经过几十年对无外磁场条件下无耗散输运的探索，最近在磁性拓扑绝缘体（TI）薄膜中实现了量子反常霍尔效应（QAHE）。然而，QAHE的普适相图及其与量子霍尔效应（QHE）的关系还有待研究。本文报道了在六层五层（Cr0.12Bi0.26Sb0.62）2 Te 3薄膜中，在矫顽场下观察到的巨纵向电阻峰和零霍尔电导平台，并证明了在0.3K温度下，金属-绝缘体在两个相反的QAHE平台态之间的转换.此外，通用QAHE相图是通过角度相关的测量实现的。我们的结果表明，量子相变在QAHE和QHE制度是在同一普适类，但微观细节是不同的。此外，QAHE绝缘态的实现揭示了探索量子相位相关物理和应用的新方法。
英文摘要：
After decades of searching for the dissipationless transport in the absence of any external magnetic field, quantum anomalous Hall effect (QAHE) was recently achieved in magnetic topological insulator (TI) films. However, the universal phase diagram of QAHE and its relation with quantum Hall effect (QHE) remain to be investigated. Here, we report the experimental observation of the giant longitudinal resistance peak and zero Hall conductance plateau at the coercive field in the 6 quintuple-layer (Cr0.12Bi0.26Sb0.62)2Te3 film, and demonstrate the metal-to-insulator switching between two opposite QAHE plateau states up to 0.3 K. Moreover, the universal QAHE phase diagram is realized through the angle-dependent measurements. Our results address that the quantum phase transitions in both QAHE and QHE regimes are in the same universality class, yet the microscopic details are different. In addition, the realization of the QAHE insulating state unveils new ways to explore quantum phase-related physics and applications.
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 all-sputtered BiSb topological insulator - perpendicularly magnetized Co/Pt multilayers. Despite fabricated by the indus…
We analyze the complex impact of the local magnetic spin texture on the transverse Hall-type voltage in device structures utilized to measure magnetoresistance effects. We find a highly localized and asymmetric magnetic sensitivity in the eight-terminal geometries that are frequently used in current-induced switching experiments, for instance to probe antiferromagnetic materials. Using current-induced switching of antiferromagnetic NiO/Pt as an example, we estimate the change in the spin Hall magnetoresistance signal associated with switching events based on the domain switching patterns obser…
Topological insulators (TIs) with spin momentum locked topological surface states (TSS) are expected to exhibit a giant spin-orbit torque (SOT) in the TI/ferromagnet systems. To date, the TI SOT driven magnetization switching is solely reported in a Cr doped TI at 1.9 K. Here, we directly show giant SOT driven magnetization switching in a Bi2Se3/NiFe heterostructure at room temperature captured using a magneto-optic Kerr effect microscope. We identify a large charge to spin conversion efficiency of ~1-1.75 in the thin TI films, where the TSS is dominant. In addition, we find the current densit…
We report a proximity-driven large anomalous Hall effect in all-telluride heterostructures consisting of ferromagnetic insulator Cr2Ge2Te6 and topological insulator (Bi,Sb)2Te3. Despite small magnetization in the (Bi,Sb)2Te3 layer, the anomalous Hall conductivity reaches a large value of 0.2e2/h in accord with a ferromagnetic response of the Cr2Ge2Te6. The results show that the exchange coupling between the surface state of the topological insulator and the proximitized Cr2Ge2Te6 layer is effective and strong enough to open the sizable exchange gap in the surface state.
Spin Hall effect (SHE) induced reversal of perpendicular magnetization has attracted significant interest, due to its potential to lead to low power memory and logic devices. However, the switching requires an assisted in-plane magnetic field, which hampers its practical applications. Here, we introduce a novel approach for external-field-free spin Hall switching of a perpendicular nanomagnet by utilizing a local dipolar field arising from an adjacent in-plane magnetic layer. Robust switching of perpendicular CoFeB nanopillars in a dipole-coupled composite stack is experimentally demonstrated …
The chirality associated with broken time reversal symmetry in magnetically doped topological insulators has important implications to the quantum transport phenomena. Here we report the anomalous Hall effect studies in Mn- and Cr-doped Bi$_2$Te$_3$ topological insulators with varied thickness and doping content. By tracing the chirality of the Hall loops, we find that the Mn-type anomalous Hall effect with clockwise chirality is strengthened by the reduction of film thickness, which is opposite to that of the Cr-type anomalous Hall effect with counterclockwise chirality. We provide a phenomen…
We investigate fast-pulse switching of in-plane-magnetized magnetic tunnel junctions (MTJs) within 3-terminal devices in which spin-transfer torque is applied to the MTJ by the giant spin Hall effect. We measure reliable switching, with write error rates down to $10^{-5}$, using current pulses as short as just 2 ns in duration. This represents the fastest reliable switching reported to date for any spin-torque-driven magnetic memory geometry, and corresponds to a characteristic time scale that is significantly shorter than predicted possible within a macrospin model for in-plane MTJs subject t…
An electric charge near the surface of a topological insulator induces an image magnetic monopole. Here, we show that if the topological insulator surface has a negative curvature, namely in the case of a semispherical cavity, the induced Hall current reverses its rotation as the electric charge crosses the semisphere geometric focus. Such a reversion is shown to be equivalent of inverting the charge of the image magnetic monopole. We also discuss upon the case of a semicylindrical cavity, where Hall current reversion appears to be feasible of probing in realistic experiments.
We quantitatively evaluate a spin anomalous Hall effect (SAHE), generating spin angular momentum flow (spin current, $J_{\rm s}$), in an L1$\rm_{0}$-FePt ferromagnet by exploiting giant magnetoresistance devices with L1$\rm_{0}$-FePt / Cu / Ni$\rm_{81}$Fe$\rm_{19}$ . From the ferromagnetic resonance linewidth modulated by the charge current ($J_{\rm c}$) injection, the spin anomalous Hall angle ($ α_{\rm SAH} $) is obtained to be 0.25 $ \pm $ 0.03. The evaluation of $ α_{\rm SAH} $ at different configurations between $J_{\rm c}$ and magnetization enables us to discuss the symmetry of SAHE and …
Negative capacitance field-effect transistors (NC-FETs) have attracted wide interest as promising candidates for steep-slope devices, and sub-60 mV/decade switching has been demonstrated in NC-FETs with various device structures and material systems. However, the detailed mechanisms of the observed steep-slope switching in some of these experiments are under intense debate. Here we show that sub-60 mV/decade switching can be observed in a WS2 transistor with a metal-insulator-metal-insulator-semiconductor (MIMIS) structure - without any ferroelectric component. This structure resembles an NC-F…
Fundamental research and technological applications of topological insulators are hindered by the rarity of materials exhibiting a robust topologically non-trivial phase, especially in two dimensions. Here, by means of extensive first-principles calculations, we propose a novel quantum spin Hall insulator with a sizeable band gap of $\sim$0.5 eV that is a monolayer of Jacutingaite, a naturally occurring layered mineral first discovered in 2008 in Brazil and recently synthesised. This system realises the paradigmatic Kane-Mele model for quantum spin Hall insulators in a potentially exfoliable t…
Quantized Anomalous Hall Effect in Magnetic Topological Insulators
霍尔效应、反常霍尔效应和自旋霍尔效应分别是由洛伦兹力和自旋轨道耦合引起的固体中的基本输运过程。近年来，人们发现了量子形式的霍尔效应和自旋霍尔效应。然而，量子化反常霍尔（QAH）效应尚未在实验上实现。在QAH绝缘体中，自发磁矩和自旋-轨道耦合结合产生拓扑非平凡的电子结构，导致量子化的霍尔效应而无需任何外部磁场。在这项工作中，基于最先进的第一性原理计算，我们预测的辉碲铋矿半导体Bi $_2$ Te $_3$，Bi $_2$ Se $_3$，和Sb $_2$ Te $_3$形成磁有序的绝缘体时，掺杂过渡金属元素（Cr或Fe），在鲜明对比，传统的稀磁半导体中，自由载流子是必要的调解磁耦合。二维薄膜中的磁序产生了以有限的陈数为特征的拓扑电子结构，具有量子化的霍尔电导$e^{2}/h$。长期追求的QAH绝缘体状态的实验实现可以在室温下实现稳健的无耗散电荷传输。
Magnetization switching by spin-orbit torque (SOT) via spin Hall effect represents as a competitive alternative to that by spin-transfer torque (STT) used for magnetoresistive random access memory (MRAM), as it does not require high-density current to go through the tunnel junction. For perpendicular MRAM, however, SOT driven switching of the free layer requires an external in-plane field, which poses limitation for viability in practical applications. Here we demonstrate field-free magnetization switching of a perpendicular magnet by utilizing an Iridium (Ir) layer. The Ir layer not only prov…
A theoretical formula is derived for the threshold current to switch a perpendicular magnetization in a ferromagnet by the spin Hall effect. The numerical simulation of the Landau-Lifshitz-Gilbert equation indicates that magnetization switching is achieved when the steady-state solution of the magnetization in the presence of the current is outside an energetically unstable region. Based on the numerical result, an analytical theory deriving the threshold current is developed by focusing on the first-order perturbation to the unstable state. The analytical formula clarifies that the magnitude …
A mechanism for phonon Hall effect (PHE) in non-magnetic insulators under an external magnetic field is theoretically studied. PHE is known in (para)magnetic compounds, where the magnetic moments and spin-orbit interaction play an essential role. In sharp contrast, we here show that a non-zero Berry curvature of acoustic phonons is induced by an external magnetic field due to the correction to the adiabatic Born-Oppenheimer approximation. This results in the finite thermal Hall conductivity $κ_H$ in nonmagnetic band insulators. Our estimate of $κ_H$ for a simple model gives $κ_H \sim 1.0\times…
Electrical currents at the surface or edge of a topological insulator are intrinsically spin-polarized. We show that such surface/edge currents can be used to switch the orientation of a molecular magnet weakly coupled to the surface or edge of a topological insulator. For the edge of a two-dimensional topological insulator as well as for the surface of a three-dimensional topological insulator the application of a well-chosen surface/edge current can lead to a complete polarization of the molecule if the molecule's magnetic anisotropy axis is appropriately aligned with the current direction. …
Electric-field control of magnetization dynamics is fundamentally and technologically important for future spintronic devices. Here, based on electric-field control of both magnetic anisotropy and spin--orbit torque, two distinct methods are presented for switching the magnetization in topological insulator (TI)/magnetic-TI hybrid systems. The magnetic anisotropy energy in magnetic TIs is formulated analytically as a function of the Fermi energy, and it is confirmed that the out-of-plane magnetization is always favored for the partially occupied surface band. Also proposed is a transistor-like…
Voltage Controlled Magnetic Anisotropy Based Low Energy Switching of a Ferromagnet on a Topological Insulator
我们提出了一种新的存储器件，它包括一个薄的铁磁层的Fe沉积在拓扑绝缘体薄膜，Bi 2 Se 3。铁磁层具有垂直各向异性，这是由于MgO沉积在Fe的顶面上。当电流在Bi2Se3的表面上通过时，Bi2Se3的表面变为自旋极化，并且在铁磁体中的d电子与在Bi2Se3的表面上传导电流的电子之间发生强交换相互作用。部分电流通过铁磁体分流，这在铁磁体中产生自旋转移力矩。自旋转移力矩和交换相互作用力矩与压控磁各向异性（VCMA）的组合允许铁磁体的超低能量切换。我们进行微磁模拟和预测的顺序为2.5 ns的开关时间和开关能量的顺序为0.45fJ的铁磁位与43kBT的热稳定性。拓扑绝缘体上的垂直各向异性铁磁体的这种超低能量和高速VCM诱导的切换可以用于能量高效的存储器设计。
We study responses to metric perturbation in topological insulator models. In this paper we introduce a novel quantity, Hall viscosity to particle density ratio, which is analogous to the viscosity to entropy ratio suggested by AdS/CFT correspondence. This quantity corresponds to the filling fraction which characterizes the quantum Hall states, and hence it could be discussed in Haldane's zero-field quantum Hall system. We also consider dissipationless viscosity in the time reversal invariant quantum spin Hall system, which is related to a spin current.
A key feature of the topological surface state under a magnetic field is the presence of the zeroth Landau level at the zero energy. Nonetheless, it has been challenging to probe the zeroth Landau level due to large electron-hole puddles smearing its energy landscape. Here, by developing ultra-low-carrier density topological insulator Sb$_2$Te$_3$ films, we were able to reach an extreme quantum limit of the topological surface state and uncover a hidden phase at the zeroth Landau level. First, we discovered an unexpected quantum-Hall-to-insulator-transition near the zeroth Landau level. Then, …
Electronic states with non-trivial topology host a number of novel phenomena with potential for revolutionizing information technology. The quantum anomalous Hall effect provides spin-polarized dissipation-free transport of electrons, while the quantum spin Hall effect in combination with superconductivity has been proposed as the basis for realizing decoherence-free quantum computing. We introduce a new strategy for realizing these effects, namely by hole and electron doping kagome lattice Mott insulators through, for instance, chemical substitution. As an example, we apply this new approach …
Spin Hall effect, an electric generation of spin current, allows for efficient control of magnetization. Recent theory revealed that orbital Hall effect creates orbital current, which can be much larger than spin Hall-induced spin current. However, orbital current cannot directly exert a torque on a ferromagnet, requiring a conversion process from orbital current to spin current. Here, we report two effective methods of the conversion through spin-orbit coupling engineering, which allows us to unambiguously demonstrate orbital-current-induced spin torque, or orbital Hall torque. We find that o…
We study an unconventional quantum Hall effect for the surface states of ultrathin Floquet topological insulators in a perpendicular magnetic field. The resulting band structure is modified by photon dressing and the topological property is governed by the low-energy dynamics of a single surface. An exchange of symmetric and antisymmetric surface states occurs by reversing the light's polarization. We find a novel quantum Hall state in which the zeroth Landau level undergoes a phase transition from a trivial insulator state, with Hall conductivity $σ_{yx}=0$ at zero Fermi energy, to a Hall ins…
The recently introduced classification of two-dimensional insulators in terms of topological crystalline invariants has been applied so far to "obstructed" atomic insulators characterized by a mismatch between the centers of the electronic Wannier functions and the ionic positions. We extend this notion to quantum spin Hall insulators in which the ground state cannot be described in terms of time-reversal symmetric localized Wannier functions. A system equivalent to graphene in all its relevant electronic and topological properties except for a real-space obstruction is identified and studied …
Fundamental insight into the nature of the quantum phase transition from a superconductor to an insulator in two dimensions, or from one plateau to the next or to an insulator in quantum Hall effect, has been revealed through the study of its scaling behavior. Here, we report on the experimental observation of a quantum phase transition from a quantum-anomalous-Hall (QAH) insulator to an Anderson insulator in a magnetic topological insulator by tuning the chemical potential. Our experiment demonstrates the existence of scaling behavior from which we extract the critical exponent for this quant…
We study spin conductivity of the surface states in a thin film of a topological insulator with Kubo formulas. Hybridization between the different sides of the film opens a gap at the Dirac point. We found that in the gapped region spin conductivity remains finite. In the gapless region near the band gap spin conductivity is enhanced. These findings make a thin film of a topological insulator as a promising material for spintronic applications.
