Electric Field Control of Spin–Orbit Torque Magnetization Switching in a Spin–Orbit Ferromagnet Single Layer

Abstract To achieve a desirable magnitude of spin–orbit torque (SOT) for magnetization switching and realize multifunctional spin logic and memory devices utilizing SOT, controlling the SOT manipulation is vitally important. In conventional SOT bilayer systems, researchers have tried to control the magnetization switching behavior via interfacial oxidization, modulation of spin–orbit effective field, and effective spin Hall angle; however, the switching efficiency is limited by the interface quality. A current‐induced effective magnetic field in a single layer of a ferromagnet with strong spin–orbit interactions, the so‐called spin–orbit ferromagnet, can be utilized to induce SOT. In spin–orbit ferromagnet systems, electric field application has the potential for manipulating the spin–orbit interactions via carrier concentration modulation. In this work, it is demonstrated that SOT magnetization switching can be successfully controlled via an external electric field using a (Ga, Mn)As single layer. By applying a gate voltage, the switching current density can be solidly and reversibly manipulated with a large ratio of 14.5%, which is ascribed to the successful modulation of the interfacial electric field. The findings of this work help further the understanding of the magnetization switching mechanism and advance the development of gate‐controlled SOT devices.


DOI: 10.1002/advs.202301540
showing great potential for the realization of spintronic memory devices with better stability, higher scalability, faster information processing speed, and lower energy consumption. To further enhance the SOT magnetization switching efficiency, researchers have explored various effective methods. First, the most generally used approach is to find materials with a large spin Hall angle SH that can generate a large spin current, which can be utilized to effectively decrease the critical switching current density J c . [1][2][3][4][5] Those materials with large SH are utilized in bilayer systems, where the spin current generated in a nonmagnetic layer is injected into the adjacent ferromagnetic layer and exerts a torque to switch the magnetization. In bilayer systems, the SOT magnetization switching can be manipulated by controlling the interfacial oxidization, [6,7] modulating the spin-orbit interaction and the effective spin Hall angle. [8][9][10][11] However, the spin injection is limited by the interface quality, which hinders further decreases in J c . To overcome this limitation, a new class of materials called spin-orbit ferromagnets, including ferromagnetic alloy, ferromagnetic topological insulators and the ferromagnetic semiconductor Mn-doped GaAs ((Ga, Mn)As), have recently been found to be very promising for highly efficient magnetization switching due to the strong spin-orbit-induced effective magnetic field, the intrinsic bulk inversion asymmetry and the appropriate saturated magnetization. [12][13][14][15] Especially in (Ga, Mn)As, an extremely low J c (4.6 × 10 4 A cm −2 ) has been demonstrated by suppressing the contribution of the field-like term with a current-induced magnetic field. [16] In a ferromagnetic alloy FePt single layer, a field-free magnetization switching was achieved and a platform was introduced to engineer large SOTs for lower-power spintronics devices by a composition gradient, while the switching ratio is limited and the J c still needs to be decreased. [17][18][19] In ferromagnetic topological insulators, electric field application has been demonstrated to control J c via modulation of the density and type of surface carriers. [15,[20][21] However, the switching process is still improvable in terms of the switching hysteresis and its completeness. [15] To achieve a desirable magnitude and realize multifunctional SOT spin logic and memory devices with a simple structure and high efficiency, manipulating the SOT in an appropriate spin-orbit ferromagnet single layer is strongly required. The single-crystalline ferromagnetic semiconductor (Ga, Mn)As is one of the best material systems for this purpose, where the Dresselhaus and Rashba effective fields The channel width of the crossbar is 0.5 μm, and the channel length is 2 μm. The yellow parts are the capping layers on the electrodes consisting of Au (100 nm)/Cr (5 nm), which also work as heat sinks. The current J flows in the (Ga 0.94 , Mn 0.06 )As layer with perpendicular magnetization from the source electrode (S) to the drain electrode (D), and the Hall resistance R H is obtained by measuring the Hall voltage V H along the [110] direction orthogonal to the S-D direction. An electric field is applied by the gate voltage V g . b) Dresselhauslike (red) and Rashba-like (light blue) effective magnetic fields (H D and H R , respectively) for hole momenta along different crystallographic directions in the tensile-strained (Ga 0.94 , Mn 0.06 )As thin film. (k x , k y , and k z ) is the wave vector of holes.
(H D and H R ) induced by the spin-orbit interactions contribute to an in-plane spin component that can exert a strong torque on the magnetization. [13] In addition to the conventional Dresselhaus and Rashba spin-orbit terms, there is also a contribution to the spin-orbit interaction resulting from the interface inversion asymmetry. [22] Because the interfacial spin-orbit fields are demonstrated to be strongly influenced by the internal electric field, [10,11] external electric field application is expected to achieve effective manipulation of the SOT in (Ga, Mn)As.
In this Article, we demonstrate that the SOT magnetization switching behavior in a ferromagnetic (Ga, Mn)As single layer can be manipulated by applying an electric field using a solid gate electrode, as shown in Figure 1a. By changing the sign and magnitude of the gate voltage V g , the interfacial electric field and hole concentration of (Ga, Mn)As are manipulated, enhancing or suppressing the spin-orbit interactions. Because the spin-orbit interactions couple the spin of a hole with its momentum and generate H D and H R (Figure 1b), [23][24][25][26] H D and H R are very sensitive to the applied electric field. By applying a positive V g , we show that the enhancement of H D and H R contributes to an increase in the SOT switching efficiency, decreasing J c . Our findings provide a promising method for efficient modulation of SOT switching by applying an electric field to a single spin-orbit ferromagnetic layer.

Magnetization Reversal in the Au/Cr/AlO x /(Ga, Mn)As System
The sample structure examined in this study is (Ga 0.94 , Mn 0.06 )As (7 nm)/In 0.3 Ga 0.7 As (500 nm)/GaAs (50 nm) grown on a GaAs (001) substrate by molecular beam epitaxy (MBE). Due to the 500 nm thick lattice-relaxed insulating In 0.3 Ga 0.7 As layer, a tensile strain is applied to the (Ga 0.94 , Mn 0.06 )As thin film, inducing perpendicular magnetic anisotropy (PMA). As shown in Figure 1a, the film was patterned into a crossbar (red parts in Figure 1a) with a size of 0.5 μm (width) × 2 μm (length) by electron beam lithography for transport measurements. The Au (100 nm)/Cr (5 nm) electrodes (yellow parts in Figure 1a), which also work as heat sinks, were deposited with electron beam evaporation. For the solid gate electrode, 40 nm thick AlO x was deposited by atomic layer deposition at 150°C as a dielectric layer (see Figure  S1 in the Supporting Information) Through characterization of the anomalous Hall effect (AHE), the PMA is confirmed by measuring the Hall resistance R H with sweeping of a magnetic field H z applied perpendicular to the film plane. In Figure 2a, the R H -H z curve (see the black curve) shows an obvious square-like character, where R H varies between approximately ±0.6 kΩ. The coercivity H c is 300 Oe, as shown in the square-like R H -H z curve, and we see an obvious anisotropic magnetoresistance (AMR) effect (see the red curve in Figure 2a), where the resistance R reaches the maximum value when the magnetization starts to be reversed by H z .
In addition to a magnetic field, a current J can also be utilized to switch the magnetization. As shown in Figure 2b, with the help of a small external magnetic field H ext = 300 Oe for deterministic magnetization reversal, R H can be changed between ±0.6 kΩ by sweeping J along the in-plane direction, which is consistent with the AHE result in Figure 2a; this result indicates that the magnetization can be fully reversed between the +z and −z directions with a rotation angle of 180°by J. For J // [110] (see the black curve in Figure 2b and the illustration of torques in Figure 2c), the spin component̂x induced by the effective field is along the [110] direction, as shown in Figure 1b, which exerts an anti-damping torquêe xt on the magnetic moment.̂e xt is proportional tom ×̂x ×m, and the direction of̂S T is the same as that of̂x. Here,m ×̂x ×m represents the unit magnetization vector. With the assistance of the torquêe xt induced by H ext , i.e.,̂e xt = −m ×Ĥ ext (here,Ĥ ext represents the vector of H ext ),̂S T overcomes the torquêa n induced by the perpendicular anisotropy field H an , i.e.,̂a n = −m ×Ĥ an (here,Ĥ an represents the vector of H an ), and reverses the magnetic moment when  10] direction, which is parallel tô ext and opposite tôa n . Therefore, with increasing J,̂S T is enhanced, and magnetization reversal occurs. Here, we note that a small hysteresis window appears when J is between 12 × 10 5 and 17 × 10 5 A cm −2 along the [1 " 10] direction (see the black curve in Figure 2b), which might result from slight phase separation of the (Ga 0.94 , Mn 0.06 )As layer.
In the magnetization switching behavior shown in Figure 2b, J c is 8.2 × 10 5 A cm −2 at 40 K for J // [110]. By changing J toward the [110] direction, J c is found to be increased to 10.5 × 10 5 A cm −2 . This occurs because H R is induced in the Au/Cr/AlO x /(Ga, Mn)As system by the breaking of the structure inversion symmetry with the 40 nm thick AlO x layer and the Au/Cr electrode. As shown in Figure 1b

Manipulation of SOT Magnetization Switching via a Gate Electric Field
To achieve manipulation of the SOT magnetization switching with an electric field, we applied a gate voltage V g to the gate electrode shown in Figure 1a. First, we measured the electrical characteristics of the crossbar device, where the source-drain current I SD was measured as a function of the source-drain voltage V SD at 40 K by applying various V g of 0, ±1, ±5, ±10, ±15, and ± 20 V, as shown in Figure 3a. Here, V SD ranging from +0.1 to −0.1 V was applied with a step of 0.001 V. The I SD -V SD curves in Figure 3a show an obvious ohmic character, meaning that ohmic contacts are formed in the crossbars. The contacts remained in good condition and were not destroyed during the measurements. By applying V g , we found that I SD was varied, indicating that I SD can be manipulated by V g . To more clearly understand the change in I SD when applying different V g , I SD modulation ratios at various V g are plotted in Figure 3b based on the results shown in Figure 3a. Here, the modulation ratio is defined by ∆I SD /I SD (V g = 0) × 100%, where ∆I SD is the I SD modulation defined by ∆I SD = I SD (V g ) − I SD (V g = 0). In Figure 3b, an obvious I SD change that is modulated by V g occurs. For V g < 0, the I SD modulation ratio is positive, indicating that the negative V g increases the hole concentration in the (Ga 0.94 , Mn 0.06 )As layer. In contrast, for V g > 0, the I SD modulation ratio is negative, resulting from the decrease in the hole concentration in the (Ga 0.94 , Mn 0.06 )As thin film.
Next, SOT magnetization switching was induced by sweeping J along the [110] direction with the application of a V g of ±10 V, as shown in Figure 3c. From the results, the application of the positive V g = +10 V decreases J c from 8.2 × 10 5 to 7.6 × 10 5 A cm −2 , which means that the SOT switching efficiency is enhanced for V g > 0. Meanwhile, for V g = −10 V, J c increases to 8.7 × 10 5 A cm −2 , indicating that the negative V g hinders the switching process to some extent. Hence, by applying the electric field (V g = ±10 V), J c can be efficiently modulated by ≈14.5% [=(8.7 − 7.6)/7.6 × 100%]. Figure 3d shows the manipulation of the SOT switching (J // [110]) at different V g of ±5, ±10, ±15, and ± 20 V at 40 K (see Figure S3 in the Supporting Information for details), from which we can conclude that a positive V g decreases J c and that a negative V g increases J c . These results indicate that the magnetization switching behavior is solidly reversibly modulated via the electric field. Here, we note that the modulation of the J c is not linearly correlated with the application of V g , which may be attributed to the extremely thin depletion layer and a limited modulation ratio of the practical interfacial electric field under V g smaller than 20 V. To further enhance the modulation ratio under larger V g , further studies are needed.

Mechanism of the Electric Field Control of the SOT Magnetization Switching
The physical mechanism of the electric field modulation of the SOT magnetization switching in the (Ga, Mn)As layer can be attributed to the successful modulation of the interfacial electric field E. As shown in Figure 4a, when V g is 0, an internal electric field E 0 is generated because of the existence of a thin depletion layer in the (Ga 0.94 , Mn 0.06 )As layer in the vicinity of the AlO x layer, as shown in Figure 4d. By applying a positive V g , the depletion is enhanced, as shown in Figure 4e, which generates an additional interfacial electric field E 1 that points in the same direction as E 0 , as shown in Figure 4b. Therefore, the total E becomes larger and contributes to a strong spin-orbit interaction, which enhances H R and H D . Then, H R and H D induce a large spin component along the in-plane direction, which exerts a strong SOT on the magnetization and enables a highly efficient switching process with a small J c . When V g is negative, holes accumulate near the interface between the AlO x and (Ga, Mn)As layers based on a capacitor model, which increases the hole concentration near the AlO x layer, as shown in Figure 4f. Then, the direction of E 1 is reversed, as shown in Figure 4c, and the total E is suppressed. The suppressed E weakens H R and H D , resulting in a decrease in the strength of the SOT. Therefore, the magnetization switching process is suppressed, and J c increases. In addition, it should be noticed that the Oersted field is demonstrated to be negligibly small in the 7 nm thick (Ga 0.94 , Mn 0.06 )As single layer. [16] By changing the direction of J from [110] to [110], the J c modulation ratio obtained by applying V g decreases from 14.5%  Figure 5a, where J c is estimated to be 10.3 × 10 5 A cm −2 at V g = +10 V and 10.8 × 10 5 A cm −2 at V g = −10 V. The decrease in the J c modulation ratio indicates that both H D and H R are influenced by V g and that the total manipulation effect is much stronger  for J // [110]. This is reasonable because H D and H R point in the same direction for J // [110], and the modulation effects are superimposed. In contrast, when applying J along the [110] axis, the directions of H D and H R are opposite, which reduces the modulation effect obtained by applying the gate electric field because the total enhancement or suppression effects of H D and H R cancel out. Hence, a small modulation ratio of J c is realized.
To check the influence of the modulation of H c by the gate bias voltage, R H is measured by sweeping H z along the [001] direction at V g = ±10 V. As shown in Figure 5b,c, with changing V g , H c is nearly constant at approximately 300 Oe regardless of whether the current is applied along the [ " 110] or [110] direction, indicating that H c is not a determining factor in the electric field control of the SOT switching. In addition, Figure 5c shows that R H varies between ±0.587 kΩ when sweeping H z at V g = +10 V. At V g = −10 V, R H varies between ±0.571 kΩ. Therefore, R H can be slightly modulated by V g with a modulation ratio of only 2.8% [=(0.587 − 0.571)/0.571 ×100%)]. Additionally, from the results shown in Figure 3a, R is estimated to be 193 kΩ at V g = +10 V and 186 kΩ at V g = −10 V. In ferromagnets, where R S is the anomalous Hall coefficient and is proportional to either R or R 2 , depending on the AHE mechanism (skew or side-jump scattering). [27] M is the magnetization, R 0 is the ordinary Hall coefficient, and B is the magnetic field. If R S is proportional to R, then the saturation magnetization can be considered to be slightly modulated by  Figure 5b (H c = 300 Oe) and Figure 5c (coercivity H c ′ = 7580 Oe), a 2.3°[ =arcsin (300/7580)] misalignment of the magnetic field occurs due to the misalignment of the magnet and/or the sample, resulting in an additional AHE signal. Therefore, an out-of-plane component of the external magnetic field with a value of 12 Oe (=300 × sin(2.3°)) exists during the current-induced SOT switching, but it is negligibly small. Here, the three curves shown in Figure 5c can be found to overlap with each other, which means that H an is constant when changing V g and that the influence of the modulation of H an can also be excluded as a determining factor in the successful manipulation of the SOT switching via the electric field.

Conclusions
In this work, the manipulation of SOT magnetization switching via a gate electric field is achieved, which can be ascribed to the successful modulation of the interfacial electric field. By applying a positive V g , the strength of the electric field is enhanced, which strengthens the total effective field in (Ga, Mn)As and assists the magnetization switching. In contrast, a negative V g results in a smaller effective field, which decreases the switching efficiency and increases J c . This finding provides an approach toward reversible modulation of the SOT magnetization switching in a single layer of a spin-orbit ferromagnet via electric fields, which will advance the development of energy-efficient gate-controlled spintorque devices and help further the understanding of the switching mechanism.

Experimental Section
Sample Preparation: A 7 nm thick (Ga 0.94 , Mn 0.06 )As thin film was grown on a semi-insulating GaAs (001) substrate in an ultrahigh-vacuum MBE system. After removal of the surface oxide layer of the GaAs substrate at 580°C, a 50 nm thick GaAs buffer layer was grown to obtain an atomically smooth surface. After that, the substrate was cooled to 450°C, and a 500 nm thick In 0.3 Ga 0.7 As layer was grown to induce a tensile strain in the (Ga 0.94 , Mn 0.06 )As layer, giving rise to PMA. Then, the sample was cooled to approximately 290°C for growth of the 7 nm thick (Ga 0.94 , Mn 0.06 )As layer. The growth process was monitored in situ by means of reflection high-energy electron diffraction. The Curie temperature T C of the (Ga 0.94 , Mn 0.06 )As thin film was estimated to be 75 K. After the device fabrication process, the T C increased to 112 K, which might be caused by the annealing process resulting from the increase in the sample temperature during the device fabrication process (see Figure S2 in the Supporting Information).
Transport Measurements: For the SOT measurements, a Keithley 2636A was used as the current source for applying a direct current, and a Keithley 2400 was used for applying a gate voltage. The Hall voltage was measured with another Keithley 2400. The measurements were carried out at 40 K.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.