We theoretically study the magnetoresistance (MR) of two-dimensional massless Dirac electrons as found on the surface of three-dimensional topological insulators (3D TIs) that is capped by a ferromagnetic insulator (FI). We calculate charge and spin transport by Kubo and Boltzmann theories, taking into account the ladder-vertex correction and the in-scattering due to normal and magnetic disorder. The induced exchange splitting is found to generate an electric conductivity that depends on the magnetization orientation, but its form is very different from both the anisotropic and spin Hall MR. The in-plane MR vanishes identically for non-magnetic disorder, while out-of-plane magnetizations cause a large MR ratio. On the other hand, we do find an in-plane MR and planar Hall effect in the presence of magnetic disorder aligned with the FI magnetization. Our results may help understand recent transport measurements on TI|FI systems.
We study the anomalous Hall-like effect (AHLE) and the effective anisotropic magnetoresistance (EAMR) in antiferromagnetic γ -IrMn3/Y3Fe5O12(YIG) and Pt/YIG heterostructures. For γ -IrMn3/YIG, the EAMR and the AHLE resistivity change sign with temperature due to the competition between the spin Hall magnetoresistance (SMR) and the magnetic proximity effect (MPE) induced by the interfacial antiferromagnetic uncompensated magnetic moment. In contrast, for Pt/YIG the AHLE resistivity changes sign with temperature whereas no sign change is observed in the EAMR. This is because the MPE and the SMR …
We demonstrate the existence of Giant proximity magnetoresistance (PMR) effect in a graphene spin valve where spin polarization is induced by a nearby magnetic insulator. PMR calculations were performed for yttrium iron garnet (YIG), cobalt ferrite (CFO), and two europium chalcogenides EuO and EuS. We find a significant PMR (up to 100%) values defined as a relative change of graphene conductance with respect to parallel and antiparallel alignment of two proximity induced magnetic regions within graphene. Namely, for high Curie temperature (Tc) CFO and YIG insulators which are particularly impo…
Due to its two dimensional nature, ferromagnetism and charge doping can be induced by proximity and electric field effects in graphene. Taking advantage of these features, we propose an electrically engineered spin valve by combining two magnetic insulators (using EuO, EuS, or YIG) and three coating gates. Two top gates are used to cancel the heavy electron doping's in these magnets and one back gate is used to utilize the normal or half-metallic ferromagnetisms. We demonstrate that, when the second top gate is tuned to utilize the insulating or spin insulating states, huge giant magnetoresist…
According to Onsager's principle, electrical resistance $R$ of general conductors behaves as an even function of external magnetic field $B$. Only in special circumstances, which involve time reversal symmetry (TRS) broken by ferromagnetism, the odd component of $R$ against $B$ is observed. This unusual phenomenon, called odd-parity magnetoresistance (OMR), was hitherto subtle (< 2%) and hard to control by external means. Here, we report a giant OMR as large as 27% in edge transport channels of an InAs quantum well, which is magnetized by a proximity effect from an underlying ferromagnetic sem…
We demonstrate single atom anisotropic magnetoresistance on the surface of a topological insulator, arising from the interplay between the helical spin-momentum-locked surface electronic structure and the hybridization of the magnetic adatom states. Our first-principles quantum transport calculations based on density functional theory for Mn on Bi$_2$Se$_3$ elucidate the underlying mechanism. We complement our findings with a two dimensional model valid for both single adatoms and magnetic clusters, which leads to a proposed device setup for experimental realization. Our results provide an exp…
The evolution of information technology has been driven by the discovery of new forms of large magnetoresistance (MR), such as giant magnetoresistance (GMR) and tunnelling magnetoresistance (TMR) in magnetic multilayers. Recently, new types of MR have been observed in much simpler bilayers consisting of ferromagnetic (FM)/nonmagnetic (NM) thin films; however, the magnitude of MR in these materials is very small (0.01 ~ 1%). Here, we demonstrate that NM/FM bilayers consisting of a NM InAs quantum well conductive channel and an insulating FM (Ga,Fe)Sb layer exhibit giant proximity magnetoresista…
Studies of negative magnetoresistance in novel materials have recently been in the forefront of spintronic research. Here, we report an experimental observation of the temperature dependent negative magnetoresistance in Bi2Te3 topological insulator (TI) nanowires at ultralow temperatures (20 mK). We find a crossover from negative to positive magnetoresistance while increasing temperature under longitudinal magnetic field. We observe a large negative magnetoresistance which reaches -22% at 8T. The interplay between negative and positive magnetoresistance can be understood in terms of the compet…
We report a metal-insulator like transition in single crystalline 3D topological insulator Bi2Te3 at a temperature of 230K in presence of an external magnetic field applied normal to the surface. This transition becomes more prominent at larger magnetic field strength with the residual resistance value increasing linearly with the magnetic field. At low temperature, the magnetic field dependence of the magnetoresistance shows a transition from logarithmic to linear behavior and the onset magnetic field value for this transition decreases with increasing temperature. The logarithmic magnetoresi…
Large unsaturated magnetoresistance (XMR) with magnitude about 1000% is observed in topological insulator candidate TaSe3 from our high field (up to 38 T) measurements. Two oscillation modes, associated with one hole pocket and two electron pockets in the bulk, respectively, are detected from our Shubnikov-de Hass (SdH) measurements, consistent with our first-principles calculations. With the detailed Hall measurements performed, our two-band model analysis exhibits an imperfect density ratio n_h/n_e closing 0.9 at T< 20 K , which suggests that the carrier compensations account for the XMR in …
We report current-direction dependent or unidirectional magnetoresistance (UMR) in magnetic/nonmagnetic topological insulator (TI) heterostructures, Cr$_x$(Bi$_{1-y}$Sb$_y$)$_{2-x}$Te$_3$/(Bi$_{1-y}$Sb$_y$)$_2$Te$_3$, that is several orders of magnitude larger than in other reported systems. From the magnetic field and temperature dependence, the UMR is identified to originate from the asymmetric scattering of electrons by magnons. In particular, the large magnitude of UMR is an outcome of spin-momentum locking and a small Fermi wavenumber at the surface of TI. In fact, the UMR is maximized ar…
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…
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,…
The theory of magnetoresistance of the edge state of a two-dimensional topological insulator is developed. The magnetic field violates the time-reversal invariance. Magnetoresistance arises due to the energy gap opened by a magnetic field parallel to the sample surface. The combined action of impurities and the magnetic field causes backscattering of edge electrons. Although impurities are necessary for scattering, sufficiently strong interaction with impurities leads to the suppression of backscattering.
Absence of backscattering and occurrence of weak anti-localization are two characteristic features of topological insulators. We find that the introduction of defects results in the appearance of a negative contribution to magnetoresistance in the topological insulator BiSbTeSe2, at temperatures below 50 K. Our analysis shows that the negative magnetoresistance originates from an increase in the density of defect states created by introduction of disorder, which leaves the surface states unaffected. We find a decrease in the magnitude of the negative magnetoresistance contribution with increas…
Ultra-thin Pt films grown on insulating ferrimagnetic CoFe2O4 (111) epitaxial films display a magnetoresistance upon rotating the magnetization of the magnetic layer. We report here X-ray magnetic circular dichroism (XMCD) recorded at Pt-L2,3 and Pt-M3 edges. The results indicate that the Pt magnetic moment, if any, is below the detection limit (< 0.001 μ$_B$/Pt), thus strongly favoring the view that the presence of CoFe2O4 does not induce the formation of magnetic moments in Pt. Therefore, the observed magnetoresistance cannot be attributed to some sort of proximity-induced magnetic moments a…
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 report magnetoresistance for current flow through iron/topological insulator (Fe/TI) and Fe/evaporated-oxide/TI contacts when a magnetic field is used to initially orient the magnetic alignment of the incorporated ferromagnetic Fe bar, at temperatures ranging from 100 K to room temperature. This magnetoresistance is associated with the relative orientation of the Fe bar magnetization and spin-polarization of electrons moving on the surface of the TI with helical spin-momentum locking. The magnitude of the observed magnetoresistance is relatively large compared to that observed in prior work…
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…
The recently discovered antiferromagnetic topological insulator MnBi$_2$Te$_4$ hosts a variety of exotic topological quantum phases such as the axion insulator and Chern insulator states. Here we report systematic gate voltage dependent magneto transport studies in six septuple-layer MnBi$_2$Te$_4$. In p-type carrier regime, we observe positive linear magnetoresistance when MnBi$_2$Te$_4$ is polarized in the ferromagnetic state by an out-of-plane magnetic field. Whereas in n-type regime, distinct negative magnetoresistance behaviors are observed. The magnetoresistance in both regimes is highly…
We report an electric field-induced in-plane magnetoresistance of an atomically flat paramagnetic insulator|platinum (Pt) interface at low temperatures with an ionic liquid gate. Transport experiments as a function of applied magnetic field strength and direction obey the spin Hall magnetoresistance phenomenology with perpendicular magnetic anisotropy. Our results establish the utility of ionic gating as an alternative method to control spintronic devices without using ferromagnets.
We observe an unusual behavior of the spin Hall magnetoresistance (SMR) measured in a Pt ultra-thin film deposited on a ferromagnetic insulator, which is a tensile-strained LaCoO3 (LCO) thin film with the Curie temperature Tc=85K. The SMR displays a strong magnetic-field dependence below Tc, with the SMR amplitude continuing to increase (linearly) with increasing the field far beyond the saturation value of the ferromagnet. The SMR amplitude decreases gradually with raising the temperature across Tc and remains measurable even above Tc. Moreover, no hysteresis is observed in the field dependen…
We study the temperature dependence of spin Hall magnetoresistance (SMR) in antiferromagnetic insulator (AFI)/metal bilayer systems. We calculate the amplitude of the SMR signal by using a quantum Monte Carlo simulation and examine how the SMR depends on the amplitude of the spin, thickness of the AFI layer, and randomness of the exchange interactions. Our results for simple quantum spin models provide a useful starting point for understanding SMR measurements on atomic layers of magnetic compounds.
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…
This article aims at giving a general presentation of spintronics, an important field of research developing today along many new directions in physics of condensed matter. We tried to present simply the physical phenomena involved in spintronics -- no equations but many schematics. We also described the applications of spintronics, those of today and those expected to have an important impact on the next developments of the information and communication technologies.
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…
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 report a systematic first-principles investigation of the influence of different magnetic insulators on the magnetic proximity effect induced in graphene. Four different magnetic insulators are considered: two ferromagnetic europium chalcogenides namely EuO and EuS and two ferrimagnetic insulators yttrium iron garnet (YIG) and cobalt ferrite (CFO). The obtained exchange-splitting varies from tens to hundreds of meV. We also find an electron doping induced by YIG and europium chalcogenides substrates, that shift the Fermi level up to 0.78 eV and 1.3 eV respectively, whereas hole doping up to…
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…
Inducing long-range magnetic order in three-dimensional topological insulators can gap the Diraclike metallic surface states, leading to exotic new phases such as the quantum anomalous Hall effect or the axion insulator state. These magnetic topological phases can host robust, dissipationless charge and spin currents or unique magnetoelectric behavior, which can be exploited in low-energy electronics and spintronics applications. Although several different strategies have been successfully implemented to realize these states, to date these phenomena have been confined to temperatures below a f…
We theoretically investigate tunneling magnetoresistance (TMR) devices, which are probing the spin-momentum coupled nature of surface states of the three-dimensional topological insulator Bi$_{2}$Se$_{3}$. Theoretical calculations are performed based on a realistic tight-binding model for Bi$_{2}$Se$_{3}$. We study both three dimensional devices, which exploit the surface states of Bi$_{2}$Se$_{3}$, as well as two-dimensional devices, which exploit the edge states of thin Bi$_{2}$Se$_{3}$ strips. We demonstrate that the material properties of Bi$_{2}$Se$_{3}$ allow a TMR ratio at room temperat…
We investigate spin-charge conversion phenomena in hybrid structures of topological insulator (TI) thin films and magnetic insulators. We find an anisotropic inverse spin-galvanic effect (ISGE) that yields a highly tunable spin-orbit torque (SOT). Concentrating on the quasiballistic limit, we also predict a giant anisotropic magnetoresistance (AMR) at low dopings. These effects, which have no counterparts in thick TIs, depend on the simultaneous presence of the hybridization between the surface states and the in-plane magnetization. Both the ISGE and AMR exhibit a strong dependence on the magn…
An intriguing phenomenon in topological semimetals and topological insulators is the negative magnetoresistance (MR) observed when a magnetic field is applied along the current direction. A prevailing understanding to the negative MR in topological semimetals is the chiral anomaly, which, however, is not well defined in topological insulators. We calculate the MR of a three-dimensional topological insulator, by using the semiclassical equations of motion, in which the Berry curvature explicitly induces an anomalous velocity and orbital moment. Our theoretical results are in quantitative agreem…
The emergence of topological order in graphene is in great demand for the realization of quantum spin Hall states. Recently, it is theoretically proposed that the spin textures of surface states in topological insulator can be directly transferred to graphene by means of proximity effect. Here we report the observations of the topological proximity effect in the graphene-topological insulator Bi2Se3 heterojunctions via magnetotransport measurements. The coupling between the p_z orbitals of graphene and the p orbitals of surface states on the Bi2Se3 bottom surface can be enhanced by applying pe…
Anomalous Hall-like signals in platinum in contact with magnetic insulators are common observations that could be explained by either proximity magnetization or spin Hall magnetoresistance. In this work, longitudinal and transverse magnetoresistances are measured in a pure gold thin film on the ferrimagnetic insulator Y$_3$Fe$_5$O$_{12}$ (Yttrium Iron Garnet, YIG). We show that both the longitudinal and transverse magnetoresistances have quantitatively consistent scaling in YIG/Au and in a YIG/Pt reference system when applying the Spin Hall magnetoresistance framework. No contribution of an an…
Electrical resistivities can be different for charge currents travelling parallel or perpendicular to the magnetization in magnetically ordered conductors or semiconductors, resulting in the well-known planar Hall effect and anisotropic magnetoresistance. Here, we study the analogous anisotropic magnetotransport behavior for magnons in a magnetic insulator Y$_{3}$Fe$_{5}$O$_{12}$. Electrical and thermal magnon injection, and electrical detection methods are used at room temperature with transverse and longitudinal geometries to measure the magnon planar Hall effect and anisotropic magnetoresis…
A new mechanism of bi-linear magnetoresistance (BMR) is studied theoretically within the minimal model describing surface electronic states in topological insulators (TIs). The BMR appears as a consequence of the second-order response to electric field, and depends linearly on both electric field (current) and magnetic field. The mechanism is based on the interplay of current-induced spin polarization and scattering processes due to peculiar spin-orbit defects. The proposed mechanism is compared to that based on a Fermi surface warping, and is shown to be dominant at lower Fermi energies. We p…
