⇦Chinese Physics Letters, 2022, Vol. 39, No. 3, Article code 037303Express Letter Orbit-Transfer Torque Driven Field-Free Switching of Perpendicular Magnetization Xing-Guo Ye (叶兴国)†, Peng-Fei Zhu (朱鹏飞)†, Wen-Zheng Xu (徐文正)†, Nianze Shang (尚念泽), Kaihui Liu (刘开辉), and Zhi-Min Liao (廖志敏)* Affiliations State Key Laboratory for Mesoscopic Physics and Frontiers Science Center for Nano-optoelectronics, School of Physics, Peking University, Beijing 100871, China Received 11 February 2022; accepted 15 February 2022; published online 16 February 2022 †These authors contributed equally to this work.
*Corresponding author. Email: liaozm@pku.edu.cn Citation Text: Ye X G, Zhu P F, Xu W Z et al. 2022 Chin. Phys. Lett. 39 037303    Abstract The reversal of perpendicular magnetization (PM) by electric control is crucial for high-density integration of low-power magnetic random-access memory. Although the spin-transfer torque and spin-orbit torque technologies have been used to switch the magnetization of a free layer with perpendicular magnetic anisotropy, the former has limited endurance because of the high current density directly through the junction, while the latter requires an external magnetic field or unconventional configuration to break the symmetry. Here we propose and realize the orbit-transfer torque (OTT), that is, exerting torque on the magnetization using the orbital magnetic moments, and thus demonstrate a new strategy for current-driven PM reversal without external magnetic field. The perpendicular polarization of orbital magnetic moments is generated by a direct current in a few-layer WTe$_{2}$ due to the existence of nonzero Berry curvature dipole, and the polarization direction can be switched by changing the current polarity. Guided by this principle, we construct the WTe$_{2}$/Fe$_{3}$GeTe$_{2}$ heterostructures to achieve the OTT driven field-free deterministic switching of PM.
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 DOI:10.1088/0256-307X/39/3/037303 © 2022 Chinese Physics Society Article Text Magnetic random-access memory (MRAM)[1–4] as a type of non-volatile memory has advantages of high speed, low power consumption and high reliability, which is recently being developed by using magnetic tunnel junction (MTJ) with perpendicular magnetic anisotropy (PMA) for further scaling down.[5] The perpendicular magnetization (PM) reversal of the free layer is the key operation of data writing in MRAM.[6] The magnetization switch driven by spin-transfer torque effect[7–10] has been implemented in two-terminal MTJ, which challenges its durability due to the high-density current passing through the junction. Thereafter, three-terminal spin-orbit torque (SOT)[11–28] devices have been developed, where the magnetization switching is caused by interfacial spin accumulations coming from spin Hall effect,[13,14] Rashba effect,[12] or the topological surface states.[16] However, an external magnetic field is usually needed for the PM switching driven by SOT effect,[15] although a few experiments have demonstrated the SOT-induced filed-free PM switching by introducing interfacial exchange bias[22] or structure asymmetry,[17,25] which is unfavorable for realistic applications. In this Letter, we propose and demonstrate the orbit-transfer torque (OTT) effect to obtain the current-driven field-free PM switching. Instead of spin degree of freedom, the OTT effect exploits the polarization of orbital magnetic moment of Bloch electrons.[29] Orbit-Transfer Torque as a New Strategy for PM Switching. The recently discovered Berry curvature dipole[30] in van der Waals materials offers an ideal platform to generate the perpendicularly polarized orbital magnetic moments by applying dc current,[31] formulated as ${\boldsymbol m} \propto ({\boldsymbol D}\cdot {\boldsymbol E)}\hat{\boldsymbol z}$, where ${\boldsymbol D}$ is the Berry curvature dipole and ${\boldsymbol E}$ is the applied electric field. Similar to the SOT, OTT also has two components, i.e., field-like torque $T_{\rm FL}\sim {\boldsymbol M}\times \hat{\boldsymbol m}$, and antidamping-like torque $T_{\rm AD}\sim {\boldsymbol M}\times (\hat{\boldsymbol m}{\times \boldsymbol M)}$ (Ref. [23]), where ${\boldsymbol M}$ is the magnetization of adjacent magnetic layer, and $\hat{\boldsymbol m}$ is the unit vector of polarized orbital magnetic moment. For perpendicularly polarized $\hat{\boldsymbol m}$, nonzero antidamping-like torque would emerge as long as ${\boldsymbol M}$ has a slight deviation from the perpendicular direction. For ferromagnetic materials with PMA, either spin wave excitation[32] or spin fluctuations can produce a perturbation of spin orientation deviating from the perpendicular direction. Therefore, the OTT can force the magnetization to prefer along the orbital polarization direction, as shown in Figs. 1(a) and 1(b). A simplified analysis is carried out to search the candidate materials to generate OTT. First, we focus on the two-dimensional (2D) layered materials, where the dimension constraint forces the orbital magnetic moment along out-of-plane direction. Second, for 2D materials with nonzero Berry curvature dipole, such as bilayer[33] or few-layer WTe$_{2}$ (Ref. [34]), and strained WSe$_{2}$ (Ref. [35]), current can induce the polarization of orbital magnetic moment.[31] As shown in Fig. 1(c), Berry curvature distributes asymmetrically in one single valley in these materials, forming a Berry curvature dipole. Applying a parallel dc current, the orbital magnetic moment is thus polarized. Further, as shown in Fig. 1(d), when the applied current polarity is reversed, the polarization direction of the orbital magnetic moment is also reversed. Guided by this principle, we constructed the few-layer WTe$_{2}$/Fe$_{3}$GeTe$_{2}$ heterostructures (see Device Fabrication in the Supplemental Material), where the few-layer WTe$_{2}$ with nonzero Berry curvature dipole is used to generate the polarization of orbital magnetic moment by applying current, and the few-layer Fe$_{3}$GeTe$_{2}$ is used as the ferromagnetic layer with PMA.[36] Field-free current-driven magnetization switching has been demonstrated as a result of the OTT effect at the heterostructure interface. The measurement results of four devices, device A in the main text and devices B–D in Figs. S7–S9 and Table S1 in the Supplemental Material, are presented.
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Fig. 1. Illustration of orbit-transfer torque. [(a), (b)] For the ferromagnetism (FM)/non-magnetic material (NM) heterostructure, the polarization of orbital magnetic moment can result in orbit-transfer torque that acts on the magnetization, and the up and down magnetization states can be switched by changing the current direction. [(c), (d)] Illustration of current-induced polarization of orbital magnetic moment in systems with nonzero Berry curvature dipole. The orbital magnetic moment is denoted by green arrow. Bloch electrons with opposite Berry curvature are denoted by red and blue, respectively. $I_{\rm e}$ is the electron current, $D$ is the Berry curvature dipole, $\varepsilon$ is the energy, and $k$ is the wavevector.
Polarization of Orbital Magnetic Moment Manifested by Nonlinear Hall Effect. WTe$_{2}$ is a 2D layered van der Waals material belonging to the transition metal dichalcogenide family, with T$_{\rm d}$-phase as its stable structure.[37] Monolayer T$_{\rm d}$-WTe$_{2}$ consists of a layer of W atoms sandwiched between two layers of Te atoms in a distorted octahedral coordination, as shown in Fig. 2(a). WTe$_{2}$ possesses various exotic phases, including Weyl semimetal,[38] gate-tunable superconductivity,[39,40] quantum spin Hall insulator,[41,42] and possible exciton insulator,[43] depending on its thickness. Its bulk crystal has space group $Pmn2_{1}$, which possesses a mirror symmetry along $b$ axis mirror line [red line in Fig. 2(a)] and a glide mirror symmetry along $a$ axis mirror line.[34] These two mirror symmetries recover an inversion symmetry in the $ab$ plane, leading to vanishing Berry curvature dipole in the WTe$_{2}$ bulk. However, since the glide mirror symmetry involves a half-cell translation, it is generally broken at the surfaces, giving rise to nonzero Berry curvature dipole at surfaces.[44] Because the mirror symmetry with $bc$ plane as mirror plane still exists at the surface, it constrains the Berry curvature dipole in WTe$_{2}$ along $a$ axis direction. The nonzero Berry curvature dipole in few-layer WTe$_{2}$ has been observed in previous experiments,[34] evidenced by the nonlinear Hall effect.
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Fig. 2. Nonlinear Hall effect in WTe$_{2}$/Fe$_{3}$GeTe$_{2}$ heterostructures. (a) Crystal structure of T$_{\rm d}$-WTe$_{2}$. The red line corresponds to the mirror line in the $ab$ plane, which persists at the surface. (b) The optical image of device A, which consists of a WTe$_{2}$/Fe$_{3}$GeTe$_{2}$ heterostructure. The crystalline axes are aligned with electrodes. The $\theta$ is defined as the angle between the current direction and the baseline direction of the electrode pair, which is approximately along the $b$ axis of WTe$_{2}$. For device A, the baseline direction is $\sim$$1.3^{\circ}$ misaligned with $b$ axis. (c) Schematic of the measurement configuration for nonlinear Hall effect. (d) The angle-dependence of the second-order nonlinear Hall effect at 1.8 K. The red line is the fitting curve.
The optical image of fabricated WTe$_{2}$/Fe$_{3}$GeTe$_{2}$ heterostructure, device A, is shown in Fig. 2(b). The thickness of WTe$_{2}$ and Fe$_{3}$GeTe$_{2}$ measured by an atomic force microscope is 11.9 and 11.2 nm, respectively (see Fig. S1). The multiple electrodes were designed as a circular disc configuration, which was utilized to implement the angle-dependent measurements. By identifying long, straight edges of WTe$_{2}$ and combining with polarized Raman spectroscopy, the crystalline axes were aligned with the electrodes, where the misalignment is $\sim$$1.3^{\circ}$ for device A (see Fig. S2). The angle $\theta$ is defined in Fig. 2(b), where $\theta =0^{\circ}$ approximately corresponds to $b$ axis; while $\theta =90^{\circ}$ approximately corresponds to $a$ axis. The device shows two carrier transport properties and large magnetoresistance with electron mobility $\sim$2203 cm$^{2}$/V$\cdot$s (see Fig. S3). Since nonzero Berry curvature dipole emerges at the interface, when applying an electric field, it would give rise to the polarization of orbital magnetic moment, expressed as ${\boldsymbol m} \propto ({\boldsymbol D}\cdot {\boldsymbol E)}\hat{\boldsymbol z}$ (Refs. [31,45]). When an ac current $I^{\omega}$ with frequency $\omega$ is applied, the induced orbital magnetization will have the alternating characteristic of frequency $\omega$, further resulting in a second-harmonic anomalous Hall voltage $V_{\rm H}^{2\omega}$ with frequency $2\omega$, known as the nonlinear Hall effect,[35] as illustrated in Fig. 2(c). The results are displayed in Fig. S4(a), and quadric $I^{\omega }-V_{\rm H}^{2\omega}$ characteristics are observed. Moreover, the nonlinear Hall voltage shows the maximum at $\theta =90^{\circ}$ approximately along $a$ axis and is nearly zero at $\theta =0^{\circ}$ approximately along $b$ axis [see Fig. 2(d)]. This angle dependence is consistent with the fact that the Berry curvature dipole in few-layer WTe$_{2}$ is along the crystal $a$ axis. Orbit-Transfer Torque in WTe$_{2}$/Fe$_{3}$GeTe$_{2}$ Heterostructures. The hysteresis loops of Hall resistance ($R_{xy}$) of the WTe$_{2}$/Fe$_{3}$GeTe$_{2}$ heterostructure were measured by sweeping the out-of-plane magnetic field at various temperatures. From the Arrott plots (see Fig. S5), it is found that the Curie temperature is $\sim $180 K, corresponding to that of 14-layer Fe$_{3}$GeTe$_{2}$ based on the previous work.[36] As shown in Fig. 3(a) and Fig. S6, the $R_{xy}$ hysteresis loops with sharp transitions are clearly observed, consistent with the PMA characteristics of Fe$_{3}$GeTe$_{2}$ (Refs. [36,46]). To demonstrate the field-free switching of magnetization in the Fe$_{3}$GeTe$_{2}$ layer through OTT, a pulse-like dc current $I_{\rm p}$ was injected into the heterostructure at $\theta =90^{\circ}$ approximately along $a$ axis, and the $R_{xy}$ was measured after the pulse $I_{\rm p}$ was removed. As shown in Fig. 3(b), current-induced $R_{xy}$ change is clearly observed at 130 K. The height of the $R_{xy}$–$I_{\rm p}$ loop agrees well with that of the $R_{xy}$–$H$ loop in Fig. 3(a), indicating the deterministic PM switching. Therefore, the $R_{xy}$–$I_{\rm p}$ loops indicate that the upward and downward magnetization states in Fe$_{3}$GeTe$_{2}$ can be switched between each other by injecting opposite currents. Since no external magnetic field is applied, such PM switching is failed to be attributed to the SOT effect in WTe$_{2}$ (Ref. [27]). The current induced PM switching agrees well with the OTT effect, that is, the torque exerted by the perpendicularly polarized orbital magnetic moments.
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Fig. 3. Orbit-transfer torque induced field-free perpendicular magnetization switching in WTe$_{2}$/Fe$_{3}$GeTe$_{2}$ heterostructure. (a) Hall resistance as a function of magnetic field at 130 K. The hysteresis loop is used for reference to identify the magnetization states. (b) Hall resistance as a function of pulse current $I_{\rm p}$ at 130 K. Before sweeping $I_{\rm p}$ from zero to large positive or negative values, the magnetization state is initialized by magnetic field. (c) Upper: a series of current pulse with amplitude $\pm 8$ mA is injected at 130 K. The red arrows indicate the deliberately programmed disturbing current pulses. Lower: the corresponding changes in Hall resistance. (d) Temperature dependence of the current-driven magnetization switching. The curves are shifted for clarity. (e) The temperature dependence of critical switching current density. The $J_{\rm c}$ corresponds to the current density at which resistance changes by more than half, and $J_{\rm on}$ corresponds to the current density at the onset of resistance change. The data in this figure were measured when the current was applied approximately along $a$ axis at $\theta =90^{\circ}$.
A sequence of current pulse with amplitude $\pm 8$ mA at 130 K and $\theta =90^{\circ}$ was injected into this heterostructure, as shown in Fig. 3(c). Current pulse with opposite polarity yields terminate states with saturated magnetization along opposite directions (up or down). Once the magnetization state is finalized, the disturbing current pulse will not affect the magnetization state, as indicated by the red arrows in Fig. 3(c). Such robust magnetization switching against perturbations indicates the application potential in MRAM. Temperature dependence of this current-induced PM switching is further investigated, as shown in Fig. 3(d). Two critical switching current densities $J_{\rm c}$ and $J_{\rm on}$ are defined, where $J_{\rm c}$ corresponds to the current density at which resistance changes by more than half, and $J_{\rm on}$ corresponds to the current density at the onset of resistance change. Both $J_{\rm c}$ and $J_{\rm on}$ are taken as the averages for up-to-down and down-to-up PM switching. As shown in Fig. 3(e), the $J_{\rm c}$ and $J_{\rm on}$ decrease upon increasing temperature, consistent with the fact that the effective PMA field in Fe$_{3}$GeTe$_{2}$ decreases upon increasing temperature. Synergistic Effect of Spin-Orbit Torque and Orbit-Transfer Torque. The above results indicate the OTT-driven PM switching as the current was applied along $a$ axis of WTe$_{2}$. It would be very different as the pulse current $I_{\rm p}$ is applied at $\theta =0^{\circ}$ approximately along $b$ axis, where the current direction is perpendicular to the Berry curvature dipole and there is almost no current induced orbital magnetism. As shown in Fig. 4(a), no deterministic switching is observed when $I_{\rm p}$ is along $b$ axis at 130 K. Instead of switching between upward and downward PM states, $I_{\rm p}$ along $b$ axis yields a terminate state with nearly zero Hall resistance. This is well understood by the SOT-induced multi-domain scenario.[28] Since SOT forces the magnetization lying in plane, when removing pulse current and thus SOT, multi-domains with magnetization randomly upward or downward would emerge, leading to nearly zero Hall resistance. Thus, the OTT is absent, and SOT dominates when $I_{\rm p}$ is along $b$ axis, as expected. Using the disc distributed electrode structure of the device, angle dependence of current-driven magnetization switching was investigated at 130 K, as shown in Fig. 4(b). It is found that the deterministic switching can be obtained within a large angle window due to the nonzero current component along $a$ axis, as shown by the $R_{xy}$–$I_{\rm p}$ loops at $\theta =120^{\circ}$ and $60^{\circ}$ in Fig. 4(b). As for the current along direction closer to $b$ axis, that is, $\theta =30^{\circ}$ and $150^{\circ}$, the $R_{xy}$–$I_{\rm p}$ loops only shows partially switching without reaching the saturated magnetization states, which suggests the coexistence of SOT and OTT. The angle-dependent critical switching current density is shown in Fig. 4(c). The $J_{\rm c}$ is failed to be fitted in the form of $1/\cos(\theta -90^{\circ})$ when only considering the current component parallel to $a$ axis. Because the bulk states can also contribute to the SOT due to intrinsic spin-orbit coupling and the OTT only comes from the interface due to the need of symmetry breaking, the strength of SOT should be larger than that of OTT in the WTe$_{2}$/Fe$_{3}$GeTe$_{2}$ device. Therefore, the SOT may dominate the onset change of magnetic states, but the deterministic switching is achieved through OTT. The angle dependence of the onset switching current density $J_{\rm on}$ is consistent with the anisotropy of spin-orbit coupling in bulk WTe$_{2}$, which possesses the largest strength along $b$ axis.[27] It is worth noting that the critical switching current at $\theta =60^{\circ}$ and $120^{\circ}$ shows a smaller value than that at $\theta =90^{\circ}$, suggesting that the synergy of SOT and OTT is more effective for the PM switching. It is worth noting that some works point out that out-of-plane spin accumulation may occur together with SOT in WTe$_{2}$ (Ref. [47]). Although this out-of-plane spin accumulation is a possible origination of the field-free perpendicular magnetization switching, it can be ruled out in our work due to the following two reasons. First, our results demonstrate the anisotropic angle dependence of the magnetization switching, which is not expected for the mechanism of out-of-plane spin accumulation. In contrast, this angle dependence is naturally explained by OTT. Second, the SOT in WTe$_{2}$ was reported to be mainly contributed by bulk states,[27] however, our results show that the switching critical current density is almost the same in samples with different thicknesses (see Table S1), indicating a surface origin of the antidamping torque. This surface origin is also well consistent with the mechanism of OTT.
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Fig. 4. Angle-dependence of current-driven magnetization switching in WTe$_{2}$/Fe$_{3}$GeTe$_{2}$ heterostructure. (a) Hall resistance as a function of pulse current $I_{\rm p}$ at 130 K. $I_{\rm p}$ is applied at $\theta =0^{\circ}$ approximately along $b$ axis. Before sweeping $I_{\rm p}$ from zero to large positive or negative values, the magnetization state is initialized by magnetic field. (b) The $R_{xy}$–$I_{\rm p}$ loops at 130 K with $I_{\rm p}$ applied along different angle $\theta$. The curves are shifted for clarity. (c) The critical switching current density as a function of angle $\theta$.
Outlook. Our work demonstrates the OTT as a new strategy for field-free magnetization switching in PMA ferromagnets, which utilizes the orbital magnetic moment of Bloch electrons rather than spins, thus extending the concept from spintronics to orbitronics and their hybrid. Through symmetry analysis, we propose that besides few-layer WTe$_{2}$, 2D materials with nonzero Berry curvature dipole,[48] including bilayer WTe$_{2}$ (Ref. [33]), strained WSe$_{2}$ (Ref. [35]), few-layer MoTe$_{2}$ (Ref. [49]), and corrugated bilayer graphene,[50] are candidates to realize OTT. Moreover, the temperature dependence of current-driven switching indicates that OTT is robust against temperature. By building heterostructures using PMA materials with Curie temperature above 300 K, such as few-layer CrTe$_{2}$ (Ref. [51]), room-temperature PM switching through OTT can be achieved, promising for realistic applications. Acknowledgment. This work was supported by the National Natural Science Foundation of China (Grant Nos. 91964201 and 61825401). References Electric-field control of ferromagnetismCurrent-Induced Switching of Domains in Magnetic Multilayer DevicesCurrent-induced magnetization reversal in magnetic nanowiresThe emergence of spin electronics in data storageMagnetic recording: advancing into the futurePerpendicular switching of a single ferromagnetic layer induced by in-plane current injectionEmission of spin waves by a magnetic multilayer traversed by a currentCurrent-driven excitation of magnetic multilayersSpin transfer torquesSpin transfer torque devices utilizing the giant spin Hall effect of tungstenEvidence for reversible control of magnetization in a ferromagnetic material by means of spin–orbit magnetic fieldCurrent-driven spin torque induced by the Rashba effect in a ferromagnetic metal layerSpin-Torque Switching with the Giant Spin Hall Effect of TantalumCurrent-Induced Switching of Perpendicularly Magnetized Magnetic Layers Using Spin Torque from the Spin Hall EffectSymmetry and magnitude of spin–orbit torques in ferromagnetic heterostructuresSpin-transfer torque generated by a topological insulatorSwitching of perpendicular magnetization by spin–orbit torques in the absence of external magnetic fieldsMagnetization switching through giant spin–orbit torque in a magnetically doped topological insulator heterostructureAn antidamping spin–orbit torque originating from the Berry curvatureA spin–orbit torque switching scheme with collinear magnetic easy axis and current configurationElectrical switching of an antiferromagnetMagnetization switching by spin–orbit torque in an antiferromagnet–ferromagnet bilayer systemCurrent-induced spin-orbit torques in ferromagnetic and antiferromagnetic systemsControl of spin–orbit torques through crystal symmetry in WTe2/ferromagnet bilayersElectric field control of deterministic current-induced magnetization switching in a hybrid ferromagnetic/ferroelectric structureSpin currents and spin–orbit torques in ferromagnetic trilayersAll-electric magnetization switching and Dzyaloshinskii–Moriya interaction in WTe2/ferromagnet heterostructuresCurrent-driven magnetization switching in a van der Waals ferromagnet Fe 3 GeTe 2Berry phase, hyperorbits, and the Hofstadter spectrum: Semiclassical dynamics in magnetic Bloch bandsQuantum Nonlinear Hall Effect Induced by Berry Curvature Dipole in Time-Reversal Invariant MaterialsValley magnetoelectricity in single-layer MoS2Spin-Wave Theory of Ferromagnetic Thin FilmsObservation of the nonlinear Hall effect under time-reversal-symmetric conditionsNonlinear anomalous Hall effect in few-layer WTe2Strain Tunable Berry Curvature Dipole, Orbital Magnetization and Nonlinear Hall Effect in WSe 2 Monolayer*Gate-tunable room-temperature ferromagnetism in two-dimensional Fe3GeTe2The crystal structures of WTe 2 and high-temperature MoTe 2Large, non-saturating magnetoresistance in WTe2Electrically tunable low-density superconductivity in a monolayer topological insulatorGate-induced superconductivity in a monolayer topological insulatorQuantum spin Hall state in monolayer 1T'-WTe2Observation of the quantum spin Hall effect up to 100 kelvin in a monolayer crystalLandau quantization and highly mobile fermions in an insulatorBerry curvature dipole current in the transition metal dichalcogenides familyStrain Engineering of the Berry Curvature Dipole and Valley Magnetization in Monolayer MoS 2 The current modulation of anomalous Hall effect in van der Waals Fe 3 GeTe 2 /WTe 2 heterostructuresUnconventional Charge–Spin Conversion in Weyl‐Semimetal WTe 2Nonlinear Hall effectsElectrically tuneable nonlinear anomalous Hall effect in two-dimensional transition-metal dichalcogenides WTe 2 and MoTe 2Hall effects in artificially corrugated bilayer graphene without breaking time-reversal symmetryRoom-temperature intrinsic ferromagnetism in epitaxial CrTe2 ultrathin films
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