The family of topological Hall effects for electrons in skyrmion crystals

Hall effects of electrons can be produced by an external magnetic field, spin–orbit coupling or a topologically non-trivial spin texture. The topological Hall effect (THE) – caused by the latter – is commonly observed in magnetic skyrmion crystals. Here, we show analogies of the THE to the conventional Hall effect (HE), the anomalous Hall effect (AHE), and the spin Hall effect (SHE). In the limit of strong coupling between conduction electron spins and the local magnetic texture the THE can be described by means of a fictitious, “emergent” magnetic field. In this sense the THE can be mapped onto the HE caused by an external magnetic field. Due to complete alignment of electron spin and magnetic texture, the transverse charge conductivity is linked to a transverse spin conductivity. They are disconnected for weak coupling of electron spin and magnetic texture; the THE is then related to the AHE. The topological equivalent to the SHE can be found in antiferromagnetic skyrmion crystals. We substantiate our claims by calculations of the edge states for a finite sample. These states reveal in which situation the topological analogue to a quantized HE, quantized AHE, and quantized SHE can be found.     

A field theoretical approach to the anomalous hall effect in semiconductors

The anomalous Hall effect for polarized electrons in semiconductors is calculated by a field theoretical method. The results obtained are essentially equivalent to those of Luttinger except for minor generalizations (the treatment of collisions is not limited to the first term in a Born expansion and the conductivity is calculated at finite frequency). The main purpose is to set a very simple formulation that can be used to treat more complicated problems, e.g. anomalous Hall effect in the presence of a magnetic field or with a resonant precessing spin magnetization. The existence of two distinct contributions to the anomalous Hall effect is clearly shown, one of which is missed in the transport equation formulation. The order of magnitude of each contribution is discussed for two different experimental situations.     

Anisotropic hysteretic Hall effect and magnetic control of chiral domains in the chiral spin states of Pr2Ir2O7

We uncover a strong anisotropy in both the anomalous Hall effect (AHE) and the magnetoresistance of the chiral spin states of Pr(2)Ir(2)O(7). The AHE appearing below 1.5 K at a zero magnetic field shows hysteresis which is most pronounced for fields cycled along the [111] direction. This hysteresis is compatible with the field-induced growth of domains composed by the 3-in 1-out spin states which remain coexisting with the 2-in 2-out spin ice manifold once the field is removed. Only for fields applied along the [111] direction, we observe a large positive magnetoresistance and Shubnikov-de Haas oscillations above a metamagnetic critical field. These observations suggest the reconstruction of the electronic structure of the conduction electrons by the field-induced spin texture.     

Topological Hall effect in pyrochlore lattice with varying density of spin chirality

The three-site spin correlation, S(i)·(S(j)×S(k)) on the neighboring triangular sites i, j and k, termed scalar spin chirality, can endow the conduction electron with a quantum Berry phase and resultant transverse (Hall) transport. The paramagnetic barely metallic state was prepared in hole-doped Y2Mo2O7 with pyrochlore lattice using a high-pressure synthesis method, which is further endowed with the spin chirality by partially replacing Y site with Tb (content x). The local spin chirality formed by the adjacent three Tb Ising moments on the pyrochlore lattice can couple to the conduction electrons to give rise to the topological Hall effect whose magnitude increases in proportion to x3 or the density of the Tb-moment triangular clusters.     

Skyrmion strings and the anomalous Hall effect in CrO2

Topological (or singularity point) defects are thought to play a crucial role in the phase transitions of 3D spin systems, as they do in such 2D systems as the XY model. In double-exchange ferromagnets the conduction electrons are strongly coupled with core spins through Hund's rule, and, in the presence of a nontrivial spin texture, acquire a Berry phase contribution to the anomalous Hall effect. We combine Hall effect and magnetization data on CrO2 with a thermodynamical scaling hypothesis to confirm that the critical behavior of the topological-spin-defect density is consistent with that of the heat capacity. This analysis is the first experimental confirmation of the topological character of critical fluctuations.     

自旋轨道耦合系统中的自旋流与自旋霍尔效应

作为自旋电子学的重要研究内容,如何在固态系统中产生、操控以及探测自旋流引起了研究人员的广泛兴趣.基于自旋轨道耦合的自旋霍尔效应为在非磁性半导体中产生自旋流提供了一种有效途径.然而,在具有自旋轨道耦合的系统中,自旋流并不守恒.如何理解这点并恰当地表述相应的连续性方程,成为自旋输运研究的基本问题之一.本文主要综述自旋轨道耦合系统中自旋流与自旋霍尔效应方面的研究进展.引入SU(2)规范势后,自旋流满足协变形式的连续性方程,该方程保证了SU(2)Kubo公式在不同规范固定下的自洽性.利用SU(2)场强张量,可以直接得到自旋密度和自旋流在SU(2)外场中受到的白旋力,该力在只有U(1)磁场时对应于Stern-Gerlach力.由于依赖杂质散射的外在自旋霍尔效应很难被利用,内在自旋霍尔效应的概念被提出:在非磁半导体中,U(1)电场会诱导出自旋流并导致系统边缘处的自旋积累.自旋霍尔效应已经在半导体和金属材料中被观察到.虽然在干净的二维电子气中自旋霍尔电导率是一普适常数e/8π,但杂质对它的影响却引起了人们的高度关注.通过引入退相干效应,自旋霍尔效应中杂质效应的一些令人困惑的理论结果,则得到清晰的解释.此外,本文还将介绍具有层间隧穿的双层二维电子气中的自旋输运现象.在能量简并点附近,自旋霍尔电导率和隧穿白旋电导率均会出现共振现象.当两层间的杂质势强度存在差异时,隧穿自旋电导率随门压的变化曲线呈现出非对称性,显示出自旋二极管效应.     

自旋轨道耦合系统中的自旋流与自旋霍尔效应

作为自旋电子学的重要研究内容,如何在固态系统中产生、操控以及探测自旋流引起了研究人员的广泛兴趣。基于自旋轨道耦合的自旋霍尔效应为在非磁性半导体中产生自旋流提供了一种有效途径。然而,在具有自旋轨道耦合的系统中,自旋流并不守恒。如何理解这点并恰当地表述相应的连续性方程,成为自旋输运研究的基本问题之一。本文主要综述自旋轨道耦合系统中自旋流与自旋霍尔效应方面的研究进展。引入SU(2)规范势后,自旋流满足协变形式的连续性方程,该方程保证了SU(2)Kubo公式在不同规范固定下的自洽性。利用SU(2)场强张量,可以直接得到自旋密度和自旋流在SU(2)外场中受到的自旋力,该力在只有U(1)磁场时对应于Stern-Gerlach力。由于依赖杂质散射的外在自旋霍尔效应很难被利用,内在自旋霍尔效应的概念被提出:在非磁半导体中,U(1)电场会诱导出自旋流并导致系统边缘处的自旋积累。自旋霍尔效应已经在半导体和金属材料中被观察到。虽然在干净的二维电子气中自旋霍尔电导率是一普适常数e/8π,但杂质对它的影响却引起了人们的高度关注。通过引入退相干效应,自旋霍尔效应中杂质效应的一些令人困惑的理论结果,则得到清晰的解释。此外,本文还将介绍具有层间隧穿的双层二维电子气中的自旋输运现象。在能量简并点附近,自旋霍尔电导率和隧穿自旋电导率均会出现共振现象。当两层间的杂质势强度存在差异时,隧穿自旋电导率随门压的变化曲线呈现出非对称性,显示出自旋二极管效应。     

Topological Hubbard model and its high-temperature quantum Hall effect

The quintessential two-dimensional lattice model that describes the competition between the kinetic energy of electrons and their short-range repulsive interactions is the repulsive Hubbard model. We study a time-reversal symmetric variant of the repulsive Hubbard model defined on a planar lattice: Whereas the interaction is unchanged, any fully occupied band supports a quantized spin Hall effect. We show that at 1/2 filling of this band, the ground state develops spontaneously and simultaneously Ising ferromagnetic long-range order and a quantized charge Hall effect when the interaction is sufficiently strong. We ponder on the possible practical applications, beyond metrology, that the quantized charge Hall effect might have if it could be realized at high temperatures and without external magnetic fields in strongly correlated materials.     

Strong orbital exchange scattering in (La1−xNdx)Sn3

In the dilute alloys (La_1-xNd_x)Sn₃ a large anomalous contribution to the zero field Hall constant has been found, which is proportional to the magnetic susceptibility of the Nd³⁺ ions. On the other hand no corresponding effect appears in (La_1-xGd_x)Sn₃. We conclude that the observed anomalous Hall effect is due to the orbital exchange scattering of the conduction electrons by the Nd-impurities. The coupling energy of this interaction is found to be of the same order of magnitude or even larger than that of the isotropic spin exchange interaction     

Intrinsic spin hall effect induced by quantum phase transition in HgCdTe quantum wells

The spin Hall effect can be induced by both extrinsic impurity scattering and intrinsic spin-orbit coupling in the electronic structure. The HgTe/CdTe quantum well has a quantum phase transition where the electronic structure changes from normal to inverted. We show that the intrinsic spin Hall effect of the conduction band vanishes on the normal side, while it is finite on the inverted side. By tuning the Cd content, the well width, or the bias electric field across the quantum well, the intrinsic spin Hall effect can be switched on or off and tuned into resonance under experimentally accessible conditions.     

Two-dimensional transport and strong spin-orbit interaction in SrMnSb_2

We have carried out magneto-transport measurements for single crystal SrMnSb_2. Clear Shubnikov-de Haas oscillations were resolved at relatively low magnetic field around 4 T, revealing a quasi-2D Fermi surface. We observed a development of quantized plateaus in Hall resistance(R_(xy)) at high pulsed fields up to 60 T. Due to the strong 2D confinement and layered properties of the samples, we interpreted the observation as bulk quantum Hall effect that is contributed by the parallel 2D conduction channels. Moreover, the spin degeneracy was lifted leading to Landau level splitting. The presence of anisotropic g factor and the formation of the oscillation beating pattern reveal a strong spin-orbit interaction in the SrMnSb_2 system.     

The lattices with the continuous vorticity as a model for fractional quantum hall effect

It was shown that the including spin of 2d electrons at high magnetic field is possible to remove the divergences in the cores of the vortex lattice and construct the topologically stable states. These states can be considered as the lattices of skyrmions where the unit cell is mapped on the whole sphere of spin directions. That gives the gapped ground state for electrons and can be used as a model for fractional quantum Hall effect.     

Charge Hall effect generated by spin-polarized current injected into Rashba spin orbit coupling media

Using the Keldysh Green’s function method, we study theoretically the electron accumulation induced by the inverse spin Hall effect in a spin valve structure in which a clean quantum wire formed from a 2D electron gas (2DEG) with Rashba/Dresselahaus spin orbit interaction (SOI) is connected to two ferromagnet electrodes. In a nonequilibrium situation when a spin current with an out-of plane (the 2DEG plane) spin polarization is driven through the SOI region by an external voltage, non-equilibrium electron accumulation or a Hall voltage forms at the two lateral sides of the quantum wire and exhibits an oscillation along the wire like the Rashba spin precession; the magnetization directions of FMs affect the Hall voltage and their parallel or antiparallel alignment along the normal direction of the 2DEG plane is most favorable to the Hall voltage. In an equilibrium situation, two planar magnetizations which are not collinear can generate an electron accumulation/a Hall voltage too. When one of the FM electrodes is replaced by a normal metal (NM), the electron accumulation is still present along the wire and its magnitude remains nearly unchanged in the biased case, whereas in the unbiased case it is reduced significantly and even vanishes.     

Optical polarization of nuclei and ODNMR in GaAs/AlGaAs quantum wells

Optical orientation of electrons was used to polarize the crystal lattice nuclei in quantum-size heterostructures and to study the effect of the conduction band spin splitting on the spin states of quasi-two-dimensional (2D) electrons drifting in an external electric field. High (～1%) nuclear polarization was registered using polarized luminescence and ODNMR in single GaAs/AlGaAs quantum wells. Measurement was made of the hyperfine interaction fields created by polarized nuclei on electrons and by electrons on nuclei. The spin-lattice relaxation of nuclei on the non-degenerate 2D electron gas was calculated. A comparison of the theoretical and experimental longitudinal relaxation times permitted the conclusion that the localized charge carriers are responsible for nuclear polarization in quantum wells in the temperature range of 2–77 K. A new effect has been studied, i.e. induction of an effective magnetic field acting on 2D electron spins when electrons drift in an external electric field in the quantum well plane. This effective field B_eff is due to the spin splitting of the conduction band of 2D electrons. The paper discusses possible registration of an ODNMR signal when the field B_eff is modulated by an electric current during optical orientation.     

半导体中自旋轨道耦合及自旋霍尔效应

本文主要评述和介绍半导体微结构中自旋轨道耦合的研究和最近的研究进展。我们细致地讨论了半导体微结构中自旋轨道耦合的物理起源和窄带隙半导体量子阱中的自旋霍尔效应。我们发现目前国际上广泛采用的线性Rashba模型在较大的电子平面波矢处失效:即自旋轨道耦合导致的能带自旋劈裂不再随电子波矢的增加而增加,而是开始下降,即出现强烈的非线性行为。这种非线性的行为起源于导带和价带间耦合的减弱。这种非线性行为还会导致电子的D’yakonov-Perel’自旋弛豫速率在较高能量处下降,与线性模型的结果完全相反。在此基础上,我们构造统一描述电子和空穴自旋霍尔效应的理论框架。我们的方法可以非微扰地计入自旋轨道耦合对本征自旋霍尔效应的影响。我们将此方法应用于强自旋轨道耦合的情形,即窄带隙CdHgTe/CdTe半导体量子阱。我们发现调节外电场或量子阱的阱宽可以作为导致量子相变和本征自旋霍尔效应的开关。我们的工作可能会为区别和实验验证本征自旋霍尔效应提供物理基础。     

Growth and transport properties of CaFeAsF_(1-x) single crystals

Using self-flux method,we have successfully grown the parent phase of the single crystals of CaFeAsF1-x.The X-ray di?raction indicates good crystallinity.In-plane resistivity shows a bad metallic behavior with a sharp drop of resistivity at about T SDW=119K.This anomaly is associated with the possible spin density wave(SDW)order.Interestingly near T SDW,the resistivity exhibits a cusp-like feature,which may be understood as the strong coupling effect between the electrons and the antiferromagnetic(AF)spin fluctuations.A reduction of fluorine or application of a high pressure will suppress the SDW feature and induce superconductivity.Hall effect measurements reveal a positive Hall coefficient below T SDW indicating a dominant role of the hole-like charge carriers in the parent phase.Strong magnetoresistance has been observed below T SDW suggesting multiple conduction channels of the charge carriers.     

Effect of the nuclear hyperfine field on the 2D electron conductivity in the quantum Hall regime

The effect of the nuclear hyperfine interaction on the dc conductivity of 2D electrons under quantum Hall effect conditions at filling factor ν=1 is observed for the first time. The local hyperfine field enhanced by dynamic nuclear polarization is monitored via the Overhauser shift of the 2D conduction electron spin resonance in AlGaAs/GaAs multiquantum-well samples. The experimentally observed change in the dc conductivity resulting from dynamic nuclear polarization is in agreement with a thermal activation model incorporating the Zeeman energy change due to the hyperfine interaction. The relaxation decay time of the dc conductivity is, within experimental error, the same as the relaxation time of the nuclear spin polarization determined from the Overhauser shift. These findings unequivocally establish the nuclear spin origins of the observed conductivity change. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 1, 58–63 (10 January 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Spin cloud induced around an elastic scatterer by the intrinsic spin hall effect

Similar to the Landauer electric dipole created around an impurity by the electric current, a spin polarized cloud of electrons can be induced by the intrinsic spin Hall effect near a spin independent elastic scatterer. It is shown that in the ballistic range around the impurity, such a cloud appears in the case of Rashba spin-orbit interaction, even though the bulk spin Hall current is absent.     

Ettingshausen effect around a Landau level filling factor nu = 3 studied by dynamic nuclear polarization

A spin current perpendicular to the electric current is investigated around a Landau level filling factor nu=3 in a GaAs/AlGaAs two-dimensional electron system. Measurements of dynamic nuclear polarization in the vicinity of the edge of a specially designed Hall bar sample indicate that the direction of the spin current with respect to the Hall electric field reverses its polarity at nu=3, where the dissipative current carried by holes in the spin up Landau level is replaced with that by electrons in the spin down Landau level.     

Dynamics of localized spins coupled to the conduction electrons with charge and spin currents

The dynamics of the localized spins coupled to the conduction electrons is studied theoretically in the wide range of magnitudes of the charge and spin currents including the regime which has never been explored but is now possible in terms of the pure spin-current injection methods, e.g., the spin Hall effect and spin battery. The equations of motion for the two-spin system are investigated in detail, and its phase diagram of the dynamics is presented. It is found that the dynamics depends sensitively upon the relative magnitudes of the charge and spin currents; i.e., it shows steady state, periodic motion, and even chaotic behavior. The extension to the multispin system and its implications including a possible "spin-current detector" are also discussed.