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 the f-sum rule.
The unidirectional magnetoresistance (UMR) is one of the most complex spin-dependent transport phenomena in ferromagnet/non-magnet bilayers, which involves spin injection and accumulation due to the spin Hall effect (SHE) or Rashba-Edelstein effect (REE), spin-dependent scattering, and magnon scattering at the interface or in the bulk of the ferromagnet. While UMR in metallic bilayers has been studied extensively in very recent years, its magnitude is as small as 10$^-$$^5$, which is too small for practical applications. Here, we demonstrate a giant UMR effect in a heterostructure of BiSb topo…
Unidirectional magnetoresistance driven by nonequilibrium antiferromagnetic magnons
South China University of Technology（华南理工大学）；Norwegian University of Science and Technology（挪威科技大学）；Peking University（北京大学）；Nanyang Technological University（南洋理工大学）
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…
The structure inversion asymmetry at surfaces and interfaces give rise to the Rashba spin-orbit interaction (SOI), that breaks the spin degeneracy of surface or interface states. Hence, when an electric current runs through a surface or interface, this Rashba effect generates an effective magnetic field acting on the electron spin. This provides an additional tool to manipulate the spin state in materials such as Si and Ge that, in their bulk form, possess inversion symmetry (or lack structural inersion asymmetry). The existence of Rashba states could be demonstrated by photoemission spectrosc…
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…
Relating magnetotransport properties to specific spin textures at surfaces or interfaces is an intense field of research nowadays. Here, we investigate the variation of the electrical resistance of Ge(111) grown epitaxially on semi-insulating Si(111) under the application of an external magnetic field. We find a magnetoresistance term which is linear in current density j and magnetic field B, hence odd in j and B, corresponding to a unidirectional magnetoresistance. At 15 K, for I = 10 $μ$A (or j = 0.33 A/m) and B = 1 T, it represents 0.5 % of the zero field resistance, a much higher value com…
Twisted bilayer graphene (TBG) exhibits fascinating correlation-driven phenomena like the superconductivity and Mott insulating state, with flat bands and a chiral lattice structure. We find by quantum transport calculations that the chirality leads to a giant unidirectional magnetoresistance (UMR) in TBG, where the unidirectionality refers to the resistance change under the reversal of the direction of the current or magnetic field. We point out that flat bands significantly enhance this effect. The UMR increases quickly upon reducing the twist angle and reaches about 20\% for an angle of 1.5…
Spin-dependent transport phenomena due to relativistic spin-orbit coupling and broken space-inversion symmetry are often difficult to interpret microscopically, in particular when occurring at surfaces or interfaces. Here we present a theoretical and experimental study of spin-orbit torque and unidirectional magnetoresistance in a model room-temperature ferromagnet NiMnSb with inversion asymmetry in the bulk of this half-heusler crystal. Besides the angular dependence on magnetization, the competition of Rashba and Dresselhaus-like spin-orbit couplings results in the dependence of these effect…
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…
We report the observation of a unidirectional magnetoresistance (UMR) that originates from the nonequilibrium orbital momentum induced by an electric current in a naturally oxidized Cu/Co bilayer. The orbital-UMR scales with the torque efficiency due to the orbital Rashba-Edelstein effect upon changing the Co thickness and temperature, reflecting their common origin. We attribute the UMR to orbital-dependent electron scattering and orbital-to-spin conversion in the ferromagnetic layer. In contrast to the spin-current induced UMR, the magnon contribution to the orbital-UMR is absent in thin Co …
The spin Hall magnetoresistance (SMR) and anomalous Hall effect (AHE) are observed in a Cr2O3/Ta structure. The structural and surface morphology of Cr2O3/Ta bilayers have been investigated. Temperature dependence of longitudinal and transverse resistances measurements confirm the relationship between SMR and AHE signals in Cr2O3/Ta structure. By means of temperature dependent magnetoresistance measurements, the physical origin of SMR in the Cr2O3/Ta structure is revealed, and the contribution to the SMR from the spin current generated by AHE has been proved. The so-called boundary magnetizati…
To date, magnetic proximity effect (MPE) has only been conclusively observed in ferromagnet (FM) based systems. We report the observation of anomalous Hall effect and anisotropic magnetoresistance in angular dependent magnetoresistance (ADMR) measurements in Pt on antiferromagnetic (AF) $α$-Fe$_2$O$_3$(0001) epitaxial films at 10 K, which provide evidence for the MPE. The Néel order of $α$-Fe$_2$O$_3$ and the induced magnetization in Pt show a unique ADMR compared with all other FM and AF systems. A macrospin response model is established and can explain the AF spin configuration and all main …
The anomalous Hall effect, observed in conducting ferromagnets with broken time-reversal symmetry, offers the possibility to couple spin and orbital degrees of freedom of electrons in ferromagnets. In addition to charge, the anomalous Hall effect also leads to spin accumulation at the surfaces perpendicular to both the current and magnetization direction. Here we experimentally demonstrate that the spin accumulation, subsequent spin backflow, and spin-charge conversion can give rise to a different type of spin current related magnetoresistance, dubbed here as the anomalous Hall magnetoresistan…
The interplay between electronic transport and antiferromagnetic order has attracted a surge of interest as recent studies have shown that a moderate change in the spin orientation of a collinear antiferromagnet may have a significant effect on the electronic band structure. Among numerous electrical probes to read out such magnetic order, unidirectional magnetoresistance (UMR), where the resistance changes under the reversal of the current direction, can provide rich insights into the transport properties of spin-orbit coupled systems. However, UMR has never been observed in antiferromagnets …
Transverse acoustic waves in an inhomogeneous medium are analogues to electromagnetic waves and will exhibit topological behavior due to the Berry gauge potential in the momentum space due to inhomogeneity. The inhomogeneous (or gradient) medium can be created using an applied strain gradient in a semiconductor thin film (silicon) since the phonon frequency and dispersion will be a function of the local strain along the strain gradient direction. As a consequence, topological phonon mediated spin and heat transport can be engineered in the semiconductor thin films. Here, we present evidence of…
Spin Hall magnetoresistance (SMR) and magnon excitation magnetoresistance (MMR) that all generate via the spin Hall effect and inverse spin Hall effect in a nonmagnetic material are always related to each other. However, the influence of magnon excitation for SMR is often overlooked due to the negligible MMR. Here, we investigate the SMR in Pt/Y3Fe5O12 (YIG) bilayers from 5 to 300K, in which the YIG are treated after Ar+-ion milling. The SMR in the treated device is smaller than in the non-treated. According to theoretical simulation, we attribute this phenomenon to the reduction of the interf…
Half-Heusler compounds have attracted significant attention because of their topologically non-trivial electronic structure, which leads to unusual electron transport properties. We thoroughly investigated the magnetotransport properties of high-quality single crystals of two half-Heusler phases, TbPtBi and HoPtBi, in pursuit of the characteristic features of topologically non-trivial electronic states. Both studied compounds are characterized by the giant values of transverse magnetoresistance with no sign of saturation in magnetic field up to 14 T. HoPtBi demonstrates the Shubnikov-de Haas e…
The spin Hall magnetoresistance (SMR) phenomenon includes the fundamental physics of spin current, and originates from spin accumulation at an interface owing to the spin Hall effect. Although bilayers are the simplest structure exhibiting SMR, these exploit spin accumulation at only one side of a layer. Herein, trilayers of CoFe2O4/Pt/CoFe2O4 were fabricated and their spin Hall magnetoresistance was investigated. The trilayer structure featuring a thin Pt layer exhibited an SMR ratio four times that of a CoFe2O4/Pt bilayer. Further, the SMR ratio exhibited a dependence on Pt layer thickness t…
Reading the magnetic state of antiferromagnetic (AFM) thin films is key for AFM spintronic devices. We investigate the underlying physics behind the spin Hall magnetoresistance (SMR) of bilayers of platinum and insulating AFM hematite (α-Fe2O3) and find an SMR efficiency of up to 0.1%, comparable to ferromagnetic based structures. To understand the observed complex SMR field dependence, we analyse the effect of misalignments of the magnetic axis that arise during growth of thin films, by electrical measurements and direct magnetic imaging, and find that a small deviation can result in signific…
Antiferromagnetic anisotropy determination by spin Hall magnetoresistance
提出了一种测量反铁磁绝缘体（AFI）磁各向异性的电学方法。当具有强自旋-轨道相互作用的金属膜，例如，铂（Pt）沉积在AFI上，由于自旋霍尔磁阻（SMR），其电阻应受到AFI N单元矢量方向的影响。因此，受外部磁场和磁各向异性两者影响的AFI N eel矢量的方向反映在Pt的电阻中。考虑SMR，计算了Pt电阻与AFI的磁场角度关系，表明在强磁场中，通过监测Pt电阻，可以从实验上获得反铁磁各向异性。对Pt/Cr2 O3、Pt/NiO和Pt/CoO等实际体系进行了计算。
We investigate the observation of negative spin Hall magnetoresistance (SMR) in antiferromagnetic Cr2O3/Ta bilayers at low temperature. The sign of the SMR signals is changed from positive to negative monotonously from 300 K to 50 K. The change of the signs for SMR is related with the competitions between the surface ferromagnetism and bulky antiferromagnetic of Cr2O3. The surface magnetizations of Cr2O3 (0001) is considered to be dominated at higher temperature, while the bulky antiferromagnetics gets to be robust with decreasing of temperature. The slopes of the abnormal Hall curves coincide…
The magnetic state of heavy metal Pt thin films in proximity to the ferrimagnetic insulator Y$_{3}$Fe$_{5}$O$_{12}$ has been investigated systematically by means of x-ray magnetic circular dichroism and x-ray resonant magnetic reflectivity measurements combined with angle-dependent magnetotransport studies. To reveal intermixing effects as the possible cause for induced magnetic moments in Pt, we compare thin film heterostructures with different order of the layer stacking and different interface properties. For standard Pt layers on Y$_{3}$Fe$_{5}$O$_{12}$ thin films, we do not detect any sta…
Magnetotransport investigation of a half-Heusler antiferromagnet DyPdBi revealed hallmark features of Weyl semimetal: huge negative longitudinal magnetoresistance and planar Hall effect. Both effects have recently been linked to chiral magnetic anomaly - axial charge pumping between Weyl nodes. Magnetoresistance (MR) of single crystals of DyPdBi is very pronounced. In magnetic field longitudinal to electrical current direction it reaches -80% and its relative difference with respect to that measured in transverse field (expressed as anisotropic magnetoresistance) is extremely strong: -60% at 1…
A comprehensive magnetotransport study including resistivity ($ρ_{xx}$) at various fields, isothermal magnetoresistance and Hall resistivity ($ρ_{xy}$) has been carried out at different temperatures on the Co$_{2}$TiAl Heusler alloy. Co$_{2}$TiAl alloy shows a paramagnetic (PM) to ferromagnetic (FM) transition below the curie temperature (T$_{C}$) $\sim$ 125 K. In the FM region, resistivity and magnetoresistance reveals a spin flip electron-magnon scattering and the Hall resistivity unveils the anomalous Hall resistivity ($ρ_{xy}^{AH}$). Scaling of anomalous Hall resistivity with resistivity e…
We report the observation of the three-dimensional angular dependence of the spin Hall magnetoresistance (SMR) in a bilayer of the epitaxial antiferromagnetic insulator NiO(001) and the heavy metal Pt, without any ferromagnetic element. The detected angular-dependent longitudinal and transverse magnetoresistances are measured by rotating the sample in magnetic fields up to 11 T, along three orthogonal planes (xy-, yz- and xz-rotation planes, where the z-axis is orthogonal to the sample plane). The total magnetoresistance has contributions arising from both the SMR and ordinary magnetoresistanc…
Giant Domain-Wall Hall Magnetoresistance in Magnetic Topological Semimetal
Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Guangdong Provincial Key Laboratory of Optical Information Materials and Technology, Institute for Advanced Materials, South China Academy of Advanced Optoelectronics, South China Normal University（华南师范大学）
We investigate the spin Hall magnetoresistance in thin film bilayer heterostructures of the heavy metal Pt and the antiferromagnetic insulator NiO. While rotating an external magnetic field in the easy plane of NiO, we record the longitudinal and the transverse resistivity of the Pt layer and observe an amplitude modulation consistent with the spin Hall magnetoresistance. In comparison to Pt on collinear ferrimagnets, the modulation is phase shifted by 90° and its amplitude strongly increases with the magnitude of the magnetic field. We explain the observed magnetic field-dependence of the spi…
We present the Co-Gd composition dependence of the spin-Hall magnetoresistance (SMR) and anisotropic magnetoresistance (AMR) for ferrimagnetic Co100-xGdx / Pt bilayers. With Gd concentration x, its magnetic moment increasingly competes with the Co moment in the net magnetization. We find a nearly compensated ferrimagnetic state at x = 24. The AMR changes sign from positive to negative with increasing x, vanishing near the magnetization compensation. On the other hand, the SMR does not vary significantly even where the AMR vanishes. These experimental results indicate that very different scatte…
We theoretically investigated the magnetoresistance (MR) and planar Hall effect (PHE) in Weyl semimetals based on the semiclassical Boltzmann theory, focusing on the fine structure of the band dispersion. We identified that the negative longitudinal MR and sign change in the PHE occur because of the negative off-diagonal effective-mass with no topological effects or chiral anomaly physics. Our results highlight the crucial role of the off-diagonal effective-mass, which can cause anomalous galvanomagnetic effects. We propose that the PHE creates a dip in their temperature dependence, which enab…
The semiclassical transport theory is especially powerful for investigating galvanomagnetic effects. Generally, the semiclassical theory is applicable only in weak fields because it does not consider Landau quantization. Herein, we extend the conventional semiclassical theory by considering Landau quantization through the field dependence of carrier density in semimetals. The extended semiclassical theory is applicable even in strong fields, where Landau quantization is noticeable. Using this new approach, we explain the qualitative change in the angular dependence of transverse magnetoresista…
We analyze the experimentally obtained spin-current-related magnetoresistance in epitaxial Pt/Co bilayers by using a drift-diffusion model that incorporates both bulk spin Hall effect and interfacial Rashba-Edelstein effect (REE). The magnetoresistance analysis yields, for the Pt/Co interface, a temperature-independent Rashba parameter in the order of 1e-11 eV m that agrees with theoretical calculations, along with an effective interfacial REE thickness of several angstroms which is in overall consistency with our previous spin-orbit torque analysis. In particular, our results suggest that bot…
Asymmetric magnetoresistance in 3$d$-5$d$ based La$_{0.67}$Ca$_{0.33}$MnO$_3$/SrIrO$_3$ bilayer: The role of unidirectional anisotropy
Jawaharlal Nehru University（贾瓦哈拉尔·尼赫鲁大学）；Indian Institute of Technology, Hauz Khaz（印度理工学院豪兹卡兹校区）；Special Centre for Nanoscience, Jawaharlal Nehru University（贾瓦哈拉尔·尼赫鲁大学纳米科学特别中心）；UGC-DAE Consortium for Scientific Research, Indore（印度古物与考古学联合会-原子能部科学研究中心）
We present here a way to modulate the anisotropic magnetoresistance (AMR) by anomalous Hall signal and thus measure the domain wall (DW) motion velocity at near-coercivity. We study the magnetization relaxation at the constant field in the longitudinal (Rxx) Hall geometry. We observed asymmetric Rxx peaks that appear at the DW pinning fields. This unusual magnetoresistance behavior is explained by considering the AMR modulation by the anomalous Hall voltage. In the proposed method, using the magnetization relaxation, the real-time DW velocity measurement is much easier in comparison to the oth…
We have studied the spin Hall magnetoresistance (SMR), the magnetoresistance within the plane transverse to the current flow, of Pt/Co bilayers. We find that the SMR increases with increasing Co thickness: the effective spin Hall angle for bilayers with thick Co exceeds the reported values of Pt when a conventional drift-diffusion model is used. An extended model including spin transport within the Co layer cannot account for the large SMR. To identify its origin, contributions from other sources are studied. For most bilayers, the SMR increases with decreasing temperature and increasing magne…
