Theoretical Study on Anisotropic Magnetoresistance Effects of Arbitrary Directions of Current and Magnetization for Ferromagnets: Application to Transverse Anisotropic Magnetoresistance Effect
Satoshi Kokado, Masakiyo Tsunoda
备注:
31 pages, 5 figures, J. Phys. Soc. Jpn. (2022), accepted
发表信息:
J. Phys. Soc. Jpn. 91, 044701 (2022) [open access]
We develop a theory of the anisotropic magnetoresistance (AMR) effects of arbitrary directions of current and magnetization for ferromagnets. Here, we use the electron scattering theory with the $s$--$s$ and $s$--$d$ scattering processes, where $s$ is the conduction electron state and $d$ is the localized d states. The resistivity due to electron scattering is expressed by the probability density of the d states of the current direction. The d states are numerically obtained by applying the exact diagonalization method to the Hamiltonian of the d states with the exchange field, crystal field, and spin--orbit interaction. Using the theory, we investigate the transverse AMR (TAMR) effect for strong ferromagnets with a crystal field of cubic or tetragonal symmetry. The cubic systems exhibit the fourfold symmetric TAMR effect, whereas the tetragonal systems show the twofold and fourfold symmetric TAMR effect. On the basis of the above results, we also comment on the experimental results of the TAMR effect for Fe$_4$N.
We study the dependence of perpendicular-current magnetoresistance in magnetic multilayers on the angle between the magnetizations of the layers. This dependence varies with the thickness of one of the layers, and is different for multilayers with two and three magnetic layers. We derive a system of equations representing an extension of the two-current series resistor model, and show that the angular dependence of magnetoresistance gives information about the noncollinear spin-transport in ferromagnets.
The anisotropic magnetoresistance (AMR) in thin permalloy strips was calculated at each steps during magnetization by the finite element method. The magnetization at equilibrium under different external fields was obtained by micromagnetic simulations, while the resistance with different magnetization was obtained by solving the Poisson equations iteratively until self-consistence. We find that the relation between magnetization and AMR deviates from the Stoner-Wohlfarth prediction when the magnetization is reduced from saturation. The reason is that the demagnetization is not necessarily from…
In order to elucidate the nature of ferromagnetic signatures observed in (Zn,Co)O we have examined experimentally and theoretically magnetic properties and spin-dependent quantum localization effects that control low-temperature magnetoresistance. Our findings, together with a through structural characterization, substantiate the model assigning spontaneous magnetization of (Zn,Co)O to uncompensated spins at the surface of antiferromagnetic nanocrystal of Co-rich wurtzite (Zn,Co)O. The model explains a large anisotropy observed in both magnetization and magnetoresistance in terms of spin hamil…
Giant magnetoresistance (GMR) of sequentially evaporated Fe-Ag structures have been investigated. Direct experimental evidence is given that inserting ferromagnetic layers into a granular structure significantly enhances the magnetoresistance. The increase of the GMR effect is attributed to spin polarization effects. The large enhancement (up to more than a fourfold value) and the linear variation of the GMR in low magnetic fields are explained by scattering of the spin polarized conduction electrons on paramagnetic grains.
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Difference in density of states for the spin's majority and minority bands in a ferromagnet changes the electrostatic potential along the domains, introducing the discontinuities of the potential at domain boundaries. The value of discontinuity oscillates with number of domains. Discontinuity depends on the positions of domain walls, their motion or collapse of domain walls in applied magnetic field. Large values of magnetoresistance are explained in terms of spin-accumulation. We suggest a new type of domain walls in nanowires of itinerant ferromagnets, in which the magnetization vector chang…
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We observe a dc voltage peak at ferromagnetic resonance (FMR) in samples consisting of a single ferromagnetic (FM) layer grown epitaxially on the $\mathit{n-}$GaAs (001) surface. The FMR peak is detected as an interfacial voltage with a symmetric line shape and is present in samples based on various FM/$n$-GaAs hetrostructures, including Co$_{2}$MnSi/$n$-GaAs, Co$_{2}$FeSi/$n$-GaAs and Fe/$n$-GaAs. We show that the interface bias voltage dependence of the FMR signal is identical to that of the tunneling anisotropic magnetoresistance (TAMR) over most of the bias range. Furthermore, we show how …
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Magnetization reversal mechanisms and impact of magnetization direction are studied in square arrays of interconnected circular permalloy nanorings using MOKE, local imaging, numerical simulations and transport techniques.
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We study current-driven magnetization switching in nanofabricated magnetic trilayers, varying the magnetoresistance in three different ways. First, we insert a strongly spin-scattering layer between the magnetic trilayer and one of the electrodes, giving increased magnetoresistance. Second, we insert a spacer with a short spin-diffusion length between the magnetic layers, decreasing the magnetoresistance. Third, we vary the angle between layer magnetizations. In all cases, we find an approximately linear dependence between magnetoresistance and inverse switching current. We give a qualitative …
Recently, van der Waals (vdW) magnetic heterostructures have received increasing research attention in spintronics. However, the lack of room-temperature magnetic order of vdW material has largely impedes its development in practical spintronics devices. Inspired by the recently discovered vdW ferromagnet Fe3GaTe2, which has been shown to have magnetic order above room temperature and sizable perpendicular magnetic anisotropy, we investigate the basic electronic structure and magnetic properties of Fe3GaTe2 as well as tunneling magnetoresistance effect in magnetic tunnel junctions (MTJs) with …
The magnetization characteristic in a permalloy thin strip is investigated by electrically measuring the anisotropic magnetoresistance and ferromagnetic resonance in in-plane and out-of-plane configurations. Our results indicate that the magnetization vector can rotate in the film plane as well as out of the film plane by changing the intensity of external magnetic field of certain direction. The magnetization characteristic can be explained by considering demagnetization and magnetic anisotropy. Our method can be used to obtain the demagnetization factor, saturated magnetic moment and the mag…
A drastic modification of electronic band structure is predicted in bilayer graphene when it is placed between two ferromagnetic insulators. Due to the exchange interaction with the proximate ferromagnet, the electronic energy dispersion in the graphene channel strongly depends on the magnetization orientation of two ferromagnetic layers, $\mathbf{M_{1}}$ and $\mathbf{M_{2}} $. While the parallel configuration $\mathbf{M_{1}}= \mathbf{M_{2}}$ leads to simple spin splitting of both conduction and valence bands, an energy gap is induced as soon as the angle $θ$ between $\mathbf{M_{1}}$ and $% \m…
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The isothermal magnetoresistance [R($θ$)] of [001] and [110] epitaxial films of La$_{2 / 3}$Sr$_{1 / 3}$MnO$_{3}$ measured as a function of the angle $θ$ between current ($\vec{I}$) and magnetic field ($\vec{H}$), both in the plane of the film, is measured at several temperatures between 10 and 300K. The magnetic easy axis of these polytypes is intimately related to the orientation of Mn - O - Mn bonds with respect to the crystallographic axis on the plane of the substrate and energy equivalence of some of these axes. The magnetization vector ($\vec{M}$) of the [001] and [110] type films is pi…
The measurements of the magnetic susceptibility, magnetization, electrical resistivity and magnetoresistance have been performed for the Fe intercalated compound Fe0.5TiS2. According to X-ray diffraction measurements the Fe0.5TiS2 compound synthesized in the present work has a monoclinic crystal structure (space group I12/m1) which results from the ordering of Fe ions and vacancies between S-Ti-S tri-layres. The changes in the heat-treatment conditions at temperatures below 1100 Celsius degrees do not lead to an order-disorder transition within the subsystem of intercalated Fe ions. It has bee…
Random hyperfine fields are essential to mechanisms of low-field magnetoresistance in organic semiconductors. Recent experiments have shown that another type of random field --- fringe fields due to a nearby ferromagnet --- can also dramatically affect the magnetoresistance. A theoretical analysis of the effect of these fringe fields is challenging, as the fringe field magnitudes and their correlation lengths are orders of magnitude larger than that of the hyperfine couplings. We extend a recent theory of organic magnetoresistance to calculate the magnetoresistance with both hyperfine and frin…
Experimental measurements show that the angular dependence of the anisotropic magnetoresistance (AMR) in L1$_0$ ordered FePt epitaxial films on the current orientation and magnetization direction is a superposition of the corresponding dependences of twofold and fourfold symmetries. The twofold AMR exhibits a strong dependence on the current orientation, whereas the fourfold term only depends on the magnetization direction in the crystal and is independent of the current orientation. First-principles calculations reveal that the fourfold AMR arises from the relaxation time anisotropy due to th…
We have measured high-field magnetization and magnetoresistance of polycrystalline samples of the A-site ordered perovskite CaCu3Ti4-xRuxO12 (x=0 - 4) utilizing a non-destructive pulsed magnet. We find that the magnetization for x=0.5, 1.0 and 1.5 is nonlinear, and tends to saturate in high fields. This is highly nontrivial because the magnetization for x=0 and 4 is linear in external field up to the highest one. We have analyzed this field dependence based on the thermodynamics of magnetic materials, and propose that the external fields delocalize the holes on the Cu2+ ions in order to maximi…
A major issue in the development of spintronic memory devices is the reduction of the power consumption for the magnetization reversal. For this purpose, the artificial control of the magnetic anisotropy of ferromagnetic materials is of great importance. Here, we demonstrate the control of the carrier-energy dependence of the magnetic anisotropy of the density of states (DOS) using the quantum size effect in a single-crystal ferromagnetic material, GaMnAs. We show that the mainly two-fold symmetry of the magnetic anisotropy of DOS, which is attributed to the impurity band, is changed to a four…
A theoretical formulation of magnetoresistance effect in a metallic ferromagnetic/nonmagnetic bilayer originated from the charge-spin conversion by the anomalous Hall effect is presented. Analytical expressions of the longitudinal and transverse resistivities in both nonmagnet and ferromagnet are obtained by solving the spin diffusion equation. The magnetoresistance generated from charge-spin conversion purely caused by the anomalous Hall effect in the ferromagnet is found to be proportional to the square of the spin polarizations in the ferromagnet and has fixed sign. We also find additional …
The electrical resistance of ferromagnetic/normal-metal (F/N) heterostructures depends on the nature of the junctions which may be tunnel barriers, point contacts, or intermetallic interfaces. For all junction types, the resistance of disordered F/N/F perpendicular spin valves as a function of the angle between magnetization vectors is shown to obey a simple universal law. The spin-current induced magnetization torque can be measured by the angular magnetoresistance of these spin valves. The results are generalized to arbitrary magnetoelectronic circuits.
We report chirality-induced current-in-plane magnetoresistance (CIP-MR) in chiral molecule/ferromagnetic metal bilayer at room temperature. The previously reported chiralityinduced current-perpendicular-to-plane magnetoresistance (CPP-MR) originates from the chiral induced spin-selectivity (CISS) effect that needs charge-current passing through the molecule. In contrast, the observed CIP-MR in the present study requires no bias charge current through the molecule. The temperature dependence of CIP-MR suggests thermally induced spin-polarization in the chiral molecules is the key for the observ…
Tunneling surface current through a thin ferromagnetic barrier in a three-dimensional topological insulator is shown to possess an extraordinary response to the orientation of barrier magnetization. In contrast to conventional magnetoresistance devices that are sensitive to the relative alignment of two magnetic layers, a drastic change in the transmission current is achieved by a single layer when its magnetization rotates by 90 degrees. Numerical estimations predict a giant magnetoresistance as large as 800 % at room temperature and the proximate exchange interaction of 40 meV in the barrier…
We report the synthesis and properties of two new insulating phases of SrFeO3-d with introduction of oxygen deficiencies in metallic SrFeO3 ; one with 0.15 < d < 0.19 (sample A)and the other above d = 0.19 (sample B). Sample A shows large negative magnetoresistance around the charged ordering (CO) temperature with magnetic anomalies seen in the temperature dependent resistivity,magnetization and M-H hysteresis loops. Sample B shows a smooth insulating behavior with no thermal hysteresis in the resistivity and with a small positive magnetoresistance. cac and cdc show multiple features associate…
I have successfully prepared (110) trilayers of \LSMO-\YBCO-\LSMO. Magnetization measurements on these samples reveal a stronger coupling between the ferromagnetic layers. The coupling is an order of magnitude higher than that seen in the case of (001) trilayers. Magnetoresistance measurements show a first order transition in the data coinciding with the antiferromagnetic regime deduced from the magnetization measurements. I have also measured the anisotropic magnetoresistance (AMR) of these samples revealing an unusually high AMR ($\sim 72000%$). I attribute such a high AMR to the pair breaki…
The influence of insertion of an ultra-thin NiO layer between the MgO barrier and ferromagnetic electrode in magnetic tunnel junctions has been investigated by measuring the tunneling magnetoresistance and the X-ray magnetic circular dichroism (XMCD). The magnetoresistance shows a high asymmetry with respect to bias voltage, giving rise to a negative value of -16% at 2.8 K. We attribute this to the formation of non-collinear spin structures in the NiO layer as observed by XMCD. The magnetic moments of the interface Ni atoms tilt from the easy axis due to exchange interaction and the tilting an…
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…
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 …
The ferromagnetic (FM) transition temperature (Tc) of a two-band Double-Exchange (DE) model for colossal magnetoresistance (CMR) materials is studied using dynamical mean-field theory (DMFT), in wide ranges of coupling constants, hopping parameters, and carrier densities. The results are shown to be in excellent agreement with Monte Carlo simulations. When the bands overlap, the value of Tc is found to be much larger than in the one-band case, for all values of the chemical potential within the energy overlap interval. A nonzero interband hopping produces an additional substantial increase of …
We studied the magnetoresistance of normal metal (NM)/ferromagnet (FM) bilayers in the linear and nonlinear (current-dependent) regimes and compared it with the amplitude of the spin-orbit torques and thermally induced electric fields. Our experiments reveal that the magnetoresistance of the heavy NM/Co bilayers (NM = Ta, W, Pt) is phenomenologically similar to the spin Hall magnetoresistance (SMR) of YIG/Pt, but has a much larger anisotropy, of the order of 0.5%, which increases with the atomic number of the NM. This SMR-like behavior is absent in light NM/Co bilayers (NM = Ti, Cu), which pre…
We derive a simple relational expression between the spin polarization ratio of resistivity, $P_ρ$, and the anisotropic magnetoresistance ratio $Δρ/ρ$, and that between the spin polarization ratio of the density of states at the Fermi energy, $P_{\rm DOS}$, and $Δρ/ρ$ for nearly half-metallic ferromagnets. We find that $P_ρ$ and $P_{\rm DOS}$ increase with increasing $|Δρ/ρ|$ from 0 to a maximum value. In addition, we roughly estimate $P_ρ$ and $P_{\rm DOS}$ for a Co$_2$FeGa$_{0.5}$Ge$_{0.5}$ Heusler alloy by substituting its experimentally observed $Δρ/ρ$ into the respective expressions.
We report the existence of a field-induced ferromagnetic transition in the magnetically ordered state (<69 K) of an intermetallic compound, Tb5Si3, and this transition is distinctly first-order at 1.8 K (near 60 kOe), whereas it appears to become second order near 20 K. The finding we stress is that the electrical resistivity becomes suddenly large in the high-field state after this transition and this is observed in the entire temperature range in the magnetically ordered state. Such an enhancement of 'positive' magnetoresistance (below 100 kOe) at the metamagnetic transition field is unexpec…
We report on the combination of current-induced spin-orbit torques and giant magnetoresistance in a single device to achieve all-electrical write and read out of the magnetization. The device consists of perpendicularly magnetized TbCo and Co layers separated by a Pt or Cu spacer. Current injection through such layers exerts spin-orbit torques and switches the magnetization of the Co layer while the TbCo magnetization remains fixed. Subsequent current injection of lower amplitude senses the relative orientation of the magnetization of the Co and TbCo layers, which results in two distinct resis…
We have investigated the anisotropic magnetoresistance (AMR) of (In,Fe)As ferromagnetic semiconductor (FMS) layers grown on semi-insulating GaAs substrates. In a 10 nm-thick (In,Fe)As layer which is insulating at low temperature, we observed crystalline AMR with two-fold and eight-fold symmetries. In a metallic 100 nm-thick (In,Fe)As layer with higher electron concentration, only two-fold symmetric crystalline AMR was observed. Our results demonstrate the macroscopic ferromagnetism in (In,Fe)As with magnetic anisotropy that depends on the electron concentration. Non-crystalline AMR is also obs…
Recent works aiming at understanding magnetotransport phenomena in ferromagnetic III-V and II-VI semiconductors are described. Theory of the anomalous Hall effect in p-type magnetic semiconductors is discussed, and the relative role of side-jump and skew-scattering mechanisms assessed for (Ga,Mn)As and (Zn,Mn)Te. It is emphasized that magnetotransport studies of ferromagnetic semiconductors in high magnetic fields make it possible to separate the contributions of the ordinary and anomalous Hall effects, to evaluate the role of the spins in carrier scattering and localization as well as to dete…
The thickness dependence of spin-orbit torque and magnetoresistance in ferromagnet/heavy-metal bilayers is studied using the first-principles non-equilibrium Green's function formalism combined with the Anderson disorder model. A systematic expansion in orthogonal vector spherical harmonics is used for the angular dependence of the torque. The damping-like torque in Co/Pt and Co/Au bilayers can be described as a sum of the spin-Hall contribution, which increases with thickness in agreement with the spin-diffusion model, and a comparable interfacial contribution. The magnetoconductance in the p…
We propose an experimental scheme to determine the spin-transfer torque efficiency excited by the spin-orbit interaction in ferromagnetic bilayers from the measurement of the longitudinal magnetoresistace. Solving a diffusive spin-transport theory with appropriate boundary conditions gives an analytical formula of the longitudinal charge current density. The longitudinal charge current has a term that is proportional to the square of the spin-transfer torque efficiency and that also depends on the ratio of the film thickness to the spin diffusion length of the ferromagnet. Extracting this cont…
We investigate theoretically the spin-independent tunneling magnetoresistance effect in a graphene monolayer modulated by two parallel ferromagnets deposited on a dielectric layer. For the parallel magnetization configuration, Klein tunneling can be observed in the transmission spectrum, but at specific oblique incident angles. For the antiparallel magnetization configuration, the transmission can be blocked by the magnetic-electric barrier provided by the ferromagnets. Such a transmission discrepancy results in a tremendous magnetoresistance ratio and can be tuned by the inclusion of an elect…
For spin-polarized junctions of ferromagnetically contacting multiple conductive paths, such as ferromagnet (FM)/atomic wires/FM and FM/carbon nanotubes/FM junctions, we theoretically investigate spin-dependent transport to elucidate the intrinsic relation between the number of paths and conduction, and to enhance the magnetoresistance (MR) ratio. When many paths are randomly located between the two FMs, electronic wave interference between the FMs appears, and then the MR ratio increases with increasing number of paths. Furthermore, at each number of paths, the MR ratio for carbon nanotubes b…
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The quasiclassical theory of a nanosize point contacts (PC) between two ferromagnets is developed. The maximum available magnetoresistance values in PC are calculated for ballistic versus diffusive transport through the area of a contact. In the ballistic regime the magnetoresistance in excess of few hundreds percents is obtained for the iron-group ferromagnets. The necessary conditions for realization of so large magnetoresistance in PC, and the experimental results by Garcia et al are discussed
SrRuO3 is an itinerant ferromagnet and in its thin film form when grown on miscut SrTiO3 it has Tc of ~ 150 K and strong uniaxial anisotropy. We measured both the Hall effect and the magnetoresistance (MR) of the films as a function of the angle between the applied field and the normal to the films at temperatures above Tc. We extracted the extraordinary Hall effect that is proportional to the perpendicular component of the magnetization and thus the MR for each angle of the applied field could be correlated with the magnitude and orientation of the induced magnetization. We successfully fit t…
In order to gain insights into the origin of colossal magneto-resistance (CMR) in manganese oxides, we performed a ^{139}La NMR study in the double-layered compound La_{1.2}Sr_{1.8}Mn_2O_7. We find that above the Curie temperature T_C=126 K, applying a magnetic field induces a long-range ferromagnetic order that persists up to T=330 K. The critical field at which the induced magnetic moment is saturated coincides with the field at which the CMR effect reaches to a maximum. Our results therefore indicate that the CMR observed above T_C in this compound is due to the field-induced ferromagnetism…
In antiferromagnetic spintronics, it is essential to separate the resistance modifications of purely magnetic origin from other effects generated by current pulses intended to switch the Néel vector. We investigate the magnetoresistance effects resulting from magnetic field induced reorientations of the staggered magnetization of epitaxial antiferromagnetic Mn2Au(001) thin films. The samples were exposed to 60 T magnetic field pulses along different crystallographic in-plane directions of Mn2Au(001), while their resistance was measured. For the staggered magnetization aligned via a spin-flop t…
We report four probe measurements of the low field magnetoresistance in single core/shell GaAs/MnAs nanowires synthesized by molecular beam epitaxy, demonstrating clear signatures of anisotropic magnetoresistance that track the field-dependent magnetization. A comparison with micromagnetic simulations reveals that the principal characteristics of the magnetoresistance data can be unambiguously attributed to the nanowire segments with a zinc blende GaAs core. The direct correlation between magnetoresistance, magnetization and crystal structure provides a powerful means of characterizing individ…
We demonstrate spin-valve magnetoresistance with a current-in-plane (CIP) configuration in (Ga,Fe)Sb / InAs (thickness $t_\mathrm{InAs}$ nm) / (Ga,Fe)Sb trilayer heterostructures, where (Ga,Fe)Sb is a ferromagnetic semiconductor (FMS) with high Curie temperature ($T_\mathrm{C}$). An MR curve with an open minor loop is clearly observed at 3.7 K in a sample with $t_\mathrm{InAs}$ = 3 nm, which originates from the parallel - antiparallel magnetization switching of the (Ga,Fe)Sb layers and spin-dependent scattering at the (Ga,Fe)Sb / InAs interfaces. The MR ratio increases (from 0.03 to 1.6%) with…