Electrical control of magnetism by electric field and current-induced torques

The remanent magnetization of ferromagnets has long been studied and used to store binary information. While early magnetic memory designs relied on magnetization switching by locally generated magnetic fields, key insights in condensed matter physics later suggested the possibility of doing it by electrical means instead. In the 1990s, Slonczewski and Berger formulated the concept of current-induced spin torques in magnetic multilayers through which a spin-polarized current generated by a first ferromagnet may be used to switch the magnetization of a second one. This discovery drove the development of spin-transfer-torque magnetic random-access memories (MRAMs). More recent fundamental research revealed other types of current-induced torques named spin-orbit torques (SOTs) and will lead to a new generation of devices including SOT MRAMs and skyrmion-based devices. Parallel to these advances, multiferroics and their magnetoelectric coupling, first investigated experimentally in the 1960s, experienced a renaissance. Dozens of multiferroic compounds with new magnetoelectric coupling mechanisms were discovered and high-quality multiferroic films were synthesized (notably of ${\mathrm{BiFeO}}_3$), also leading to novel device concepts for information and communication technology such as the magnetoelectric spin-orbit (MESO) transistor. The story of the electrical switching of magnetization, which is discussed in this review, is that of a dance between fundamental research (in spintronics, condensed matter physics, and materials science) and technology (MRAMs, MESO transistors, microwave emitters, spin diodes, skyrmion-based devices, components for neuromorphics, etc.). This pas de deux has led to major scientific and technological breakthroughs in recent decades (such as the conceptualization of pure spin currents, the observation of magnetic skyrmions, and the discovery of spin-charge interconversion effects). As a result, this field has not only propelled MRAMs into consumer electronics products but also fueled discoveries in adjacent research areas such as ferroelectrics or magnonics. In this review, recent advances in the control of magnetism by electric fields and by current-induced torques are covered. Fundamental concepts in these two directions are reviewed first, their combination is then discussed, and finally current various families of devices harnessing the electrical control of magnetic properties for various application fields are addressed. The review concludes by giving perspectives in terms of both emerging fundamental physics concepts and new directions in materials science.

Figure 1

Schematic illustrating the emergence of the Internet of things and machine learning and artificial intelligence as macroscale drivers for the beyond Moore’s law research and development. The leveling off of the various scaling laws (Dennard’s law states that as the dimensions of a device go down so does power consumption; Amdahl’s law is a principle that states that the maximum potential improvement to the performance of a system is limited by the portion of the system that cannot be improved) is described as a function of time, leading to the end of Moore’s law. Courtesy of Sasikanth Manipatruni and Debo Olaosebikan, Kepler Computing.

Figure 2

Moore’s law: the evolution of the number of transistors per chip over time.

Figure 3

Heat output over time for bipolar and CMOS transistor chips. From [143].

Figure 4

Energy consumption of information and communication technology systems over time. From [280].

Figure 5

Fundamental taxonomy of solid-state order parameters. (a) Emergence of ferromagnetism due to spontaneous time-reversal symmetry breaking, ferroelectricity due to spontaneous spatial inversion symmetry breaking, and ferroelasticity, which is characterized by a spontaneous strain, and ferrotoroidicity, which breaks both time and spatial inversion symmetry ([592]). The coexistence of at least two order parameters defines multiferroics and the coupling between them leads to magnetoelectricity, piezoelectricity, and piezomagnetism. (b) Scheme of a classical double-well energy $U$ landscape that characterizes the emergence of the order parameters (here $\eta$) described in (a). Switching between equivalent states requires an energy barrier $E(\eta )$, often described as the Landau barrier, to be overcome.

Figure 6

(a) Sketch of the ${AB\text{O}}_3$ perovskite unit cell of ${\mathrm{BiFeO}}_3$. The Bi atoms are at the corners of the cell ($A$ site), the Fe atom is at the center of the cell ($B$ site) and the oxygen atoms form an octahedron around the Fe. The polarization points along the $⟨111⟩$ plane. The three corresponding propagation directions ($k_1$, $k_2$, and $k_3$) are contained along the $(111)$ plane. (b) Sketch of the spin cycloid in which antiparallel spins are rotating in a plane defined by the polarization $P$ and the propagation vector $k$. A small canting perpendicular to the cycloidal plane and varying in space forms a coupled spin-density wave (propagating in the gray plane). (c) Small canted moment resulting from the Dzyaloshinskii-Moriya interaction; see Sec. 2e for the definition. From [140].

Figure 7

Electric-field control of antiferromagnetism in ${\mathrm{BiFeO}}_3$. (a) In-plane PFM and (b) XMLD PEEM on a central area that has been electrically switched. From [682]. (c) Reconstructed antiferromagnetic configurations from SHG images in a single ferroelectric domain and (d) after switching in plane (top left inset) and out of plane (bottom right inset). (c),(d) From [81]. (e),(f) In-plane PFM and (g),(h) corresponding scanning N-$V$ magnetometry images of two different single ferroelectric domains defined by applying an electric field to the PFM tip. (e)–(h) From [214].

Figure 8

(a) Spin-current model. Two transition metal ions $M1$ and $M2$ are separated by an O ion. $M1$ and $M2$ carry noncollinear spin moments $\overrightarrow{e_1}$ and $\overrightarrow{e_2}$. In this situation, a spin current arises and is expressed as $\overrightarrow{J_s}\propto \overrightarrow{{\mathit{e}}_1}\times \overrightarrow{{\mathit{e}}_2}$, with the direction of the $\overrightarrow{J_s}$ vector corresponding to the spin polarization. The electric polarization is then given by $\overrightarrow{\mathit{P}}\propto \overrightarrow{{\mathit{e}}_{12}}\times \overrightarrow{{\mathit{j}}_{\mathit{s}}}$, where $\overrightarrow{{\mathit{e}}_{12}}$ is the unit vector connecting $M1$ and $M2$. This mechanism is analogous to the inverse Dzyaloshinskii-Moriya interaction; see [514]. (b) $P$ and $E$ curves obtained at magnetic fields of 0 (red line) and 6 T (blue curve) for a ${\mathrm{DyMnO}}_3$ crystal, illustrating the magnetic-field control of ferroelectric in this compound. From [304].

Figure 9

Electric-field modulation of magnetization in a $Y$-type hexaferrite. (a) Periodic modulations of $M$ along the $[100]$ crystallographic direction at zero magnetic field under repeating triangular waves of $E$ applied parallel to the $[120]$ direction after preparing the system by cooling it to the measurement temperature in the electric and magnetic fields (magnetoelectric annealing). (b) Corresponding magnetization vs electric-field loops illustrating the reversal. The red and blue traces in (a) and (b) correspond to the opposite directions of the applied electric field during the magnetoelectric annealing procedure. From [76].

Figure 10

(a) Atomic resolution image of a six-unit-cell-thick ${\mathrm{BiFeO}}_3$ (BFO) layer sandwiched between epitaxial ${\mathrm{SrRuO}}_3$ (SRO) top and bottom electrodes as a representative of sub-10-nm-thick multiferroics as a model system. (b) The corresponding crystal model showing the octahedral tilts (in both the SRO and ${\mathrm{BiFeO}}_3$ layers). (c) Schematic depiction showing how the formation of a Schottky barrier at the contact metal—${\mathrm{BiFeO}}_3$ interface can lead to potential drops. (d) List of materials physics challenges and opportunities for multiferroic heterostructures.

Figure 11

Synthesis of model systems illustrating epitaxial synthesis as a pathway to create model systems at the scale of a single unit cell. (a) Reflection high-energy electron diffraction (RHEED) pattern of the growth of the ${\mathrm{La}}_{0.7}{\mathrm{Sr}}_{0.3}{\mathrm{MnO}}_3$ bottom electrode on a ${\mathrm{TiO}}_2$-terminated ${\mathrm{SrTiO}}_3$ substrate. The insertion of two unit cells of ${\mathrm{SrRuO}}_3$ leads to a conversion of the termination from the $B$ site to the $A$ site. (b) Time of flight ion scattering and recoil spectroscopy of the two types of substrate surfaces. The spectra are normalized to the Mn peak, and it is clear that the La content is much higher for one of them than for the other. (c),(d) Atomic resolution STEM images of the two types of interfaces showing that atomically sharp interfaces can be obtained. From [662].

Figure 12

Electric-field manipulation of interfacial magnetic coupling in epitaxial heterostructures. (a) 1 T, field cooled magnetic hysteresis loops at 10 K showing a strong exchange bias of 200 Oe for a ${\mathrm{La}}_{0.7}{\mathrm{Sr}}_{0.3}{\mathrm{MnO}}_3(5\mathrm{nm}){/\mathrm{BiFeO}}_3(75\mathrm{nm})$ heterostructure. (b) Magnitude of the exchange-bias field as a function of temperature and interface termination ($\mathrm{La}/\mathrm{Sr}\text{−}\mathrm{O}$vs Bi-O interfaces). (a),(b) From [661]. (c),(d) Device layouts for magnetoelectric measurements, with the corresponding SEM image shown in (e). (f) Bipolar voltage profile and the corresponding exchange bias and coercivity showing full electric-field switching of the exchange bias. (c)–(f) From [638].

Figure 13

$E$-field control of magnetism at room temperature. (a) Schematic of the magnetoelectric test structure comprising the multiferroic $\mathrm{La}\text{−}{\mathrm{BiFeO}}_3$ layer that is in contact with a CoFe-Cu-CoFe spin valve used as a readout element. (b) The normalized resistance of the spin valve as a function of applied voltage to the $\mathrm{La}\text{−}{\mathrm{BiFeO}}_3$ layer. (c) The normalized resistance vs electric field at zero magnetic field and at 100 Oe showing no significant difference, and thus illustrating that the switching of the spin valve is due to the electric field. (d) Piezoelectric hysteresis loop for the 20 nm $\mathrm{La}\text{−}{\mathrm{BiFeO}}_3$ layer showing the full switching at $\sim 500\mathrm{mV}$. Insets: XMCD-PEEM images of a Co layer that is in contact with the $\mathrm{La}\text{−}{\mathrm{BiFeO}}_3$ layer. The contrast reversal illustrates a change in the magnetization direction due to the applied voltage of 500 mV. (e) XMCD-PEEM image of a $\mathrm{CoFe}$ 10 nm $\mathrm{La}\text{−}{\mathrm{BiFeO}}_3$ test structure that has been switched by $-200\mathrm{mV}$ (dark) and $+200\mathrm{mV}$ (bright) contrast showing that the magnetization direction has mostly been switched. From [254], and [467].

Figure 14

Piezoelectric control of the magnetic anisotropy. Magnetization vs magnetic field aligned along the (a) $y$ and (b) $x$ axes in Ni thin films on $\mathrm{Pb}({\mathrm{Zr}}_x{\mathrm{Ti}}_{1-x}){\mathrm{O}}_3$-based actuators under $+30\mathrm{V}$ and $-30\mathrm{V}$ (along the $x$ axis). (c) Sketch showing that the magnetic anisotropy of the Ni thin film rotates by 90° and depends on the sign of the voltage applied to the piezoelectric actuator. (a)–(c) From [626]. (d),(e) Ferroelectric domain (left panels, birefringent contrast) and magnetic domains (right panels, magneto-optic Kerr contrast) for a CoFe thin film on a ${\mathrm{BaTiO}}_3$ substrate (d) under a vertical voltage of 120 V and (e) when the voltage is turned off. As depicted in the sketch between (d) and (e), the voltage changes the population of ferroelastic domains in ${\mathrm{BaTiO}}_3$ and, consequently, in the local strain and magnetic anisotropy. (d),(e) From [319].

Figure 15

(a) Variation of the magnetization with voltage in FeRh grown on ${\mathrm{BaTiO}}_3$ single crystals at 385 K. Inset: x-ray diffraction pattern of the $(002)$ and $(200)/(020)$ reflections of ${\mathrm{BaTiO}}_3$ as a function of voltage at 390 K. Under 60 V, the ${\mathrm{BaTiO}}_3$ is a purely $c$ domain, while it consists of mixed $a$ and $c$ domains at 0 V. (b) Sketch of the electric-field-induced magnetic phase transition at 385 K with the XMCD-PEEM image overlayed. (a),(b) From [89]. (c) Temperature dependence of the magnetic damping in FeRh thin films grown on PMN-PT. (d) Electric-field modulation of the damping at 380 K. (c),(d) From [418]. (e) Large electroresistance of FeRh thin films on ${\mathrm{BaTiO}}_3$ substrates at 376 K. (f) Principle of the experiment. (g) MCD phase images collected at 376 K at 0 and $-1\mathrm{kV}/\mathrm{cm}$ electric field. (e)–(g) From [331], and [359].

Figure 16

Epitaxial magnetoelectric superlattices from the improper ferroelectric ${\mathrm{LuFeO}}_3$. (a) Schematic of the crystal structure of a ${\mathrm{LuFeO}}_3/{\mathrm{LuFe}}_2{\mathrm{O}}_4$ superlattice. (b) Atomic resolution images of superlattices with various ${\mathrm{LuFeO}}_3/{\mathrm{LuFe}}_2{\mathrm{O}}_4$ stacking sequences. (c) Piezoforce microscopy image of a ${\mathrm{LuFeO}}_3/{\mathrm{LuFe}}_2{\mathrm{O}}_4$ superlattice showing the box-in-a-box switching of the ferroelectric polarization. (d) The corresponding XMCD-PEEM image at the Fe edge showing the switching of the magnetization state. The scale bar is $3\mathrm{\mu }\mathrm{m}$. From [411].

Figure 17

(a) Field-effect control of the hole-induced ferromagnetism in magnetic semiconductor $(\mathrm{In},\mathrm{Mn})\mathrm{As}$ field-effect transistors. The gate voltage $V_{\mathrm{G}}$ applied through the insulator controls the hole concentration in the magnetic semiconductor channel (the filled circles). Negative $V_{\mathrm{G}}$ increases hole concentration, resulting in enhancement of the ferromagnetic interaction among magnetic Mn ions, whereas positive $V_{\mathrm{G}}$ has an opposite effect. The arrow schematically shows the magnitude of the Mn magnetization. (b) Hall effect for different gate voltages. When holes are partially depleted from the channel ($V_{\mathrm{G}}=+125\mathrm{V}$), a paramagnetic response is observed (blue dash-dotted line), whereas a clear hysteresis at low fields ($<0.7\mathrm{mT}$) appears as holes are accumulated in the channel ($V_{\mathrm{G}}=-125\mathrm{V}$, red dashed line). Two Hall curves measured at $V_{\mathrm{G}}=0\mathrm{V}$ before and after the application of $-125\mathrm{V}$ (black solid line and green dotted line, respectively) are virtually identical (i.e., the effect is volatile). Inset: the same curves shown at higher magnetic fields. (c) Temperature dependence of spontaneous Hall resistance $R_{\mathrm{Hall}}^S$ under three different gate biases. $R_{\mathrm{Hall}}^S$ being proportional to the spontaneous magnetization $M_S$ indicates a $\pm 1\mathrm{K}$ modulation of $T_{\mathrm{C}}$ upon application of $V_{\mathrm{G}}=\pm 125\mathrm{V}$. $T_{\mathrm{C}}$ is determined using Arrott plots (inset). From [431].

Figure 18

(a) Magnetoelectric hysteresis curve at 100 K showing the magnetic response of the $\mathrm{Pb}(\mathrm{Zr},\mathrm{Ti}){\mathrm{O}}_3/{\mathrm{La}}_{0.8}{\mathrm{Sr}}_{0.2}{\mathrm{MnO}}_3$ system as a function of the applied electric field. The two magnetization values correspond to modulation of the magnetization of the ${\mathrm{La}}_{0.8}{\mathrm{Sr}}_{0.2}{\mathrm{MnO}}_3$ layer. Insets: the magnetic and electric states of the ${\mathrm{La}}_{0.7}{\mathrm{Sr}}_{0.3}{\mathrm{MnO}}_3$ and $\mathrm{Pb}(\mathrm{Zr},\mathrm{Ti}){\mathrm{O}}_3$ layers, respectively. The size of the arrow qualitatively indicates the magnetization amplitude. From [400]. (b) Comparison of the electric-field dependence of the remanent ferroelectric polarization $P_r$ and of the magnetic modulation per unit cell area $\mathrm{\Delta }M$ measured in a $\mathrm{Pb}(\mathrm{Zr},\mathrm{Ti}){\mathrm{O}}_3/{\mathrm{La}}_{0.7}{\mathrm{Sr}}_{0.3}{\mathrm{MnO}}_3$ bilayer. Both curves were measured consecutively at 50 K and 100 Oe. From [338].

Figure 19

(a) Schematic of an electrolytic cell containing the FePt or FePd film within an applied magnetic field $H$. The potential profile $E$ due to the applied potential $U$ is indicated by the red line. The potential drop at the Pt electrode side is much lower (compared to that of the sample surface) as a result of the Pt electrode’s large surface area. (b) Magnetization switching of the 2-nm-thick FePt film for different $U$ values between the film and the Pt counter electrode. From [627]. (c) Schematic of the sample used for a voltage-induced magnetic anisotropy change. (d) Magneto-optical Kerr ellipticity ${\eta }_k$ for different applied voltages as a function of the applied field. The thickness of the Fe film was 0.48 nm. A significant change in the hysteresis curve indicated a large change in perpendicular anisotropy following application of the bias voltage. Right inset: voltage modulation response of the Kerr ellipticity $d{\eta }_k/dV$. Left inset: magnetization direction at points $A$ and $B$ in the hysteresis curves. From [383].

Figure 20

(a) Sketch of the device for the modulation of the magnetic properties of a Co film. (b) Temperature dependence of the magnetization at $H=2\mathrm{Oe}$ under a gate voltage $V_G=-2$, 0, and $+2\mathrm{V}$. From [525].

Figure 21

(a) Normalized magnetization measured by MCD as a function of the applied electric field (trace and retrace) at 4 K and a fixed magnetic field ($+0.44\mathrm{T}$ in the top panel and $-0.44\mathrm{T}$ in the bottom panel), showing the electrical switching of the magnetic order in bilayer ${\mathrm{CrI}}_3$. Insets: the corresponding magnetic states. From [275]. (b) Uniaxial magnetic anisotropy field ($H_u=H_s^{\perp }-H_s^{\parallel }$) of multilayer ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$ as a function of temperature at different gate voltages and in the pristine case. Inset: the dependence of $T_{\mathrm{C}}$ on gate voltage. From [603]. (c) $T_{\mathrm{C}}$ of a trilayer ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$ as a function of gate voltage. From [112]. (d) $H_{\mathrm{C}}$ of a trilayer ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$ as a function of gate voltage at 10 K. From [112].

Figure 22

(a) Electric-field control of the skyrmion phase pocket in single crystal ${\mathrm{Cu}}_2{\mathrm{OSeO}}_3$. Electric and magnetic fields are parallel to the $[111]$ direction of the crystal. From [435]. (b) Schematic of the single crystal ${\mathrm{Cu}}_2{\mathrm{OSeO}}_3$ sample configuration using patterned Pt electrodes to apply in-plane electric fields of $3.6\mathrm{V}/\mathrm{\mu }\mathrm{m}$. (c) Reversible electric-field transition between the helical spin state and the skyrmion lattice visualized using Lorentz transmission electron microscopy ($T=24.7\mathrm{K}$ under an out-of-plane magnetic field of 254 Oe). (b),(c) From [253].

Figure 23

(a) Schematic diagram of the experimental setup for ferroelectric domain switching using an atomic force microscopy conductive tip and to perform Hall measurements. (b) Piezoresponse force microscopy phase images (top panels) and Hall and extracted topological Hall curves (bottom panels) of a ${\mathrm{SrRuO}}_3/{\mathrm{BaTiO}}_3$ sample for different ferroelectric poling states. The scale bar corresponds to $10\mathrm{\mu }\mathrm{m}$. (c) Difference in MFM contrast between images taken at two different magnetic fields. From [614].

Figure 24

(a) Raman spectra showing magnon modes (cyclon: ${\varphi }_2$, ${\varphi }_3$, and ${\varphi }_4$; extracyclon: ${\psi }_2$ and ${\psi }_3$) in a ${\mathrm{BiFeO}}_3$ single crystal for increasing electric fields. (b) Sketch of the magnon modes in the cycloidal order of ${\mathrm{BiFeO}}_3$. (c) Electric-field dependence of the energy of ${\psi }_2$ showing a strong and hysteretic modulation. From [495].

Figure 25

(a) PFM image of a 100-nm-thick ${\mathrm{BiFeO}}_3$ layer on a ${\mathrm{DyScO}}_3$ substrate illustrating the typical 71° stripe domains. The two broad stripes notated as $S$-$O$ are the metal layers (typically a metal with strong spin-orbit coupling such as Pt) that are used to probe the ISHE and spin Seebeck responses due to the propogation of magnons in the ${\mathrm{BiFeO}}_3$ layer, as illustrated in (b). An electric field applied between these two metal strips enables the ferroelectric polarization state of ${\mathrm{BiFeO}}_3$ to be switched. (c) Top panel: the nonlocal spin Seebeck voltage as a function of dc electric field applied to ${\mathrm{BiFeO}}_3$. Lower panel: the corresponding ferroelectric switching. (d) Summary of some areas of research, specifically a focus on ballistic spin-magnon transport in epitaxial heterostructures such as the one shown in (e). From [451].

Figure 26

Voltage-controlled reconfigurable magnonic crystal based on ${\mathrm{BiFeO}}_3/{\mathrm{La}}_{0.7}{\mathrm{Sr}}_{0.3}{\mathrm{MnO}}_3$. (a) Sketch of the setup in which spin waves are injected by an antenna and collected by the other with a $2\mathrm{\mu }\mathrm{m}$ gap in between. The ferroelectric domains are read and controlled by PFM. (b) 3D view of the actual device and PFM phase images of the gap in three different polarization configurations: down (red), up (blue), and periodic (green) with a period of 500 nm. (c) Frequency dependence of the inductance (top panel) and the phase (bottom panel) showing a 20 dB rejection at 3.54 GHz for the periodically poled configuration (green lines) as well as an accident in the phase. From [390].

Figure 27

Spin currents. Spin-polarized currents (a) flowing inside a magnetic ($F$) metal and (b) tunneling from this material. At the interface with a nonmagnetic (NM) metal, the spin polarization extends with an exponential decrease in the range of the spin diffusion length. (c) For current along $x$, emission along $z$ of a pure spin current into a magnetic or nonmagnetic layer by the SHE in a heavy metal (HM) (left panel) and by diffusion from an Edelstein polarization in the surface or interface states of a topological insulator (TI), Dirac semimetal, or Rashba 2DEG (right panel).

Figure 28

(a) Sketch of the electronic energy dispersion surfaces in the surface states of a topological insulator (Dirac cone). (b) Fermi contour at constant energy illustrating the spin-momentum locking. At any $k$ position on the contour, the spin is perpendicular to $k$. (c) Electronic dispersion surfaces of a Rashba system. (d) In contrast to the case of topological insulators, here the systems comprises two Fermi contours. On each the spin is locking perpendicular to $k$ for the spins both curling clockwise in one contour and curling counterclockwise in the other contour. (e) Charge-to-spin conversion with a topological insulator. The application of a charge current $J_c$ along $-x$ causes a shift of the Fermi contour and generates an extra population of states with spin along $y$. This generated spin density can then diffuse vertically as a spin current $J_s$. (f) Spin-to-charge conversion with a topological insulator. Spins oriented along $y$ injected into the topological insulator populate states with momentum along $x$ (which is accompanied by the ejection of spins oriented along $-y$ from states with momentum along $-x$), causing an overall shift of the Fermi contour and thus the generation of charge current along $-x$. (g) Charge-to-spin conversion in a Rashba system. The situation is similar to that in (e) except that spin densities with opposite spin polarizations are generated by the injected charge current for the inner and outer contours. However, they do not compensate, yielding the generation of a finite spin density that may diffuse vertically as a spin current. (h) Spin-to-charge conversion in a Rashba system. Again the situation is similar to that in (f), but here the injection of spins causes shifts of the Fermi contours in opposite directions, albeit without a full compensation, which results in the generation of a finite charge current.

Figure 29

(a) Concept of spin-transfer torque. A spin-polarized current (prepared by a magnetic material $F1$) is injected through a nonmagnetic layer (tunnel barrier or metal) into the magnetic material $F2$. Inside $F2$, exchange-induced precessions dephase the transverse components of injected spins and lead to a transfer of the transverse component of the injected spin current into $F2$ or, equivalently, to a torque on its magnetization. (b) Schematic of the dampinglike and fieldlike torques on a magnetization $M$ departing from its equilibrium orientation along $H_{\text{eff}}$ and precessing around $H_{\text{eff}}$ in the situation in which the dampinglike torque is the opposite of the LLG damping torque and enlarges the precessions. (c),(d) Switching by STT: In (d), macrospin simulation of the switching of the device in (c) from parallel (P) to antiparallel (AP) by the STT induced by the injection of a vertical spin current from the polarizer into the free layer. (e) Magnetization dynamics for a device of the type in (c) in the regime in which the STT generates a steady state gyration of the magnetization in the free layer (or a gyration of a magnetic vortex in the free layer; see the inset displaying the vortex core and its trajectory shown as a dashed line). (f) Experimental example of microwave power emission generated by vortex gyration. (a)–(e) Adapted from [171]. (f) From [135].

Figure 30

(a) Dampinglike ($T_{\mathrm{DL}}$) and fieldlike ($T_{\mathrm{FL}}$) SOTs induced by spin currents (polarizations indicated with small arrows) due to SHE in a heavy metal and (b) EE in a Rashba or topological 2DEG. (c) Switching in the macrospin limit is used to illustrate the symmetry of the reversal of perpendicular magnetization under the additive actions of $T_{\mathrm{DL}}$ and torque $T_B$ induced by an applied field along the current direction. Left panel: graphic showing that, for $J>0$, $T_B$ helps $T_{\mathrm{DL}}$ to reverse $M$ from up to down, especially midway when $M$ is in plane and $T_{\mathrm{DL}}=0$, regardless of the orientation of $M$ in the plane. Right panel: same applied field with $J<0$ for a reversal from down to up and a clockwise loop. Reversing the applied field leads to a counterclockwise loop. (d),(e) In the device shown in (d), (e) shows the switching loops of the ferromagnetic CoFeB layer magnetization under the conjugated actions of the spin current generated by the EE in the surface state of the topological insulator ${(\mathrm{BiSb})}_2{\mathrm{Te}}_3$ and an applied field $B_x$ in the current direction. The switching loops, which are detected using the anomalous Hall effect, are clockwise for $B_x>0$ or counterclockwise for $B_x<0$. From [636].

Figure 31

Symmetry and dynamics of the switching of a magnetic layer with PMA by SOT. Macrospin simulations of the switching by SOT of (a) in-plane and (b) out-of-plane magnetizations. Courtesy of P. Gambardella. For in-plane magnetization, the SOT progressively enlarges precessions of the magnetization around its initial orientation to finally reverse it. The long incubation time (successive precessions) leads to long switching times. For the PMA in (b), the action of SOT is immediate and can lead to much shorter switching times around or below 1 ns. (c) Switching of a ferromagnetic layer with PMA in the process of nucleation and extension of domains where snapshots of x-ray magnetic dichroism images of a dot of $\mathrm{Pt}/\mathrm{Co}/\mathrm{MgO}$ with PMA during the reversal of its magnetization by the SOT is induced by current pulses in Pt. Adapted from [36]. With an applied field along $x$ ($-x$), the SOT induces a reversal from up (down) to down (up) for positive current and from down (up) to up (down) for negative current, as in the magnetization loops. The nucleation of a reversed domain starts on the edges at a point (the dot) where the combination of the applied field and the DMI favors this nucleation. (d) Time trace of the average out-of-plane magnetization (squares) during current injection (line) derived from the images in (c). Successive pulse amplitudes of $-3.1\times 10^8$, $+4.4\times 10^8\mathrm{A}/{\mathrm{cm}}^2$, and $B_x=0.11\mathrm{T}$. From [378]. (e) Switching probability $P$ of a square of a $\mathrm{Pt}(3\mathrm{nm})/\mathrm{Co}(0.6\mathrm{nm}){/\mathrm{AlO}}_x$ layer as a function of $B_x$ at different current amplitudes of pulses of 210 ps and (f) as a function of pulse length at a fixed field of 91 mT and varying current amplitudes. From [193].

Figure 32

Current-induced switching of in-plane magnetization of a CoFeB layer by SOT generated from SHE in a Ta layer, with (a) an experimental device and (b) a switching loop at room temperature detected by TMR in a $\mathrm{CoFeB}/\mathrm{MgO}/\mathrm{CoFeB}$ MTJ. From [352]. (c) Current-induced switching of the in-plane magnetization of a CoFeB layer generated by the EE in the surface states of the Dirac semimetal $\alpha \text{−}\mathrm{Sn}$ in a $\alpha \text{−}\mathrm{Sn}/\mathrm{Ag}/\mathrm{CoFeB}$ trilayer , (d) switching loop at zero field and room temperature detected by MOKE, and (e) band structure and Dirac cone of $\alpha \text{−}\mathrm{Sn}$. (c)–(e) From [124].

Figure 33

(a) Illustration of the DMI induced by spin-orbit coupling and the breaking of inversion symmetry at the interface between a magnetic layer and a heavy metal. (b) Illustration of a left-handed chiral DW in $\mathrm{Pt}/\mathrm{CoFe}/\mathrm{MgO}$. The effective field $H_{\mathrm{SL}}$ induced by SHE in Pt moves adjacent up-down and up-down DWs in the same direction against electron flow $j_e$. Adapted from [144]. (c) Velocity of chiral DWs vs current density for several DMI values. From [570]. (d) Top panel: schematic showing that an applied in-plane field $H_L$ along the current axis can help the DMI (top arrow) or compete with it (bottom arrow) for the formation of a chiral Néel DW. Adapted from [144]. Bottom panel: dependence of the DW velocity on the sign and magnitude of the applied field along the current axis. Adapted from [144]. (e) SOT-induced velocity of Néel DWs as a function of temperature in the vicinity of the compensation temperatures $T_M$ (blue vertical line) and $T_A$ (green vertical line) for a ferrimagnetic ${\mathrm{Co}}_{44}{\mathrm{Gd}}_{56}$ layer on Pt. From [72]. (f) STT-induced velocities, up to about $3\mathrm{km}/\mathrm{s}$, for Néel DWs as a function of temperature near the compensation temperature of ${\mathrm{Mn}}_{4-x}{\mathrm{Ni}}_x\mathrm{N}$ films. From [199].

Figure 34

Current-induced motion of magnetic skyrmions. (a) Spin configuration in a Néel skyrmion. (b) Multilayer with an additive DMI at the top and bottom interfaces of the Co layers. (c) Column of coupled skyrmions in a multilayer with interfacial DMIs. (d) Magnetic force microscopy images of skyrmions in a multilayer of the type shown in (b). (a)–(d) From [373]. (e) Motion of skyrmions driven by the SOT induced by the SHE in the heavy metal below the magnetic layer. (f) SHE-induced skyrmion velocity as a function of current density in two types of multilayers. From [634]. (g) Snapshots of the SOT-driven motion of skyrmions in a $|\mathrm{Ta}10|\mathrm{Pt}8|(\mathrm{Co}1.4|\mathrm{Ru}1.2|\mathrm{Pt}0.6)\times 3|\mathrm{Pt}2.4$ multilayer induced by $7\times 10^{11}\mathrm{A}/{\mathrm{m}}^2$ pulses of 12 ns. Courtesy of N. Reyren.

Figure 35

Control of magnetism by currents in 2D magnets. (a) Illustration of a ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2/\mathrm{Pt}$ bilayer. From [620]. SOT switching of the bilayer displayed in (a) in the presence of a (b) positive or (c) negative in-plane field along the current direction. From [620]. (d) Comparison of the current densities and in-plane fields required for SOT switching in devices based on 3D magnets (CoFeB, MnGa, and TmIG) and 2D magnets (${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$ and ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$), with the best results found for $\mathrm{Ta}/{\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$. From [439]. (e) Schematic view of a ${\mathrm{CrI}}_3\text{bilayer}/{\mathrm{TaSe}}_2$ heterostructure in which the SOT induced by the interfacial current can drive the relative orientation of the magnetizations of the two ${\mathrm{CrI}}_3$ layers from parallel to antiparallel. From [130]. (f) Lorentz microscopy images of skyrmions in a ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$ film with oxidized interfaces and current-induced motion of the skyrmions. From [446].

Figure 36

Electric control of spin-charge interconversion effects in different systems. (a) GaAs band structures and spin-polarized electrons generated by circularly polarized light absorption. A high electric field induces the transition of the spin-polarized electrons from the $\mathrm{\Gamma }$ valley to the satellite $L$ valley, where part of its $p$ character provides a larger effective spin-orbit coupling. Sketches at the left and right show the optically induced SHE for the $\mathrm{\Gamma }$ valley and $L$ valley, respectively; the SHE is larger in the latter. (b) Electric-field dependence of the ${\theta }_{\text{SHE}}$ in GaAs. Right inset: enlargement at low field. Left inset: measurement configuration of the optically induced SHE. (a),(b) From [434]. (c) Resistance as a function of gate voltage ${\mathit{V}}_{\mathit{G}}$ for a 2-nm-thick Pt on YIG. (d) Output voltage detected during spin pumping at the same sample for $V_G=2$ and $-2\mathrm{V}$. (e) Normalized spin-to-charge output current as a function of $V_G$ for different Pt thicknesses. (c)–(e) From [134].

Figure 37

(a) Sketch of the nonlocal spin-valve concept for spin-charge interconversion measurement in a graphene/TMD vdW heterostructure. A current $I$ along the graphene/TMD arm ($y$ axis) generates a nonequilibrium spin density due to the EE with spins along $x$ (blue arrow) and a spin accumulation with spins out of plane (along $z$) due to the SHE with opposite orientation at opposite edges of the graphene/TMD arm (red arrows). The induced spins diffuse in graphene toward the ferromagnetic electrode $F1$ and are detected by measuring $V_{\mathit{nl}}^F=V_{\mathit{nl}}^{+}-V_{\mathit{nl}}^{-}$. The EE and SHE contributions to $V_{\mathit{nl}}^F$ are separated via spin precession by applying an external magnetic field along $z$ and $x$, respectively. (b) Spin-charge interconversion signals for the SHE (red line) and the EE (blue line) as a function of $V_G$. The sheet resistance of graphene vs $V_G$ is also plotted to show the charge neutrality point. (a),(b) From [46]. (c) Sketch of the spin-pumping experiment to quantify spin-charge interconversion in a ${\mathrm{SrTiO}}_3/{\mathrm{AlO}}_x$ 2DEG. (d) Gate dependence of the Edelstein length ${\mathit{\lambda }}_{\mathrm{IEE}}$ of a ${\mathrm{SrTiO}}_3/{\mathrm{AlO}}_x$ 2DEG at 15 K. (c),(d) From [600].

Figure 38

(a) Sketch of an interfacial ferroelectric Rashba system in which the ferroelectric accumulates or depletes the carrier into an adjacent layer with large spin-orbit coupling (top layer), thus generating a Rashba state at the interface. (b) Spin contours in the Rashba states. The chirality is reversed upon switching the ferroelectric polarization direction. (c) Ferroelectric control of the IEE. From [425].

Figure 39

Ferroelectric control of the spin-charge interconversion in GeTe investigated by spin pumping ferromagnetic resonance (FMR). (a) Setup for the study of the ferroelectric switching of the spin-charge interconversion in GeTe. Top: electrical circuit for ferroelectric switching monitored by resistance changes. Bottom: sketch of the contacts used to measure the lateral voltage proportional to the charge-current production in the same experiment. Negative (positive) voltage pulses were applied by a source-measure unit (SMU) to set the ferroelectric polarization direction ($P_{\mathrm{in}}$ or $P_{\mathrm{out}}$). (b) Hysteresis loop of the conductance vs $V_{\text{write}}$ of a $\mathrm{Au}(3\mathrm{nm})/\mathrm{Fe}(20\mathrm{nm})/\mathrm{GeTe}(15\mathrm{nm})/\mathrm{Si}$ sample. Inset: $I$-$V$ curves of the heterostructure after the application of two saturating voltage pulses at $V_{\text{write}}=-30$ and $+60\mathrm{V}$. (c),(d) FMR spectra and (e),(f) normalized current production at 300 K for the slab oriented along the $ZA$ and $ZU$ directions vs ferroelectric polarization. The dashed curves correspond to $P_{\mathrm{in}}(V_{\text{write}}<0)$ and the dotted curves correspond to $P_{\mathrm{out}}(V_{\text{write}}>0)$. The spin-pumping peak is positive (negative) for $P_{\mathrm{in}}$ and negative (positive) for $P_{\mathrm{out}}$. The green curves in (e) and (f) refer to the pristine (unpoled) states. The relatively small amplitude of the spin-pumping signal in the unpoled state is associated with a multidomain ferroelectric configuration. (g) Temperature dependence of the charge current production. From [596].

Figure 40

(a) Sketch of the sample for detecting the ferroelectric control of the IEE. (b) Gate voltage dependence of the current produced by spin-charge interconversion through the IEE in $\mathrm{NiFe}/{\mathrm{AlO}}_x/{\mathrm{SrTiO}}_3$ heterostructures after application of a large electric field to ${\mathrm{SrTiO}}_3$ to induce a ferroelectriclike state $T=7\mathrm{K}$. From [425]. (c) Schematic illustrations of tunneling pulsed ISHE measurements in the ISHE type based on a ${\mathrm{La}}_{0.7}{\mathrm{Sr}}_{0.3}{\mathrm{MnO}}_3/\mathrm{Pb}(\mathrm{Zr},\mathrm{Ti}){\mathrm{O}}_3/\mathrm{Pt}$ stack. (d) The injected pulsed tunneling current ($I_e$) generates a flow of pulsed spin-current ($J_S$) in the Pt metal, which produces a transverse pulsed ISHE voltage ($V_{t\text{−}\mathrm{pISHE}}$) at $T=10\mathrm{K}$. From [156].

Figure 41

Electric control of STT. (a) Sketch of a perpendicularly magnetized MTJ and the effect of the electric field through a voltage to the free CoFeB layer. (b) Normalized minor loops of the TMR curve at different applied bias values. Inset: full TMR curve measured at low bias. (c) Unipolar switching of the MTJ using a series of negative pulses (schematically shown in purple at the bottom) with alternating amplitudes of $-0.9$ and $-1.5\mathrm{V}$. A constant biasing magnetic field ($H_{\mathrm{bias}}$) of 55 Oe was applied in favor of the antiparallel state at $-0.9\mathrm{V}$. (d) Sketch of the hysteresis loops of the top CoFeB layer showing the unipolar switching process: magnetization $\mathrm{down}\to \mathrm{up}$ switching at $V=V_1$ (red) through STT with a greatly reduced energy barrier; magnetization $\mathrm{up}\to \mathrm{down}$ switching at $V=V_2$ (black) using another negative electric field, where $|V_2|>|V_1|$. The loop for $V=0$ is shown in blue. The vertical dotted line represents the position of the constant $H_{\mathrm{bias}}$. The moment of the bottom CoFeB is fixed pointing down. From [619].

Figure 42

Electrical control of SOT. (a) Sketch and (b) cross section TEM image of the device, a single MTJ consisting of $\mathrm{Ta}/\mathrm{CoFeB}/\mathrm{MgO}/\mathrm{CoFeB}/\mathrm{Ru}/\mathrm{CoFe}/\mathrm{IrMn}$ fabricated on a thermally oxidized Si wafer. (c) MTJ resistance as a function of the write pulse current density while applying a control voltage pulse of $+1.0\mathrm{V}$ (top panel) and $-1.0\mathrm{V}$ (bottom panel). The width of both the write current pulse and the control voltage pulse was 50 ns. No $H_{\mathrm{bias}}$ was applied during the measurement. (d) Switching phase diagram obtained by taking the resistance-write pulse current density curves. From [262].

Figure 43

Road map for spintronic logic and memory devices and advances to higher write speed, smaller size, and lower power dissipation in areas of processing in memory ranging from toggle MRAM, on the market since 2006, to STT MRAM, which is in production today, and the SOT MRAM or MESO devices expected in the coming generations. Adapted from [216].

Figure 44

(a) Ferroelectric control of the TMR in $\mathrm{Fe}/{\mathrm{BaTiO}}_3/{\mathrm{La}}_{0.7}{\mathrm{Sr}}_{0.3}{\mathrm{MnO}}_3$ tunnel junctions. Top images: orientation of the ferroelectric polarization of the tunnel barrier, which controls the spin polarization at the $\mathrm{Fe}/{\mathrm{BaTiO}}_3$ interface. Bottom panel: TMR (4.2 K, 50 mV) for both polarization states after $\pm 1\mathrm{V}$, 1 s pulses. From [191]. (b) Left panel: annular dark field scanning transmission microscopy cross section image of the $\mathrm{Co}/{\mathrm{PbTiO}}_3/{\mathrm{La}}_{0.7}{\mathrm{Sr}}_{0.3}{\mathrm{MnO}}_3$ junction. Right panel: hysteretic dependence of the TMR (10 K, 10 mV) with the polarization state of ${\mathrm{PbTiO}}_3$ controlled using various pulse voltages ($50\mathrm{\mu }\mathrm{s}$). From [368]. (c) TMR of a $\mathrm{Co}/\mathrm{PVDF}/{\mathrm{La}}_{0.6}{\mathrm{Sr}}_{0.4}{\mathrm{MnO}}_3$ junction (10 K, 10 mV) after the PVDF is polarized downward ($+1.2\mathrm{V}$) and upward ($-1.5\mathrm{V}$). From [345].

Figure 45

(a) Top image: schematic of a magnetoelectric device consisting of a ${\mathrm{Co}}_{0.9}{\mathrm{Fe}}_{0.1}/\mathrm{Cu}/{\mathrm{Co}}_{0.9}{\mathrm{Fe}}_{0.1}$ spin valve on ${\mathrm{BiFeO}}_3$. Bottom panel: two $R(V)$ loops under zero magnetic field along with a ferroelectric loop (red line) from a neighboring device. From [239]. (b) Top image: Sketch of the spin-valve (SV) stack and cross section of the device measured using scanning electron microscopy. Bottom panel: GMR loops with different applied voltages, which start with a depolarized state of the $\mathrm{Pb}(\mathrm{Zr},\mathrm{Ti}){\mathrm{O}}_3$ layer. From [334]. (c) Top image: schematic of the MTJ device structure deposited on PNM-PT. Bottom panel: repeatable bistable remanent resistance states modulated by 8 and $-1.6\mathrm{kV}{\mathrm{cm}}^{-1}$ electric-field pulses in the absence of a bias magnetic field. RA is the resistance-area product. From [84].

Figure 46

(a) Detailed structure of the MTJ and schematic top view of a sample structure with two pairs of $AA$ and $BB$ electrodes. The major axis of the elliptical device was along the $x$ axis. The pinning direction of the MTJ was along the $[100]$ direction of the PMN-PT substrate ($+x$ axis). (b) Polar curves of the angular-dependent $M_R/M_S$ of a CoFeB layer with the applied voltages 0 V, $BB$ 200 V, $AA$ 400 V, and $BB$ $-200\mathrm{V}$. The $[100]$ direction of the PMN-PT substrate corresponds to 0. The double-headed arrows indicate the direction of the magnetic easy axis. (c) Dependence of the resistance of the tunnel junction on voltage synergistically applied to the $AA$ and $BB$ electrode pairs at $H=0\mathrm{Oe}$. The reversible resistance switching between high- and low-resistance states corresponds to the antiparallel and parallel magnetization configurations of the MTJ, as illustrated in the insets, which indicate the 180° magnetization switching of the free layer driven by voltage. From [83].

Figure 47

Sketch of a MESO device. Adapted from [379].

Figure 48

(a) Scanning electron microscope image of the SO module device region. The CoFe element dimensions are $500\times 100\times 2.5{\mathrm{nm}}^3$ (length, width, and thickness). An applied charge current $I_{\mathrm{in}}$ between contact 1 and ground becomes spin-polarized and is injected in the $\mathsf{T}$-shaped Pt structure through a $100\times 100{\mathrm{nm}}^2$ junction. Owing to the ISHE, an output voltage $V_{\text{read}}=V_{\mathrm{SO}+}-V_{\mathrm{SO}-}$ is detected between contacts 2 and 3. (b) Output signal of the SO module, obtained from the transverse resistance ${\mathrm{R}}_{\mathrm{ISHE}}=V_{\text{read}}/I_{\text{in}}$ as a function of an external magnetic field $B_{\mathrm{ext}}$. The two magnetization states of the CoFe element, with an amplitude of $2\mathrm{\Delta }{R}_{\mathrm{ISHE}}$, are depicted in the insets by the yellow arrows. (c) Sketch for the full MESO operation at room temperature, without any external magnetic field applied, shown in (d). Voltage pulses $V_{\text{write}}$ drives ${\mathrm{BiFeO}}_3$ magnetization ($M_{\mathrm{BFO}}$) switching and the subsequent magnetization reversal of the ferromagnetic element $M_{\mathrm{FM}}$ . $M_{\mathrm{FM}}$ is electrically read through the ISHE in the Pt element. (d) The output signal $V_{\mathrm{read}}$ changes by $\sim 1.5\mathrm{\mu }\mathrm{V}$ for $V_{\text{write}}=\pm 3\mathrm{V}$, reflecting opposite $M_{\mathrm{FM}}$ orientations. After each pulse, the magnetization state is read three times (at intervals of 1 s) and averaged. From [601].

Figure 49

Applications of STNOs. Schematics of STNOs functioning as (a) spin oscillator for rf emission and (b) spin diode for conversion from rf to dc. From [105]. (c) Schematic of circuit with arrays of eight spin diodes used for energy harvesting and lightning the light-emitting diode (LED) on the right. From [523]. (d) Schematic of a skyrmion-based racetrack memory. From [286].