Perspective: Magnetoelectric switching in thin film multiferroic heterostructures

Since the resurgence of multiferroics research, significant advancement has been made in the theoretical and experimental investigation of the electric field control of magnetization, magnetic anisotropy, magnetic phase, magnetic domains, and Curie temperature in multiferroic heterostructures. As a result of these advances, multiferroic heterostructures are on a trajectory to impact spintronics applications through the significantly reduced energy consumption per unit area for magnetization switching (1–500 μJ cm−2) when compared to that of current-driven magnetization switching (0.2–10 mJ cm−2). Considering this potential impact, it becomes necessary to understand magnetoelectric switching dynamics and characteristic switching times. The body of experimental work investigating magnetoelectric switching dynamics is rather limited, with the majority of room temperature converse magnetoelectric switching measurements reported having employed relatively long voltage pulses. Recently, however, the field has started to consider the kinetics of the switching path in multiferroic (and ferroelectric) switching. Excitingly, the results are challenging our understanding of switching processes while offering new opportunities to engineer the magnetoelectric effect. Considering the prospects of multiferroics for beyond-CMOS applications and the possible influence on operational speed, much remains to be understood regarding magnetoelectric switching kinetics and dynamics, particularly at reduced dimensions and under the influence of boundary effects resulting from strain, electrostatics, and orientation. In this article, we review magnetoelectric switching in multiferroic heterostructures for the electric field control of magnetism. We then offer perspectives moving toward the goal of low energy-delay spintronics for computational applications.

[1]  K. Rabe,et al.  Ferroelectricity at the Nanoscale: Local Polarization in Oxide Thin Films and Heterostructures , 2004, Science.

[2]  R. Ramesh,et al.  Electric-field control of local ferromagnetism using a magnetoelectric multiferroic (Nature Materials (2008) 7, (478-482)) , 2008 .

[3]  F. Y. Huang Effect of strain transfer on critical thickness for epitaxial layers grown on compliant substrate , 2000 .

[4]  M. Fiebig,et al.  Probing Ferroelectric Domain Engineering in BiFeO3 Thin Films by Second Harmonic Generation , 2015, Advanced materials.

[5]  Ho Won Jang,et al.  Ferroelastic switching for nanoscale non-volatile magnetoelectric devices. , 2010, Nature materials.

[6]  C. Vaz,et al.  Magnetoelectric Effects in Complex Oxides with Competing Ground States , 2009 .

[7]  Nicola A. Spaldin,et al.  The toroidal moment in condensed-matter physics and its relation to the magnetoelectric effect , 2008 .

[8]  Lena F. Kourkoutis,et al.  Atomically engineered ferroic layers yield a room-temperature magnetoelectric multiferroic , 2016, Nature.

[9]  H-S Philip Wong,et al.  Memory leads the way to better computing. , 2015, Nature nanotechnology.

[10]  T. Zhao,et al.  Low voltage performance of epitaxial BiFeO3 films on Si substrates through lanthanum substitution , 2008 .

[11]  Sergei V. Kalinin,et al.  Deterministic control of ferroelastic switching in multiferroic materials. , 2009, Nature nanotechnology.

[12]  E. Mishina,et al.  THz Electric Field-Induced Second Harmonic Generation in Inorganic Ferroelectric , 2017, Scientific Reports.

[13]  D. M. Evans,et al.  Magnetic switching of ferroelectric domains at room temperature in multiferroic PZTFT , 2013, Nature Communications.

[14]  Uwe Bauer,et al.  Magneto-ionic control of interfacial magnetism. , 2014, Nature materials.

[15]  Ilya Krivorotov,et al.  Deep subnanosecond spin torque switching in magnetic tunnel junctions with combined in-plane and perpendicular polarizers , 2011 .

[16]  M. Fiebig Revival of the magnetoelectric effect , 2005 .

[17]  M. Trassin Low energy consumption spintronics using multiferroic heterostructures , 2016, Journal of physics. Condensed matter : an Institute of Physics journal.

[18]  S. Cheong,et al.  Multiferroics: a magnetic twist for ferroelectricity. , 2007, Nature materials.

[19]  Manuel Bibes,et al.  Spintronics with multiferroics , 2008 .

[20]  S. Cheong,et al.  Insulating interlocked ferroelectric and structural antiphase domain walls in multiferroic YMnO3. , 2010, Nature materials.

[21]  Non-volatile voltage control of magnetization and magnetic domain walls in magnetostrictive epitaxial thin films , 2012, 1208.3567.

[22]  H. Ohno,et al.  Magnetization vector manipulation by electric fields , 2008, Nature.

[23]  C. Nan,et al.  Multiferroic Heterostructures Integrating Ferroelectric and Magnetic Materials , 2016, Advanced materials.

[24]  A. Tulapurkar,et al.  Large voltage-induced magnetic anisotropy change in a few atomic layers of iron. , 2009, Nature nanotechnology.

[25]  J. Scott Room-temperature multiferroic magnetoelectrics , 2013 .

[26]  J. Melngailis,et al.  Dynamics of ferroelastic domains in ferroelectric thin films , 2003, Nature materials.

[27]  T. Kampfrath,et al.  Antiferromagnetic opto-spintronics , 2017, 1705.10600.

[28]  M. Kunz,et al.  Directed assembly of nano-scale phase variants in highly strained BiFeO3 thin films , 2012 .

[29]  Reduction in critical current for spin transfer switching in perpendicular anisotropy spin valves using an in-plane spin polarizer , 2009 .

[30]  C. Ross,et al.  Fast switching and signature of efficient domain wall motion driven by spin-orbit torques in a perpendicular anisotropy magnetic insulator/Pt bilayer , 2017 .

[31]  M. Mochizuki,et al.  Numerical Simulation of Spin-Chirality Switching in Multiferroics via Intense Electromagnon Excitations , 2011, 1102.3762.

[32]  Mark R. Freeman,et al.  Advances in Magnetic Microscopy , 2001, Science.

[33]  Chang-Beom Eom,et al.  Strain Tuning of Ferroelectric Thin Films , 2007 .

[34]  D. Vanderbilt,et al.  Full magnetoelectric response of Cr2O3 from first principles , 2012, 1207.5873.

[35]  Asif Islam Khan,et al.  Single crystal functional oxides on silicon , 2015, Nature Communications.

[36]  Dimitrie Culcer,et al.  Universal intrinsic spin Hall effect. , 2004, Physical review letters.

[37]  Robert E. Jones,et al.  Ferroelectric non-volatile memories for low-voltage, low-power applications , 1995 .

[38]  Ryoichi Nakatani,et al.  Magnetoelectric switching of perpendicular exchange bias in Pt/Co/α-Cr2O3/Pt stacked films , 2015 .

[39]  M. Yi,et al.  Voltage-driven charge-mediated fast 180 degree magnetization switching in nanoheterostructure at room temperature , 2017, npj Computational Materials.

[40]  P. Mandal,et al.  Tilt engineering of spontaneous polarization and magnetization above 300 K in a bulk layered perovskite , 2015, Science.

[41]  T. Nozaki,et al.  Magnetoelectric switching energy in Cr2O3/Pt/Co perpendicular exchange coupled thin film system with small Cr2O3 magnetization , 2017 .

[42]  W. Brower,et al.  Dielectric Constant ofCr2O3Crystals , 1963 .

[43]  J. Park,et al.  Control of spin-orbit torques through crystal symmetry in WTe2/ferromagnet bilayers , 2017 .

[44]  Dmitri E. Nikonov,et al.  Benchmarking of Beyond-CMOS Exploratory Devices for Logic Integrated Circuits , 2015, IEEE Journal on Exploratory Solid-State Computational Devices and Circuits.

[45]  R. Ramesh,et al.  Epitaxial BiFeO3 Multiferroic Thin Film Heterostructures , 2003, Science.

[46]  C. Nan,et al.  Purely electric-field-driven perpendicular magnetization reversal. , 2015, Nano letters.

[47]  A. Sepulveda,et al.  Strain-mediated 180° switching in CoFeB and Terfenol-D nanodots with perpendicular magnetic anisotropy , 2017 .

[48]  John G. Jones,et al.  Acoustically actuated ultra-compact NEMS magnetoelectric antennas , 2017, Nature Communications.

[49]  T. Lu,et al.  Electrically induced enormous magnetic anisotropy in Terfenol-D/lead zinc niobate-lead titanate multiferroic heterostructures , 2012 .

[50]  Junhao Chu,et al.  Surface magnetoelectric effect in ferromagnetic metal films. , 2008, Physical review letters.

[51]  Kaushik Roy,et al.  MESL: Proposal for a Non-volatile Cascadable Magneto-Electric Spin Logic , 2016, Scientific Reports.

[52]  Jörg Raabe,et al.  Spatially and time-resolved magnetization dynamics driven by spin-orbit torques. , 2017, Nature nanotechnology.

[53]  L. Martin,et al.  Switching kinetics in epitaxial BiFeO3 thin films , 2010 .

[54]  Ilya Grinberg,et al.  Intrinsic ferroelectric switching from first principles , 2016, Nature.

[55]  N. Mathur,et al.  Multiferroic and magnetoelectric materials , 2006, Nature.

[56]  M D Rossell,et al.  Reversible electric control of exchange bias in a multiferroic field-effect device. , 2010, Nature materials.

[57]  Yoichi Shiota,et al.  Induction of coherent magnetization switching in a few atomic layers of FeCo using voltage pulses. , 2011, Nature materials.

[58]  G. Carman,et al.  Single domain spin manipulation by electric fields in strain coupled artificial multiferroic nanostructures. , 2013, Physical review letters.

[59]  C. Vaz Electric field control of magnetism in multiferroic heterostructures , 2011, Journal of physics. Condensed matter : an Institute of Physics journal.

[60]  Rui Zhang,et al.  Complete set of properties of 0.92Pb(Zn1/3Nb2/3)O3–0.08PbTiO3 single crystal with engineered domains , 2003 .

[61]  R. Waser,et al.  Scaling of structure and electrical properties in ultrathin epitaxial ferroelectric heterostructures , 2006 .

[62]  N. D. Mathur,et al.  Ferroelectric Control of Spin Polarization , 2010, Science.

[63]  C. Ahn,et al.  Origin of the magnetoelectric coupling effect in Pb(Zr0.2Ti0.8)O{3}/La{0.8}Sr{0.2}MnO{3} Multiferroic heterostructures. , 2010, Physical review letters.

[64]  Peter Francis Carcia,et al.  Perpendicular magnetic anisotropy in Pd/Co thin film layered structures , 1985 .

[65]  A. Minor,et al.  Observation of polar vortices in oxide superlattices , 2016, Nature.

[66]  Lin F. Yang,et al.  Electric-field control of nonvolatile magnetization in Co40Fe40B20/Pb(Mg(1/3)Nb(2/3))(0.7)Ti(0.3)O3 structure at room temperature. , 2012, Physical review letters.

[67]  Andrew M. Rappe,et al.  Thin-film ferroelectric materials and their applications , 2017 .

[68]  Kang L. Wang,et al.  Electric-poling-induced magnetic anisotropy and electric-field-induced magnetization reorientation in magnetoelectric Ni/(011) [Pb(Mg1/3Nb2/3)O3](1-x)-[PbTiO3]x heterostructure , 2011 .

[69]  N. Spaldin Multiferroics: from the cosmically large to the subatomically small , 2017 .

[70]  T. Zhao,et al.  Electrical control of antiferromagnetic domains in multiferroic BiFeO3 films at room temperature , 2006, Nature materials.

[71]  M. Fiebig,et al.  Magnetoelectric Force Microscopy on Antiferromagnetic 180∘ Domains in Cr2O3 , 2017, Materials.

[72]  Sebastiaan van Dijken,et al.  Electric-field control of magnetic domain wall motion and local magnetization reversal , 2011, Scientific Reports.

[73]  C. Nan,et al.  Full 180° Magnetization Reversal with Electric Fields , 2014, Scientific Reports.

[74]  Dmitri E. Nikonov,et al.  Magnetoelectric spin wave amplifier for spin wave logic circuits , 2009 .

[75]  Yurong Yang,et al.  Near room-temperature multiferroic materials with tunable ferromagnetic and electrical properties , 2014, Nature Communications.

[76]  D. Ralph,et al.  Spin-torque ferromagnetic resonance induced by the spin Hall effect. , 2010, Physical review letters.

[77]  Yurong Yang,et al.  Prediction of a novel magnetoelectric switching mechanism in multiferroics. , 2014, Physical review letters.

[78]  J. Robertson,et al.  Electronic and magnetic properties of Ti2O3, Cr2O3, and Fe2O3 calculated by the screened exchange hybrid density functional , 2012, Journal of physics. Condensed matter : an Institute of Physics journal.

[79]  C. Nan,et al.  Universality of the surface magnetoelectric effect in half-metals , 2009 .

[80]  M. Fiebig,et al.  The evolution of multiferroics , 2016 .

[81]  Shuichi Murakami,et al.  Dissipationless Quantum Spin Current at Room Temperature , 2003, Science.

[82]  Dmitri E. Nikonov,et al.  Electric-field-induced magnetization reversal in a ferromagnet-multiferroic heterostructure. , 2011, Physical review letters.

[83]  A. Tagantsev,et al.  Controlling domain wall motion in ferroelectric thin films. , 2015, Nature nanotechnology.

[84]  Jeffrey Bokor,et al.  Electrically driven magnetic domain wall rotation in multiferroic heterostructures to manipulate suspended on-chip magnetic particles. , 2015, ACS nano.

[85]  J. Nowak,et al.  Spin torque switching of perpendicular Ta∣CoFeB∣MgO-based magnetic tunnel junctions , 2011 .

[86]  M. Bibes,et al.  Ultrathin oxide films and interfaces for electronics and spintronics , 2011 .

[87]  R. Ramesh,et al.  Electric field control of magnetism using BiFeO3-based heterostructures , 2014 .

[88]  M. Fiebig,et al.  Ferroic nature of magnetic toroidal order , 2014, Nature Communications.

[89]  D C Ralph,et al.  Nanosecond-Timescale Low Energy Switching of In-Plane Magnetic Tunnel Junctions through Dynamic Oersted-Field-Assisted Spin Hall Effect. , 2016, Nano letters.

[90]  Ce-Wen Nan,et al.  Multiferroic magnetoelectric composite nanostructures , 2010 .

[91]  Aurelien Manchon,et al.  Nonequilibrium intrinsic spin torque in a single nanomagnet , 2008 .

[92]  M. Fiebig,et al.  Time-resolved imaging of magnetoelectric switching in multiferroic MnWO4 , 2011, 1103.2066.

[93]  R. Whatmore,et al.  Magnetic Field-Induced Ferroelectric Switching in Multiferroic Aurivillius Phase Thin Films at Room Temperature , 2013 .

[94]  D. Ralph,et al.  Spin-Torque Switching with the Giant Spin Hall Effect of Tantalum , 2012, Science.

[95]  D. Ralph,et al.  Current-induced switching of perpendicularly magnetized magnetic layers using spin torque from the spin Hall effect. , 2012, Physical review letters.

[96]  A. Bhalla,et al.  Dielectric and pyroelectric properties in the Pb(Mg1/3Nb2/3)O3-PbTiO3 system , 1989 .

[97]  Wei-gang Wang,et al.  Electric-field-assisted switching in magnetic tunnel junctions. , 2012, Nature materials.

[98]  Andrew M Rappe,et al.  Ferroelectric polarization reversal via successive ferroelastic transitions. , 2015, Nature materials.

[99]  Caroline A Ross,et al.  Current-induced switching in a magnetic insulator. , 2017, Nature materials.

[100]  D. Ralph,et al.  Low-damping sub-10-nm thin films of lutetium iron garnet grown by molecular-beam epitaxy , 2016, 1609.04753.

[101]  Dominik M. Juraschek,et al.  Dynamical Multiferroicity , 2016, 1612.06331.

[102]  Fröhlich,et al.  Second harmonic generation and magnetic-dipole-electric-dipole interference in antiferromagnetic Cr2O3. , 1994, Physical review letters.

[103]  Ce-Wen Nan,et al.  Design of a Voltage‐Controlled Magnetic Random Access Memory Based on Anisotropic Magnetoresistance in a Single Magnetic Layer , 2012, Advanced materials.

[104]  C. Nan,et al.  Understanding and designing magnetoelectric heterostructures guided by computation: progresses, remaining questions, and perspectives , 2017, npj Computational Materials.

[105]  Shan X. Wang,et al.  Nanoscale control of exchange bias with BiFeO3 thin films. , 2008, Nano letters.

[106]  K. Bouzehouane,et al.  Mechanisms of exchange bias with multiferroic BiFeO3 epitaxial thin films. , 2007, Physical review letters.

[107]  Nan Zhang,et al.  Electric field control of deterministic current-induced magnetization switching in a hybrid ferromagnetic/ferroelectric structure. , 2016, Nature materials.

[108]  V. Garcia,et al.  Electric-field control of magnetic order above room temperature. , 2014, Nature materials.

[109]  Dmitri E. Nikonov,et al.  Material Targets for Scaling All Spin Logic , 2012, ArXiv.

[110]  C. Nan,et al.  Recent Progress in Multiferroic Magnetoelectric Composites: from Bulk to Thin Films , 2011, Advanced materials.

[111]  Chi H. Lee,et al.  Ultrafast polarization switching in thin-film ferroelectrics , 2004 .

[112]  Jong-Ryul Jeong,et al.  Field-free switching of perpendicular magnetization through spin-orbit torque in antiferromagnet/ferromagnet/oxide structures. , 2016, Nature nanotechnology.

[113]  Satadeep Bhattacharjee,et al.  Ultrafast switching of the electric polarization and magnetic chirality in BiFeO3 by an electric field. , 2014, Physical review letters.

[114]  F. Freimuth,et al.  Symmetry and magnitude of spin-orbit torques in ferromagnetic heterostructures. , 2013, Nature nanotechnology.

[115]  Robert A. Buhrman,et al.  Spin-torque-driven ballistic precessional switching with 50 ps impulses , 2011 .

[116]  D. Ralph,et al.  Spin transfer torques , 2007, 0711.4608.

[117]  Tao Wu,et al.  Electrical control of reversible and permanent magnetization reorientation for magnetoelectric memory devices , 2011 .

[118]  A. Marty,et al.  Electric Field-Induced Modification of Magnetism in Thin-Film Ferromagnets , 2007, Science.

[119]  S. Auffret,et al.  Ultrafast magnetization switching by spin-orbit torques , 2013, 1310.5586.

[120]  Tahir Ghani,et al.  Voltage induced magnetostrictive switching of nanomagnets: Strain assisted strain transfer torque random access memory , 2014 .

[121]  Hyunsoo Yang,et al.  Hf thickness dependence of spin-orbit torques in Hf/CoFeB/MgO heterostructures , 2016 .

[122]  Qinghua Zhang,et al.  Electric-field control of tri-state phase transformation with a selective dual-ion switch , 2017, Nature.

[123]  L. Martin,et al.  Advances in the growth and characterization of magnetic, ferroelectric, and multiferroic oxide thin films , 2010 .

[124]  Ashok Kumar,et al.  Near-room temperature relaxor multiferroic , 2010 .

[125]  C. Nan,et al.  Multiferroic Magnetoelectric Composites: Historical Perspective, Status, and Future Directions , 2008, Progress in Advanced Dielectrics.

[126]  Dmitri E. Nikonov,et al.  Benchmarking spintronic logic devices based on magnetoelectric oxides , 2014 .

[127]  Ruijuan Xu,et al.  Enhanced Electrical Resistivity and Properties via Ion Bombardment of Ferroelectric Thin Films , 2016, Advanced materials.

[128]  R. Ramesh,et al.  Deterministic switching of ferromagnetism at room temperature using an electric field , 2014, Nature.

[129]  J. Bokor,et al.  Large resistivity modulation in mixed-phase metallic systems , 2015, Nature Communications.

[130]  Qian Niu,et al.  Berry phase effects on electronic properties , 2009, 0907.2021.

[131]  M. Fiebig,et al.  Observation of ferrotoroidic domains , 2007, Nature.

[132]  Christian Binek,et al.  Magnetoelectric switching of exchange bias. , 2005, Physical review letters.

[133]  Stephen Jesse,et al.  Three‐State Ferroelastic Switching and Large Electromechanical Responses in PbTiO3 Thin Films , 2017, Advanced materials.

[134]  S. Cheong,et al.  Direct visualization of magnetoelectric domains. , 2014, Nature materials.

[135]  E. Markiewicz,et al.  Dielectric properties of BiFeO3 ceramics obtained from mechanochemically synthesized nanopowders , 2011 .

[136]  E. Salje,et al.  Magnetoelastic coupling and multiferroic ferroelastic/magnetic phase transitions in the perovskite KMnF_{3} , 2012 .

[137]  R. Dynes,et al.  Full electric control of exchange bias. , 2013, Physical review letters.

[138]  T. Nozaki,et al.  Observation of magnetoelectric effect in Cr2O3/Pt/Co thin film system , 2014 .

[139]  Meilin Liu,et al.  Epitaxial Lift‐Off of Centimeter‐Scaled Spinel Ferrite Oxide Thin Films for Flexible Electronics , 2017, Advanced materials.

[140]  E. Tsymbal,et al.  Magnetoelectric effect at the Fe 3 O 4 /BaTiO 3 (001) interface: A first-principles study , 2008 .

[141]  Yang Shen,et al.  Optimizing direct magnetoelectric coupling in Pb(Zr,Ti)O3/Ni multiferroic film heterostructures , 2015 .

[142]  Amit Kumar,et al.  Magnon Sidebands and Spin-Charge Coupling in Bismuth Ferrite Probed by Nonlinear Optical Spectroscopy , 2009 .

[143]  R. Whatmore,et al.  Direct visualization of magnetic-field-induced magnetoelectric switching in multiferroic Aurivillius phase thin films , 2017 .

[144]  Qinghua Zhang,et al.  Electric-field control of ferromagnetism through oxygen ion gating , 2017, Nature Communications.

[145]  Naoki Shimomura,et al.  Isothermal electric switching of magnetization in Cr2O3/Co thin film system , 2015 .

[146]  W. B. Zeper,et al.  Perpendicular magnetic anisotropy and magneto-optical Kerr effect of vapor-deposited Co/Pt-layered structures , 1989 .

[147]  Kang L. Wang,et al.  Switching of perpendicular magnetization by spin-orbit torques in the absence of external magnetic fields. , 2013, Nature nanotechnology.

[148]  W. Cao,et al.  Polarization reversal study using ultrasound , 2001 .

[149]  A. Rushforth,et al.  Magnetostrictive thin films for microwave spintronics , 2013, Scientific Reports.

[150]  U. V. Waghmare,et al.  First-principles study of spontaneous polarization in multiferroic BiFeO 3 , 2005 .

[151]  Joo-Von Kim,et al.  Real-space imaging of non-collinear antiferromagnetic order with a single-spin magnetometer , 2017, Nature.

[152]  A. Naeemi,et al.  Strain-Mediated Magnetization Reversal Through Spin-Transfer Torque , 2017, IEEE Transactions on Magnetics.

[153]  Neil M. White,et al.  Experimental investigation into the effect of substrate clamping on the piezoelectric behaviour of thick-film PZT elements , 2004 .

[154]  K. Yamauchi,et al.  Interface effects at a half-metal/ferroelectric junction , 2007, 0707.1665.

[155]  A. Tagantsev,et al.  Effect of mechanical boundary conditions on phase diagrams of epitaxial ferroelectric thin films , 1998 .

[156]  G. Carman,et al.  Nanoscale magnetic ratchets based on shape anisotropy , 2017, Nanotechnology.

[157]  Xiufeng Han,et al.  Giant electrical modulation of magnetization in Co40Fe40B20/Pb(Mg1/3Nb2/3)0.7Ti0.3O3(011) heterostructure , 2014, Scientific Reports.

[158]  A. Fert,et al.  Tunnel junctions with multiferroic barriers. , 2007, Nature materials.

[159]  A. Loidl,et al.  Characteristics of ferroelectric-ferroelastic domains in Néel-type skyrmion host GaV4S8 , 2017, Scientific Reports.

[160]  Jing Wang,et al.  Non-volatile ferroelastic switching of the Verwey transition and resistivity of epitaxial Fe3O4/PMN-PT (011) , 2013, Scientific Reports.

[161]  Denys Makarov,et al.  Purely antiferromagnetic magnetoelectric random access memory , 2016, Nature Communications.

[162]  D. Khomskii,et al.  Classifying multiferroics: Mechanisms and effects , 2009 .

[163]  M. J. Lee,et al.  Interface ferromagnetism and orbital reconstruction in BiFeO3-La(0.7)Sr(0.3)MnO3 heterostructures. , 2010, Physical review letters.

[164]  Hideo Ohno,et al.  Control of magnetism by electric fields. , 2015, Nature nanotechnology.

[165]  J. Katine,et al.  Ultrafast switching in magnetic tunnel junction based orthogonal spin transfer devices , 2010 .

[166]  Ming Liu,et al.  Voltage control of magnetism in multiferroic heterostructures , 2014, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[167]  H. Ohno,et al.  Electrical Manipulation of Magnetization Reversal in a Ferromagnetic Semiconductor , 2003, Science.

[168]  Mark Hoffman,et al.  Neutron diffraction study of the polarization reversal mechanism in [111]c-oriented Pb(Zn1∕3Nb2∕3)O3−xPbTiO3 , 2007 .

[169]  A. Herklotz,et al.  Strain controlled ferroelectric switching time of BiFeO3 capacitors , 2012 .

[170]  D. Tenne,et al.  Emergence of room-temperature ferroelectricity at reduced dimensions , 2015, Science.

[171]  C. Vicario,et al.  Large-Amplitude Spin Dynamics Driven by a THz Pulse in Resonance with an Electromagnon , 2014, Science.

[172]  D. Pierce,et al.  Interfacial coupling in multiferroic/ferromagnet heterostructures , 2013, 1304.5394.

[173]  Non-volatile ferroelectric control of ferromagnetism in (Ga,Mn)As. , 2008, Nature materials.

[174]  Ilya Krivorotov,et al.  Low writing energy and sub nanosecond spin torque transfer switching of in-plane magnetic tunnel junction for spin torque transfer random access memory , 2011 .

[175]  V. Gopalan,et al.  Fast Magnetic Domain-Wall Motion in a Ring-Shaped Nanowire Driven by a Voltage. , 2016, Nano letters.

[176]  C. Binek,et al.  Robust isothermal electric switching of interface magnetization: A route to voltage-controlled spintronics , 2010, 1004.3763.

[177]  M. Bibes,et al.  Multiferroics: towards a magnetoelectric memory. , 2008, Nature materials.

[178]  A. P. Pyatakov,et al.  Crafting the magnonic and spintronic response of BiFeO3 films by epitaxial strain. , 2013, Nature materials.

[179]  R. Ramesh,et al.  Multiferroics: progress and prospects in thin films. , 2007, Nature materials.

[180]  Supriyo Bandyopadhyay,et al.  Reversible strain-induced magnetization switching in FeGa nanomagnets: Pathway to a rewritable, non-volatile, non-toggle, extremely low energy straintronic memory , 2015, Scientific Reports.

[181]  A critical analysis of the feasibility of pure strain-actuated giant magnetostrictive nanoscale memories , 2015, 1508.00629.

[182]  P. Stamenov,et al.  Designing switchable polarization and magnetization at room temperature in an oxide , 2015, Nature.

[183]  S. van Dijken,et al.  Size dependence of domain pattern transfer in multiferroic heterostructures. , 2013, Physical review letters.

[184]  E. Ascher,et al.  Some Properties of Ferromagnetoelectric Nickel‐Iodine Boracite, Ni3B7O13I , 1966 .