We have investigated the effect of unidirectional periodic potential modulation on the fractional quantum Hall (FQH) states located within the filling factor range $1<ν<2$. We find that odd-numerator FQH states are strongly suppressed, while the even-numerator ones are less affected or even enhanced, by the introduction of the modulation. In the picture of the composite fermions (CFs), the behaviors are equivalent to the suppression of the spin splitting of the CFs by the modulation. We discuss the origin of the suppression and the possible modulation-induced phase transition from the FQH state to the stripe state.
We perform electronic measurements of unidirectional spin Hall magnetoresistance (USMR) in a Permalloy/Pt bilayer, in conjunction with magneto-optical Brillouin light spectroscopy of spin current-driven magnon population. We show that the current dependence of USMR closely follows the dipolar magnon density, and that both dependencies exhibit the same scaling over a large temperature range of 80-400 K. These findings demonstrate a close relationship between spin current-driven magnon generation and USMR, and indicate that the latter is likely dominated by the dipolar magnons.
We predict a spin anomalous-Hall unidirectional magnetoresistance (AH-UMR) in conducting bilayers composed of a ferromagnetic layer and a nonmagnetic layer, which does $\textit{not}$ rely on the spin Hall effect in the normal metal layer$-$in stark contrast to the well-studied unidirectional spin-Hall magnetoresistance$-$but, instead, arises from the spin anomalous Hall effect in the ferromagnetic layer. Physically, it is the charge-spin conversion induced by the spin anomalous Hall effect that conspires with the structural inversion asymmetry to generate a net nonequilibrium spin density in t…
Recent studies evidence 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…
The large spin orbit coupling in topological insulators results in helical spin-textured Dirac surface states that are attractive for topological spintronics. These states generate an efficient spin-orbit torque on proximal magnetic moments at room temperature. However, memory or logic spin devices based upon such switching require a non-optimal three terminal geometry, with two terminals for the writing current and one for reading the state of the device. An alternative two terminal device geometry is now possible by exploiting the recent discovery of a unidirectional spin Hall magnetoresista…
We have observed commensurability oscillations (CO) in the Hall resistance $R_{yx}$ of a unidirectional lateral superlattice (ULSL). The CO, having small amplitudes ($\sim$ 1 $Ω$) and being superposed on a roughly three-orders of magnitude larger background, are obtained by directly detecting the difference in $R_{yx}$ between the ULSL area and the adjacent unmodulated two-dimensional electron gas area, and then extracting the odd part with respect to the magnetic field. The CO thus obtained are compared with a theoretical calculation and turn out to have the amplitude much smaller than the th…
Unidirectional spin Hall magnetoresistance (USMR) has been widely reported in the heavy metal / ferromagnet (HM/FM) bilayer systems. We observe the USMR in the Pt/α-Fe2O3 bilayers where the α-Fe2O3 is an antiferromagnetic (AFM) insulator. Systematic field and temperature dependent measurements confirm the magnonic origin of the USMR. The appearance of AFM-USMR is driven by the imbalance of creation and annihilation of AFM magnons by spin orbit torque due to thermal random field. However, unlike its ferromagnetic counterpart, theoretical modeling reveals that the USMR in Pt/α-Fe2O3 is determine…
Dependence of Modulation Amplitude on Electron Density in Unidirectional Lateral Superlattices: The Effect of the Thickness of the Two-dimensional Electron Gas
Thanks to its unique symmetry, the unidirectional spin Hall and Rashba-Edelstein magnetoresistance (USRMR) is of great fundamental and practical interest, particularly in the context of reading magnetization states in two-terminal spin-orbit torque switching memory and logic devices. Recent studies show that topological insulators could improve USRMR amplitude. However, the topological insulator device configurations studied so far in this context, namely ferromagnetic metal/topological insulator bilayers and magnetically doped topological insulators, suffer from current shunting by the metall…
Magnetoresistive effects are usually invariant upon inversion of the magnetization direction. In noncentrosymmetric conductors, however, nonlinear resistive terms can give rise to a current dependence that is quadratic in the applied voltage and linear in the magnetization. Here we demonstrate that such conditions are realized in simple bilayer metal films where the spin-orbit interaction and spin-dependent scattering couple the current-induced spin accumulation to the electrical conductivity. We show that the longitudinal resistance of Ta|Co and Pt|Co bilayers changes when reversing the polar…
We develop a model for the magnonic contribution to the unidirectional spin Hall magnetoresistance (USMR) of heavy metal/ferromagnetic insulator bilayer films. We show that diffusive transport of Holstein-Primakoff magnons leads to an accumulation of spin near the bilayer interface, giving rise to a magnoresistance which is not invariant under inversion of the current direction. Unlike the electronic contribution described by Zhang and Vignale [Phys. Rev. B 94, 140411 (2016)], which requires an electrically conductive ferromagnet, the magnonic contribution can occur in ferromagnetic insulators…
Many Heusler compounds are predicted to be ferromagnetic half metals in the bulk, which makes them promising compounds for spintronics. However, for devices the transport spin polarization at specific interfaces requires optimization. We show that investigations of the unidirectional magnetoresistance provide an alternative approach to access this quantity. Based on a Wheatstone-bridge design we probed the unidirectional magnetoresistance of Co2MnSi/(Ag, Cu, or Cr)(0.5 nm)/Pt (or Ta) multilayers and separate the spin-dependent unidirectional spin Hall magnetoresistance from other contributions…
A nonlinear magnetoresistance - called unidirectional spin-Hall magnetoresistance - is recently experimentally discovered in metallic bilayers consisting of a heavy metal and a ferromagnetic metal. To study the fundamental mechanism of the USMR, both ferromagnetic and heavy metallic layer thickness dependence of the USMR are presented in a Pt/Co/AlOx trilayer at room temperature. To avoid ambiguities, second harmonic Hall measurements are used for separating spin-Hall and thermal contributions to the non-linear magnetoresistance. The experimental results are fitted by using a drift-diffusion t…
We present a detailed analysis of harmonic longitudinal and Hall voltage measurements for in-plane magnetized Pt/Co/Ta and Ta/Co/Pt trilayers in reference to Pt/Co and Ta/Co bilayers. Enhancement of spin-orbit torques (SOTs) and unidirectional spin Hall magnetoresistance (USMR) is achieved by introducing the second heavy metal (HM) with the opposite sign of the spin Hall angle. The extracted SOT efficiencies are larger for the trilayers as compared to the bilayers, confirming the enhanced values reported for the trilayers with perpendicularly magnetized Co. The maximum effective spin Hall angl…
Commensurability oscillations in the rf conductivity of unidirectional lateral superlattices: measurement of anisotropic conductivity by coplanar waveguide
Recent experiments have revealed nonlinear features of the magnetoresistance in metallic bilayers consisting of a heavy-metal (HM) and a ferromagnetic metal (FM). A small change in the lon- gitudinal resistance of the bilayer has been observed when reversing the direction of either the applied in-plane current or the magnetization. We attribute such nonlinear transport behavior to the spin-polarization dependence of the electron mobility in the FM layer acting in concert with the spin accumulation induced in that layer by the spin Hall current originating in the bulk of the HM layer. An explic…
Chiral edge plasmons in quantum anomalous Hall insulators
Beijing Forestry University（北京林业大学）；Beijing Institute of Technology（北京理工大学）；Chinese Academy of Sciences（中国科学院）；University of Science and Technology of China（中国科学技术大学）
The electromotive forces induced by surface acoustic waves (SAWs) are investigated in ferromagnetic thin films. CoFeB thin films deposited on LiNbO$_3$ substrates are patterned into Hall-bars to study the acoustoelectric transport properties of the device. The longitudinal and transverse dc voltages that develop in the Hall bars, which are parallel and orthogonal to the flow of the SAW, respectively, are measured under application of an in-plane magnetic field. The longitudinal voltage scales linearly with the SAW power and reverses its polarity upon changing the direction to which the SAW pro…
Real-space Observation of Unidirectional Charge Density Wave and Complex Structural Modulation in the Pnictide Superconductor Ba$_{1-x}$Sr$_x$Ni$_2$As$_2$
本文利用扫描隧道显微镜在实空间观测 Ba$_{1-x}$Sr$_x$Ni$_2$As$_2$ 中单向电荷密度波与结构调制，发现 Sr 替代抑制 CDW 并稳定 1×2 超结构，从而增强超导电性。
Quantum spin-Hall edges are envisaged as next-generation transistors, yet they exhibit dissipationless transport only over short distances. Here we show that in a diffusive sample, where charge puddles with odd spin cause back-scattering, a magnetic field drastically increases the mean free path and drives the system into the ballistic regime with a Landauer-Buttiker conductance. A strong non-linear non-reciprocal current emerges in the diffusive regime with opposite signs on each edge, and vanishes in the ballistic limit. We discuss its detection in state-of-the-art experiments.
Unidirectional magnetoresistance (UMR) in a ferromagnetic bilayer due to the spin Hall effects (SHEs) provides a facile means of probing in-plane magnetization to avoid complex magnetic tunnel junctions. However, the UMR signal is very weak and usually requires a lock-in amplifier for detection even in the bilayer involving Ta or Pt with a large spin Hall angle (SHA). Here we report a type of UMR, termed as the anomalous UMR (AUMR), in a single CoFeB layer without any adjacent SHE layers, where the UMR signal is about 10 times larger than that in Ta/CoFeB structures and can be detected by usin…
Phenomenology similar to the nonreciprocal charge transport violating Onsagers reciprocity relations can develop in directionally inhomogeneous conducting films with nonuniform Hall coefficient along the current trajectory. The effect is demonstrated in ferromagnetic CoPd films and analyzed in comparison with the unidirectional magnetoresistance phenomena. We suggest to use an engineered inhomogeneity for spintronics applications and present the concept of mixed symmetry Hall devices in which transverse to current Hall signal is measured in a longitudinal contacts arrangement. Magnetization re…
Integer quantum Hall effect and Hofstadter's butterfly spectra in three-dimensional metals in external periodic modulations
我们认为Hofstadter蝴蝶效应伴随着量子霍尔效应，这与Koshino {\it et al.} [Phys. Rev. Lett. {\bf 86}，1062（2001）]可以在完全不同的系统中实现--施加有弱外部周期性调制的3D金属（例如，声波）。也就是说，由于施加的磁场$\Vec{B}$，两个周期性势的影响干扰朗道量子化，通常导致分形能隙作为$\Vec{B}$的倾斜角的函数，计算伴随的量子化霍尔张量。这一现象源于这样一个事实，即虽然本系统与3D紧束缚系统具有不同的蝴蝶物理起源，但数学形式是非常等效的。
We consider a system of weakly coupled wires with quantum Hall effect (QHE) and in the presence of a spatially periodic modulation of the chemical potential along the wire, equivalent to a charge density wave (CDW). We investigate the competition between the two effects which both open a gap. We show that by changing the ratio between the amplitudes of the CDW modulation and the tunneling between wires, one can switch between non-topological CDW-dominated phase to topological QHE-dominated phase. Both phases host edge states of chiral and non-chiral nature robust to on-site disorder. However, …
We observe geometric resonance features of composite fermions on the flanks of the even denominator ν = 1/2 fractional quantum Hall state in high-mobility two-dimensional electron and hole systems confined to wide GaAs quantum wells and subjected to a weak, strain-induced, unidirectional periodic potential modulation. The features provide a measure of how close to ν = 1/2 the system stays single-component and supports a composite fermion Fermi sea before transitioning into a ν = 1/2 fractional quantum Hall state, presumably the two-component Ψ331 state.
High quality chromium (Cr) doped three-dimensional topological insulator (TI) Sb2Te3 films are grown via molecular beam epitaxy on heat-treated insulating SrTiO3(111) substrates. We report that the Dirac surface states are insensitive to Cr doping, and a perfect robust long-range ferromagnetic order is unveiled in epitaxial Sb2-xCrxTe3 films. The anomalous Hall effect is modulated by applying a bottom gate, contrary to the ferromagnetism in conventional diluted magnetic semiconductors (DMSs), here the coercivity field is not significantly changed with decreasing carrier density. Carrier-indepe…
The longitudinal conductance of mesoscopic Hall samples with arbitrary disorder and periodic modulations
本文利用Kubo-Landauer方法计算了置于强垂直磁场中的二维电子系统在周期调制和无序势作用下的纵向（两端）电导。散射问题被改写为一组非均匀的，耦合的线性方程组，使我们能够找到从有限大小的系统计算的传输概率;结果是准确的非相互作用的电子。我们的方法充分考虑了无序和周期调制的影响，无论它们的相对强度如何，只要朗道能级混合可以忽略不计。特别是，我们专注于周期性调制和那些无序的影响之间的相互作用。这似乎是理解最近实验的相关机制[S。Melinte { \em et al}，Phys. Rev. Lett. { \bf 92}，036802（2004）]，我们的数值结果与这些实验结果定性一致。我们开发的数值技术可以直接推广到多终端的几何形状，以及其他多通道散射问题。
We consider a system of weakly coupled one-dimensional wires forming a three-dimensional stack in the presence of a spatially periodic modulation of the chemical potential along the wires, equivalent to a charge density wave (CDW). An external static magnetic field is applied parallel to the wire axes. We show that, for a certain parameter regime, due to interplay between the CDW and magnetic field, the system can support a second-order topological phase characterized by the presence of chiral quasi-1D Quantum Hall Effect (QHE) hinge modes. Interestingly, we demonstrate that direction of propa…
We report on Cr doping effect in Mn3Sn polycrystalline films with both uniform and modulation doping. It is found that Cr doping with low concentration does not cause notable changes to the structural and magnetic properties of Mn3Sn, but it significantly enhances the anomalous Hall conductivity, particularly for modulation-doped samples at low temperature. A Hall conductivity as high as 184.8 Ω-1 cm-1 is obtained for modulation-doped samples at 50 K, in a sharp contrast to vanishingly small values for undoped samples at the same temperature. We attribute the enhancement to the change of Fermi…
A Tomonaga-Luttinger (TL) liquid is known as an integrable system, in which a non-equilibrium many-body state survives without relaxing to a thermalized state. This intriguing characteristic is tested experimentally in copropagating quantum Hall edge channels at bulk filling factor nu = 2. The unidirectional transport allows us to investigate the time evolution by measuring the spatial evolution of the electronic states. The initial state is prepared with a biased quantum point contact, and its spatial evolution is measured with a quantum-dot energy spectrometer. We find strong evidences for a…
We propose a realization of perfect valley filters based on the chiral domain-wall channels between a quantum anomalous Hall insulator and a quantum valley Hall insulator. Uniquely, all these channels reside in the same valley and propagate unidirectionally, $100\%$ valley-polarizing passing-by carriers without backscattering. The valley index, the chirality, and the number of the channels are protected by topological charges, controllable by external fields, and detectable by circular dichroism.
Resistively detected NMR (RDNMR) based on dynamic nuclear polarization (DNP) in a quantum Hall ferromagnet (QHF) is a highly-sensitive method for the discovery of fascinating quantum Hall phases; however, the mechanism of this DNP and in particular the role of quantum Hall edge states in it are unclear. Here we demonstrate the important but previously unrecognized effect of chiral edge modes on the nuclear spin polarization. A side-by-side comparison of the RDNMR signals from Hall bar and Corbino disk configurations allows us to distinguish the contributions of bulk and edge states to DNP in Q…
We report on a possible optical tuning of the spin Hall conductivity in mono-layer transition metal dichalcogenides. Light beams of frequencies much higher than the energy scale of the system (the \textit{off-resonant} condition) does not excite electrons but rearranges the band structure. The rearrangement is quantitatively established using the Floquet formalism. For such a system of mono-layer transition metal dichalcogenides, the spin Hall conductivity (calculated with the Kubo expression in presence of disorder) exhibits a drop at higher frequencies and lower intensities. Finally, we comp…
