Two-dimensional (2D) Rashba systems have been intensively studied in the last decade due to their unconventional physics, tunability capabilities, and potential for spin-charge interconversion when compared to conventional heavy metals. With the advent of a new generation of spin-based logic and memory devices, the search for Rashba systems with more robust and larger conversion efficiencies is expanding. Conventionally, demanding techniques such as angle- and spin-resolved photoemission spectroscopy are required to determine the Rashba parameter $α_{R}$ that characterizes these systems. Here, we introduce a simple method that allows a quantitative extraction of $α_{R}$, through the analysis of the bilinear response of angle-dependent magnetotransport experiments. This method is based on the modulation of the Rashba-split bands under a rotating in-plane magnetic field. We show that our method is able to correctly yield the value of $α_{R}$ for a wide range of Fermi energies in the 2D electron gas at the LaAlO$_{3}$/SrTiO$_{3}$ interface. By applying a gate voltage, we observe a maximum $α_{R}$ in the region of the band structure where interband effects maximize the Rashba effect, consistently with theoretical predictions.
We report the observation of magnetoresistance originating from Rashba spin-orbit coupling (SOC) in a metallic heterostructure: the Rashba-Edelstein (RE) magnetoresistance. We show that the simultaneous action of the direct and inverse RE effects in a Bi/Ag/CoFeB trilayer couples current-induced spin accumulation to the electric resistance. The electric resistance changes with the magnetic-field angle, reminiscent of the spin Hall magnetoresistance, despite the fact that bulk SOC is not responsible for the magnetoresistance. We further found that, even when the magnetization is saturated, the …
We predict two spin-dependent transport phenomena in two-dimensional electron systems, which are induced by spatially fluctuating Rashba spin-orbit interaction. When the electron gas is magnetized, the random Rashba interaction leads to the anomalous Hall effect. An example of such a system is a narrow-gap magnetic semiconductor-based symmetric quantum well. We show that the anomalous Hall conductivity reveals a strongly nonlinear dependence on the magnetization, decreasing exponentially at large spin density. We also show that electron scattering from a fluctuating Rashba field in a two-dimen…
We study anisotropic magnetoresistance (AMR) in a spin-polarized two-dimensional electron gas with Rashba spin-orbit coupling and nonmagnetic disorder collision. We show that AMR exists, arising from the combined effect of in-plane magnetization, spin-orbit coupling, and nonmagnetic remote disorder scattering. Further, numerical evaluation demonstrates that the smoothness of the remote disorder can strongly affect AMR, and this AMR is sensitive to the electron density. Large magnitude of AMR ($\approx24%$) is obtained for low density system with strong spin-orbit splitting.
The magnetoresistance of a three-dimensional Rashba material placed on top of a ferromagnetic insulator is theoretically investigated. In addition to the intrinsic Rashba spin-orbit interaction, we also consider extrinsic spin-orbit coupling via side-jump and skew scattering, and the Elliott-Yafet spin relaxation mechanism. The latter is anisotropic due to the mass anisotropy which reflects the noncentrosymmetric crystal structure of three-dimensional Rashba metals. A quasiclassical approach is employed to derive a set of coupled spin-diffusion equations, which are supplemented by boundary con…
Bilinear magnetoresistance is a nonlinear transport phenomenon that scales linearly with the electric and magnetic fields, and appears in nonmagnetic systems with strong spin-orbit coupling, such as topological insulators (TIs). Using the semiclassical Boltzmann theory and generalized relaxation time approximation, we consider in detail the bilinear magnetoresistance in an effective model describing surface states of three-dimensional topological insulators. We show that the presence of magnetic impurities remarkably modifies the BMR signal. In general, scattering on magnetic impurities reduce…
In addition to the topologically protected linear dispersion, a band-bending-confined two-dimensional electron gas with tunable Rashba spin-splitting (RSS) was found to coexist with the topological surface states on the surface of topological insulators (TIs). Here, we report the observation of large bilinear magnetoresistance (BMR) in Bi2Se3 films decorated with transition metal atoms. The magnitude of the BMR sensitively depends on the type and amount of atoms deposited, with a maximum achieved value close to those of strong Rashba semiconductors. Our first-principles calculations reproduce …
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…
We predict a magnetoresistance induced by the interfacial Rashba spin-orbit coupling in normal metal|ferromagnetic insulator bilayer. It depends on the angle between current and magnetization directions identically to the "spin Hall magnetoresistance" mechanism caused by a combined action of spin Hall and inverse spin Hall effects. Due to the identical phenomenology it is not obvious whether the magnetoresistance reported by Nakayama et al. is a bulk metal or interface effect. The interfacial Rashba induced magnetoresistance may be distinguished from the bulk metal spin Hall magnetoresistance …
The Rashba effect leads to a chiral precession of the spins of moving electrons while the Dzyaloshinskii-Moriya interaction (DMI) generates preference towards a chiral profile of local spins. We predict that the exchange interaction between these two spin systems results in a 'chiral' magnetoresistance depending on the chirality of the local spin texture. We observe this magnetoresistance by measuring the domain wall (DW) resistance in a uniquely designed Pt/Co/Pt zigzag wire, and by changing the chirality of the DW with applying an in-plane magnetic field. A chirality-dependent DW resistance …
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…
We present a theoretical study on the effect of radiation on the mangetoresistance of two-dimensional electron systems with strong Rashba spint-orbit coupling. We want to study the interplay between two well-known effects in these electron systems: the radiation-induced resistance oscillations and the typical beating pattern of systems with intense Rashba interaction. We analytically derive an exact solution for the electron wave function corresponding to a total Hamiltonian with Rashba and radiation terms. We consider a perturbation treatment for elastic scattering due to charged impurities t…
The effects of the spin-orbit interaction on the tunneling magnetoresistance of magnetic tunnel junctions are investigated. A model in which the experimentally observed two-fold symmetry of the anisotropic tunneling magnetoresistance (TAMR) originates from the interference between Dresselhaus and Bychkov-Rashba spin-orbit couplings is formulated. Bias induced changes of the Bychkov-Rashba spin-orbit coupling strength can result in an inversion of the TAMR. The theoretical calculations are in good agreement with the TAMR experimentally observed in epitaxial Fe/GaAs/Au tunnel junctions.
The momentum dependent splitting of spin-bands in an electronic system is known as the "Rashba effect". Systems with the "Rashba effect" possess a Dirac point in momentum space. An electron in a cyclotron orbit enclosing that Dirac point in the reciprocal space gains a "Berry phase". We report here the Shubnikov-de-Haas oscillations (SdH) at the conducting interface of EuO-KTaO$_3$ (KTO). Observed SdH oscillations suggest the presence of two Fermi surfaces. For both the Fermi surfaces, we have seen the presence of a non-trivial "Berry phase" suggesting that the surfaces enclose the "Dirac poin…
Anisotropic magnetoresistance of two-dimensional Rashba systems with in-plane Zeeman field and point-like disorder
Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院量子材料与技术研究所）；Institut für Theorie der Kondensierten Materie, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院凝聚态理论研究所）；Department of Physics and Astronomy, Ohio University（俄亥俄大学物理与天文学系）
Among the perovskite oxide family, KTaO$_3$ (KTO) has recently attracted considerable interest as a possible system for the realization of the Rashba effect. In this work, we improvise a novel conducting interface by juxtaposing KTO with another insulator, namely LaVO$_3$ (LVO) and report planar Hall effect (PHE) and anisotropic magnetoresistance (AMR) measurements. This interface exhibits a signature of strong spin-orbit coupling. Our experimental observation of two fold AMR at low magnetic fields can be intuitively understood using a phenomenological theory for a Rashba spin-split system. At…
We argue that edge electrons in monolayer WTe$_2$ can possess a "cooperative" orbital moment (COM) that critically impacts its edge magnetoresistance behavior. Arising from the cooperative action of both Rashba and Ising spin orbit coupling, COM quickly achieves large magnitudes (of order few Bohr magnetons) even for relatively small spin-orbit coupling strengths. As we explain, such large COM magnitudes arise from an unconventional cooperative spin canting of edge spins when Rashba and Ising spin orbit coupling act together. Strikingly, COM can compete with spin moments to produce an unusual …
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…
We reveal that the interplay between Rashba spin-orbit coupling and proximity-induced magnetization in a two-dimensional electron gas leads to peculiar transport properties and large anisotropy of magnetoresistance. While the related tunneling anisotropic magnetoresistance (TAMR) has been extensively studied before, we predict an effect with a different origin arising from the evolution of a resonant condition with the in-plane rotation of magnetization and having a much larger magnitude. The resonances in the tunneling emerge from a spin-parity-time symmetry of the scattering states. However,…
Spin-orbit effects appearing in topological insulators (TI) and at Rashba interfaces are currently revolutionizing how we can manipulate spins and have led to several newly discovered effects, from spin-charge interconversion and spin-orbit torques to novel magnetoresistance phenomena. In particular, a puzzling magnetoresistance has been evidenced, bilinear in electric and magnetic fields. Here, we report the observation of bilinear magnetoresistance (BMR) in strained HgTe, a prototypical TI. We show that both the amplitude and sign of this BMR can be tuned by controlling, with an electric gat…
The present paper theoretically investigates magnetoresistance curves in quasiperiodic magnetic multilayers for two different growth directions, namely [110] and [100]. We considered identical ferromagnetic layers separated by non-magnetic layers with two different thicknesses chosen based on the Fibonacci sequence. Using parameters for Fe/Cr multilayers, four terms were included in our description of the magnetic energy: Zeeman, cubic anisotropy, bilinear and biquadratic couplings. The minimum energy was determined by the gradient method and the equilibrium magnetization directions found were…
The Rashba spin-orbit coupling in carbon nanotubes and its effect on spin-dependent transport properties are analyzed theoretically. We focus on clean non-interacting nanotubes with tunable number of subbands $N$. The peculiar band structure is shown to allow in principle for Datta-Das oscillatory behavior in the tunneling magnetoresistance as a function of gate voltage, despite the presence of multiple bands. We discuss the conditions for observing Datta-Das oscillations in carbon nanotubes.
Rashba interfaces yield efficient spin-charge interconversion and give rise to nonreciprocal transport phenomena. Here, we report magnetotransport experiments in few-nanometer-thick films of PdCoO$_2$, a delafossite oxide known to display a large Rashba splitting and surface ferromagnetism. By analyzing the angle dependence of the first- and second-harmonic longitudinal and transverse resistivities, we identify a Rashba-driven unidirectional magnetoresistance that competes with the anomalous Nernst effect below the Curie point. We estimate a Rashba coefficient of 0.75 {\pm} 0.3 eV Å and argue …
A microscopic expression of the residual electrical resistivity tensor is derived in linear response theory for Rashba electrons scattering at a magnetic impurity with cylindrical or non-cylindrical potential. The behavior of the longitudinal and transversal residual resistivity is computed for an Fe impurity at the Au(111) surface. We studied the evolution of the resistivity tensor elements as function of the Rashba spin-orbit strength and the magnetization direction of the impurity. We found that the absolute values of longitudinal resistivity reduces with increasing spin-orbit strength of t…
We study the magnetoelectric and magnetothermal transport properties of noncentrosymmetric metals using semiclassical Boltzmann transport formalism by incorporating the effects of Berry curvature and orbital magnetic moment. These effects impart quadratic-B dependence to the magnetoelectric and magnetothermal conductivities, leading to intriguing phenomena such as planar Hall effect, negative magnetoresistance, planar Nernst effect and negative Seebeck effect. The transport coefficients associated with these effects show the usual oscillatory behavior with respect to the angle between the appl…
We theoretically investigate a new kind of nonlinear magnetoresistance on the surface of three-dimensional topological insulators (TIs). At variance with the unidirectional magnetoresistance (UMR) effect in magnetic bilayers, this nonlinear magnetoresistance does not rely on a conducting ferromagnetic layer and scales linearly with both the applied electric and magnetic fields; for this reason, we name it bilinear magneto-electric resistance (BMER). We show that the sign and the magnitude of the BMER depends sensitively on the orientation of the current with respect to the magnetic field as we…
We report experiments on epitaxially grown Fe/GaAs/Au tunnel junctions demonstrating that the tunneling anisotropic magnetoresistance (TAMR) effect can be controlled by a magnetic field. Theoretical modelling shows that the interplay of the orbital effects of a magnetic field and the Dresselhaus spin-orbit coupling in the GaAs barrier leads to an independent contribution to the TAMR effect with uniaxial symmetry, whereas the Bychkov-Rashba spin-orbit coupling does not play a role. The effect is intrinsic to barriers with bulk inversion asymmetry.
In ferromagnet/normal-metal bilayers, the sensitivity of the spin Hall magnetoresistance and the spin Nernst magnetothermopower to the boundary conditions at the interface is of central importance. In general, such boundary conditions can be substantially affected by current-induced spin polarizations. In order to quantify the role of the latter, we consider a Rashba two-dimensional electron gas with a ferromagnet attached to one side of the system. The geometry of such a system maximizes the effect of current-induced spin polarization on the boundary conditions, and the spin Hall magnetoresis…
In a one-dimensional weak-link wire the spin-orbit interaction (SOI) alone cannot generate a nonzero spin current. We show that a Zeeman field acting in the wire in conjunction with the Rashba SOI there does yield such a current, whose magnitude and direction depend on the direction of the field. When this field is not parallel to the effective field due to the SOI, both the charge and the spin currents oscillate with the length of the wire. Measuring the oscillating anisotropic magnetoresistance can thus yield information on the SOI strength. These features are tuned by applying a magnetic an…
The Rashba-Edelstein effect stems from the interaction between the electron's spin and its momentum induced by spin-orbit interaction at an interface or a surface. It was shown that the inverse Rashba-Edelstein effect can be used to convert a spin- into a charge current. Here, we demonstrate that a Bi/Ag Rashba interface can even drive an adjacent ferromagnet to resonance. We employ a spin-torque ferromagnetic resonance excitation/detection scheme which was developed originally for a bulk spin-orbital effect, the spin Hall effect. In our experiment, the direct Rashba-Edelstein effect generates…
The effects of the spin-orbit interaction on the tunneling magnetoresistance of ferromagnet/semiconductor/normal metal tunnel junctions are investigated. Analytical expressions for the tunneling anisotropic magnetoresistance (TAMR) are derived within an approximation in which the dependence of the magnetoresistance on the magnetization orientation in the ferromagnet originates from the interference between Bychkov-Rashba and Dresselhaus spin-orbit couplings that appear at junction interfaces and in the tunneling region. We also investigate the transport properties of ferromagnet/semiconductor/…
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 electric-field tunable Rashba spin-orbit coupling at the LaAlO3/SrTiO3 interface shows potential applications in spintronic devices. However, different gate dependence of the coupling strength has been reported in experiments. On the theoretical side, it has been predicted that the largest Rashba effect appears at the crossing point of the $d_{xy}$ and $d_{xz,yz}$ bands. In this work, we study the tuneability of the Rashba effect in LaAlO3/SrTiO3 by means of back-gating. The Lifshitz transition was crossed multiple times by tuning the gate voltage so that the Fermi energy is tuned to appro…
The effects of structural (Rashba) and bulk (Dresselhaus) spin-orbit interaction terms on the low-field magnetoresistance are investigated in high-quality two dimensional systems. The weak localization theory accounting for both of these terms valid in the whole range of magnetic fields is proposed. The suppresion of antilocalization correction as Rashba and Dresselhaus terms strengths approach each other is demonstrated. The effect of cubic in the wavevector spin-splitting term is analyzed.
We present magnetoresistance measurements performed on ultrathin films of amorphous Ni and Fe. In these films the Curie temperature drops to zero at small thickness, making it possible to study the effect of ferromagnetism on localization. We find that non-ferromagnetic films are characterized by positive magnetoresistance. This is interpreted as resulting from weak antilocalization due to strong Bychkov-Rashba spin orbit scattering. As the films become ferromagnetic the magnetoresistance changes sign and becomes negative. We analyze our data to identify the individual contributions of weak lo…
We consider the effect of the Rashba spin-orbital interaction and space charge in a ferromagnet-insulator/semiconductor/insulator-ferromagnet junction where the spin current is severely affected by the doping, band structure and charge screening in the semiconductor. In diffusion region, if the the resistance of the tunneling barriers is comparable to the semiconductor resistance, the magnetoresistance of this junction can be greatly enhanced under appropriate doping by the co-ordination between the Rashba effect and screened Coulomb interaction in the nonequilibrium transport processes within…
A magnetoresistance effect induced by the Rashba spin-orbit interaction was predicted, but not yet observed, in bilayers consisting of normal metal and ferromagnetic insulator. Here, we present an experimental observation of this new type of spin-orbit magnetoresistance (SOMR) effect in a bilayer structure Cu[Pt]/Y3Fe5O12 (YIG), where the Cu/YIG interface is decorated with nanosize Pt islands. This new MR is apparently not caused by the bulk spin-orbit interaction because of the negligible spin-orbit interaction in Cu and the discontinuity of the Pt islands. This SOMR disappears when the Pt is…
We intercalate a van der Waals heterostructure of graphene and hexagonal Boron Nitride with Au, by encapsulation, and show that Au at the interface is two dimensional. A charge transfer upon current annealing indicates redistribution of Au and induces splitting of the graphene bandstructure. The effect of in plane magnetic field confirms that splitting is due to spin-splitting and that spin polarization is in the plane, characteristic of a Rashba interaction with magnitude approximately 25 meV. Consistent with the presence of intrinsic interfacial electric field we show that the splitting can …
Using the Landauer-Bütikker formalism, we study the graphene magneto-transport in the presence of Rashba spin-orbit interaction (RSOI). We show that the angle resolved transmission probability in the proposed structures can be tuned by the RSOI strength. The transmission spectrum show Klein tunneling in the parallel (P) magnetization configuration which can be blocked by the RSOI. This effect is also observable for the anti-parallel (AP) magnetization configuration in different incident angle. The numerical results shows that the spin-polarized conductance strongly depends on the strength of t…
Hanle magnetoresistance (HMR) is a type of magnetoresistance where interplay of the spin Hall effect, Hanle-type spin precession, and spin-dependent scattering at the top/bottom surfaces in a heavy metal controls the effect. In this study, we modulate HMR in ultrathin Pt by ionic gating, where the surface Rashba field created by a strong electric field at the interface between the ionic gate and Pt plays the dominant role in the modulation. This finding can facilitate investigations of gate-tunable, spin-related effects and fabrication of spin devices.
Spin Hall and Edelstein effects in a ballistic quantum dot with Rashba spin-orbit coupling
CNR-SPIN（意大利国家研究委员会自旋物理研究所）；Università di Salerno（萨莱诺大学）；Dipartimento di Fisica ”E.R. Caianiello”, Università di Salerno（萨莱诺大学埃·R·卡亚涅洛物理系）；INFN, Sezione di Napoli, Gruppo collegato di Salerno（意大利国家核物理研究所那不勒斯分部萨莱诺协作组）；Dipartimento di Fisica, Università della Calabria（卡拉布里亚大学物理系）；Dipartimento di Fisica Ettore Pancini, Università degli Studi di Napoli Federico II（那不勒斯费德里科二世大学埃托雷·潘奇尼物理系）；AGH University of Krakow, Faculty of Physics and Applied Computer Science（克拉科夫AGH科技大学物理与应用计算机科学系）
We demonstrate a current tunable Rashba spin orbit interaction in LaAlO3/SrTiO3 (LAO/STO) quasi two dimensional electron gas (2DEG) system. Anisotropic magnetoresistance (AMR) measurements are employed to detect and understand the current-induced Rashba field. The effective Rashba field scales with the current and a value of 2.35 T is observed for a dc-current of 200 uA. The results suggest that LAO/STO heterostructures can be considered for spin orbit torque based magnetization switching.
Magnetotransport measurements are a popular way of characterizing the electronic structure of topological materials and often the resulting datasets cannot be described by the well-known Drude model due to large, non-parabolic contributions. In this work, we focus on the effects of magnetic fields on topological materials through a Zeeman term included in the model Hamiltonian. To this end, we re-evaluate the simplifications made in the derivations of the Drude model and pinpoint the scattering time and Fermi velocity as Zeeman-term dependent factors in the conductivity tensor. The driving mec…
Recent experimental work on Au thin films demonstrated signs of charge current-induced spin polarization through open circuit voltage measurements. In this study, we are investigating the underlying mechanism(s) that induces this measured signal in the Au devices. We determine the theoretically expected spin polarization from both Rashba-Edelstein effect and bulk spin Hall effect. The discrepancy in the scaling of the measured signal as a function of the thickness of the Au thin film in the two cases is our key to differentiate between the two effects when compared to experimental data. Experi…
Over the regime of the radiation-induced zero-resistance states and associated oscillatory magnetoresistance, we propose a low magnetic field analog of quantum-Hall-limit techniques for the electrical detection of electron spin- and nuclear magnetic- resonance, dynamical nuclear polarization via electron spin resonance, and electrical characterization of the nuclear spin polarization via the Overhauser shift. In addition, beats observed in the radiation-induced oscillatory-magnetoresistance are developed into a method to measure and control the zero-field spin splitting due to the Bychkov-Rash…
The propensity of some materials and multilayers to have a magnetic field dependent resistance, called magnetoresistance, has found commercial applications such as giant magnetoresistance harddisk read heads. But magnetoresistance can also be a powerful probe of electronic and magnetic interactions in matter. For example, magnetoresistance can be used to analyze multiband conductivity, conduction inhomogeneity, localized magnetic moments, and (fractional) Landau level structure. For materials with strong spin-orbit interaction, magnetoresistance can be used as a probe for weak antilocalization…
We report a systematic study on Edelstein magnetoresistance (Edelstein MR) in Co25Fe75/Cu/Bi2O3 heterostructures with a strong spin-orbit interaction at the Cu/Bi2O3 interface. We succeed in observing a significant dependence of the Edelstein MR on both Cu layer thickness and temperature, and also develop a general analytical model considering distinct bulk and interface contributions on spin relaxation. Our analysis, based on the above model, quantitatively illustrates a unique property of the spin transport near the Rashba interface, revealing a prominent role of the spin relaxation process …
We investigate the behavior of both pure spin and spin-polarized currents measured with four probe non-local and two probe local configurations up to room temperature and under external gate voltage in a lateral graphene transistor, produced using a standard large-scale microfabrication process. The high spin diffusion length of pristine graphene in the channel, measured both directly and by the Hanle effect, and the tuning of relation between electrode resistance area present in the device architecture, allowed us to observe local tunnel magnetoresistance at room temperature, a new finding fo…
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 …
