is a rare earth ion comprising at least one of La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, or Y.

9. The device of claim 1, wherein at least one of the first AFM layer and second AFM layer comprises a perovskite structured AFM oxide.

10. The device of claim 9, wherein the AFM oxide comprises REFeO3, where RE comprises a rare earth element.

11. The device of claim 10, wherein the rare earth element comprises at least one of Y, La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu.

12. The device of claim 1, wherein the first and second terminals comprise a topological insulator.

13. The device of claim 12, wherein the first and second terminals comprise at least one of Bi2Se3, BiSb, a-Sn, Bi2Te3, or BiSbTe3.

14. The device of claim 1, wherein at least one of the first and second terminals has a resistivity of 50 micro Ohms-cm to 100 milli Ohms-cm.

15. The device of claim 1, wherein a lattice parameter of the multiferroic layer is matched to a lattice parameter of at least one of the first AFM layer and the second AFM layer.

16. An information storage element, comprising the MESO memory device of claim 1, wherein the information storage element is configured as a non-destructive read out nonvolatile memory element.

17. A method for fabricating a magnetoelectric spin-orbit (MESO) memory device, comprising:depositing a first AFM layer on a substrate;depositing a multiferroic layer on the first AFM layer;depositing a second AFM layer on the multiferroic layer; anddepositing a spin-orbit (S-O) metal layer on the second AFM layer.

18. The method of claim 17, wherein the layers are deposited via sputtering, pulsed laser deposition, molecular beam epitaxy, atomic layer deposition, or metal-organic chemical vapor deposition.

19. An information storage method, comprising:providing the MESO memory device of claim 1; andwriting information to the MESO memory device via the steps of:applying an electric field to the AFM magnon heterostructure via a differential voltage between the first and second terminals; andstoring a data bit as a confined magnon in the multiferroic layer via the spin Hall effect.

20. The method of claim 19, further comprising reading information from the MESO memory device via the steps of:applying an electrical current to the first terminal;transferring the momentum to the confined magnon in the multiferroic layer; creating an output voltage via inverse spin Hall effect in the second terminal; and measuring the output voltage;206595-0002-00WOwherein the confined magnon generates the output voltage via the AFM magnon heterostructure.

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