Current-Nonlinear Hall Effect and Spin-Orbit Torque Magnetization Switching in a Magnetic Topological Insulator

Magnetic parity violation and parity-time-reversal-symmetric magnets

Parity-time-reversal symmetry (PTsymmetry), a symmetry for the combined operations of space inversion (P) and time reversal (T), is a fundamental concept of physics and characterizes the functionality of materials as well asPandTsymmetries. In particular, thePT-symmetric systems can be found in the centrosymmetric crystals undergoing the parity-violating magnetic order which we call the odd-parity magnetic multipole order. While this spontaneous order leavesPTsymmetry intact, the simultaneous violation ofPandTsymmetries gives rise to various emergent responses that are qualitatively different from those allowed by the nonmagneticP-symmetry breaking or by the ferromagnetic order. In this review, we introduce candidates hosting the intriguing spontaneous order and overview the characteristic physical responses. Various off-diagonal and/or nonreciprocal responses are identified, which are closely related to the unusual electronic structures such as hidden spin-momentum locking and asymmetric band dispersion.

Highly Efficient Spin-Orbit Torque Switching in Bi2Se3/Fe3GeTe2 van der Waals Heterostructures

Topological insulators (TIs) have shown promise as a spin-generating layer to switch the magnetization state of ferromagnets via spin-orbit torque (SOT) due to charge-to-spin conversion efficiency of the TI surface states that arises from spin-momentum locking. However, when TIs are interfaced with conventional bulk ferromagnetic metals, the combination of charge transfer and hybridization can potentially destroy the spin texture and hamper the possibility of accessing the TI surface states. Here, we fabricate an all van der Waals (vdW) heterostructure consisting of molecular beam epitaxy grown bulk-insulating Bi2Se3 and exfoliated 2D metallic ferromagnet Fe3GeTe2 (FGT) with perpendicular anisotropy. By detecting the magnetization state of the FGT via anomalous Hall effect and magneto-optical Kerr effect measurements, we determine the critical switching current density for magnetization switching to be Jc ≈ 1.2 × 106 A/cm2, the lowest reported for the switching of a perpendicular anisotropy ferromagnet using Bi2Se3. From second harmonic Hall measurements, we further determine the SOT efficiency (ξDL) to be in the range of 1.8 ± 0.3 and 1.4 ± 0.08 between 5 and 150 K, comparable to the highest values reported for Bi2Se3. Our density functional theory calculations find that the weak interlayer interactions at the Bi2Se3/FGT interface lead to a weakened dipole at the interface and suppress the proximity induced magnetic moment on Bi2Se3. This enables direct access to the TI surface states contributed by the first quintuple layer, where the spins are singly degenerate with significant net in-plane spin polarization. Our results highlight the clear advantage of all-vdW heterostructures with weak interlayer interactions that can enhance SOT efficiency and minimize critical current density, an important step toward realizing next generation low-power nonvolatile memory and spintronic devices.

Electrical switching of the edge current chirality in quantum anomalous Hall insulators

A quantum anomalous Hall (QAH) insulator is a topological phase in which the interior is insulating but electrical current flows along the edges of the sample in either a clockwise or counterclockwise direction, as dictated by the spontaneous magnetization orientation. Such a chiral edge current eliminates any backscattering, giving rise to quantized Hall resistance and zero longitudinal resistance. Here we fabricate mesoscopic QAH sandwich Hall bar devices and succeed in switching the edge current chirality through thermally assisted spin-orbit torque (SOT). The well-quantized QAH states before and after SOT switching with opposite edge current chiralities are demonstrated through four- and three-terminal measurements. We show that the SOT responsible for magnetization switching can be generated by both surface and bulk carriers. Our results further our understanding of the interplay between magnetism and topological states and usher in an easy and instantaneous method to manipulate the QAH state.

Thermally generated spin current in the topological insulator Bi2Se3

We present measurements of thermally generated transverse spin currents in the topological insulator Bi2Se3, thereby completing measurements of interconversions among the full triad of thermal gradients, charge currents, and spin currents. We accomplish this by comparing the spin Nernst magneto-thermopower to the spin Hall magnetoresistance for bilayers of Bi2Se3/CoFeB. We find that Bi2Se3 does generate substantial thermally driven spin currents. A lower bound for the ratio of spin current density to thermal gradient is [Formula: see text] = (4.9 ± 0.9) × 106 [Formula: see text], and a lower bound for the magnitude of the spin Nernst ratio is -0.61 ± 0.11. The spin Nernst ratio for Bi2Se3 is the largest among all materials measured to date, two to three times larger compared to previous measurements for the heavy metals Pt and W. Strong thermally generated spin currents in Bi2Se3 can be understood via Mott relations to be due to an overall large spin Hall conductivity and its dependence on electron energy.

Spin-Orbit Torques and Spin Hall Magnetoresistance Generated by Twin-Free and Amorphous Bi0.9 Sb0.1 Topological Insulator Films

Topological insulators have attracted great interest as generators of spin-orbit torques (SOTs) in spintronic devices. Bi1-x Sbx is a prominent topological insulator that has a high charge-to-spin conversion efficiency. However, the origin and magnitude of the SOTs induced by current-injection in Bi1-x Sbx remain controversial. Here, the investigation of the SOTs and spin Hall magnetoresistance resulting from charge-to-spin conversion in twin-free epitaxial layers of Bi0.9 Sb0.1 (0001) coupled to FeCo are investigated, and compared with those of amorphous Bi0.9 Sb0.1 . A large charge-to-spin conversion efficiency of 1 in the first case and less than 0.1 in the second is found, confirming crystalline Bi0.9 Sb0.1 as a strong spin-injector material. The SOTs and spin Hall magnetoresistance are independent of the direction of the electric current, indicating that charge-to-spin conversion in single-crystal Bi0.9 Sb0.1 (0001) is isotropic despite the strong anisotropy of the topological surface states. Further, it is found that the damping-like SOT has a non-monotonic temperature dependence with a minimum at 20 K. By correlating the SOT with resistivity and weak antilocalization measurements, charge-spin conversion is concluded to occur via thermally excited holes from the bulk states above 20 K, and conduction through the isotropic surface states with increasing spin polarization due to decreasing electron-electron scattering below 20 K.

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

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.

Giant Magnetochiral Anisotropy in Weyl Semimetal WTe_{2} Induced by Diverging Berry Curvature

The concept of Berry curvature is essential for various transport phenomena. However, an effect of the Berry curvature on magnetochiral anisotropy, i.e., nonreciprocal magnetotransport, is still elusive. Here, we report that the Berry curvature induces the large magnetochiral anisotropy. In Weyl semimetal WTe_{2}, we observe the strong enhancement of the magnetochiral anisotropy when the Fermi level is located near the Weyl points. Notably, the maximal figure of merit γ[over ¯] reaches 1.2×10^{-6}  m^{2} T^{-1} A^{-1}, which is the largest ever reported in bulk materials. Our semiclassical calculation shows that the diverging Berry curvature at the Weyl points strongly enhances the magnetochiral anisotropy.

Large magnetoelectric resistance in the topological Dirac semimetal α-Sn

The spin-momentum locking of surface states in topological materials can produce a resistance that scales linearly with magnetic and electric fields. Such a bilinear magnetoelectric resistance (BMER) effect offers a new approach for information reading and field sensing applications, but the effects demonstrated so far are too weak or for low temperatures. This article reports the first observation of BMER effects in topological Dirac semimetals; the BMER responses were measured at room temperature and were substantially stronger than those reported previously. The experiments used topological Dirac semimetal α-Sn thin films grown on silicon substrates. The films showed BMER responses that are 10⁶ times larger than previously measured at room temperature and are also larger than those previously obtained at low temperatures. These results represent a major advance toward realistic BMER applications. Significantly, the data also yield the first characterization of three-dimensional Fermi-level spin texture of topological surface states in α-Sn.

Zero Magnetic Field Plateau Phase Transition in Higher Chern Number Quantum Anomalous Hall Insulators

The plateau-to-plateau transition in quantum Hall effect under high magnetic fields is a celebrated quantum phase transition between two topological states. It can be achieved by either sweeping the magnetic field or tuning the carrier density. The recent realization of the quantum anomalous Hall (QAH) insulators with tunable Chern numbers introduces the channel degree of freedom to the dissipation-free chiral edge transport and makes the study of the quantum phase transition between two topological states under zero magnetic field possible. Here, we synthesized the magnetic topological insulator (TI)/TI pentalayer heterostructures with different Cr doping concentrations in the middle magnetic TI layers using molecular beam epitaxy. By performing transport measurements, we found a potential plateau phase transition between C=1 and C=2 QAH states under zero magnetic field. In tuning the transition, the Hall resistance monotonically decreases from h/e^{2} to h/2e^{2}, concurrently, the longitudinal resistance exhibits a maximum at the critical point. Our results show that the ratio between the Hall resistance and the longitudinal resistance is greater than 1 at the critical point, which indicates that the original chiral edge channel from the C=1 QAH state coexists with the dissipative bulk conduction channels. Subsequently, these bulk conduction channels appear to self-organize and form the second chiral edge channel in completing the plateau phase transition. Our study will motivate further investigations of this novel Chern number change-induced quantum phase transition and advance the development of the QAH chiral edge current-based electronic and spintronic devices.

Ultrahigh efficient spin orbit torque magnetization switching in fully sputtered topological insulator and ferromagnet multilayers

Spin orbit torque (SOT) magnetization switching of ferromagnets with large perpendicular magnetic anisotropy has a great potential for the next generation non-volatile magnetoresistive random-access memory (MRAM). It requires a high performance pure spin current source with a large spin Hall angle and high electrical conductivity, which can be fabricated by a mass production technique. In this work, we demonstrate ultrahigh efficient and robust SOT magnetization switching in fully sputtered BiSb topological insulator and perpendicularly magnetized Co/Pt multilayers. Despite fabricated by the magnetron sputtering instead of the laboratory molecular beam epitaxy, the topological insulator layer, BiSb, shows a large spin Hall angle of θSH = 10.7 and high electrical conductivity of σ = 1.5 × 105 Ω-1 m-1. Our results demonstrate the feasibility of BiSb topological insulator for implementation of ultralow power SOT-MRAM and other SOT-based spintronic devices.

Quantum transport and potential of topological states for thermoelectricity in Bi2Te3thin films

This paper reviews recent developments in quantum transport and it presents current efforts to explore the contribution of topological insulator boundary states to thermoelectricity in Bi₂Te₃thin films. Although Bi₂Te₃has been used as a thermoelectric material for many years, it is only recently that thin films of this material have been synthesized as 3D topological insulators with interesting physics and potential applications related to topologically protected surface states. A major bottleneck in Bi₂Te₃thin films has been eliminating its bulk conductivity while increasing its crystal quality. The ability to grow epitaxial films with high crystal quality and to fabricate sophisticated Bi₂Te₃-based devices is attractive for implementing a variety of topological quantum devices and exploring the potential of topological states to improve thermoelectric properties. Special emphasis is laid on preparing low-defect-density Bi₂Te₃epitaxial films, gate-tuning of normal-state transport and Josephson supercurrent in topological insulator/superconductor hybrid devices. Prospective quantum transport experiments on Bi₂Te₃thin-film devices are discussed as well. Finally, an overview of current progress on the contribution of topological insulator boundary states to thermoelectricity is presented. Future explorations to reveal the potential of topological states for improving thermoelectric properties of Bi₂Te₃films and realizing high-performance thermoelectric devices are discussed.

Nonreciprocal Transport in a Bilayer of MnBi2Te4 and Pt

MnBi₂Te₄ (MBT) is the first intrinsic magnetic topological insulator with the interaction of spin-momentum locked surface electrons and intrinsic magnetism, and it exhibits novel magnetic and topological phenomena. Recent studies suggested that the interaction of electrons and magnetism can be affected by the Mn-doped Bi₂Te₃ phase at the surface due to inevitable structural defects. Here, we report an observation of nonreciprocal transport, that is, current-direction-dependent resistance, in a bilayer composed of antiferromagnetic MBT and nonmagnetic Pt. The emergence of the nonreciprocal response below the Néel temperature confirms a correlation between nonreciprocity and intrinsic magnetism in the surface state of MBT. The angular dependence of the nonreciprocal transport indicates that nonreciprocal response originates from the asymmetry scattering of electrons at the surface of MBT mediated by magnon. Our work provides an insight into nonreciprocity arising from the correlation between magnetism and Dirac surface electrons in intrinsic magnetic topological insulators.

Theory of unidirectional magnetoresistance and nonlinear Hall effect

We study the unidirectional magnetoresistance (UMR) and the nonlinear Hall effect (NLHE) in the ferromagnetic Rashba model. For this purpose we derive expressions to describe the response of the electric current quadratic in the applied electric field. We compare two different formalisms, namely the standard Keldysh nonequilibrium formalism and the Moyal-Keldysh formalism, to derive the nonlinear conductivities of UMR and NLHE. We find that both formalisms lead to identical numerical results when applied to the ferromagnetic Rashba model. The UMR and the NLHE nonlinear conductivities tend to be comparable in magnitude according to our calculations. Additionally, their dependencies on the Rashba parameter and on the quasiparticle broadening are similar. The nonlinear zero-frequency response considered here is several orders of magnitude higher than the one at optical frequencies that describes the photocurrent generation in the ferromagnetic Rashba model. Additionally, we compare our Keldysh nonequilibrium expression in the independent-particle approximation to literature expressions of the UMR that have been obtained within the constant relaxation time approximation of the Boltzmann formalism. We find that both formalisms converge to the same analytical formula in the limit of infinite relaxation time. However, remarkably, we find that the Boltzmann result does not correspond to the intraband term of the Keldysh expression. Instead, the Boltzmann result corresponds to the sum of the intraband term and an interband term that can be brought into the form of an effective intraband term due to thef-sum rule.

Magnetic memory driven by topological insulators

Giant spin-orbit torque (SOT) from topological insulators (TIs) provides an energy efficient writing method for magnetic memory, which, however, is still premature for practical applications due to the challenge of the integration with magnetic tunnel junctions (MTJs). Here, we demonstrate a functional TI-MTJ device that could become the core element of the future energy-efficient spintronic devices, such as SOT-based magnetic random-access memory (SOT-MRAM). The state-of-the-art tunneling magnetoresistance (TMR) ratio of 102% and the ultralow switching current density of 1.2 × 10⁵ A cm⁻² have been simultaneously achieved in the TI-MTJ device at room temperature, laying down the foundation for TI-driven SOT-MRAM. The charge-spin conversion efficiency θ_SH in TIs is quantified by both the SOT-induced shift of the magnetic switching field (θ_SH = 1.59) and the SOT-induced ferromagnetic resonance (ST-FMR) (θ_SH = 1.02), which is one order of magnitude larger than that in conventional heavy metals. These results inspire a revolution of SOT-MRAM from classical to quantum materials, with great potential to further reduce the energy consumption.

It remains challenging to integrate topological insulators (TI) with magnetic tunnel junctions (MTJ) for spintronics applications. Here, the authors achieve a large tunneling magnetoresistance ratio and a low switching current density in a TI-MTJ device at room temperature, very promising for TI-driven magnetic memory.

Spin-Orbit Torque in Van der Waals-Layered Materials and Heterostructures

Spin-orbit torque (SOT) opens an efficient and versatile avenue for the electrical manipulation of magnetization in spintronic devices. The enhancement of SOT efficiency and reduction of power consumption are key points for the implementation of high-performance SOT devices, which strongly rely on the spin-orbit coupling (SOC) strength and magnetic properties of ferromagnetic/non-magnetic heterostructures. Recently, van der Waals-layered materials have shown appealing properties for use in efficient SOT applications. On the one hand, transition-metal dichalcogenides, topological insulators, and graphene-based heterostructures possess appreciable SOC strength. This feature can efficiently converse the charge current into spin current and result in large SOT. On the other hand, the newly discovered layered magnetic materials provide ultra-thin and gate-tunable ferromagnetic candidates for high-performance SOT devices. In this review, the latest advancements of SOT research in various layered materials are summarized. First, a brief introduction of SOT is given. Second, SOT studies of various layered materials and heterostructures are summarized. Subsequently, progresses on SOT-induced magnetization switching are presented. Finally, current challenges and prospects for future development are suggested.

Switching of a Magnet by Spin-Orbit Torque from a Topological Dirac Semimetal

Recent experiments show that topological surface states (TSS) in topological insulators (TI) can be exploited to manipulate magnetic ordering in ferromagnets. In principle, TSS should also exist for other topological materials, but it remains unexplored as to whether such states can also be utilized to manipulate ferromagnets. Herein, current-induced magnetization switching enabled by TSS in a non-TI topological material, namely, a topological Dirac semimetal α-Sn, is reported. The experiments use an α-Sn/Ag/CoFeB trilayer structure. The magnetization in the CoFeB layer can be switched by a charge current at room temperature, without an external magnetic field. The data show that the switching is driven by the TSS of the α-Sn layer, rather than spin-orbit coupling in the bulk of the α-Sn layer or current-produced heating. The switching efficiency is as high as in TI systems. This shows that the topological Dirac semimetal α-Sn is as promising as TI materials in terms of spintronic applications.

Current-induced switching of proximity-induced ferromagnetic surface states in a topological insulator

Electrical manipulation of magnetization could be an essential function for energy-efficient spintronics technology. A magnetic topological insulator, possessing a magnetically gapped surface state with spin-polarized electrons, not only exhibits exotic topological phases relevant to the quantum anomalous Hall state but also enables the electrical control of its magnetic state at the surface. Here, we demonstrate efficient current-induced switching of the surface ferromagnetism in hetero-bilayers consisting of the topological insulator (Bi_1-xSb_x)₂Te₃ and the ferromagnetic insulator Cr₂Ge₂Te₆, where the proximity-induced ferromagnetic surface states play two roles: efficient charge-to-spin current conversion and emergence of large anomalous Hall effect. The sign reversal of the surface ferromagnetic states with current injection is clearly observed, accompanying the nearly full magnetization reversal in the adjacent insulating Cr₂Ge₂Te₆ layer of an optimal thickness range. The present results may facilitate an electrical control of dissipationless topological-current circuits.

Electrical manipulation of magnetization in devices made of topological materials may be an essential route towards future spintronics technology. Here, Mogi et al. show efficient current-induced switching of surface ferromagnetism in hetero-bilayers of topological insulator (Bi_1-xSb_x)₂Te₃ and ferromagnetic insulator Cr₂Ge₂Te₆.

Roadmap of spin-orbit torques

Spin-orbit torque (SOT) is an emerging technology that enables the efficient manipulation of spintronic devices. The initial processes of interest in SOTs involved electric fields, spin-orbit coupling, conduction electron spins and magnetization. More recently interest has grown to include a variety of other processes that include phonons, magnons, or heat. Over the past decade, many materials have been explored to achieve a larger SOT efficiency. Recently, holistic design to maximize the performance of SOT devices has extended material research from a nonmagnetic layer to a magnetic layer. The rapid development of SOT has spurred a variety of SOT-based applications. In this Roadmap paper, we first review the theories of SOTs by introducing the various mechanisms thought to generate or control SOTs, such as the spin Hall effect, the Rashba-Edelstein effect, the orbital Hall effect, thermal gradients, magnons, and strain effects. Then, we discuss the materials that enable these effects, including metals, metallic alloys, topological insulators, two-dimensional materials, and complex oxides. We also discuss the important roles in SOT devices of different types of magnetic layers, such as magnetic insulators, antiferromagnets, and ferrimagnets. Afterward, we discuss device applications utilizing SOTs. We discuss and compare three-terminal and two-terminal SOT-magnetoresistive random-access memories (MRAMs); we mention various schemes to eliminate the need for an external field. We provide technological application considerations for SOT-MRAM and give perspectives on SOT-based neuromorphic devices and circuits. In addition to SOT-MRAM, we present SOT-based spintronic terahertz generators, nano-oscillators, and domain wall and skyrmion racetrack memories. This paper aims to achieve a comprehensive review of SOT theory, materials, and applications, guiding future SOT development in both the academic and industrial sectors.

Current-Induced Spin-Orbit Torques for Spintronic Applications

Control of magnetization in magnetic nanostructures is essential for development of spintronic devices because it governs fundamental device characteristics such as energy consumption, areal density, and operation speed. In this respect, spin-orbit torque (SOT), which originates from the spin-orbit interaction, has been widely investigated due to its efficient manipulation of the magnetization using in-plane current. SOT spearheads novel spintronic applications including high-speed magnetic memories, reconfigurable logics, and neuromorphic computing. Herein, recent advances in SOT research, highlighting the considerable benefits and challenges of SOT-based spintronic devices, are reviewed. First, the materials and structural engineering that enhances SOT efficiency are discussed. Then major experimental results for field-free SOT switching of perpendicular magnetization are summarized, which includes the introduction of an internal effective magnetic field and the generation of a distinct spin current with out-of-plane spin polarization. Finally, advanced SOT functionalities are presented, focusing on the demonstration of reconfigurable and complementary operation in spin logic devices.

The Material Efforts for Quantized Hall Devices Based on Topological Insulators

A topological insulator (TI) is a kind of novel material hosting a topological band structure and plenty of exotic topological quantum effects. Achieving quantized electrical transport, including the quantum Hall effect (QHE) and the quantum anomalous Hall effect (QAHE), is an important aspect of realizing quantum devices based on TI materials. Intense efforts are made in this field, in which the most essential research is based on the optimization of realistic TI materials. Herein, the TI material development process is reviewed, focusing on the realization of quantized transport. Especially, for QHE, the strategies to increase the surface transport ratio and decrease the threshold magnetic field of QHE are examined. For QAHE, the evolution history of magnetic TIs is introduced, and the recently discovered magnetic TI candidates with intrinsic magnetizations are discussed in detail. Moreover, future research perspectives on these novel topological quantum effects are also evaluated.

Strongly Surface State Carrier-Dependent Spin-Orbit Torque in Magnetic Topological Insulators

The topological surface states (TSS) in topological insulators (TIs) can exert strong spin-orbit torque (SOT) on adjacent magnetization, offering great potential in implementing energy-efficient magnetic memory devices. However, there are large discrepancies among the reported spin Hall angle values in TIs, and its temperature dependence still remains elusive. Here, the spin Hall angle in a modulation-doped Cr-Bi_x Sb_{2- x} Te₃ (Cr-BST) film is quantitatively determined via both transport and optic approaches, where consistent results are obtained. A large spin Hall angle of ≈90 in the modulation-doped Cr-BST film is demonstrated at 2.5 K, and the spin Hall angle drastically decreases to 0.3-0.5 as the temperature increases. Moreover, by tuning the top TSS carrier concentration, a competition between the top and bottom TSS in contributing to SOT is observed. The above phenomena can account for the large discrepancies among the previously reported spin Hall angle values and reveal the unique role of TSS in generating SOT.

The spin Hall effect of Bi-Sb alloys driven by thermally excited Dirac-like electrons

We have studied the charge to spin conversion in Bi_1-x Sb _x /CoFeB heterostructures. The spin Hall conductivity (SHC) of the sputter-deposited heterostructures exhibits a high plateau at Bi-rich compositions, corresponding to the topological insulator phase, followed by a decrease of SHC for Sb-richer alloys, in agreement with the calculated intrinsic spin Hall effect of Bi_1-x Sb _x . The SHC increases with increasing Bi_1-x Sb _x thickness before it saturates, indicating that it is the bulk of the alloy that predominantly contributes to the generation of spin current; the topological surface states, if present, play little role. Unexpectedly, the SHC is found to increase with increasing temperature, following the trend of carrier density. These results suggest that the large SHC at room temperature, with a spin Hall efficiency exceeding 1 and an extremely large spin current mobility, is due to increased number of thermally excited Dirac-like electrons in the L valley of the narrow gap Bi_1-x Sb _x alloy.

Resonant Photovoltaic Effect in Doped Magnetic Semiconductors

The rectified nonlinear response of a clean, time-reversal symmetric, undoped semiconductor to an ac electric field includes a well known intrinsic shift current. We show that when Kramers degeneracy is broken, a distinct second order rectified response appears due to Bloch state anomalous velocities in a system with an oscillating Fermi surface. This effect, which we refer to as the resonant photovoltaic effect, produces a resonant galvanic current peak at the interband absorption threshold in doped semiconductors or semimetals with approximate particle-hole symmetry. We evaluate the resonant photovoltaic effect for a model of the surface states of a magnetized topological insulator.

Room-Temperature Spin-Orbit Torque from Topological Surface States

Spin-momentum locked surface states in topological insulators (TIs) provide a promising route for achieving high spin-orbit torque (SOT) efficiency beyond the bulk spin-orbit coupling in heavy metals (HMs). However, in previous works, there is a huge discrepancy among the quantitative SOTs from TIs in various systems determined by different methods. Here, we systematically study the SOT in the TI(HM)/Ti/CoFeB/MgO systems by the same method, and make a conclusive assessment of SOT efficiency for TIs and HMs. Our results demonstrate that TIs show more than one order of magnitude higher SOT efficiency than HMs even at room temperature, at the same time the switching current density as low as 5.2×10^{5}  A cm^{-2} is achieved with (Bi_{1-x}Sb_{x})_{2}Te_{3}. Furthermore, we investigate the relationship between SOT efficiency and the position of Fermi level in (Bi_{1-x}Sb_{x})_{2}Te_{3}, where the SOT efficiency is significantly enhanced near the Dirac point, with the most insulating bulk and conducting surface states, indicating the dominating SOT contribution from topological surface states. This work unambiguously demonstrates the ultrahigh SOT efficiency from topological surface states.

Surface state transport in double-gated and magnetized topological insulators with hexagonal warping effects

We explore the scattering of Dirac electrons in a double-gated topological insulator in the presence of magnetic proximity effects and warped surface states. It is found that a magnetic field can shift the Dirac cone in momentum space and deform the constant-energy contour, or opens up a band gap at the Dirac point, depending on the magnetization orientation. The double gate voltage induces quantum wells and/or quantum barriers on the surface of topological insulators, generating surface resonant tunnelling states. It is found that the hexagonal warping effect can increase the electronic transport at high energies when the constant-energy contour exhibits a snowflake shape. The energy-dependent conductances in the parallel and antiparallel magnetic configurations exhibit out-of-phase oscillations due to the quantum interference of propagating waves in the region between the two magnetized segments. Although the conductance spectrum of the double-well structure is higher than that of the double-barrier structure, the magnetoresistance ratio versus the separation distance between the two magnetized barriers exhibits pronounced oscillations due to the resonant tunnelling states. We show that the surface state transport can be controlled by the exchange field and gate voltage without breaking time reversal symmetry, suggesting that the double gated and magnetized topological insulators can be utilized to achieve a large magnetoresistance ratio with a tunable sign.

Spin-Orbit Torque Switching of a Nearly Compensated Ferrimagnet by Topological Surface States

Utilizing spin-orbit torque (SOT) to switch a magnetic moment provides a promising route for low-power-dissipation spintronic devices. Here, the SOT switching of a nearly compensated ferrimagnet Gd_x (FeCo)_{1- x} by the topological insulator [Bi₂ Se₃ and (BiSb)₂ Te₃ ] is investigated at room temperature. The switching current density of (BiSb)₂ Te₃ (1.20 × 10⁵ A cm^-2 ) is more than one order of magnitude smaller than that in conventional heavy-metal-based structures, which indicates the ultrahigh efficiency of charge-spin conversion (>1) in topological surface states. By tuning the net magnetic moment of Gd_x (FeCo)_{1- x} via changing the composition, the SOT efficiency has a significant enhancement (6.5 times) near the magnetic compensation point, and at the same time the switching speed can be as fast as several picoseconds. Combining the topological surface states and the nearly compensated ferrimagnets provides a promising route for practical energy-efficient and high-speed spintronic devices.

Magnetization switching using topological surface states

Topological surface states (TSSs) in a topological insulator are expected to be able to produce a spin-orbit torque that can switch a neighboring ferromagnet. This effect may be absent if the ferromagnet is conductive because it can completely suppress the TSSs, but it should be present if the ferromagnet is insulating. This study reports TSS-induced switching in a bilayer consisting of a topological insulator Bi₂Se₃ and an insulating ferromagnet BaFe₁₂O₁₉. A charge current in Bi₂Se₃ can switch the magnetization in BaFe₁₂O₁₉ up and down. When the magnetization is switched by a field, a current in Bi₂Se₃ can reduce the switching field by ~4000 Oe. The switching efficiency at 3 K is 300 times higher than at room temperature; it is ~30 times higher than in Pt/BaFe₁₂O₁₉. These strong effects originate from the presence of more pronounced TSSs at low temperatures due to enhanced surface conductivity and reduced bulk conductivity.

Nonlinear Planar Hall Effect

An intriguing property of a three-dimensional (3D) topological insulator (TI) is the existence of surface states with spin-momentum locking, which offers a new frontier of exploration in spintronics. Here, we report the observation of a new type of Hall effect in a 3D TI Bi_{2}Se_{3} film. The Hall resistance scales linearly with both the applied electric and magnetic fields and exhibits a π/2 angle offset with respect to its longitudinal counterpart, in contrast to the usual angle offset of π/4 between the linear planar Hall effect and the anisotropic magnetoresistance. This novel nonlinear planar Hall effect originates from the conversion of a nonlinear transverse spin current to a charge current due to the concerted actions of spin-momentum locking and time-reversal symmetry breaking, which also exists in a wide class of noncentrosymmetric materials with a large span of magnitude. It provides a new way to characterize and utilize the nonlinear spin-to-charge conversion in a variety of topological quantum materials.

Unidirectional Magneto-Resistance in Modulation-Doped Magnetic Topological Insulators

Nonlinear unidirectional spin Hall magnetoresistance (USMR) has been reported in heavy metal/ferromagnet bilayers, which could be employed as an effective method in detecting the magnetization orientation in spintronic devices with two-terminal geometry. Recently, another unidirectional magnetoresistance (UMR) was reported in magnetic topological insulator (TI)-based heterostructures at cryogenic temperature, whose amplitude is orders of magnitude larger than the USMR measured in heavy metal-based magnetic heterostructures at room temperature. Here, we report the UMR effect in the modulation-doped magnetic TI structures. This UMR arises due to the interplay between the magnetic dopant's magnetization and the current-induced surface spin polarization, when they are parallel or antiparallel to each other in the TI material. By varying the dopant's position in the structure, we reveal that the UMR is mainly originating from the interaction between the magnetization and the surface spin-polarized carriers (not bulk carriers). Furthermore, from the magnetic field-, the angular rotation-, and the temperature-dependence, we highlight the correlation between the UMR effect and the magnetism in the structures. The large UMR versus current ratio in TI-based magnetic bilayers promises the easy readout in TI-based spintronic devices with two-terminal geometry.

Current-driven magnetization switching in ferromagnetic bulk Rashba semiconductor (Ge,Mn)Te

Multiferroic materials with both ferroelectric and ferromagnetic orders provide a promising arena for the electrical manipulation of magnetization through the mutual correlation between those ferroic orders. Such a concept of multiferroics may expand to semiconductor with both broken symmetries of spatial inversion and time reversal, that is, polar ferromagnetic semiconductors. Here, we report the observation of current-driven magnetization switching in one such example, (Ge,Mn)Te thin films. The ferromagnetism caused by Mn doping opens an exchange gap in original massless Dirac band of the polar semiconductor GeTe with Rashba-type spin-split bands. The anomalous Hall conductivity is enhanced with increasing hole carrier density, indicating that the contribution of the Berry phase is maximized as the Fermi level approaches the exchange gap. By means of pulse-current injection, the electrical switching of the magnetization is observed in the (Ge,Mn)Te thin films as thick as 200 nm, pointing to the Rashba-Edelstein effect of bulk origin. The efficiency of this effect strongly depends on the Fermi-level position owing to the efficient spin accumulation at around the gap. The magnetic bulk Rashba system will be a promising platform for exploring the functional correlations among electric polarization, magnetization, and current.

Ultrafast Spin-to-Charge Conversion at the Surface of Topological Insulator Thin Films

Strong spin-orbit coupling, resulting in the formation of spin-momentum-locked surface states, endows topological insulators with superior spin-to-charge conversion characteristics, though the dynamics that govern it have remained elusive. Here, an all-optical method is presented, which enables unprecedented tracking of the ultrafast dynamics of spin-to-charge conversion in a prototypical topological insulator Bi₂ Se₃ /ferromagnetic Co heterostructure, down to the sub-picosecond timescale. Compared to pure Bi₂ Se₃ or Co, a giant terahertz emission is observed in the heterostructure that originates from spin-to-charge conversion, in which the topological surface states play a crucial role. A 0.12 ps timescale is identified that sets a technological speed limit of spin-to-charge conversion processes in topological insulators. In addition, it is shown that the spin-to-charge conversion efficiency is temperature independent in Bi₂ Se₃ as expected from the nature of the surface states, paving the way for designing next-generation high-speed optospintronic devices based on topological insulators at room temperature.

Spin-momentum locking and spin-orbit torques in magnetic nano-heterojunctions composed of Weyl semimetal WTe2

Spin–orbit torque has recently been intensively investigated for the purposes of manipulating the magnetization in magnetic nano-devices and understanding fundamental physics. Therefore, the search for novel materials or material combinations that exhibit a strong enough spin-torque effect has become one of the top priorities in this field of spintronics. Weyl semimetal, a new topological material that features open Fermi arc with strong spin–orbit coupling and spin–momentum locking effect, is naturally expected to exhibit an enhanced spin-torque effect in magnetic nano-devices. Here we observe a significantly enhanced spin conductivity, which is associated with the field-like torque at low temperatures. The enhancement is obtained in the b-axis WTe₂/Py bilayers of nano-devices but not observed in the a-axis of WTe₂/Py nano-devices, which can be ascribed to the enhanced spin accumulation by the spin–momentum locking effect of the Fermi arcs of the Weyl semimetal WTe₂.

The Fermi arcs, topological surface states of Weyl semimetals can enable the intriguing spin control and facilitate topological spintronics. Here the authors report the spin-orbit torque at the interface of WTe₂/Py and attribute it to the enhanced spin accumulation by the spin-momentum locking effect of the Fermi arcs of WTe₂.

Origins of the Unidirectional Spin Hall Magnetoresistance in Metallic Bilayers

Recent studies evidenced the emergence of asymmetric electron transport in layered conductors owing to the interplay between electrical conductivity, magnetization, and the spin Hall or Rashba-Edelstein effects. Here, we investigate the unidirectional magnetoresistance (UMR) caused by the current-induced spin accumulation in Co/Pt and CoCr/Pt bilayers. We identify three competing mechanisms underpinning the resistance asymmetry, namely, interface and bulk spin-dependent electron scattering and electron-magnon scattering. Our measurements provide a consistent description of the current, magnetic field, and temperature dependence of the UMR and show that both positive and negative UMR can be obtained by tuning the interface and bulk spin-dependent scattering.

Current-induced dynamics of skyrmion strings

Dynamics of string-like objects is an important issue in a broad range of physical systems, including vortex lines in superconductors, viscoelastic polymers, and superstrings in elementary particle physics. In noncentrosymmetric magnets, string forms of magnetic skyrmions are present as topological spin objects, and their current-induced dynamics has recently attracted intense interest. We show in the chiral magnet MnSi that the current-induced deformation dynamics of skyrmion strings results in transport response associated with the real-space Berry phase. Prominent nonlinear Hall signals emerge above the threshold current only in the skyrmion phase. We clarify the mechanism for these nonlinear Hall signals by adopting spin density wave picture to describe the moving skyrmion lattice; deformation of skyrmion strings occurs in an asymmetric manner due to the Dzyaloshinskii-Moriya interaction, which leads to the nonreciprocal nonlinear Hall response originating from an emergent electromagnetic field. This finding reveals the dynamical nature of string-like objects and consequent transport outcomes in noncentrosymmetric systems.

Field-Free Programmable Spin Logics via Chirality-Reversible Spin-Orbit Torque Switching

Spin-orbit torque (SOT)-induced magnetization switching exhibits chirality (clockwise or counterclockwise), which offers the prospect of programmable spin-logic devices integrating nonvolatile spintronic memory cells with logic functions. Chirality is usually fixed by an applied or effective magnetic field in reported studies. Herein, utilizing an in-plane magnetic layer that is also switchable by SOT, the chirality of a perpendicular magnetic layer that is exchange-coupled with the in-plane layer can be reversed in a purely electrical way. In a single Hall bar device designed from this multilayer structure, three logic gates including AND, NAND, and NOT are reconfigured, which opens a gateway toward practical programmable spin-logic devices.

Direct visualization of current-induced spin accumulation in topological insulators

Charge-to-spin conversion in various materials is the key for the fundamental understanding of spin-orbitronics and efficient magnetization manipulation. Here we report the direct spatial imaging of current-induced spin accumulation at the channel edges of Bi2Se3 and BiSbTeSe2 topological insulators as well as Pt by a scanning photovoltage microscope at room temperature. The spin polarization is along the out-of-plane direction with opposite signs for the two channel edges. The accumulated spin direction reverses sign upon changing the current direction and the detected spin signal shows a linear dependence on the magnitude of currents, indicating that our observed phenomena are current-induced effects. The spin Hall angle of Bi2Se3, BiSbTeSe2, and Pt is determined to be 0.0085, 0.0616, and 0.0085, respectively. Our results open up the possibility of optically detecting the current-induced spin accumulations, and thus point towards a better understanding of the interaction between spins and circularly polarized light.

Quantized chiral edge conduction on domain walls of a magnetic topological insulator

Electronic ordering in magnetic and dielectric materials forms domains with different signs of order parameters. The control of configuration and motion of the domain walls (DWs) enables nonvolatile responses against minute external fields. Here, we realize chiral edge states (CESs) on the magnetic DWs of a magnetic topological insulator. We design and fabricate the magnetic domains in the quantum anomalous Hall state with the tip of a magnetic force microscope and prove the existence of the chiral one-dimensional edge conduction along the prescribed DWs through transport measurements. The proof-of-concept devices based on reconfigurable CESs and Landauer-Büttiker formalism are realized for multiple-domain configurations with well-defined DW channels. Our results may lead to the realization of low-power-consumption spintronic devices.

Tailoring tricolor structure of magnetic topological insulator for robust axion insulator

Exploration of novel electromagnetic phenomena is a subject of great interest in topological quantum materials. One of the unprecedented effects to be experimentally verified is the topological magnetoelectric (TME) effect originating from an unusual coupling of electric and magnetic fields in materials. A magnetic heterostructure of topological insulator (TI) hosts such exotic magnetoelectric coupling and can be expected to realize the TME effect as an axion insulator. We designed a magnetic TI with a tricolor structure where a nonmagnetic layer of (Bi, Sb)₂Te₃ is sandwiched by a soft ferromagnetic Cr-doped (Bi, Sb)₂Te₃ and a hard ferromagnetic V-doped (Bi, Sb)₂Te₃. Accompanied by the quantum anomalous Hall (QAH) effect, we observe zero Hall conductivity plateaus, which are a hallmark of the axion insulator state, in a wide range of magnetic fields between the coercive fields of Cr- and V-doped layers. The resistance of the axion insulator state reaches as high as 10⁹ ohms, leading to a gigantic magnetoresistance ratio exceeding 10,000,000% upon the transition from the QAH state. The tricolor structure of the TI may not only be an ideal arena for the topologically distinct phenomena but can also provide magnetoresistive applications for advancing dissipation-less topological electronics.