Orbit-Transfer Torque Driven Field-Free Switching of Perpendicular Magnetization

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 D is the Berry curvature dipole and 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 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 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).

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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 WTe₂ (Ref.[34]), and strained WSe₂ (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 WTe₂/Fe₃GeTe₂ heterostructures (see Device Fabrication in the Supplemental Material), where the few-layer WTe₂ with nonzero Berry curvature dipole is used to generate the polarization of orbital magnetic moment by applying current, and the few-layer Fe₃GeTe₂ 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.

Polarization of Orbital Magnetic Moment Manifested by Nonlinear Hall Effect. WTe₂ is a 2D layered van der Waals material belonging to the transition metal dichalcogenide family, with T_d-phase as its stable structure.^[37] Monolayer T_d-WTe₂ 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). WTe₂ 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 Pmn2₁, 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 WTe₂ 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 WTe₂ along a axis direction. The nonzero Berry curvature dipole in few-layer WTe₂ has been observed in previous experiments,^[34] evidenced by the nonlinear Hall effect.

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The optical image of fabricated WTe₂/Fe₃GeTe₂ heterostructure, device A, is shown in Fig. 2(b). The thickness of WTe₂ and Fe₃GeTe₂ 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 WTe₂ and combining with polarized Raman spectroscopy, the crystalline axes were aligned with the electrodes, where the misalignment is ∼1.3° for device A (see Fig. S2). The angle θ is defined in Fig. 2(b), where θ = 0° approximately corresponds to b axis; while θ = 90° approximately corresponds to a axis. The device shows two carrier transport properties and large magnetoresistance with electron mobility ∼2203 cm²/V⋅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^ω with frequency ω is applied, the induced orbital magnetization will have the alternating characteristic of frequency ω, further resulting in a second-harmonic anomalous Hall voltage ${V}_{{\rm{H}}}^{2\omega }$ with frequency 2ω, 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 θ = 90° approximately along a axis and is nearly zero at θ = 0° approximately along b axis [see Fig. 2(d)]. This angle dependence is consistent with the fact that the Berry curvature dipole in few-layer WTe₂ is along the crystal a axis.

Orbit-Transfer Torque in WTe₂/Fe₃GeTe₂ Heterostructures. The hysteresis loops of Hall resistance (R_xy ) of the WTe₂/Fe₃GeTe₂ 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 ∼ 180 K, corresponding to that of 14-layer Fe₃GeTe₂ 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 Fe₃GeTe₂ (Refs.[36,46]). To demonstrate the field-free switching of magnetization in the Fe₃GeTe₂ layer through OTT, a pulse-like dc current I_p was injected into the heterostructure at θ = 90° approximately along a axis, and the R_xy was measured after the pulse I_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_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_p loops indicate that the upward and downward magnetization states in Fe₃GeTe₂ 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 WTe₂ (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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A sequence of current pulse with amplitude ± 8 mA at 130 K and θ = 90° 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_c and J_on are defined, where J_c corresponds to the current density at which resistance changes by more than half, and J_on corresponds to the current density at the onset of resistance change. Both J_c and J_on are taken as the averages for up-to-down and down-to-up PM switching. As shown in Fig. 3(e), the J_c and J_on decrease upon increasing temperature, consistent with the fact that the effective PMA field in Fe₃GeTe₂ 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 WTe₂. It would be very different as the pulse current I_p is applied at θ = 0° 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_p is along b axis at 130 K. Instead of switching between upward and downward PM states, I_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_p is along b axis, as expected.

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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_p loops at θ = 120° and 60° in Fig. 4(b). As for the current along direction closer to b axis, that is, θ = 30° and 150°, the R_xy –I_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_c is failed to be fitted in the form of 1/cos(θ – 90°) 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 WTe₂/Fe₃GeTe₂ 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_on is consistent with the anisotropy of spin-orbit coupling in bulk WTe₂, which possesses the largest strength along b axis.^[27] It is worth noting that the critical switching current at θ = 60° and 120° shows a smaller value than that at θ = 90°, 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 WTe₂ (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 WTe₂ 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.

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 WTe₂, 2D materials with nonzero Berry curvature dipole,^[48] including bilayer WTe₂ (Ref.[33]), strained WSe₂ (Ref.[35]), few-layer MoTe₂ (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 CrTe₂ (Ref.[51]), room-temperature PM switching through OTT can be achieved, promising for realistic applications.

Acknowledgment