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.

Multiferroics are materials that possess more than one ferroic order, such as ferroelectricty,1,2 (anti)ferromagnetism (AFM),1–3 ferroelasticity,4–6 and ferrotoroidicity.7–9 As most single phase multiferroic materials have ordering temperatures well below room temperature or have weak ferromagnetic (FM) order,10 it is essential to consider composite structures, such as ferromagnet/ferroelectric bilayers, where the constituents are not multiferroic, yet both orders are sustained at room temperature.11–14 Though intrinsic multiferroic materials were initially discovered in the 1950s and 1960s,15 early 21st century advances in in thin film deposition,1,16,17 and physical descriptions of correlations between two or more ferroic orders18–21 sparked a renaissance of multiferroics research. This has resulted in the demonstration of coupling between spin, charge, lattice, and orbital degrees of freedom in thin film multiferroic heterostructures for nanoscale devices.25–32 For magnetoelectronics (ME), the coupling between ferroelectric and magnetic orders (magnetoelectricity) in multiferroics is a significant focus33–36 as this enables the transduction of electric and magnetic energy via the magnetic field control of electrical polarization (the direct magnetoelectric effect −αDME=P/H)37,38 and the electric field control of magnetism (the converse magnetoelectric effect −αCME=μ0M/E).24,39 The transduction between electric and magnetic energy opens the door for exciting applications in bio- and magnetic field- sensing,40,41 nanoscale actuation,42,43 and low-energy consumption computational technologies.22,33,44,45

In recent years, there has been a push to develop new computing technologies with improved switching energy, delay, and scaling behavior when compared to CMOS.46 The field of spintronics has gained traction for beyond-CMOS memory and logic applications due to advantages that derive from the high density, high reliability, non-volatility, and Si compatibility of the devices.34,44,47 The short comings of spintronic devices, however, tend to stem from the significant energy dissipation in spin torque switching where the injection of a spin-polarized current into a magnetic layer drives the motion of a magnetic domain wall or changes the magnetic state of a multilayer device.35,48–52 As the current densities for current driven magnetic reversal typically fall in the range of 105–107 A cm−2, the energy dissipation per unit area per switch tends to be in the range of 1–10 mJ cm−2 and makes resistive losses primarily responsible for the energy consumption.51–53 Instead, the use of magnetoelectric multiferroic materials has been proposed as a pathway to ultra-low energy, non-volatile memory and logic through the electric field control of magnetism.25–32 Early experiments using multiferroic heterostructures have demonstrated energy dissipation per unit area per switch in the range of 1–500 μ J cm−2 (not considering contributions from parasitic losses or magnetic fields).22,54 These measurements indicate the potential impact that thin film multiferroics heterostructures can have on the energy consumption of spintronic devices.

In this article, we provide a brief synopsis of magnetoelectric switching in composite and single phase multiferroic heterostructures for the room temperature electric field control of magnetism. As many excellent reviews on multiferroics,33,55 magnetoelectrics,56,57 and electric field control of magnetism58–60 are already available,12,16,17,61 we focus on recent developments and perspectives for the future of the field. Furthermore, as energy efficient switching of magnetization for spintronics is a goal, we discuss and tabulate recent results. In particular, for device applications, we not only consider energy dissipation, but developments regarding magnetoelectric switching kinetics and dynamics that influence the magnetoelectric effect and will impact device switching time and reliability. While recent advances in the discovery of new room-temperature, single phase, magnetoelectric multiferroics are promising,27,62–66 the material palette is still quite limited.67 Thus, we further provide a perspective regarding hybrid devices based around a combined magnetoelectric-spin orbit torque (SOT) switching44,45,61 to offer additional possibilities toward highly scalable, energy efficient beyond-CMOS technologies.44,45,61,68

The converse magnetoelectric coupling coefficient governs the efficiency by which a material can convert electrical energy into magnetic and is thus a critical parameter for device considerations. The largest converse magnetoelectric coefficients reported to date are observed in heterostructures.57 Magnetoelectric heterostructures for the electric field control of magnetism can roughly be divided into four categories: ionically coupled, charge coupled, strain coupled, and exchange coupled. Schematics of these mechanisms are illustrated in Fig. 1.

FIG. 1.

Coupling mechanisms of magnetoelectric heterostructures (a) Schematic showing magnetoionic control of a ferromagnetic thin film. Here, an electric field (E) causes O2− ion migration at the boundary and changes the phase of the oxide ferromagnet. (b) Diagram of a charge-coupled magnetoelectric heterostructure. An applied E changes the population of the spin dependent density of states (DOS) modifying the magnetization in the metallic FM layer. (c) Schematic of strain-mediated switching in a composite heterostructure. Application of E induces a ferroelastic strain (ε) through the converse piezoelectric effect. The strain changes the magnetic anisotropy axis of the magnetostrictive magnet because of mechanical coupling to the ferroelectric. (d) Schematic of the exchange biased magnetoelectric composite. The surface moments of the magnetoelectric antiferromagnet (ME AFM) impose themselves on the soft ferromagnetic layer, resulting in a strong magnetism that tracks the orientation of the magnetic order in the magnetoelectric. Application of an electric field switches the orientation of the moments in the antiferromagnet and the exchange coupled ferromagnet.

FIG. 1.

Coupling mechanisms of magnetoelectric heterostructures (a) Schematic showing magnetoionic control of a ferromagnetic thin film. Here, an electric field (E) causes O2− ion migration at the boundary and changes the phase of the oxide ferromagnet. (b) Diagram of a charge-coupled magnetoelectric heterostructure. An applied E changes the population of the spin dependent density of states (DOS) modifying the magnetization in the metallic FM layer. (c) Schematic of strain-mediated switching in a composite heterostructure. Application of E induces a ferroelastic strain (ε) through the converse piezoelectric effect. The strain changes the magnetic anisotropy axis of the magnetostrictive magnet because of mechanical coupling to the ferroelectric. (d) Schematic of the exchange biased magnetoelectric composite. The surface moments of the magnetoelectric antiferromagnet (ME AFM) impose themselves on the soft ferromagnetic layer, resulting in a strong magnetism that tracks the orientation of the magnetic order in the magnetoelectric. Application of an electric field switches the orientation of the moments in the antiferromagnet and the exchange coupled ferromagnet.

Close modal

In magnetoionic heterostructures, the magnetism of the FM layer is manipulated through voltage-dependent chemical modification of the material. This is often through migration of O2– to control interface magnetization69 or the phase of the oxide FM.70,71 Though these systems can boast large magnetization changes (on the order of 2 μB per ion),71 reported switching times are slow69 (∼100 s) and magnetic switching has not been shown; thus, applicability for electronic devices may be limited and will not be discussed further here.

In charge coupled magnetoelectric heterostructures, the carrier population of the magnetic layer is altered72,73 to produce changes in magnetic saturation,74–76 anisotropy,77,78 coercive field,79,80 and coercivity.81 This effect is especially notable in the so-called half-metallic ferromagnets with large band polarization, such as (La0.67Sr0.33)MnO3,3,82 and Heusler alloys.83,84 As the converse magnetoelectric coefficients in charge coupled heterostructures are typically much smaller than the strain or exchange coupled counterparts,57 they will not be discussed further in this perspective but are mentioned for completeness.

In strain coupled heterostructures, a magnetostrictive ferromagnetic layer is strained by a piezoelectric/ferroelectric crystal85 to produce changes in magnetic anisotropy,86–88 control magnetic phase,32,89,90 or induce 90° switching of magnetization91–94 (Fig. 2). Recent experiments with strain-mediated composite magnetoelectrics have employed conductive magnets with large magnetostrictive coefficients (λ) such as Terfenol-D85,91 (λ ∼ 1200 ppm), Galfenol (Fe1-xGax)92,93 (λ ∼ 250 ppm), FeRh89 (ferromagnet-antiferromagnet transition), CoFeB91,95 (λ ∼ 50 ppm), and Ni96 (λ ∼ −34 ppm). Using these magnetostrictive alloys, researchers have achieved magnetoelectric operations with energy dissipation per area per switch on the order of 1–100 μ J cm−2, 96 ranking the technology among the best potential post-CMOS devices.46 Additionally, there is favorable scaling with shrinking magnet size. A lateral decrease in the magnet size is expected to decrease the energy dissipation due to the expected reduction in capacitance.44,68 Thinner films experience more homogenous strain transfer,97 which would allow magnetostrictive/ferroelectric heterostructures to function with lower threshold voltages. Beyond the ∼42 kbT anisotropy barrier limit that ensures thermal stability, there may be an additional functional limit to the scaling of ultrathin magnetic films. If surface or interface magnetic anisotropies become dominant, the magnetic layer will favor a different magnetic orientation [e.g., Co below ∼1–1.5 nm (Refs. 98 and 99)], which may not be compatible with the composite heterostructure. The use of conductive ferromagnets additionally provides the opportunity for current-based read techniques, such as magnetoresistance,100 magnetic tunnel junctions (MTJ),101 and the anomalous Hall effect,102 to probe electric field modulations of the magnetic properties. Devices of this type necessitate the use of high piezoelectric coefficient crystals, typically relaxor-type PbTiO3 derivatives such as Pb(ZrTi)O3 (PZT)3,37,96 and Pb(MgNb)O3-PbTiO3 (PMN-PT).95,103,104 Additionally, this mechanism is extremely sensitive to the interface between the two constituents as it requires efficient transfer of strain across the interface. Recently, by depositing material epitaxially to maximize strain transfer between the layers,105 Parkes et al. have shown electric field-controlled non-volatile 90° switching in a Galfenol film,92 as shown in Fig. 2(a). Researchers have also shown, in highly epitaxial structures, voltage control of the magnetic state in FeRh, toggling between ferromagnetic and antiferromagnetic states through strain-mediated switching of a piezoelectric substrate89 [Fig. 2(b)]. These epitaxial structures are among the best reported magnetoelectric coefficients.

FIG. 2.

Demonstrations of strain-mediated magnetoelectric switching. (a) Magneto-Optical Kerr Effect (MOKE) images showing reversible, strain dependent magnetization orientation of an Fe0.8Ga0.2/PMN-PT heterostructure. The greyscale contrast in the images shows the domain structure and the red arrows show the magnetization direction. (b) Electric field modulated resistive switching of an FeRh/PMN-PT heterostructure. (c) Resistivity as a function of switching event corresponding to the resistive (and magnetic) states marked in (b), showing a strain-mediated, non-volatile 5% change in resistance with an applied voltage pulse. Part (a) adapted from Ref. 92. Parts (b) and (c) adapted from Ref. 89.

FIG. 2.

Demonstrations of strain-mediated magnetoelectric switching. (a) Magneto-Optical Kerr Effect (MOKE) images showing reversible, strain dependent magnetization orientation of an Fe0.8Ga0.2/PMN-PT heterostructure. The greyscale contrast in the images shows the domain structure and the red arrows show the magnetization direction. (b) Electric field modulated resistive switching of an FeRh/PMN-PT heterostructure. (c) Resistivity as a function of switching event corresponding to the resistive (and magnetic) states marked in (b), showing a strain-mediated, non-volatile 5% change in resistance with an applied voltage pulse. Part (a) adapted from Ref. 92. Parts (b) and (c) adapted from Ref. 89.

Close modal

As the switching in strain-based composites is driven by the piezoelectric/ferroelectric, magnetoelectric device switching is limited by the dynamics and energy consumption of ferroelectric polarization switching,23,35,39 placing the maximum device speed to be on the order of 10–100s of ps.106,107 Additionally, for devices that rely on reorienting the magnetization direction, strain based magnetoelectric composites are limited to 90° switching of magnetization by electric field unless sequential voltages are applied. Opportunities may exist, however, for circumventing this limitation by harnessing kinetic and dynamic switching features of ferroelectrics, which are discussed further below. Current experiments with strain-driven composites often utilize a magnetostrictive thin film deposited on a large piezoelectric single crystal,3,37,94,96,103 yet this poses a challenge for eventual device integration as the energy consumption will scale with the volume of the ferroelectric.108–110 The use of ferroelectric/piezoelectric thin films is necessary for eventual device applications at the 10–100 nm scale and achieving the lowest energy dissipation per switch. The reduced dimension offers an additional level of control of the ferroelectric for functional110–113 and performance106,107,113 optimization. The challenge with this, however, is epitaxial clamping of the ferroelectric film to the substrate, which significantly reduces piezoelectric coefficients and limits the strains that can be achieved.114–116 Reports suggest that this effect can be mitigated through patterning of the ferroelectric to reduce boundary effects114,117 or chemical exfoliation to alleviate epitaxial strain,118,119 yet these techniques have yet to see widespread adoption for magnetoelectric device applications.

In exchange coupled multiferroic heterostructures, a single phase magnetoelectric antiferromagnet is coupled to a ferromagnetic layer through interface exchange coupling (Fig. 3). Magnetoelectric switching of the antiferromagnetic layer can then switch the sign of the bias field or magnetization of the heterostructure, the most famous examples of this being BiFeO322,29,39,120 and Cr2O3.24,121 Examples of this switching are shown in Figs. 3(a) and 3(b). Single phase multiferroic materials, such as BiFeO3, tend to have low converse magnetoelectric coefficients due to their small ferromagnetic moment that results from the canted antiferromagnetic order.55,122–125 Thus, single phase magnetoelectric heterostructures are employed using conductive ferromagnetic layers, such as Co,23 CoFe,22,126 and Ni,96 which exchange couple to the magnetic order of the multiferroic. This effectively amplifies the weak magnetic moment of the multiferroic and further paves the way for integration of magnetoelectric multiferroics with existing spintronic technologies to reduce the energy consumption required for magnetization switching.45 

FIG. 3.

Demonstrations of exchange-bias-mediated magnetoelectric coupling in multiferroic heterostructures. (a) XMCD image showing ferromagnetic domains in a multiferroic BiFeO3 heterostructure, before and after electrical switching. The red and blue arrows indicate the magnetization direction. (b) Magnetic hysteresis showing switching of exchange bias in (Pd/Co)3 deposited on a Cr2O3 single crystal. As the antiferromagnetic layer is magnetoelectrically switched with voltage in a static 150 mT magnetic field, the horizontal shift of the hysteresis changes sign. Part (a) adapted from Ref. 22. Part (b) adapted from Ref. 132.

FIG. 3.

Demonstrations of exchange-bias-mediated magnetoelectric coupling in multiferroic heterostructures. (a) XMCD image showing ferromagnetic domains in a multiferroic BiFeO3 heterostructure, before and after electrical switching. The red and blue arrows indicate the magnetization direction. (b) Magnetic hysteresis showing switching of exchange bias in (Pd/Co)3 deposited on a Cr2O3 single crystal. As the antiferromagnetic layer is magnetoelectrically switched with voltage in a static 150 mT magnetic field, the horizontal shift of the hysteresis changes sign. Part (a) adapted from Ref. 22. Part (b) adapted from Ref. 132.

Close modal

In the case of room temperature ferroelectric antiferromagnetic BiFeO3, the antiferromagnetic structure cants due to the Dzyaloshinskii-Moriya interaction, a spin-orbit mediated antisymmetric exchange (E=D·M1×M2) between nearest neighbor magnetic moments M1 and M2. D is the Dzyaloshinskii-Moriya vector and has symmetry constraints such that it points along the polar axis of BiFeO3. The result of the antisymmetric exchange is a weak moment that forms a long-range spin cycloid127 or, with enough epitaxial strain, a uniform canted moment.128 Due to the D vector being oriented along the polar axis of BiFeO3, the antiferromagnetic and canted moment structure has been observed to track the ferroelectric polarization in ferroelastic (non-180°) switching events. Thus, the moments of an exchange coupled ferromagnet not only amplify the effective moment but also correlate with the ferroelectric domain structure of the multiferroic.23,35,39,126,129 This coupling between the magnetic and ferroelectric domain structure then permits the electric field control of the magnetization through the control of the ferroelectric polarization [Fig. 3(a)]. This observation would imply that magnetoelectric device switching is limited by the dynamics and energy consumption of ferroelectric polarization switching,23,35,39 placing the maximum device speed to be on the order of 10–100s of ps.106,107 Exchange coupled magnetoelectric devices utilizing BiFeO3 have reached energies per operation of 240–500 μ J cm−2, the energy dissipated in half a ferroelectric hysteresis loop, PsVC where Ps is the saturation polarization and Vc is the coercive switching voltage. To minimize this inherent loss mechanism, the ferroelectric must be engineered to obtain a smaller polarization or coercive voltage. Researchers have attempted this through La substitution130 on the Bi site of BiFeO3; however, the influence of heavy La doping on the magnetoelectric properties is currently unknown.

Cr2O3 is a non-ferroelectric antiferromagnetic material which shows a linear magnetoelectric effect above room temperature.131 While not multiferroic, the persistence of a magnetoelectric effect to above room temperature makes it a promising candidate for low-energy spintronics. Due to its hexagonal (Corundum) crystal structure, the magnetic moment of the Cr3+ ions points along the c-direction and leads to a perpendicular uncompensated surface magnetization. Cooling in a magnetic field, or magnetoelectric annealing of the material, can then result in a single, global, surface magnetization state independent of surface roughness.132 This perpendicular magnetization is potentially favorable for device implementation44 as an out-of-plane magnetization minimizes interactions between magnetic bits.46 Using perpendicular magnetic anisotropy (PMA) in a (Co/Pd)3 superlattice, He et al. demonstrated the isothermal, electric field switching of exchange bias resulting from the electrical switching of the surface magnetization in bulk single crystal Cr2O3.132 While magnetoelectric switching of Cr2O3 requires the synchronous application of an external electric and magnetic field, the decoupling of the magnetoelectric effect from ferroelectricity may result in a device that can reach the lowest energy consumption per operation if the DC magnetic field required for magnetoelectric switching can be provided by a nearby ferromagnet. In fact, reports of magnetoelectric switching in thin films have shown excellent energy dissipation per operation, down to 60 nJ cm−2, (as calculated from capacitive, non-parasitic losses) as reported by Kosub et al. using a proximity induced ferromagnetism in a Pt/Cr2O3 thin film heterostructure.133 Scaling this number to small devices, however, approaches the generally accepted threshold for magnetic stability (40 kBT44), implying that other loss mechanisms will become dominant. Challenges for the electric field control of magnetism using Cr2O3 thin films still remain, for instance, eliminating or circumventing the required external magnetic field102,133 for magnetoelectric switching. Again, devices including a hard magnetic layer may solve this problem by providing a static magnetic field. Additional challenges result from crystallographic twin domains in thin film Cr2O3.133–135 At the twin boundary, a decrease in the bandgap and breakdown voltage is observed134 that hinders magnetoelectric switching. The prospects of this material, however, serve to encourage further research.133,136,137

To date, the magnetoelectric coupling coefficient (α) has been used as a figure of merit for judging multiferroic systems and devices, as this governs the energy needed for magnetic switching to take place. There has, however, been little work on the timescale of the switching itself, with only a few experimental reports22,23,121 investigating the dynamics of multiferroic switching. For devices based on multiferroic materials to be competitive for post-CMOS technologies,33,44,68,72 switching must be on the order of 1 ns (Refs. 34 and 46) or less and the kinetics and dynamics of magnetoelectric switching must become a major subject of research. The relevant switching metrics for some representative devices are reproduced here in Table I. The energies per operation presented here were calculated assuming capacitive losses as the dominant loss mechanism in an idealized device.

TABLE I.

Experimental converse magnetoelectric switching metrics.

SystemTypeRequired field (kV cm-1)Pulse widthEnergy dissipation (mJ cm-2)α(reported units)
Terf-D/PZN-PT85  Strain 600 DC 3.2a 580 Oe cm kV−1 
CoFeB/PMN-PT91,95 Strain 17.5 DC 2.7a b 
FeRh/PMN-PT89  Strain 6.7 1 s 1.0a 1.6 × 10−5 s m−1 (Ref. 32
FeGa/PMN-PT92  Strain b DC b b 
CoFe/BFO22,54 Exchange 400c 10 ms 0.48 1 × 10−7 s m−1 
Co/BFO23  Exchange 400 b 0.28a 5 × 10−11 s m−1c 
(Co-Pt)/Cr2O3121  Exchange 1750d 100 ns 3.2 × 10−2a,d b 
Pt/Cr2O3133  Proximity 75e DC 5.9 × 10−5a,e b 
SystemTypeRequired field (kV cm-1)Pulse widthEnergy dissipation (mJ cm-2)α(reported units)
Terf-D/PZN-PT85  Strain 600 DC 3.2a 580 Oe cm kV−1 
CoFeB/PMN-PT91,95 Strain 17.5 DC 2.7a b 
FeRh/PMN-PT89  Strain 6.7 1 s 1.0a 1.6 × 10−5 s m−1 (Ref. 32
FeGa/PMN-PT92  Strain b DC b b 
CoFe/BFO22,54 Exchange 400c 10 ms 0.48 1 × 10−7 s m−1 
Co/BFO23  Exchange 400 b 0.28a 5 × 10−11 s m−1c 
(Co-Pt)/Cr2O3121  Exchange 1750d 100 ns 3.2 × 10−2a,d b 
Pt/Cr2O3133  Proximity 75e DC 5.9 × 10−5a,e b 
a

Calculated with E/A=12ϵϵ0V2/d using a bulk dielectric constant138–141 and the reported geometry. Contributions from parasitic losses and a magnetic field, if applied, are not included.

b

Values not reported.

c

Calculated from reported device parameters.

d

Requires a magnetic field of 10 kOe.

e

Requires a magnetic field of 6.28 kOe.

In recent years, there has been a significant amount of work investigating magnetoelectric effects in single phase and composite systems;12,16,17,55 however, most of this work has focused on the states before and after switching with relatively long, or even DC, voltage pulses. Despite the immense effort, relatively little work has been done to determine the role of magnetoelectric switching kinetics and dynamics in the magnetoelectric effect and its role in magnetization switching. Whether magnetoelectric switching yields a thermodynamically driven transition or one that harnesses dynamic sequences through well synchronized voltage pulses, as in VCMA structures,81,101 the dynamics of the magnetoelectric switching must be investigated for future device applications, as devices are typically benchmarked according to their energy-delay product.34,46 Additionally, non-trivial switching kinetics observed in oxide ferroelectrics and multiferroics142,143 offer a potential playground for the engineering of magnetoelectric devices. The careful investigation of dynamic magnetoelectric switching in heterostructures may provide many new opportunities for novel spintronics applications.

For memory and logic applications, the switching time is critical for evaluation and speed of the device.34,46 Magnetoelectric switching is not only proposed to be low in energy consumption, as discussed above, but as the anticipated switching times are relatively fast (∼10 ns–100 ps),106,121,144–147 the energy-delay product appears quite promising. There is, however, a dearth of studies that consider magnetoelectric switching kinetics and dynamics,22,148,149 making switching times speculative. Additionally, experiments have shown that the electrostatic and mechanical boundary conditions1,16,150 have a strong influence on the switching of functional properties; thus, kinetic and dynamic studies as a function of boundary conditions and size will be necessary and may provide opportunities for further engineering of the magnetoelectric effect. As an example, in the bulk magnetoelectric multiferroic MnWO4, the converse magnetoelectric switching occurs on a millisecond time scale,148,151 illustrating that kinetic and dynamic studies will be necessary to understand if the rather ideal projected switching times can be achieved and engineered into devices.

In many composites and single phase multiferroics, the magnetoelectric switching is determined by the switching of the ferroelectric. Lately, experimental studies using fast raster and band-excitation piezoresponse force ferroelectric domain imaging microscopy have revealed that ferroelectric switching can occur under successive ferroelastic switching.5,22,147,152 In the case of multiferroic BiFeO3, where the ferroelectric polarization and the weak ferromagnetic magnetization are coupled by the Dzyaloshinskii-Moriya vector,39,146 it was shown that 180° ferroelectric switching in an anisotropically strained film with two ferroelectric domain variants occurred under a two-step switching.22,23 Density functional theory calculations of the kinetic switching barriers have shown that polarization switching through rotation has a significantly lower energy barrier than direct switching, where the polarization goes through and inversion center and P = 0 (Fig. 4). Prior to this experimental observation, thermodynamic considerations, which inherently assume that polarization switching occurs in a single step, concluded that it would be impossible to achieve deterministic 180° electric-field-induced switching without some other changes in the system.

FIG. 4.

Successive multi-stage magnetoelectric switching. (a) DFT calculated energy barrier (upper panel), Bi shift from the position center (center panel), and oxygen octahedral rotation (bottom panel). Calculated barrier energies for direct switching (green) and multi-stage switching (black) reveal that the energy barrier for sequential polarization rotation is significantly lower. The oxygen octahedra, representing the weak magnetic moment of BiFeO3, follow the successive polarization rotations while direct polarization switching leaves the octahedral rotation invariant. (b) Spatial map of the number of ferroelectric switching events that occurs during polarization reversal of an anisotropically strained, two-variant BiFeO3 thin film. (c) PFM image taken during the intermediate stage of polarization switching (left) with a schematic of the eight possible polarization directions of BiFeO3 and colorized to matched to the PFM image to indicate the local polarization direction (right). The correlations between matrix and emergent domains suggest that electrostatic and elastic boundary conditions influence the multi-stage switching. Scale bars are 500 nm. Adapted from Ref. 22.

FIG. 4.

Successive multi-stage magnetoelectric switching. (a) DFT calculated energy barrier (upper panel), Bi shift from the position center (center panel), and oxygen octahedral rotation (bottom panel). Calculated barrier energies for direct switching (green) and multi-stage switching (black) reveal that the energy barrier for sequential polarization rotation is significantly lower. The oxygen octahedra, representing the weak magnetic moment of BiFeO3, follow the successive polarization rotations while direct polarization switching leaves the octahedral rotation invariant. (b) Spatial map of the number of ferroelectric switching events that occurs during polarization reversal of an anisotropically strained, two-variant BiFeO3 thin film. (c) PFM image taken during the intermediate stage of polarization switching (left) with a schematic of the eight possible polarization directions of BiFeO3 and colorized to matched to the PFM image to indicate the local polarization direction (right). The correlations between matrix and emergent domains suggest that electrostatic and elastic boundary conditions influence the multi-stage switching. Scale bars are 500 nm. Adapted from Ref. 22.

Close modal

Multi-stage ferroelastic switching has also been observed in other rhombohedral and tetragonal ferroelectric systems,147,152–155 indicating that the successive switching may be more common than direct switching in general. Indeed, in PbTiO3-based materials, it has been explicitly shown that 90° or 180° switching can proceed through a degenerate intermediate polarization147 that is highly dependent on the strain state.152 In (111)-oriented PbZr0.2Ti0.8O3 films, 180° polarization reversal was mediated by the formation of a metastable twinned domain structure with a high density of 90° domain walls, showing the multi-step switching event.147 Intrinsic multi-stage, successive ferroelastic switching events may enable the 180° magnetization switching in strain coupled composites,156,157 as only 90° switching of magnetization should be possible in a single switching event. Nanoscale magnetoelectric motors and calculations for 180° electric field driven magnetization switching in composites have thus far required multi-electrodes with synchronized voltage pulses to create a rotating strain that rotates in the plane.158 As the strain rotates stepwise in multistage ferroelastic switching, it may enable magnetoelectric switching and magnetization reversal with only single electrodes and one voltage pulse. It is, however, unclear how quickly this multistage switching occurs and how it depends on the magnitude of the electric field. Recent theoretical works predict switching times on the order of 20 ps (Refs. 106 and 147) and experimental work with PbTiO3- and BiFeO3-based thin film capacitors has shown values on the order of 100–500 ps,107,159 yet further work is needed to explore this phenomenon and apply these metrics to a wider variety of systems.

Early work on the magnetoelectric dynamics in magnetoelectric Cr2O3 showed absorption peaks consistent with the selection rules for a magnetoelectric dipole transition at ∼1014 Hz,131 as measured through second harmonic generation. This indicates that the magnetoelectric coupling has an electronic component and can be quite fast, the question is then the strength of the effect and its interaction with a coupled magnetization. Computational work on Cr2O3 has shown that the electronic contribution to the magnetoelectric effect is significant, yet still dominated by the ionic contribution,160 which would presumably still place operational frequencies in the ∼1012 Hz range (∼1 ps per operation). Recent experimental work has demonstrated magnetoelectric switching in Cr2O3 thin films using electric field pulses in the range of 100 ns;121 thus, further questions reside regarding just how quickly magnetoelectric switching events can occur in thin films and in the presence of materials related defects. Recent developments in scanning probe microscopy techniques, such as band excitation and magnetoelectric force microscopy,135,161,162 may shed light on magnetoelectric dynamics, as these techniques could allow mapping of energy dissipation mechanisms on the nanoscale and enable domain engineering for efficient switching in non-ferroelectric magnetoelectrics such as Cr2O3. Several challenges hinder dynamic measurements of these materials. One challenge is that the antiferromagnetic order is relatively difficult to probe. Nonlinear optics, neutron microscopy, and X-ray microscopy provide access to the antiferromagnetic state. Outside of requiring large scale facilities for the case of neutron microscopy and X-ray microscopy, the techniques are challenged in either spatial resolution or temporal resolution55,131,163,164 as domain sizes in ferroelectric and multiferroics can be of 50 to 150 nm (Refs. 22 and 165) and dynamics in the pico- to femtosecond range. To investigate the atomic-scale dynamics of antiferromagnetic and magnetoelectric systems in the pico- to femtosecond range,131,166 the development of ultrafast microscopy with high spatial resolution would be extremely valuable.167 

Resonant magnetoelectric excitation of multiferroic, orthorhombic TbMnO3 was performed optically in the terahertz range, showing that an ultrafast (at ∼2 ps) spin deflection of ∼4% occurred, yet this is far from a 180° reversal.168 In the case of room temperature multiferroic BiFeO3, little has been done on the converse magnetoelectric switching dynamics of single films and heterostructures beyond a quasi-static regime,22,150 leaving the speeds unknown.169 Concerning multiferroic and magnetoelectric systems, information on dynamics is sparse in contrast to the observation of equilibrium switching states.

Hybrid magnetoelectric-spin-orbit torque (ME-SOT) heterostructures, consisting of a composite magnetoelectric with a spin-orbit torque layer, may offer the opportunity to combine the respective advantages of magnetoelectric and spin-orbit torque switching, namely, high temperature operation, low-energy consumption, and fast, deterministic 180° magnetization switching. Figure 5 shows recent computational work considering current-driven spin-orbit torque switching of a magnetostrictive magnet from a saddle point state, initialized by strain-mediated magnetoelectric switching.45 Figure 5(a) illustrates the three stages of the proposed hybrid ME-SOT switching with simulations of the projected magnetization onto the x, y, and z directions. The magnetoelectric effect rotates the magnetization by 90° from the anisotropy axis (x direction). A current-driven spin-orbit torque is applied via the spin Hall effect (SHE) of a heavy metal layer as the voltage driving the piezo-strain is reduced and drives the magnetization the remaining 90° to achieve full 180° switching (magnetization along –x direction). Interestingly, such a hybrid switch may decrease the current pulse width for reliable spin-orbit torque switching by a factor of ∼10–1000, depending on the anisotropy and damping parameter of the magnetostrictive layer, as seen in Fig. 5(b). The reduced pulse width is a consequence of eliminating the precessional motion in early stage spin-orbit torque switching by the initialization from the magnetoelectric effect. While the magnitude of the pulse current for reliable switching can be reduced, by ∼50x in certain cases,61 the reduction will depend on the properties of the ferromagnet. To better describe and motivate hybrid multiferroic - spin torque heterostructures, we will briefly review the state of spin-torque switching before providing additional perspectives.

FIG. 5.

Schematics and simulations of strain-mediated magnetization reversal through spin torque. (a) Illustration and simulation of the three stages (initial magnetization, strain introduction, and reversal through spin torque) of strain-mediated magnetization reversal with spin torque. (b). Spin torque switching probability for magnetization initialized in x, y, and z directions, as defined in (a) with x being the easy axis, as a function of the spin current pulse width. By initializing the magnetization to one of the two high-energy states, say through magnetoelectric switching, the switching current pulse width can be decreased by a factor of ∼10–1000. This pulse width reduction is achieved by eliminating the magnetic precession in the early stage of spin torque driven magnetization reversal. Inset: Minimum pulse width versus error rate for a magnetization initialized along the y direction. Depending on the ratio of in-plane to out-of-plane magnetic anisotropy energies, the magnitude to the pulse current may also be reduced for switching. Adapted from Ref. 45.

FIG. 5.

Schematics and simulations of strain-mediated magnetization reversal through spin torque. (a) Illustration and simulation of the three stages (initial magnetization, strain introduction, and reversal through spin torque) of strain-mediated magnetization reversal with spin torque. (b). Spin torque switching probability for magnetization initialized in x, y, and z directions, as defined in (a) with x being the easy axis, as a function of the spin current pulse width. By initializing the magnetization to one of the two high-energy states, say through magnetoelectric switching, the switching current pulse width can be decreased by a factor of ∼10–1000. This pulse width reduction is achieved by eliminating the magnetic precession in the early stage of spin torque driven magnetization reversal. Inset: Minimum pulse width versus error rate for a magnetization initialized along the y direction. Depending on the ratio of in-plane to out-of-plane magnetic anisotropy energies, the magnitude to the pulse current may also be reduced for switching. Adapted from Ref. 45.

Close modal

To lead into a discussion of hybrid multiferroic - spin torque heterostructures, a brief discussion of spin-torque switching is given. Current control of magnetization can be achieved by the conversion of charge current into spin current with subsequent injection of the spin current into a ferromagnetic layer.170 The traditional method of spin injection is to use a magnetic layer or heterostructure to polarize an incident current, such as in a magnetic tunnel junction79 (MTJ). More recently, however, the field has begun to take advantage of spin-orbit phenomena to convert charge current into spin current.50 One such mechanism for injecting spin current into a magnetic layer is through the use of the intrinsic spin Hall effect (SHE).171,172 In intrinsic SHE metals such as Pt and Ta, the transverse spin current generation is high, approximately 5% to 15% of the applied electrical current.173,174 The transverse spin diffusion can then exert a torque on an adjacent magnetic material to induce precession or switching. A thorough review of the physics of these intrinsic transport phenomena is presented by Xiao et al.170 

Traditionally, current-based switching is enabled through the deposition of MTJ/spin-valve heterostructures, illustrated in Figs. 6(a) and 6(b). In isolation, out-of-plane currents are applied for both reading and writing the state (parallel or antiparallel), with the threshold write current often being orders of magnitude higher than the read current. This process is typically less efficient than the SHE, as outlined in a quantitative comparison between select spin torque switching experiments in Table II. Spin-orbit driven, or spin-orbit torque (SOT), switching studies, illustrated in Figs. 6(c)–6(e), are typically done using Hall voltage,49,176 resonant magnetoresistance,173,174 or perpendicular magnetoresistance51,177–179 measurements. An example of a Hall structure for spin-orbit torque measurements is given in Fig. 6(d). In this case, an injected charge current results in the precession of the magnetization in the top layer, a result of spin-orbit generated spin injection, affecting the anomalous Hall conductivity of the magnetic layer.

FIG. 6.

Spin torque switching in an MTJ/Spin Valve. (a) Schematic showing use of a magnetic layer as an in-plane spin polarizer. Current (J) through a pinned ferromagnetic (FM) layer becomes spin polarized and exerts a torque on a second, free, ferromagnetic layer. (b) Probability of switching in a MTJ plotted against pulse time and amplitude. The Parallel (P) - Antiparallel (AP) switching asymmetry is characteristic of MTJ heterostructures. Additionally, there is a sharp increase in threshold current past the 1 GHz (1 ns) threshold, due to the magnetization dynamics. (c) Schematic showing current-driven switching via the spin Hall effect. (d) Typical Hall bar structure of a spin Hall device, with a spin current generating layer (here Pt) and ferromagnetic sensor (here Co). (e) The spin torque strength is detected through the modulation of the anomalous Hall conductivity in the ferromagnetic layer from the induced magnetic precession. Part (b) adapted from Ref. 175. Parts (d) and (e) adapted from Ref. 48.

FIG. 6.

Spin torque switching in an MTJ/Spin Valve. (a) Schematic showing use of a magnetic layer as an in-plane spin polarizer. Current (J) through a pinned ferromagnetic (FM) layer becomes spin polarized and exerts a torque on a second, free, ferromagnetic layer. (b) Probability of switching in a MTJ plotted against pulse time and amplitude. The Parallel (P) - Antiparallel (AP) switching asymmetry is characteristic of MTJ heterostructures. Additionally, there is a sharp increase in threshold current past the 1 GHz (1 ns) threshold, due to the magnetization dynamics. (c) Schematic showing current-driven switching via the spin Hall effect. (d) Typical Hall bar structure of a spin Hall device, with a spin current generating layer (here Pt) and ferromagnetic sensor (here Co). (e) The spin torque strength is detected through the modulation of the anomalous Hall conductivity in the ferromagnetic layer from the induced magnetic precession. Part (b) adapted from Ref. 175. Parts (d) and (e) adapted from Ref. 48.

Close modal
TABLE II.

Experimental spin torque switching metrics.

SystemTypePulse widthEnergy dissipation (mJ cm−2)External mag. field (Oe)
CoFeB/MgO/CoFeB/Ru/CoFe/PtMn51  MTJ 500 ps 4.2a 1000 
Ta/CoFeB/MgO/CoFeB179  MTJ 5 ns 11.3a … 
PtMn/CoFe/Ru/CoFeB/MgO/CoFeB175  MTJ 700 ps 10.9a … 
[CoFe/Pd]3/CoFe/Cu/Co/[Pd/Co]5177  Spin valve 10 ns 3.9e2a 130 
Pt/[CoPt]4/Co/Cu/Co/Cu/Py/Cu/Py178  Spin valve 100 ps 7.2a … 
TmIG/Pt49  SOT 20 ns 0.23a 
Pt/Hf/FeCoB/Ru/FeCoB184  SOT 430 ps 0.65a 25 
Pt/Co185  SOT 2 ns 43.9a 940 
SystemTypePulse widthEnergy dissipation (mJ cm−2)External mag. field (Oe)
CoFeB/MgO/CoFeB/Ru/CoFe/PtMn51  MTJ 500 ps 4.2a 1000 
Ta/CoFeB/MgO/CoFeB179  MTJ 5 ns 11.3a … 
PtMn/CoFe/Ru/CoFeB/MgO/CoFeB175  MTJ 700 ps 10.9a … 
[CoFe/Pd]3/CoFe/Cu/Co/[Pd/Co]5177  Spin valve 10 ns 3.9e2a 130 
Pt/[CoPt]4/Co/Cu/Co/Cu/Py/Cu/Py178  Spin valve 100 ps 7.2a … 
TmIG/Pt49  SOT 20 ns 0.23a 
Pt/Hf/FeCoB/Ru/FeCoB184  SOT 430 ps 0.65a 25 
Pt/Co185  SOT 2 ns 43.9a 940 
a

Calculated from reported device parameters.

While spin-orbit torque provides a mechanism for reduced switching energy with respect to traditional spin transfer torque (STT) switching, it still requires a significant current density to supply the spin-torque necessary to overcome damping and drive 180° switching of the magnetization.173,180 The demonstrated threshold current density for deterministic switching is on the order of 106–108 A cm−2, and is dependent on multiple factors, including intrinsic material properties, the geometry of the magnetization with respect to the polarization orientation of the spin current, and the interface quality.48,49,135 The lowest energy dissipation per switch per area has been demonstrated using a magnetic insulator with perpendicular magnetic anisotropy and a Pt layer that generates an in-plane polarized spin current. In such a geometry, the write current density, assuming transparent interfaces, would be of the form

Jwrite=2eμ0MsHkt1θSH,

where e is the electron charge, is the reduced Planck's constant, μ0 is the permeability of free space,Ms,t, and Hk are the saturation magnetization, thickness, and the out-of-plane magnetic anisotropy field of the ferromagnetic layer, and θSH is the spin Hall angle (a measure of charge to spin current conversion efficiency) of the spin Hall layer. The equation highlights the role of material parameters in the energy dissipation for spin-orbit torque switching. Due to symmetry constraints, the most pervasive spin Hall materials are confined to generating in-plane polarized spin currents.181 The most energy efficient spin-orbit torque switching is expected to occur through out-of-plane antidamping torques that would arise from out-of-plane polarized spin currents injected to a perpendicularly magnetized layer which would lead to expected write current densities of the form

Jwrite=2eμ0MsHktα1θSH,

where α is the magnetic damping parameter of the ferromagnetic layer and is a quantity less than unity. Recent experimental work on 2-dimensional TaTe2 has demonstrated out-of-plane antidumping torques in connection to mirror plane symmetry breaking.182 This motivates future work on low-symmetry materials with large spin-orbit coupling. In terms of switching speeds, due to the precessional nature of magnetic moments,50,173,183 purely magnetic switching, such as in a tunneling (MTJ) or spin transfer torque (STT) device, occurs on the order of 1–10 ns.49 Recently, 100 ps (Ref. 48) was demonstrated in a spin Hall bilayer system, at the cost of increasing current density magnitude ( ∼ 108 A cm−2). With current densities in the range of 106–108 A cm−2, energy dissipation remains high, typically ranging from 1–10 mJ cm−2.175,178,179

Electric field control of magnetization with magnetoelectric materials provides a route to ultra-low power switching of a magnetization with favorable scaling.22,34,44,55 There is, however, a dearth of single phase multiferroics with unambiguous magnetoelectric coupling at room temperature and the largest and most robust room temperature magnetoelectric effects to date have been demonstrated in composite multiferroics32,57,103 utilizing strain- or exchange-bias-mediated lamellar heterostructures. From thermodynamic symmetry considerations, however, only 90° switching of magnetization should be possible with the application of a single electric field pulse. Indeed, experimental work on the strain-mediated magnetoelectric effect in composite multiferroics has shown that the magnetic energy landscape can be modified by a sufficient anisotropic strain to reversibly reorient the magnetization easy axis by 90°.86,92,104 Without the aid of kinetics or precisely synchronized voltages,156,157 deterministic strain-mediated magnetoelectric switching of a magnetization by 180° (desired for maximum readout signal) may be unrealizable.

For efficient converse magnetoelectric switching in composites, magnets with large magnetostriction coefficients are necessary.13,14 This creates implications for reducing the energy dissipation through current driven spin-orbit torques as the write current density for spin-orbit torque switching scales linearly with α, the magnetic damping parameter of the ferromagnet. The large spin-lattice coupling in materials with large magnetostriction coefficients results in a large magnetic damping parameter (α ∼0.2, compared to ∼0.03 for most ferromagnetic metals and ∼0.003 for magnetic insulators)186,187 which will increase the switching current threshold (in the simplified case where all other parameters are fixed). As shown in Fig. 6, however, this may decrease the precession time, increasing the speed of the device and lowering the energy-delay product. These factors offer opportunities for material optimization and the hybrid device scheme enables new possibilities for low-energy dissipation and fast spintronic logic and memory.

Hybrid ME-SOT heterostructures can also provide novel ways to integrate strain and charge induced phenomena into spin-orbit torque devices for added functionalities (Table III). In terms of reduced threshold switching currents and energy dissipation, spin-orbit torque is most efficient when the magnetic anisotropy of the ferromagnetic is perpendicular to the film plane. Unfortunately, the spin-orbit torque on a magnet from heavy metal layers such as Pt, W, or Ta in this geometric configuration can only generate stochastic switching of the out-of-plane magnetization,180 a detriment for devices. The degeneracy can be broken by breaking the in-plane symmetry and this has recently been demonstrated with an in-plane magnetic field,180 an in-plane oxidation gradient,188 and an in-plane exchange bias field.189 Using a hybrid ME-SOT heterostructure consisting of a Pt/Co/Ni/Co/Pt multilayer on ferroelectric PMN-PT, the deterministic switching of a magnetic multilayer with perpendicular magnetic anisotropy has been reported using Pt as the spin Hall layer (Fig. 7).190 In this hybrid ME-SOT heterostructure, the in-plane degeneracy is broken by a lateral gradient of the out-of-plane electric field at the Pt/PMN-PT interface due to the ferroelectric polarization of PMN-PT. The interpretation is that the electric field gradient creates a spatially inhomogeneous Rashba-like spin-orbit coupling that results in a spatially inhomogeneous spin current. This inhomogeneous spin current mixes with the spin current generated by the spin Hall effect to enable switching of the magnetization (Fig. 7). It was found that a modified Landau-Lifshitz-Gilbert equation of the form

Mt=γM×Heff+αMsM×MtγcM×Jsx,

where the modification includes a torque from a gradient in the spin current density (Js/x) as the final term, describing the unidirectional switching behavior of the magnetization experimentally observed.190 Excitingly, the sign of spatially inhomogeneous charge mediated torque was found to be switchable with in-plane electric field, indicating that the origin of this effect is due to the ferroelectric polarization.

TABLE III.

Hybrid magnetoelectric-spintronic devices.a

SystemRequired stress (MPa)Current density (A cm−2)Current pulse widthEnergy dissipation (mJ cm−2)
Strain assisted ST61  350 4.5 × 105 1 ns 4.1 × 10−2b 
Strain mediated ST45  … 7.0 × 107 1–100 ps 0.521c 
SystemRequired stress (MPa)Current density (A cm−2)Current pulse widthEnergy dissipation (mJ cm−2)
Strain assisted ST61  350 4.5 × 105 1 ns 4.1 × 10−2b 
Strain mediated ST45  … 7.0 × 107 1–100 ps 0.521c 
a

All values in this table are obtained from computational results.

b

Calculated from reported device parameters.

c

Calculated using device geometry from Ref. 173.

FIG. 7.

Charge-mediated spatially inhomogeneous spin currents. (a) Schematic of hybrid multiferroic-spin torque structure, consisting of a Pt spin Hall layer as the Hall cross and a Co/Ni/Co/Pt magnetic pillar with perpendicular magnetic anisotropy (PMA) in the center of the cross. PMN-PT bias electrodes are also shown. (b) Spin torque switching of a PMA magnet without the presence of an in-plane magnetic field (Hx) is non-deterministic by symmetry. (c) Schematic of the out-of-plane electric field gradient at the Pt/PMN-PT interface due to the ferroelectric polarization. The out-of-plane electric field, when combined with the spin Hall effect, creates a spatially inhomogeneous spin current which enables deterministic current driven spin-orbit torques switching. The gradient of the spin current density changes sign with bias voltage to the PMN-PT enabling the handedness of the spin-orbit torques switching to be controlled. Adapted from Ref. 170.

FIG. 7.

Charge-mediated spatially inhomogeneous spin currents. (a) Schematic of hybrid multiferroic-spin torque structure, consisting of a Pt spin Hall layer as the Hall cross and a Co/Ni/Co/Pt magnetic pillar with perpendicular magnetic anisotropy (PMA) in the center of the cross. PMN-PT bias electrodes are also shown. (b) Spin torque switching of a PMA magnet without the presence of an in-plane magnetic field (Hx) is non-deterministic by symmetry. (c) Schematic of the out-of-plane electric field gradient at the Pt/PMN-PT interface due to the ferroelectric polarization. The out-of-plane electric field, when combined with the spin Hall effect, creates a spatially inhomogeneous spin current which enables deterministic current driven spin-orbit torques switching. The gradient of the spin current density changes sign with bias voltage to the PMN-PT enabling the handedness of the spin-orbit torques switching to be controlled. Adapted from Ref. 170.

Close modal

The work in Ref. 190 demonstrates the charge-mediation of spin-orbit phenomena in hybrid ME-SOT heterostructures and opens the floor to the discovery of other novel coupling to spin-orbit torques through voltage controlled strain, spin, and charge. In fact, a recent theoretical study191 suggests that in-plane biaxial effective magnetic fields generated by the strain-mediated magnetoelectric effect in composites may also provide the in-plane symmetry breaking required to enable deterministic current-driven spin-orbit torque switching. Exciting possibilities exist for the exploration other novel coupling and properties in hybrid ME-SOT heterostructures for magnetoelectronics.

In conclusion, magnetoelectric heterostructures enable energy efficient magnetic switching via the electric field control of magnetism. The field has shown novel magnetoelectric switching stemming from strain and exchange coupling that has open exciting possibilities for device engineering and fundamental investigations. Moving forward, magnetoelectric switching kinetics and dynamics are likely to provide information that is critical for complete understanding of magnetoelectric coupling and device engineering efforts. As the palette of single phase room temperature multiferroics with demonstrated magnetoelectric coupling is limited, utilizing composites with spin-orbit torques may offer another potential avenue for deterministic low-energy and fast control over magnetization by harnessing the strengths of each mechanism. Recently, it has been proposed that hybrid devices can provide advantage reduced current requirements61 and switching times45 or lead to other novel mechanisms to influence spin-orbit torque switching. This work was supported by IMRA America.

1.
J.
Wang
,
J. B.
Neaton
,
H.
Zheng
,
V.
Nagarajan
,
S. B.
Ogale
,
B.
Liu
,
D.
Viehland
,
V.
Vaithyanathan
,
D. G.
Schlom
,
U. V.
Waghmare
,
N. A.
Spaldin
,
K. M.
Rabe
,
M.
Wuttig
, and
R.
Ramesh
,
Science
299
,
1719
(
2003
).
2.
T.
Choi
,
Y.
Horibe
,
H. T.
Yi
,
Y. J.
Choi
,
W.
Wu
, and
S.-W.
Cheong
,
Nat. Mater.
9
,
253
(
2010
).
3.
C. A. F.
Vaz
,
J.
Hoffman
,
Y.
Segal
,
J. W.
Reiner
,
R. D.
Grober
,
Z.
Zhang
,
C. H.
Ahn
, and
F. J.
Walker
,
Phys. Rev. Lett.
104
,
127202
(
2010
).
4.
M. A.
Carpenter
,
E. K. H.
Salje
, and
C. J.
Howard
,
Phys. Rev. B
85
,
224430
(
2012
).
5.
N.
Balke
,
S.
Choudhury
,
S.
Jesse
,
M.
Huijben
,
Y. H.
Chu
,
A. P.
Baddorf
,
L. Q.
Chen
,
R.
Ramesh
, and
S. V.
Kalinin
,
Nat. Nanotechnol.
4
,
868
(
2009
).
6.
Á.
Butykai
,
S.
Bordács
,
I.
Kézsmárki
,
V.
Tsurkan
,
A.
Loidl
,
J.
Döring
,
E.
Neuber
,
P.
Milde
,
S. C.
Kehr
, and
L. M.
Eng
,
Sci. Rep.
7
,
44663
(
2017
).
7.
A. S.
Zimmermann
,
D.
Meier
, and
M.
Fiebig
,
Nat. Commun.
5
,
4796
(
2014
).
8.
B. B.
Van Aken
,
J.-P.
Rivera
,
H.
Schmid
, and
M.
Fiebig
,
Nature
449
,
702
(
2007
).
9.
N. A.
Spaldin
,
M.
Fiebig
, and
M.
Mostovoy
,
J. Phys. Condens. Matter
20
,
434203
(
2008
).
10.
W.
Eerenstein
,
N. D.
Mathur
, and
J. F.
Scott
,
Nature
442
,
759
(
2006
).
11.
Y.
Wang
,
J.
Hu
,
Y.
Lin
, and
C.-W.
Nan
,
NPG Asia Mater.
2
,
61
(
2010
).
12.
C.-W.
Nan
,
M. I.
Bichurin
,
S.
Dong
,
D.
Viehland
, and
G.
Srinivasan
,
J. Appl. Phys.
103
,
031101
(
2008
).
13.
J.
Ma
,
J.
Hu
,
Z.
Li
, and
C.-W.
Nan
,
Adv. Mater.
23
,
1062
(
2011
).
14.
J.-M.
Hu
,
L.-Q.
Chen
, and
C.-W.
Nan
,
Adv. Mater.
28
,
15
(
2016
).
15.
E.
Ascher
,
H.
Rieder
,
H.
Schmid
, and
H.
Stössel
,
J. Appl. Phys.
37
,
1404
(
1966
).
16.
L. W.
Martin
,
Y.-H.
Chu
, and
R.
Ramesh
,
Mater. Sci. Eng., R
68
,
89
(
2010
).
17.
R.
Ramesh
and
N. A.
Spaldin
,
Nat. Mater.
6
,
21
(
2007
).
18.
N. A.
Spaldin
,
Nat. Rev. Mater.
2
,
17017
(
2017
).
19.
D. M.
Juraschek
,
M.
Fechner
,
A. V.
Balatsky
, and
N. A.
Spaldin
,
Phys. Rev. Mater.
1
,
014401
(
2017
).
20.
D.
Khomskii
,
Physics
2
,
20
(
2009
).
21.
S.-W.
Cheong
and
M.
Mostovoy
,
Nat. Mater.
6
,
13
(
2007
).
22.
J. T.
Heron
,
J. L.
Bosse
,
Q.
He
,
Y.
Gao
,
M.
Trassin
,
L.
Ye
,
J. D.
Clarkson
,
C.
Wang
,
J.
Liu
,
S.
Salahuddin
,
D. C.
Ralph
,
D. G.
Schlom
,
J.
Íñiguez
,
B. D.
Huey
, and
R.
Ramesh
,
Nature
516
,
370
(
2014
).
23.
T.
Gao
,
X.
Zhang
,
W.
Ratcliff
,
S.
Maruyama
,
M.
Murakami
,
A.
Varatharajan
,
Z.
Yamani
,
P.
Chen
,
K.
Wang
,
H.
Zhang
,
R.
Shull
,
L. A.
Bendersky
,
J.
Unguris
,
R.
Ramesh
, and
I.
Takeuchi
,
Nano Lett.
17
,
2825
(
2017
).
24.
P.
Borisov
,
A.
Hochstrat
,
X.
Chen
,
W.
Kleemann
, and
C.
Binek
,
Phys. Rev. Lett.
94
,
117203
(
2005
).
25.
Y.-H.
Chu
,
L. W.
Martin
,
M. B.
Holcomb
,
M.
Gajek
,
S.-J.
Han
,
Q.
He
,
N.
Balke
,
C.-H.
Yang
,
D.
Lee
,
W.
Hu
,
Q.
Zhan
,
P.-L.
Yang
,
A.
Fraile-rodríguez
,
A.
Scholl
,
S. X.
Wang
, and
R.
Ramesh
,
Nat. Mater.
7
,
678
(
2008
).
26.
T.
Zhao
,
A.
Scholl
,
F.
Zavaliche
,
K.
Lee
,
M.
Barry
,
A.
Doran
,
M. P.
Cruz
,
Y. H.
Chu
,
C.
Ederer
,
N. A.
Spaldin
,
R. R.
Das
,
D. M.
Kim
,
S. H.
Baek
,
C. B.
Eom
, and
R.
Ramesh
,
Nat. Mater.
5
,
823
(
2006
).
27.
J. A.
Mundy
,
C. M.
Brooks
,
M. E.
Holtz
,
J. A.
Moyer
,
H.
Das
,
A. F.
Rébola
,
J. T.
Heron
,
J. D.
Clarkson
,
S. M.
Disseler
,
Z.
Liu
,
A.
Farhan
,
R.
Held
,
R.
Hovden
,
E.
Padgett
,
Q.
Mao
,
H.
Paik
,
R.
Misra
,
L. F.
Kourkoutis
,
E.
Arenholz
,
A.
Scholl
,
J. A.
Borchers
,
W. D.
Ratcliff
,
R.
Ramesh
,
C. J.
Fennie
,
P.
Schiffer
,
D. A.
Muller
, and
D. G.
Schlom
,
Nature
537
,
523
(
2016
).
28.
P.
Yu
,
J.-S.
Lee
,
S.
Okamoto
,
M. D.
Rossell
,
M.
Huijben
,
C.-H.
Yang
,
Q.
He
,
J. X.
Zhang
,
S. Y.
Yang
,
M. J.
Lee
,
Q. M.
Ramasse
,
R.
Erni
,
Y.-H.
Chu
,
D. A.
Arena
,
C.-C.
Kao
,
L. W.
Martin
, and
R.
Ramesh
,
Phys. Rev. Lett.
105
,
027201
(
2010
).
29.
S. M.
Wu
,
S. A.
Cybart
,
D.
Yi
,
J. M.
Parker
,
R.
Ramesh
, and
R. C.
Dynes
,
Phys. Rev. Lett.
110
,
067202
(
2013
).
30.
M.
Gajek
,
M.
Bibes
,
S.
Fusil
,
K.
Bouzehouane
,
J.
Fontcuberta
,
A.
Barthélémy
, and
A.
Fert
,
Nat. Mater.
6
,
296
(
2007
).
31.
V.
Garcia
,
M.
Bibes
,
L.
Bocher
,
S.
Valencia
,
F.
Kronast
,
A.
Crassous
,
X.
Moya
,
S.
Enouz-Vedrenne
,
A.
Gloter
,
D.
Imhoff
,
C.
Deranlot
,
N. D.
Mathur
,
S.
Fusil
,
K.
Bouzehouane
, and
A.
Barthélémy
,
Science
327
,
1106
(
2010
).
32.
R. O.
Cherifi
,
V.
Ivanovskaya
,
L. C.
Phillips
,
A.
Zobelli
,
I. C.
Infante
,
E.
Jacquet
,
V.
Garcia
,
S.
Fusil
,
P. R.
Briddon
,
N.
Guiblin
,
A.
Mougin
,
A. A.
Ünal
,
F.
Kronast
,
S.
Valencia
,
B.
Dkhil
,
A.
Barthélémy
, and
M.
Bibes
,
Nat. Mater.
13
,
345
(
2014
).
33.
M.
Bibes
and
A.
Barthélémy
,
Nat. Mater.
7
,
425
(
2008
).
34.
D. E.
Nikonov
and
I. A.
Young
,
J. Mater. Res.
29
,
2109
(
2014
).
35.
J. T.
Heron
,
D. G.
Schlom
, and
R.
Ramesh
,
Appl. Phys. Rev.
1
,
021303
(
2014
).
36.
H.
Béa
,
M.
Gajek
,
M.
Bibes
, and
A.
Barthélémy
,
J. Phys. Condens. Matter
20
,
434221
(
2008
).
37.
D. M.
Evans
,
A.
Schilling
,
A.
Kumar
,
D.
Sanchez
,
N.
Ortega
,
M.
Arredondo
,
R. S.
Katiyar
,
J. M.
Gregg
, and
J. F.
Scott
,
Nat. Commun.
4
,
1534
(
2013
).
38.
L.
Keeney
,
T.
Maity
,
M.
Schmidt
,
A.
Amann
,
N.
Deepak
,
N.
Petkov
,
S.
Roy
,
M. E.
Pemble
, and
R. W.
Whatmore
,
J. Am. Ceram. Soc.
96
,
2339
(
2013
).
39.
J. T.
Heron
,
M.
Trassin
,
K.
Ashraf
,
M.
Gajek
,
Q.
He
,
S. Y.
Yang
,
D. E.
Nikonov
,
Y. H.
Chu
,
S.
Salahuddin
, and
R.
Ramesh
,
Phys. Rev. Lett.
107
,
217202
(
2011
).
40.
L.
Huang
,
D.
Wen
,
Z.
Zhong
,
H.
Zhang
, and
F.
Bai
, preprint arXiv:14054076 Cond-Mat (
2014
).
41.
T.
Nan
,
H.
Lin
,
Y.
Gao
,
A.
Matyushov
,
G.
Yu
,
H.
Chen
,
N.
Sun
,
S.
Wei
,
Z.
Wang
,
M.
Li
,
X.
Wang
,
A.
Belkessam
,
R.
Guo
,
B.
Chen
,
J.
Zhou
,
Z.
Qian
,
Y.
Hui
,
M.
Rinaldi
,
M. E.
McConney
,
B. M.
Howe
,
Z.
Hu
,
J. G.
Jones
,
G. J.
Brown
, and
N. X.
Sun
,
Nat. Commun.
8
,
296
(
2017
).
42.
J.
Cui
,
S. M.
Keller
,
C.-Y.
Liang
,
G. P.
Carman
, and
C. S.
Lynch
,
Nanotechnology
28
,
08LT01
(
2017
).
43.
H.
Sohn
,
M. E.
Nowakowski
,
C.
Liang
,
J. L.
Hockel
,
K.
Wetzlar
,
S.
Keller
,
B. M.
McLellan
,
M. A.
Marcus
,
A.
Doran
,
A.
Young
,
M.
Kläui
,
G. P.
Carman
,
J.
Bokor
, and
R. N.
Candler
,
ACS Nano
9
,
4814
(
2015
).
44.
S.
Manipatruni
,
D. E.
Nikonov
, and
I. A.
Young
,
Phys. Rev. Appl.
5
,
014002
(
2016
).
45.
N.
Kani
,
J. T.
Heron
, and
A.
Naeemi
,
IEEE Trans. Magn.
53
,
4300808
(
2017
).
46.
D. E.
Nikonov
and
I. A.
Young
,
IEEE J. Explor. Solid-State Comput. Devices Circuits
1
,
3
(
2015
).
47.
H.-S. P.
Wong
and
S.
Salahuddin
,
Nat. Nanotechnol.
10
,
191
(
2015
).
48.
K.
Garello
,
C. O.
Avci
,
I. M.
Miron
,
M.
Baumgartner
,
A.
Ghosh
,
S.
Auffret
,
O.
Boulle
,
G.
Gaudin
, and
P.
Gambardella
,
Appl. Phys. Lett.
105
,
212402
(
2014
).
49.
C. O.
Avci
,
E.
Rosenberg
,
M.
Baumgartner
,
L.
Beran
,
A.
Quindeau
,
P.
Gambardella
,
C. A.
Ross
, and
G. S. D.
Beach
,
Appl. Phys. Lett.
111
,
072406
(
2017
).
50.
D. C.
Ralph
and
M. D.
Stiles
,
J. Magn. Magn. Mater.
320
,
1190
(
2008
).
51.
H.
Liu
,
D.
Bedau
,
D.
Backes
,
J. A.
Katine
,
J.
Langer
, and
A. D.
Kent
,
Appl. Phys. Lett.
97
,
242510
(
2010
).
52.
G. E.
Rowlands
,
T.
Rahman
,
J. A.
Katine
,
J.
Langer
,
A.
Lyle
,
H.
Zhao
,
J. G.
Alzate
,
A. A.
Kovalev
,
Y.
Tserkovnyak
,
Z. M.
Zeng
,
H. W.
Jiang
,
K.
Galatsis
,
Y. M.
Huai
,
P. K.
Amiri
,
K. L.
Wang
,
I. N.
Krivorotov
, and
J.-P.
Wang
,
Appl. Phys. Lett.
98
,
102509
(
2011
).
53.
C. O.
Avci
,
A.
Quindeau
,
C.-F.
Pai
,
M.
Mann
,
L.
Caretta
,
A. S.
Tang
,
M. C.
Onbasli
,
C. A.
Ross
, and
G. S. D.
Beach
,
Nat. Mater.
16
,
309
(
2017
).
54.
S.
Manipatruni
,
D. E.
Nikonov
,
C.-C.
Lin
,
P.
Bhagwati
,
Y. L.
Huang
,
A. R.
Damodaran
,
Z.
Chen
,
R.
Ramesh
, and
I. A.
Young
, preprint arXiv:180108280 Cond-Mat (
2018
).
55.
M.
Fiebig
,
T.
Lottermoser
,
D.
Meier
, and
M.
Trassin
,
Nat. Rev. Mater.
1
,
16046
(
2016
).
56.
M.
Fiebig
,
J. Phys. Appl. Phys.
38
,
R123
(
2005
).
57.
J.-M.
Hu
,
C.-G.
Duan
,
C.-W.
Nan
, and
L.-Q.
Chen
,
Npj Comput. Mater.
3
,
18
(
2017
).
58.
F.
Matsukura
,
Y.
Tokura
, and
H.
Ohno
,
Nat. Nanotechnol.
10
,
209
(
2015
).
59.
M.
Liu
and
N. X.
Sun
,
Philos. Trans. R. Soc. A
372
,
20120439
(
2014
).
60.
C. A. F.
Vaz
,
J. Phys. Condens. Matter
24
,
333201
(
2012
).
61.
A.
Khan
,
D. E.
Nikonov
,
S.
Manipatruni
,
T.
Ghani
, and
I. A.
Young
,
Appl. Phys. Lett.
104
,
262407
(
2014
).
62.
D. A.
Sanchez
,
A.
Kumar
,
N.
Ortega
,
R. S.
Katiyar
, and
J. F.
Scott
,
Appl. Phys. Lett.
97
,
202910
(
2010
).
63.
H. J.
Zhao
,
W.
Ren
,
Y.
Yang
,
J.
Íñiguez
,
X. M.
Chen
, and
L.
Bellaiche
,
Nat. Commun.
5
,
4021
(
2014
).
64.
M. J.
Pitcher
,
P.
Mandal
,
M. S.
Dyer
,
J.
Alaria
,
P.
Borisov
,
H.
Niu
,
J. B.
Claridge
, and
M. J.
Rosseinsky
,
Science
347
,
420
(
2015
).
65.
P.
Mandal
,
M. J.
Pitcher
,
J.
Alaria
,
H.
Niu
,
P.
Borisov
,
P.
Stamenov
,
J. B.
Claridge
, and
M. J.
Rosseinsky
,
Nature
525
,
363
(
2015
).
66.
F.
Ahmad
,
M.
Tuhin
,
S.
Michael
,
D.
Nitin
,
R.
Saibal
,
E.
Pemble Martyn
,
W.
Whatmore Roger
, and
K.
Lynette
,
J. Am. Ceram. Soc.
100
,
975
(
2017
).
67.
J. F.
Scott
,
NPG Asia Mater.
5
,
e72
(
2013
).
68.
A.
Jaiswal
and
K.
Roy
,
Sci. Rep.
7
,
39793
(
2017
).
69.
U.
Bauer
,
L.
Yao
,
A. J.
Tan
,
P.
Agrawal
,
S.
Emori
,
H. L.
Tuller
,
S.
van Dijken
, and
G. S. D.
Beach
,
Nat. Mater.
14
,
174
(
2015
).
70.
H.-B.
Li
,
N.
Lu
,
Q.
Zhang
,
Y.
Wang
,
D.
Feng
,
T.
Chen
,
S.
Yang
,
Z.
Duan
,
Z.
Li
,
Y.
Shi
,
W.
Wang
,
W.-H.
Wang
,
K.
Jin
,
H.
Liu
,
J.
Ma
,
L.
Gu
,
C.
Nan
, and
P.
Yu
,
Nat. Commun.
8
,
2156
(
2017
).
71.
N.
Lu
,
P.
Zhang
,
Q.
Zhang
,
R.
Qiao
,
Q.
He
,
H.-B.
Li
,
Y.
Wang
,
J.
Guo
,
D.
Zhang
,
Z.
Duan
,
Z.
Li
,
M.
Wang
,
S.
Yang
,
M.
Yan
,
E.
Arenholz
,
S.
Zhou
,
W.
Yang
,
L.
Gu
,
C.-W.
Nan
,
J.
Wu
,
Y.
Tokura
, and
P.
Yu
,
Nature
546
,
124
(
2017
).
72.
A.
Khitun
,
D. E.
Nikonov
, and
K. L.
Wang
,
J. Appl. Phys.
106
,
123909
(
2009
).
73.
C.-G.
Duan
,
J. P.
Velev
,
R. F.
Sabirianov
,
Z.
Zhu
,
J.
Chu
,
S. S.
Jaswal
, and
E. Y.
Tsymbal
,
Phys. Rev. Lett.
101
,
137201
(
2008
).
74.
D.
Chiba
,
M.
Yamanouchi
,
F.
Matsukura
, and
H.
Ohno
,
Science
301
,
943
(
2003
).
75.
I.
Stolichnov
,
S. W. E.
Riester
,
H. J.
Trodahl
,
N.
Setter
,
A. W.
Rushforth
,
K. W.
Edmonds
,
R. P.
Campion
,
C. T.
Foxon
,
B. L.
Gallagher
, and
T.
Jungwirth
,
Nat. Mater.
7
,
464
(
2008
).
76.
M. K.
Niranjan
,
J. P.
Velev
,
C.-G.
Duan
,
S. S.
Jaswal
, and
E. Y.
Tsymbal
,
Phys. Rev. B
78
,
104405
(
2008
).
77.
M.
Yi
,
H.
Zhang
, and
B.-X.
Xu
,
Npj Comput. Mater.
3
,
38
(
2017
).
78.
D.
Chiba
,
M.
Sawicki
,
Y.
Nishitani
,
Y.
Nakatani
,
F.
Matsukura
, and
H.
Ohno
,
Nature
455
,
515
(
2008
).
79.
W.-G.
Wang
,
M.
Li
,
S.
Hageman
, and
C. L.
Chien
,
Nat. Mater.
11
,
64
(
2012
).
80.
Y.
Shiota
,
T.
Nozaki
,
F.
Bonell
,
S.
Murakami
,
T.
Shinjo
, and
Y.
Suzuki
,
Nat. Mater.
11
,
39
(
2012
).
81.
M.
Weisheit
,
S.
Fähler
,
A.
Marty
,
Y.
Souche
,
C.
Poinsignon
, and
D.
Givord
,
Science
315
,
349
(
2007
).
82.
H. J. A.
Molegraaf
,
J.
Hoffman
,
C. A. F.
Vaz
,
S.
Gariglio
,
D.
van der Marel
,
C. H.
Ahn
, and
J.-M.
Triscone
,
Adv. Mater.
21
,
3470
(
2009
).
83.
C.-G.
Duan
,
C.-W.
Nan
,
S. S.
Jaswal
, and
E. Y.
Tsymbal
,
Phys. Rev. B
79
,
140403
(
2009
).
84.
K.
Yamauchi
,
B.
Sanyal
, and
S.
Picozzi
,
Appl. Phys. Lett.
91
,
062506
(
2007
).
85.
M.
Liu
,
S.
Li
,
Z.
Zhou
,
S.
Beguhn
,
J.
Lou
,
F.
Xu
,
T.
Jian Lu
, and
N. X.
Sun
,
J. Appl. Phys.
112
,
063917
(
2012
).
86.
T. H. E.
Lahtinen
,
K. J. A.
Franke
, and
S.
van Dijken
,
Sci. Rep.
2
,
258
(
2012
).
87.
K. J. A.
Franke
,
D.
López González
,
S. J.
Hämäläinen
, and
S.
van Dijken
,
Phys. Rev. Lett.
112
,
017201
(
2014
).
88.
M.
Buzzi
,
R. V.
Chopdekar
,
J. L.
Hockel
,
A.
Bur
,
T.
Wu
,
N.
Pilet
,
P.
Warnicke
,
G. P.
Carman
,
L. J.
Heyderman
, and
F.
Nolting
,
Phys. Rev. Lett.
111
,
027204
(
2013
).
89.
Y.
Lee
,
Z. Q.
Liu
,
J. T.
Heron
,
J. D.
Clarkson
,
J.
Hong
,
C.
Ko
,
M. D.
Biegalski
,
U.
Aschauer
,
S. L.
Hsu
,
M. E.
Nowakowski
,
J.
Wu
,
H. M.
Christen
,
S.
Salahuddin
,
J. B.
Bokor
,
N. A.
Spaldin
,
D. G.
Schlom
, and
R.
Ramesh
,
Nat. Commun.
6
,
5959
(
2015
).
90.
M.
Liu
,
J.
Hoffman
,
J.
Wang
,
J.
Zhang
,
B.
Nelson-Cheeseman
, and
A.
Bhattacharya
,
Sci. Rep.
3
,
1876
(
2013
).
91.
Q.
Wang
,
X.
Li
,
C.-Y.
Liang
,
A.
Barra
,
J.
Domann
,
C.
Lynch
,
A.
Sepulveda
, and
G.
Carman
,
Appl. Phys. Lett.
110
,
102903
(
2017
).
92.
D. E.
Parkes
,
S. A.
Cavill
,
A. T.
Hindmarch
,
P.
Wadley
,
F.
McGee
,
C. R.
Staddon
,
K. W.
Edmonds
,
R. P.
Campion
,
B. L.
Gallagher
, and
A. W.
Rushforth
,
Appl. Phys. Lett.
101
,
072402
(
2012
).
93.
H.
Ahmad
,
J.
Atulasimha
, and
S.
Bandyopadhyay
,
Sci. Rep.
5
,
18264
(
2015
).
94.
T.
Wu
,
A.
Bur
,
K.
Wong
,
P.
Zhao
,
C. S.
Lynch
,
P. K.
Amiri
,
K. L.
Wang
, and
G. P.
Carman
,
Appl. Phys. Lett.
98
,
262504
(
2011
).
95.
S.
Zhang
,
Y.
Zhao
,
X.
Xiao
,
Y.
Wu
,
S.
Rizwan
,
L.
Yang
,
P.
Li
,
J.
Wang
,
M.
Zhu
,
H.
Zhang
,
X.
Jin
, and
X.
Han
,
Sci. Rep.
4
,
3727
(
2014
).
96.
M.
Feng
,
J.
Wang
,
J.-M.
Hu
,
J.
Wang
,
J.
Ma
,
H.-B.
Li
,
Y.
Shen
,
Y.-H.
Lin
,
L.-Q.
Chen
, and
C.-W.
Nan
,
Appl. Phys. Lett.
106
,
072901
(
2015
).
97.
F. Y.
Huang
,
Appl. Phys. Lett.
76
,
3046
(
2000
).
98.
P. F.
Carcia
,
A. D.
Meinhaldt
, and
A.
Suna
,
Appl. Phys. Lett.
47
,
178
(
1985
).
99.
W. B.
Zeper
,
FJ. a M.
Greidanus
,
P. F.
Carcia
, and
C. R.
Fincher
,
J. Appl. Phys.
65
,
4971
(
1989
).
100.
J.-M.
Hu
,
Z.
Li
,
L.-Q.
Chen
, and
C.-W.
Nan
,
Adv. Mater.
24
,
2869
(
2012
).
101.
T.
Maruyama
,
Y.
Shiota
,
T.
Nozaki
,
K.
Ohta
,
N.
Toda
,
M.
Mizuguchi
,
A. A.
Tulapurkar
,
T.
Shinjo
,
M.
Shiraishi
,
S.
Mizukami
,
Y.
Ando
, and
Y.
Suzuki
,
Nat. Nanotechnol.
4
,
158
(
2009
).
102.
T.
Nozaki
,
M.
Al-Mahdawi
,
S. P.
Pati
,
S.
Ye
,
Y.
Shiokawa
, and
M.
Sahashi
,
Jpn. J. Appl. Phys., Part 1
56
,
070302
(
2017
).
103.
S.
Zhang
,
Y. G.
Zhao
,
P. S.
Li
,
J. J.
Yang
,
S.
Rizwan
,
J. X.
Zhang
,
J.
Seidel
,
T. L.
Qu
,
Y. J.
Yang
,
Z. L.
Luo
,
Q.
He
,
T.
Zou
,
Q. P.
Chen
,
J. W.
Wang
,
L. F.
Yang
,
Y.
Sun
,
Y. Z.
Wu
,
X.
Xiao
,
X. F.
Jin
,
J.
Huang
,
C.
Gao
,
X. F.
Han
, and
R.
Ramesh
,
Phys. Rev. Lett.
108
,
137203
(
2012
).
104.
T.
Wu
,
A.
Bur
,
K.
Wong
,
J.
Leon Hockel
,
C.-J.
Hsu
,
H. K. D.
Kim
,
K. L.
Wang
, and
G. P.
Carman
,
J. Appl. Phys.
109
,
07D732
(
2011
).
105.
D. E.
Parkes
,
L. R.
Shelford
,
P.
Wadley
,
V.
Holý
,
M.
Wang
,
A. T.
Hindmarch
,
G.
van der Laan
,
R. P.
Campion
,
K. W.
Edmonds
,
S. A.
Cavill
, and
A. W.
Rushforth
,
Sci. Rep.
3
,
2220
(
2013
).
106.
S.
Liu
,
I.
Grinberg
, and
A. M.
Rappe
,
Nature
534
,
360
(
2016
).
107.
E. J.
Guo
,
K.
Dörr
, and
A.
Herklotz
,
Appl. Phys. Lett.
101
,
242908
(
2012
).
108.
R. E.
Jones
,
P. D.
Maniar
,
R.
Moazzami
,
P.
Zurcher
,
J. Z.
Witowski
,
Y. T.
Lii
,
P.
Chu
, and
S. J.
Gillespie
,
Thin Solid Films
270
,
584
(
1995
).
109.
M.
Trassin
,
J. Phys. Condens. Matter
28
,
033001
(
2016
).
110.
L. J.
McGilly
,
P.
Yudin
,
L.
Feigl
,
A. K.
Tagantsev
, and
N.
Setter
,
Nat. Nanotechnol.
10
,
145
(
2015
).
111.
D.
Lee
,
H.
Lu
,
Y.
Gu
,
S.-Y.
Choi
,
S.-D.
Li
,
S.
Ryu
,
T. R.
Paudel
,
K.
Song
,
E.
Mikheev
,
S.
Lee
,
S.
Stemmer
,
D. A.
Tenne
,
S. H.
Oh
,
E. Y.
Tsymbal
,
X.
Wu
,
L.-Q.
Chen
,
A.
Gruverman
, and
C. B.
Eom
,
Science
349
,
1314
(
2015
).
112.
N. A.
Pertsev
,
A. G.
Zembilgotov
, and
A. K.
Tagantsev
,
Phys. Rev. Lett.
80
,
1988
(
1998
).
113.
D. G.
Schlom
,
L.-Q.
Chen
,
C.-B.
Eom
,
K. M.
Rabe
,
S. K.
Streiffer
, and
J.-M.
Triscone
,
Annu. Rev. Mater. Res.
37
,
589
(
2007
).
114.
V.
Nagarajan
,
A.
Roytburd
,
A.
Stanishevsky
,
S.
Prasertchoung
,
T.
Zhao
,
L.
Chen
,
J.
Melngailis
,
O.
Auciello
, and
R.
Ramesh
,
Nat. Mater.
2
,
43
(
2003
).
115.
R.
Steinhausen
,
T.
Hauke
,
W.
Seifert
,
V.
Mueller
,
H.
Beige
,
S.
Seifert
, and
P.
Lobmann
, in
ISAF 1998 Proceedings of the 11th IEEE International Symposium on Applications of Ferroelectrics
(
1998
), pp.
93
96
, Cat No. 98CH36245.
116.
R. N.
Torah
,
S. P.
Beeby
, and
N. M.
White
,
J. Phys. Appl. Phys.
37
,
1074
(
2004
).
117.
V.
Nagarajan
,
J.
Junquera
,
J. Q.
He
,
C. L.
Jia
,
R.
Waser
,
K.
Lee
,
Y. K.
Kim
,
S.
Baik
,
T.
Zhao
,
R.
Ramesh
,
P.
Ghosez
, and
K. M.
Rabe
,
J. Appl. Phys.
100
,
051609
(
2006
).
118.
S. R.
Bakaul
,
C. R.
Serrao
,
M.
Lee
,
C. W.
Yeung
,
A.
Sarker
,
S.-L.
Hsu
,
A. K.
Yadav
,
L.
Dedon
,
L.
You
,
A. I.
Khan
,
J. D.
Clarkson
,
C.
Hu
,
R.
Ramesh
, and
S.
Salahuddin
,
Nat. Commun.
7
,
10547
(
2016
).
119.
L.
Shen
,
L.
Wu
,
Q.
Sheng
,
C.
Ma
,
Y.
Zhang
,
L.
Lu
,
J.
Ma
,
J.
Ma
,
J.
Bian
,
Y.
Yang
,
A.
Chen
,
X.
Lu
,
M.
Liu
,
H.
Wang
, and
C.-L.
Jia
,
Adv. Mater.
29
,
1702411
(
2017
).
120.
S. M.
Wu
,
S. A.
Cybart
,
P.
Yu
,
M. D.
Rossell
,
J. X.
Zhang
,
R.
Ramesh
, and
R. C.
Dynes
,
Nat. Mater.
9
,
756
(
2010
).
121.
K.
Toyoki
,
Y.
Shiratsuchi
,
A.
Kobane
,
C.
Mitsumata
,
Y.
Kotani
,
T.
Nakamura
, and
R.
Nakatani
,
Appl. Phys. Lett.
106
,
162404
(
2015
).
122.
H.
Béa
,
M.
Bibes
,
F.
Ott
,
B.
Dupé
,
X.-H.
Zhu
,
S.
Petit
,
S.
Fusil
,
C.
Deranlot
,
K.
Bouzehouane
, and
A.
Barthélémy
,
Phys. Rev. Lett.
100
,
017204
(
2008
).
123.
M.
Bibes
,
J. E.
Villegas
, and
A.
Barthélémy
,
Adv. Phys.
60
,
5
(
2011
).
124.
T.
Morgan
,
L.
Gabriele De
,
M.
Sebastian
, and
F.
Manfred
,
Adv. Mater.
27
,
4871
(
2015
).
125.
J.
Zhou
,
M.
Trassin
,
Q.
He
,
N.
Tamura
,
M.
Kunz
,
C.
Cheng
,
J.
Zhang
,
W.-I.
Liang
,
J.
Seidel
,
C.-L.
Hsin
, and
J.
Wu
,
J. Appl. Phys.
112
,
064102
(
2012
).
126.
M.
Trassin
,
J. D.
Clarkson
,
S. R.
Bowden
,
J.
Liu
,
J. T.
Heron
,
R. J.
Paull
,
E.
Arenholz
,
D. T.
Pierce
, and
J.
Unguris
,
Phys. Rev. B
87
,
134426
(
2013
).
127.
I.
Gross
,
W.
Akhtar
,
V.
Garcia
,
L. J.
Martínez
,
S.
Chouaieb
,
K.
Garcia
,
C.
Carrétéro
,
A.
Barthélémy
,
P.
Appel
,
P.
Maletinsky
,
J.-V.
Kim
,
J. Y.
Chauleau
,
N.
Jaouen
,
M.
Viret
,
M.
Bibes
,
S.
Fusil
, and
V.
Jacques
,
Nature
549
,
252
(
2017
).
128.
D.
Sando
,
A.
Agbelele
,
D.
Rahmedov
,
J.
Liu
,
P.
Rovillain
,
C.
Toulouse
,
I. C.
Infante
,
A. P.
Pyatakov
,
S.
Fusil
,
E.
Jacquet
,
C.
Carrétéro
,
C.
Deranlot
,
S.
Lisenkov
,
D.
Wang
,
J.-M.
Le Breton
,
M.
Cazayous
,
A.
Sacuto
,
J.
Juraszek
,
A. K.
Zvezdin
,
L.
Bellaiche
,
B.
Dkhil
,
A.
Barthélémy
, and
M.
Bibes
,
Nat. Mater.
12
,
641
(
2013
).
129.
L. W.
Martin
,
Y.-H.
Chu
,
M. B.
Holcomb
,
M.
Huijben
,
P.
Yu
,
S.-J.
Han
,
D.
Lee
,
S. X.
Wang
, and
R.
Ramesh
,
Nano Lett.
8
,
2050
(
2008
).
130.
Y. H.
Chu
,
Q.
Zhan
,
C.-H.
Yang
,
M. P.
Cruz
,
L. W.
Martin
,
T.
Zhao
,
P.
Yu
,
R.
Ramesh
,
P. T.
Joseph
,
I. N.
Lin
,
W.
Tian
, and
D. G.
Schlom
,
Appl. Phys. Lett.
92
,
102909
(
2008
).
131.
M.
Fiebig
,
D.
Fröhlich
,
B. B.
Krichevtsov
, and
R. V.
Pisarev
,
Phys. Rev. Lett.
73
,
2127
(
1994
).
132.
X.
He
,
Y.
Wang
,
N.
Wu
,
A. N.
Caruso
,
E.
Vescovo
,
K. D.
Belashchenko
,
P. A.
Dowben
, and
C.
Binek
,
Nat. Mater.
9
,
579
(
2010
).
133.
T.
Kosub
,
M.
Kopte
,
R.
Hühne
,
P.
Appel
,
B.
Shields
,
P.
Maletinsky
,
R.
Hübner
,
M. O.
Liedke
,
J.
Fassbender
,
O. G.
Schmidt
, and
D.
Makarov
,
Nat. Commun.
8
,
13985
(
2017
).
134.
Y.
Guo
,
S. J.
Clark
, and
J.
Robertson
,
J. Phys. Condens. Matter
24
,
325504
(
2012
).
135.
Y.
Geng
,
H.
Das
,
A. L.
Wysocki
,
X.
Wang
,
S.-W.
Cheong
,
M.
Mostovoy
,
C. J.
Fennie
, and
W.
Wu
,
Nat. Mater.
13
,
163
(
2014
).
136.
T.
Ashida
,
M.
Oida
,
N.
Shimomura
,
T.
Nozaki
,
T.
Shibata
, and
M.
Sahashi
,
Appl. Phys. Lett.
106
,
132407
(
2015
).
137.
T.
Ashida
,
M.
Oida
,
N.
Shimomura
,
T.
Nozaki
,
T.
Shibata
, and
M.
Sahashi
,
Appl. Phys. Lett.
104
,
152409
(
2014
).
138.
R.
Zhang
,
B.
Jiang
,
W.
Jiang
, and
W.
Cao
,
Mater. Lett.
57
,
1305
(
2003
).
139.
E.
Markiewicz
,
B.
Hilczer
,
M.
Błaszyk
,
A.
Pietraszko
, and
E.
Talik
,
J. Electroceram.
27
,
154
(
2011
).
140.
P. H.
Fang
and
W. S.
Brower
,
Phys. Rev.
129
,
1561
(
1963
).
141.
S. W.
Choi
,
R. T. R.
Shrout
,
S. J.
Jang
, and
A. S.
Bhalla
,
Ferroelectrics
100
,
29
(
1989
).
142.
S.
Saremi
,
R.
Xu
,
L. R.
Dedon
,
J. A.
Mundy
,
S.-L.
Hsu
,
Z.
Chen
,
A. R.
Damodaran
,
S. P.
Chapman
,
J. T.
Evans
, and
L. W.
Martin
,
Adv. Mater.
28
,
10750
(
2016
).
143.
A. K.
Yadav
,
C. T.
Nelson
,
S. L.
Hsu
,
Z.
Hong
,
J. D.
Clarkson
,
C. M.
Schlepütz
,
A. R.
Damodaran
,
P.
Shafer
,
E.
Arenholz
,
L. R.
Dedon
,
D.
Chen
,
A.
Vishwanath
,
A. M.
Minor
,
L. Q.
Chen
,
J. F.
Scott
,
L. W.
Martin
, and
R.
Ramesh
,
Nature
530
,
198
(
2016
).
144.
M.
Mochizuki
and
N.
Nagaosa
,
J. Phys. Conf. Ser.
320
,
012082
(
2011
).
145.
Y.
Yang
,
J.
Íñiguez
,
A.-J.
Mao
, and
L.
Bellaiche
,
Phys. Rev. Lett.
112
,
057202
(
2014
).
146.
J. B.
Neaton
,
C.
Ederer
,
U. V.
Waghmare
,
N. A.
Spaldin
, and
K. M.
Rabe
,
Phys. Rev. B
71
,
014113
(
2005
).
147.
R.
Xu
,
S.
Liu
,
I.
Grinberg
,
J.
Karthik
,
A. R.
Damodaran
,
A. M.
Rappe
, and
L. W.
Martin
,
Nat. Mater.
14
,
79
(
2015
).
148.
M.
Baum
,
J.
Leist
,
T.
Finger
,
K.
Schmalzl
,
A.
Hiess
,
L. P.
Regnault
,
P.
Becker
,
L.
Bohatý
,
G.
Eckold
, and
M.
Braden
,
Phys. Rev. B
89
,
144406
(
2014
).
149.
D.
Pantel
,
Y.-H.
Chu
,
L. W.
Martin
,
R.
Ramesh
,
D.
Hesse
, and
M.
Alexe
,
J. Appl. Phys.
107
,
084111
(
2010
).
150.
S. H.
Baek
,
H. W.
Jang
,
C. M.
Folkman
,
Y. L.
Li
,
B.
Winchester
,
J. X.
Zhang
,
Q.
He
,
Y. H.
Chu
,
C. T.
Nelson
,
M. S.
Rzchowski
,
X. Q.
Pan
,
R.
Ramesh
,
L. Q.
Chen
, and
C. B.
Eom
,
Nat. Mater.
9
,
309
(
2010
).
151.
T.
Hoffmann
,
P.
Thielen
,
P.
Becker
,
L.
Bohatý
, and
M.
Fiebig
,
Phys. Rev. B
84
,
184404
(
2011
).
152.
A. R.
Damodaran
,
S.
Pandya
,
J. C.
Agar
,
Y.
Cao
,
R. K.
Vasudevan
,
R.
Xu
,
S.
Saremi
,
Q.
Li
,
J.
Kim
,
M. R.
McCarter
,
L. R.
Dedon
,
T.
Angsten
,
N.
Balke
,
S.
Jesse
,
M.
Asta
,
S. V.
Kalinin
, and
L. W.
Martin
,
Adv. Mater.
29
,
1702069
(
2017
).
153.
L. W.
Martin
and
A. M.
Rappe
,
Nat. Rev. Mater.
2
,
16087
(
2017
).
154.
J.
Yin
and
W.
Cao
,
Appl. Phys. Lett.
79
,
4556
(
2001
).
155.
J. E.
Daniels
,
T. R.
Finlayson
,
M.
Davis
,
D.
Damjanovic
,
A. J.
Studer
,
M.
Hoffman
, and
J. L.
Jones
,
J. Appl. Phys.
101
,
104108
(
2007
).
156.
J. J.
Wang
,
J. M.
Hu
,
J.
Ma
,
J. X.
Zhang
,
L. Q.
Chen
, and
C. W.
Nan
,
Sci. Rep.
4
,
7507
(
2014
).
157.
J.-M.
Hu
,
T.
Yang
,
J.
Wang
,
H.
Huang
,
J.
Zhang
,
L.-Q.
Chen
, and
C.-W.
Nan
,
Nano Lett.
15
,
616
(
2015
).
158.
J.-M.
Hu
,
T.
Yang
,
K.
Momeni
,
X.
Cheng
,
L.
Chen
,
S.
Lei
,
S.
Zhang
,
S.
Trolier-McKinstry
,
V.
Gopalan
,
G. P.
Carman
,
C.-W.
Nan
, and
L.-Q.
Chen
,
Nano Lett.
16
,
2341
(
2016
).
159.
J.
Li
,
B.
Nagaraj
,
H.
Liang
,
W.
Cao
,
C. H.
Lee
, and
R.
Ramesh
,
Appl. Phys. Lett.
84
,
1174
(
2004
).
160.
A.
Malashevich
,
S.
Coh
,
I.
Souza
, and
D.
Vanderbilt
,
Phys. Rev. B
86
,
094430
(
2012
).
161.
P.
Schoenherr
,
L. M.
Giraldo
,
M.
Lilienblum
,
M.
Trassin
,
D.
Meier
, and
M.
Fiebig
,
Materials
10
,
1051
(
2017
).
162.
S.
Jesse
,
S. V.
Kalinin
,
R.
Proksch
,
A. P.
Baddorf
, and
B. J.
Rodriguez
,
Nanotechnology
18
,
435503
(
2007
).
163.
P.
Němec
,
M.
Fiebig
,
T.
Kampfrath
, and
A. V.
Kimel
,
Nat. Phys.
14
,
229
(
2018
).
164.
K. A.
Grishunin
,
N. A.
Ilyin
,
N. E.
Sherstyuk
,
E. D.
Mishina
,
A.
Kimel
,
V. M.
Mukhortov
,
A. V.
Ovchinnikov
,
O. V.
Chefonov
, and
M. B.
Agranat
,
Sci. Rep.
7
,
687
(
2017
).
165.
C. H.
Ahn
,
K. M.
Rabe
, and
J.-M.
Triscone
,
Science
303
,
488
(
2004
).
166.
M. O.
Ramirez
,
A.
Kumar
,
S. A.
Denev
,
N. J.
Podraza
,
X. S.
Xu
,
R. C.
Rai
,
Y. H.
Chu
,
J.
Seidel
,
L. W.
Martin
,
S.-Y.
Yang
,
E.
Saiz
,
J. F.
Ihlefeld
,
S.
Lee
,
J.
Klug
,
S. W.
Cheong
,
M. J.
Bedzyk
,
O.
Auciello
,
D. G.
Schlom
,
R.
Ramesh
,
J.
Orenstein
,
J. L.
Musfeldt
, and
V.
Gopalan
,
Phys. Rev. B
79
,
224106
(
2009
).
167.
M. R.
Freeman
and
B. C.
Choi
,
Science
294
,
1484
(
2001
).
168.
T.
Kubacka
,
J. A.
Johnson
,
M. C.
Hoffmann
,
C.
Vicario
,
S.
de Jong
,
P.
Beaud
,
S.
Grübel
,
S.-W.
Huang
,
L.
Huber
,
L.
Patthey
,
Y.-D.
Chuang
,
J. J.
Turner
,
G. L.
Dakovski
,
W.-S.
Lee
,
M. P.
Minitti
,
W.
Schlotter
,
R. G.
Moore
,
C. P.
Hauri
,
S. M.
Koohpayeh
,
V.
Scagnoli
,
G.
Ingold
,
S. L.
Johnson
, and
U.
Staub
,
Science
343
,
1333
(
2014
).
169.
S.
Bhattacharjee
,
D.
Rahmedov
,
D.
Wang
,
J.
Íñiguez
, and
L.
Bellaiche
,
Phys. Rev. Lett.
112
,
147601
(
2014
).
170.
D.
Xiao
,
M.-C.
Chang
, and
Q.
Niu
,
Rev. Mod. Phys.
82
,
1959
(
2010
).
171.
S.
Murakami
,
N.
Nagaosa
, and
S.-C.
Zhang
,
Science
301
,
1348
(
2003
).
172.
J.
Sinova
,
D.
Culcer
,
Q.
Niu
,
N. A.
Sinitsyn
,
T.
Jungwirth
, and
A. H.
MacDonald
,
Phys. Rev. Lett.
92
,
126603
(
2004
).
173.
L.
Liu
,
C.-F.
Pai
,
Y.
Li
,
H. W.
Tseng
,
D. C.
Ralph
, and
R. A.
Buhrman
,
Science
336
,
555
(
2012
).
174.
L.
Liu
,
T.
Moriyama
,
D. C.
Ralph
, and
R. A.
Buhrman
,
Phys. Rev. Lett.
106
,
036601
(
2011
).
175.
H.
Zhao
,
A.
Lyle
,
Y.
Zhang
,
P. K.
Amiri
,
G.
Rowlands
,
Z.
Zeng
,
J.
Katine
,
H.
Jiang
,
K.
Galatsis
,
K. L.
Wang
,
I. N.
Krivorotov
, and
J.-P.
Wang
,
J. Appl. Phys.
109
,
07C720
(
2011
).
176.
R.
Ramaswamy
,
X.
Qiu
,
T.
Dutta
,
S. D.
Pollard
, and
H.
Yang
,
Appl. Phys. Lett.
108
,
202406
(
2016
).
177.
R.
Law
,
E.-L.
Tan
,
R.
Sbiaa
,
T.
Liew
, and
T. C.
Chong
,
Appl. Phys. Lett.
94
,
062516
(
2009
).
178.
O. J.
Lee
,
D. C.
Ralph
, and
R. A.
Buhrman
,
Appl. Phys. Lett.
99
,
102507
(
2011
).
179.
D. C.
Worledge
,
G.
Hu
,
D. W.
Abraham
,
J. Z.
Sun
,
P. L.
Trouilloud
,
J.
Nowak
,
S.
Brown
,
M. C.
Gaidis
,
E. J.
O'Sullivan
, and
R. P.
Robertazzi
,
Appl. Phys. Lett.
98
,
022501
(
2011
).
180.
L.
Liu
,
O. J.
Lee
,
T. J.
Gudmundsen
,
D. C.
Ralph
, and
R. A.
Buhrman
,
Phys. Rev. Lett.
109
,
096602
(
2012
).
181.
K.
Garello
,
I. M.
Miron
,
C. O.
Avci
,
F.
Freimuth
,
Y.
Mokrousov
,
S.
Blügel
,
S.
Auffret
,
O.
Boulle
,
G.
Gaudin
, and
P.
Gambardella
,
Nat. Nanotechnol.
8
,
587
(
2013
).
182.
D.
MacNeill
,
G. M.
Stiehl
,
M. H. D.
Guimaraes
,
R. A.
Buhrman
,
J.
Park
, and
D. C.
Ralph
,
Nat. Phys.
13
,
300
(
2017
).
183.
A.
Manchon
and
S.
Zhang
,
Phys. Rev. B
78
,
212405
(
2008
).
184.
S. V.
Aradhya
,
G. E.
Rowlands
,
J.
Oh
,
D. C.
Ralph
, and
R. A.
Buhrman
,
Nano Lett.
16
,
5987
(
2016
).
185.
M.
Baumgartner
,
K.
Garello
,
J.
Mendil
,
C. O.
Avci
,
E.
Grimaldi
,
C.
Murer
,
J.
Feng
,
M.
Gabureac
,
C.
Stamm
,
Y.
Acremann
,
S.
Finizio
,
S.
Wintz
,
J.
Raabe
, and
P.
Gambardella
,
Nat. Nanotechnol.
12
,
980
(
2017
).
186.
P. G.
Gowtham
,
G. E.
Rowlands
, and
R. A.
Buhrman
,
J. Appl. Phys.
118
,
183903
(
2015
).
187.
C. L.
Jermain
,
H.
Paik
,
S. V.
Aradhya
,
R. A.
Buhrman
,
D. G.
Schlom
, and
D. C.
Ralph
,
Appl. Phys. Lett.
109
,
192408
(
2016
).
188.
G.
Yu
,
P.
Upadhyaya
,
Y.
Fan
,
J. G.
Alzate
,
W.
Jiang
,
K. L.
Wong
,
S.
Takei
,
S. A.
Bender
,
L.-T.
Chang
,
Y.
Jiang
,
M.
Lang
,
J.
Tang
,
Y.
Wang
,
Y.
Tserkovnyak
,
P. K.
Amiri
, and
K. L.
Wang
,
Nat. Nanotechnol.
9
,
548
(
2014
).
189.
Y.-W.
Oh
,
S.
Chris Baek
,
Y. M.
Kim
,
H. Y.
Lee
,
K.-D.
Lee
,
C.-G.
Yang
,
E.-S.
Park
,
K.-S.
Lee
,
K.-W.
Kim
,
G.
Go
,
J.-R.
Jeong
,
B.-C.
Min
,
H.-W.
Lee
,
K.-J.
Lee
, and
B.-G.
Park
,
Nat. Nanotechnol.
11
,
878
(
2016
).
190.
K.
Cai
,
M.
Yang
,
H.
Ju
,
S.
Wang
,
Y.
Ji
,
B.
Li
,
K. W.
Edmonds
,
Y.
Sheng
,
B.
Zhang
,
N.
Zhang
,
S.
Liu
,
H.
Zheng
, and
K.
Wang
,
Nat. Mater.
16
,
712
(
2017
).
191.
Q.
Wang
,
J.
Domann
,
G.
Yu
,
A.
Barra
,
K. L.
Wang
, and
G. P.
Carman
, arXiv:180201647 Cond-Mat Physicsphysics (
2017
).