In a time-reversal invariant system, while the anomalous Hall effect identically vanishes in the linear response regime due to the constraint of time-reversal symmetry on the distribution of Berry curvature, a nonlinear Hall effect can emerge in the second-order response regime if the inversion symmetry is broken to allow a nonzero Berry curvature dipole (BCD) on the Fermi surface. In this work, we study the nonlinear Hall effect of the BCD origin in two-dimensional doped insulators and semimetals belonging to the symmetry class AI which has spinless time-reversal symmetry. Despite that the class AI does not host any strong topological insulator phase in two dimensions, we find that they can still be classified as topologically obstructed insulators and trivial insulators if putting certain constraint on the Hamiltonians. When the insulator gets closer to the phase boundary of the two distinct phases, we find that the BCDs will become more prominent if the doping level is located near the band edge. Moreover, when the insulator undergoes a phase transition between the two distinct phases, we find that the BCDs will dramatically change their signs. For the semimetals without inversion symmetry, we find that the BCDs will sharply reverse their signs when the doping level crosses the Dirac points. With the shift of the locations of Dirac points in energy, the critical doping level at which the BCDs sharply reverse their signs will accordingly change. Our study reveals that class AI materials can also have interesting geometrical and topological properties, and remarkable nonlinear Hall effect can also appear in this class of materials even though the spin-orbit coupling is negligible. Our findings broaden the scope of materials to study the nonlinear Hall effect and provide new perspectives for the application of this effect.
The spin Hall effect (SHE) is highly promising for spintronic applications, and the design of materials with large SHE can enable ultra-low power memory technology. Recently, 5d-transition metal oxides have been shown to demonstrate a large SHE. Here we report large values of SHE in four 5d-transition metal anti-perovskites which makes these anti-perovskites promising spintronic materials. We demonstrate that these effects originate in the mixing of dx2-y2 and dxy orbitals caused by spin orbit coupling.
Scaling of spin Hall angle in 3d, 4d and 5d metals from Y3Fe5O12/metal spin pumping
在铁磁/非磁（FM/NM）双层膜中，自旋抽运产生的纯自旋电流在NM中产生逆自旋霍尔效应（ISHE）电压，由此可以提取NM的自旋抽运和输运特性。Y3 Fe 5 O 12（YIG）具有极低的阻尼，是微波器件和铁磁共振（FMR）自旋抽运中重要且广泛应用的FM材料。在这里，我们报告的自旋泵浦从20 nm厚的YIG薄膜到一系列的3d，4d和5d正常金属（Cu，Ag，Ta，W，Pt和Au）与不同的自旋轨道耦合强度的系统研究。从增强吉尔伯特阻尼从FMR线宽和ISHE信号的频率依赖性，自旋霍尔角和YIG/NM界面自旋混合电导定量确定这些金属。自旋霍尔角在很大程度上随原子序数的四次方而变化，证实了自旋轨道耦合在反自旋霍尔效应中的广泛作用。
Surprisingly large inverse spin Hall effect and systematic variation of spin-orbit coupling with d-orbital filling in 3d transition metals
一般认为，自旋轨道耦合（SOC）遵循Z4（原子序数）依赖性，并且仅在重元素中变得重要。因此，考虑到3d过渡金属的小Z，它们的SOC应该可以忽略不计。使用动态自旋泵的Y3 Fe 5 O 12为基础的结构，我们发现了一个系统的演化自旋霍尔角与d-轨道填充在一系列的3d金属，让人想起在5d金属中观察到的行为。特别地，Cr和Ni显示出非常大的自旋霍尔角（Pt的自旋霍尔角的一半），表明d轨道填充而不是Z在3d金属中的自旋霍尔效应（SHE）中起主导作用。这一结果丰富了我们对SHE的理解，拓宽了可用于探索SOC所能实现的丰富现象的材料范围，并为测试过渡金属中自旋轨道耦合的理论模型提供了指导。
The generation of spin and orbital currents is of crucial importance in the field of spin-orbitronics. In this work, using relativistic density functional theory and the Kubo linear-response formalism, we systematically investigate the spin Hall and orbital Hall effects for 40 monoatomic metals. The spin Hall conductivity (SHC) and orbital Hall conductivity (OHC) are computed as a function of the electrochemical potential and the influence of the spin-orbit interaction strength is also investigated. Our calculations predict a rather small OHC in $sp$ metals, but a much larger OHC in $d$-band m…
In a system with inversion symmetry broken, a second-order nonlinear Hall effect can survive even in the presence of time-reversal symmetry. In this work, we show that a giant nonlinear Hall effect can exist in twisted bilayer WTe2 system. The Berry curvature dipole of twisted bilayer WTe2 (θ = 29.4°) can reach up to ~1400 Å, which is much larger than that in previously reported nonlinear Hall systems. In twisted bilayer WTe2 system, there exists abundant band anticrossings and band inversions around the Fermi level, which brings a complicated distribution of Berry curvature, and leading to th…
We study the mechanisms of the spin Hall effect (SHE) and anomalous Hall effect (AHE) in 3$d$ ferromagnetic metals (Fe, Co, permalloy (Ni$_{81}$Fe$_{19}$; Py), and Ni) by varying their resistivities and temperature. At low temperatures where the phonon scattering is negligible, the skew scattering coefficients of the SHE and AHE in Py are related to its spin polarization. However, this simple relation breaks down for Py at higher temperatures as well as for the other ferromagnetic metals at any temperature. We find that, in general, the relation between the SHE and AHE is more complex, with th…
We use temperature-dependent Hall measurements to identify contributions of spin Hall, magnetic proximity, and sublattice effects to the anomalous Hall signal in heavy metal/ferrimagnetic insulator heterostructures with perpendicular magnetic anisotropy. This approach enables detection of both the magnetic proximity effect onset temperature and the magnetization compensation temperature and provides essential information regarding the interfacial exchange coupling. Onset of a magnetic proximity effect yields a local extremum in the temperature-dependent anomalous Hall signal, which occurs at h…
Ferroelectric-like metals are a relatively rare class of materials that have ferroelectric-like distortion and metallic conductivity. LiOsO$_3$ is the first demonstrated and the most investigated ferroelectric-like metal. The presence of free carriers makes them difficult to be studied by traditional ferroelectric techniques. In this paper, using the symmetry analysis and first-principles calculations, we demonstrate that the ferroelectric-like transition of LiOsO$_3$ can be probed by a kind of electrical transport method based on nonlinear Hall effect. The Berry curvature dipole exists in the…
We have performed precise Hall measurements for the ferrotoroidic candidate material UNi4B. Below Neel temperature TN ~ 20 K (corresponding to the ferrotoroidic transition temperature), a Hall voltage becomes finite even at zero field and changes proportional to the square of current density; by contrast, it is almost zero above TN. Moreover, we have found that a current-induced magnetization estimated from our Hall effect measurements is qualitatively consistent with the previous directly measured value. These results provide strong evidence for a magnetoelectric phenomenon uniquely in ferrot…
The theory of the nonlinear Hall effect has been established by I. Sodemann and L. Fu [Phys. Rev. Lett. 115, 216806 (2015)] in a semiclassical framework: therein, the effect appears as a geometrical property of Bloch electrons, originating from their anomalous velocity. Here I present a more general theory, addressing correlated and/or noncrystalline systems as well, where the expressions of both linear and nonlinear Hall conductivities originate from the many-electron anomalous velocity. The independent-electron results are retrieved as special cases.
Spin currents in ferromagnets afford diverse functionalities. We evaluate the extrinsic spin Hall effects of magnetic impurity scattering in ferromagnetic metals. We show that spin-dependent scattering can provide a high spin current polarized perpendicularly to the magnetization direction and is a dominant mechanism in the moderate-conductivity regime. We find that the superposition of the spin-conserve and spin-flip channels causes the spin currents. These findings suggest that optimizing alloy composition is an effective strategy to control the spin Hall effect.
Room temperature intrinsic anomalous Hall effect in disordered half-metallic ferromagnetic quaternary Heusler alloy CoRuFeSi
National Institute of Technology Andhra Pradesh（安得拉邦国立技术学院）；Indian Institute of Technology Hyderabad（海德拉巴印度理工学院）；Institute of Low Temperature and Structure Research, Polish Academy of Sciences（波兰科学院低温结构研究所）；Indian Institute of Technology Kanpur（坎普尔印度理工学院）；UGC-DAE Consortium for Scientific Research, Kolkata Centre（UGC-DAE科学研究中心加尔各答中心）
We report on the determination of the anomalous spin Hall angle in the ferromagnetic metal alloy cobalt-iron (Co$_{25}$Fe$_{75}$, CoFe). This is accomplished by measuring the spin injection/detection efficiency in a multiterminal device with nanowires of platinum (Pt) and CoFe deposited onto the magnetic insulator yttrium iron garnet (Y$_3$Fe$_5$O$_{12}$, YIG). Applying a spin-resistor model to our multiterminal spin transport data, we determine the magnon conductivity in YIG, the spin conductance at the YIG/CoFe interface and finally the anomalous spin Hall angle of CoFe as a function of its …
Detecting the orientation of the Néel vector is a major research topic in antiferromagnetic spintronics. Here we recognize the intrinsic nonlinear Hall effect, which is independent of the relaxation time, as a prominent contribution to the time-reversal-odd second order conductivity and can be used to detect the flipping of the Néel vector. In contrast, the Berry-curvature-dipole-induced nonlinear Hall effect depends linear on relaxation time and is time-reversal-even. We study the intrinsic nonlinear Hall effect in an antiferromagnetic metal: tetragonal CuMnAs, and show that its nonlinear Hal…
The Hall effects comprise one of the oldest but most vital fields in condensed matter physics, and they persistently inspire new findings, such as quantum Hall effects and topological phases of matter. The recently discovered nonlinear Hall effect is a new member of the family of Hall effects. It is characterized as a transverse Hall voltage in response to two longitudinal currents in the Hall measurement, but it does not require time-reversal symmetry to be broken. It has deep connections to symmetry and topology and, thus, opens new avenues by which to probe the spectral, symmetry and topolo…
In transition-metal dichalcogenides, electrons in the K-valleys can experience both Ising and Rashba spin-orbit couplings. In this work, we show that the coexistence of Ising and Rashba spin-orbit couplings leads to a special type of valley Hall effect, which we call spin-orbit coupling induced valley Hall effect. Importantly, near the conduction band edge, the valley-dependent Berry curvatures generated by spin-orbit couplings are highly tunable by external gates and dominate over the intrinsic Berry curvatures originating from orbital degrees of freedom under accessible experimental conditio…
Scattering by multiple scatterers sometimes gives rise to nontrivial consequences such as anomalous Hall effect. We here study a mechanism for anomalous Hall effect which originates from the correlation of nonmagnetic impurities and localized moments; a Hall effect induced by vector spin chirality. Using a scattering theory approach, we study the skew scattering induced by the scattering processes that involve two magnetic moments and a non-magnetic impurity, which is proportional to the vector spin chirality of the spins in the vicinity of the non-magnetic impurity. Furthermore, we show that …
Recently, signatures of nonlinear Hall effects induced by Berry-curvature dipoles have been found in atomically thin 1T'/Td-WTe$_2$. In this work, we show that in strained polar transition-metal dichalcogenides(TMDs) with 2H-structures, Berry-curvature dipoles created by spin degrees of freedom lead to strong nonlinear Hall effects. Under an easily accessible uniaxial strain of order 0.2%, strong nonlinear Hall signals, characterized by a Berry-curvature dipole on the order of 1Å, arise in electron-doped polar TMDs such as MoSSe, and this is easily detectable experimentally. Moreover, the magn…
We predict a nonlinear Hall effect in certain Weyl semimetals with broken inversion symmetry. When the energy dispersions about pairs of Weyl nodes are skewed -- the Weyl cones are "tilted" -- the concerted actions of the anomalous velocity and the chiral anomaly give rise to the nonlinear Hall effect. This Hall conductivity is linear in both electric and magnetic fields, and depends critically on the tilting of the Weyl cones. We also show that this effect does not rely on a finite Berry curvature dipole, in contrast to the intrinsic quantum nonlinear Hall effect that was recently observed in…
Under broken time reversal symmetry such as in the presence of external magnetic field or internal magnetization, a transverse voltage can be established in materials perpendicular to both longitudinal current and applied magnetic field, known as classical Hall effect. However, this symmetry constraint can be relaxed in the nonlinear regime, thereby enabling nonlinear anomalous Hall current in time-reversal invariant materials - an underexplored realm with exciting new opportunities beyond classical linear Hall effect. Here, using group theory and first-principles theory, we demonstrate a rema…
The orbital Hall effect provides an alternative means to the spin Hall effect to convert a charge current into a flow of angular momentum. Recently, compelling signatures of orbital Hall effects have been identified in 3d transition metals. Here, we report a systematic study of the generation, transmission, and conversion of orbital currents in heterostructures comprising 3d, 5d, and 4f metals. We show that the orbital Hall conductivity of Cr reaches giant values of the order of 5*10^5 Ohm^{-1} m^{-1} and that Pt presents a strong orbital Hall effect in addition to the spin Hall effect. Measur…
