The understanding of the characteristics of a magnetic layer in a different environment is crucial for any spintronics application. Before practical applications, thorough scrutiny of such devices is compulsory. Here we study such a potential Hall device of MgO-capped Hf/GdFeCo bilayer (FeCo-rich) for magnetization relaxation around nucleation fields at different voltage probe line widths and dc sensing currents. The device is characterized by anomalous Hall measurements in transverse and longitudinal Hall geometries for two different probe widths A (5 micrometer) and B (1 micrometer). The coercivities of the Hall loops (\r{ho}xy-H and Rxx-H) drop with increasing the sense current for both the probes. For probe B, the sharp and large drop in coercivity (\r{ho}xy-H loops) at comparatively lower sensing currents is observed, which is attributed to the negligible current shunting and presence of pinning site at B caused by the patterning process. The average domain wall velocities at various sensing currents for probe B are found to be smaller than probe A, from the transverse and longitudinal Hall geometry magnetization relaxation measurements, which agrees with pinning sites and Joule heating effect at probe B. The notch position in the pattern and the longitudinal Hall resistance curve peak shape suggest the domain wall propagation direction from probe B to probe A in the current channel. This study highlights the domain wall propagation at different nucleation fields, sensing currents, and the Hall probe aspect ratios.
Room-Temperature Highly-Tunable Coercivity and Highly-Efficient Nonvolatile Multi-States Magnetization Switching by Small Current in Single 2D Ferromagnet Fe$_3$GaTe$_2$
Giant Exfoliation Induced Magnetic Coercivity in Fe$_3$GaTe$_2$
National High Magnetic Field Laboratory（国家强磁场实验室）；Florida State University（佛罗里达州立大学）；The University of Edinburgh（爱丁堡大学）；Argonne National Laboratory（阿贡国家实验室）；Donostia International Physics Center (DIPC)（圣塞巴斯蒂安国际物理中心）；Baylor University（贝勒大学）
Large magnetic anisotropy and coercivity are key properties of functional magnetic materials and are generally associated with rare earth elements. Here we show an extreme, uniaxial magnetic anisotropy and the emergence of magnetic hysteresis in Li2(Li1-xFex)N. An extrapolated, magnetic anisotropy field of 220 Tesla and a coercivity field of over 11 Tesla at 2 Kelvin outperform all known hard-ferromagnets and single-molecule magnets (SMMs). Steps in the hysteresis loops and relaxation phenomena in striking similarity to SMMs are particularly pronounced for x << 1 and indicate the presence of n…
The phenomenological theory for "topological" Hall effect (THE) is proposed. The theory can be used for qualitative analysis of THE in the medium with arbitrary magnetization distribution. In the paper the cylindrical particle with "vortex" magnetization is considered. The hysteresis loop of THE is qualitatively different comparing to abnormal Hall effect. The estimation of THE magnitude in the "vortex" particle is made. For Co particle with 100 nm diameter the THE exceeds normal and abnormal Hall effects until an external magnetic field less than 200 Oe.
The anomalous Hall effect is investigated experimentally and theoretically for ferromagnetic thin films of Mn$_5$Ge$_3$. We have separated the intrinsic and extrinsic contributions to the experimental anomalous Hall effect, and calculated the intrinsic anomalous Hall conductivity from the Berry curvature of the Bloch states using first-principles methods. The intrinsic anomalous Hall conductivity depends linearly on the magnetization, which can be understood from the long wavelength fluctuations of the spin orientation at finite temperatures. The quantitative agreement between theory and exper…
Precise estimation of spin Hall angle as well as successful maximization of spin-orbit torque (SOT) form a basis of electronic control of magnetic properties with spintronic functionality. Until now, current-nonlinear Hall effect, or second harmonic Hall voltage has been utilized as one of the methods for estimating spin Hall angle, which is attributed to the magnetization oscillation by SOT. Here, we argue the second harmonic Hall voltage 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$_3$. From the angular, …
Measurements of the transverse Hall resistance are widely used to investigate electron transport, magnetization phenomena, and topological quantum states. Owing to the difficulty of probing transient changes of the transverse resistance, the vast majority of Hall effect experiments are carried out in stationary conditions using either dc or ac currents. Here we present an approach to perform time-resolved measurements of the transient Hall resistance during current-pulse injection with sub-nanosecond temporal resolution. We apply this technique to investigate in real-time the magnetization rev…
A theoretical formula is derived for the threshold current to switch a perpendicular magnetization in a ferromagnet by the spin Hall effect. The numerical simulation of the Landau-Lifshitz-Gilbert equation indicates that magnetization switching is achieved when the steady-state solution of the magnetization in the presence of the current is outside an energetically unstable region. Based on the numerical result, an analytical theory deriving the threshold current is developed by focusing on the first-order perturbation to the unstable state. The analytical formula clarifies that the magnitude …
The symmetry considerations that imply a non-zero anomalous Hall effect (AHE) in certain non-collinear antiferromagnets also imply both non-zero orbital magnetization and a net spin magnetization. We have explicitly evaluated the orbital magnetizations of several anomalous Hall effect antiferromagnets and find that they tend to dominate over spin magnetizations, especially so when spin-orbit interactions are weak. Because of the greater relative importance of orbital magnetization the coupling between magnetic order and an external magnetic field is unusual. We explain how magnetic fields can …
The electronic topology is generally related to the Berry curvature, which can induce the anomalous Hall effect in time-reversal symmetry breaking systems. Intrinsic monolayer transition metal dichalcogenides possesses two nonequivalent K and K' valleys, having Berry curvatures with opposite signs, and thus vanishing anomalous Hall effect in this system. Here we report the experimental realization of asymmetrical distribution of Berry curvature in a single valley in monolayer WSe2 through applying uniaxial strain to break C3v symmetry. As a result, although the Berry curvature itself is still …
We quantitatively evaluate a spin anomalous Hall effect (SAHE), generating spin angular momentum flow (spin current, $J_{\rm s}$), in an L1$\rm_{0}$-FePt ferromagnet by exploiting giant magnetoresistance devices with L1$\rm_{0}$-FePt / Cu / Ni$\rm_{81}$Fe$\rm_{19}$ . From the ferromagnetic resonance linewidth modulated by the charge current ($J_{\rm c}$) injection, the spin anomalous Hall angle ($ α_{\rm SAH} $) is obtained to be 0.25 $ \pm $ 0.03. The evaluation of $ α_{\rm SAH} $ at different configurations between $J_{\rm c}$ and magnetization enables us to discuss the symmetry of SAHE and …
We present a two-band kinetic equation method to investigate the anomalous Hall effect in a Rashba two-dimensional electron system subjected to a homogeneous magnetization. The electron-impurity scattering is taken into account in the self-consistent Born approximation. It is demonstrated that the impurity-density-free anomalous Hall conductivity arises from an intrinsic and a disorder-mediated mechanisms, associated respectively with the electron states under and near the Fermi surface. The intrinsic mechanism relates to a dc-field-induced transition process, or in other words, a linear stati…
Although much effort has been made to explore quantum anomalous Hall effect (QAHE) in both theory and experiment, the QAHE systems with tunable Chern numbers are yet limited. Here, we theoretically propose that NiAsO$_3$ and PdSbO$_3$, monolayer transitional metal oxides, can realize QAHE with tunable Chern numbers via manipulating their magnetization orientations. When the magnetization lies in the \textit{x-y} plane and all mirror symmetries are broken, the low-Chern-number (i.e., $\mathcal{C}=\pm1$) phase emerges. When the magnetization exhibits non-zero \textit{z}-direction component, the …
Magnetization switching by spin-orbit torque (SOT) via spin Hall effect represents as a competitive alternative to that by spin-transfer torque (STT) used for magnetoresistive random access memory (MRAM), as it does not require high-density current to go through the tunnel junction. For perpendicular MRAM, however, SOT driven switching of the free layer requires an external in-plane field, which poses limitation for viability in practical applications. Here we demonstrate field-free magnetization switching of a perpendicular magnet by utilizing an Iridium (Ir) layer. The Ir layer not only prov…
We experimentally investigate the current-induced magnetization reversal in Pt/[Co/Ni]$_3$/Al multilayers combining the anomalous Hall effect and magneto-optical Kerr effect techniques in crossbar geometry. The magnetization reversal occurs through nucleation and propagation of a domain of opposite polarity for a current density of the order of 0.3 TA/m$^2$. In these experiments we demonstrate a full control of each stage: i)the Ørsted field controls the domain nucleation and ii) domain-wall propagation occurs by spin torque from the Pt spin Hall effect. This scenario requires an in-plane magn…
Here, we investigate spin Hall angle of Pt in Ni80Fe20/Pt bilayer system by using a broadband spin pumping and inverse spin Hall effect measurement. An out-of-plane excitation geometry with application of external magnetic field perpendicular to the charge current direction is utilized in order to suppress unwanted galvanomagnetic effects. Magnetization precession angle on ferromagnetic resonance for wide excitation frequency range (4-14 GHz) is estimated from the rectification voltage of anisotropic magnetoresistance (AMR) and a conventional method of using microwave power in a coplanar waveg…
We theoretically report that, with \textit{in-plane} magnetization, the quantum anomalous Hall effect (QAHE) can be realized in two-dimensional atomic crystal layers with preserved inversion symmetry but broken out-of-plane mirror reflection symmetry. We take the honeycomb lattice as an example, where we find that the low-buckled structure, which makes the system satisfy the symmetric criteria, is crucial to induce QAHE. The topologically nontrivial bulk gap carrying a Chern number of $\mathcal{C}=\pm1$ opens in the vicinity of the saddle points $M$, where the band dispersion exhibits strong a…
We report a continuous phase transition between quantum-anomalous-Hall and trivial-insulator phases in a magnetic topological insulator upon magnetization rotation. The Hall conductivity transits from one plateau of quantized Hall conductivity $e^2/h$ to the other plateau of zero Hall conductivity. The transition curves taken at various temperatures cross almost at a single point, exemplifying the critical behavior of the transition. The slope of the transition curves follows a power-law temperature dependence with a critical exponent of $-0.61$. This suggests a common underlying origin in the…
The spin-orbit interaction in heavy metal/ferromagnet/oxide structures has been extensively investigated because it can be employed in manipulation of the magnetization direction by in-plane current. This implies the existence of an inverse effect, in which the conductivity in such structures should depend on the magnetization orientation. In this work, we report a systematic study of the magnetoresistance (MR) of the W/CoFeB/MgO structures and its correlation to the current-induced torque to the magnetization. We observe that the MR is independent of the angle between magnetization and curren…
Statistics of level spacing and magnetization are studied for the phase diagram of the integer quantum Hall effect in a 2D finite lattice model with Anderson disorder.
Micro-Hall magnetometry is employed to study the magnetization dynamics of a single, micron-size CrO$_2$ grain. With this technique we track the motion of a single domain wall, which allows us to probe the distribution of imperfections throughout the material. An external magnetic field along the grain's easy magnetization direction induces magnetization reversal, giving rise to a series of sharp jumps in magnetization. Supported by micromagnetic simulations, we identify the transition to a state with a single cross-tie domain wall, where pinning/depinning of the wall results in stochastic Bar…
Spin-orbit torques are studied in Ta/TbFeCo patterned structures with a bulk perpendicular magnetic anisotropy (bulk-PMA) for the first time. The current-induced magnetization switching is investigated in the presence of a perpendicular, longitudinal, or transverse field. In order to rule out Joule heating effect, switching of the magnetization is also demonstrated using current pulses. It is found that the anti-damping torque correlated with spin Hall effect is very strong, and a spin Hall angle of about 0.12 is obtained. The field-like torque related with Rashba effect is negligible in this …
We study the anomalous Hall effect and orbital magnetization in chiral antiferromagnets, constructing a simple tight-binding model on a stacked Kagome lattice structure with spin-orbit coupling and the exchange interaction between the localized spins and itinerant electrons. It is shown that the ground state is an orbital ferromagnet with the easy-plane anisotropy. The relation between the orbital magnetization and the configuration of the Weyl points are discussed.
In a two-dimensional electron gas, the quantized Hall conductance can be induced by a strong magnetic field, known as the quantum Hall effect, and it can also result from the strong exchange coupling of magnetic ions, dubbed as the "quantum anomalous Hall effect". The quantum Hall effect requires the out-of-plane magnetic field, and similarly, it is commonly believed that the magnetization should be out-of-plane for the quantum anomalous Hall effect. In the present work, we find this condition is not necessary and predict that the quantum anomalous Hall effect can also be induced by the purely…
We present a magnetization measurement probing the transition from a quantum Hall to insulating (QH-I) state for a two-dimensional electron gas in a disordered GaAs/AlGaAs heterostructure. Using a highly sensitive DC torque magnetometer, we discover an abrupt change in the orbital magnetization precisely at the critical point for the QH-I transition. Since this transition is predicted to be a second order quantum phase transition, a thermodynamic signature in magnetization is totally unexpected. The observed feature is reminiscent of the well-known de Haas-van Alphen oscillations arising from …
The dependence on temperature of the spin magnetization of a two-dimensional electron gas at filling factor unity is studied. Using classical Monte Carlo simulations we analyze the effect that the equivalence between topological and electrical charge has on the the behavior of the magnetization. We find that at intermediate temperatures the spin polarization increases in a thirty per cent due to the Hartree interaction between charge fluctuations.
We have studied the intrinsic spin Hall conductivity of 3d transition metal ferromagnets using first-principles calculations. We find the spin Hall conductivity of bcc Fe and fcc Ni, prototypes of ferromagnetic systems, depends on the direction of magnetization. The spin Hall conductivity of electrons with their spin orientation orthogonal to the magnetization are found to be larger than that when the two are parallel. For example, the former can be more than four times larger than the latter in bcc Fe. Such a difference arises due to the anisotropy of the spin current operator in the spinor s…
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 report here the results of two-dimensional electron gas based micro-Hall magnetometry measurements and micromagnetic simulations of dipolar coupled nanomagnets of Ni80Fe20 arranged in a double ring-like geometry. We observe that although magnetic force microscopy images exhibit single domain like magnetic states for the nanostructures, their reversal processes may undergo complex behavior. The details of such reversal behavior is observed as specific features in micro-Hall magnetometry data which compares well with the micromagnetic simulation data.
We theoretically demonstrate that 100\% valley-polarized transport in monolayers of MoS$_{2}$ and other group-VI dichalcogenides can be obtained using off-resonant circularly polarized light. By tuning the intensity of the off-resonant light the intrinsic band gap in one valley is reduced, while it is enhanced in the other valley, enabling single valley quantum transport. As a consequence, we predict (i) enhancement of the longitudinal electrical conductivity, accompanied by an increase in the spin-polarization of the flowing electrons, (ii) enhancement of the intrinsic spin Hall effect, toget…
Based on first-principles calculations, we find novel valley-polarized quantum anomalous Hall (VP-QAH) phases with a large gap-0.19 eV at an appropriate buckled angle and tunable topological phase transitions driven by the spontaneous magnetization within a half-hydrogenated Bi honeycomb monolayer. Depending on the magnetization orientation, four different phases can emerge, i.e., two VP-QAH phases, ferromagnetic insulating and metallic states. When the magnetization is reversed from the +$\mathbf{z}$ to -$\mathbf{z}$ directions, accompanying with a sign change in the Chern number (from -1 to …
We show that the quantum anomalous Hall effect almost always occurs in magnetic topological insulator thin films whenever the top and bottom surface layer magnetizations are parallel, independent of the interior layer magnetization configuration. Using this criteria we identify structures that have a quantum anomalous Hall effect even though they have collinear magnetic structures with no net magnetization, and discuss strategies for realizing these interesting magnetic states experimentally.
Both spin and orbital degrees of freedom contribute to the magnetic moment of isolated atoms. However, when inserted in crystals, atomic orbital moments are quenched because of the lack of rotational symmetry that protects them when isolated. Thus, the dominant contribution to the magnetization of magnetic materials comes from electronic spin. Here we show that nanoislands of quantum spin Hall insulators can host robust orbital edge magnetism whenever their highest occupied Kramers doublet is singly occupied, upgrading the spin edge current into a charge current. The resulting orbital magnetiz…
Van der Waals materials are a new platform to study two-dimensional systems, including magnetic order. Since the number of spins is relatively small, measuring the magnetization is challenging. Here we report spin Hall magnetoresistance (SMR) up to room temperature caused by the magnetic surface texture of exfoliated flakes of magnetic van der Waals materials. For the antiferromagnet FePS3 the SMR amounts to 0.1 % for an applied magnetic field of 7 T at 5 K which implies a substantial canting of the magnetic moments relative to the colinear antiferromagnetic order. The canting is substantial e…
The critical current needed to destabilize the magnetization of a perpendicular ferromagnet via the spin Hall effect is studied. Both the dampinglike and fieldlike torques associated with the spin current generated by the spin Hall effect is included in the Landau-Lifshitz-Gilbert equation to model the system. In the absence of the fieldlike torque, the critical current is independent of the damping constant and is much larger than that of conventional spin torque switching of collinear magnetic systems, as in magnetic tunnel junctions. With the fieldlike torque included, we find that the crit…
Existing investigations of the anomalous Hall effect i.e. a current flowing transverse to the electric field in the absence of an external magnetic field) are concerned with the transport current. However, for many applications one needs to know the total current, including its pure magnetization part. In this paper, we employ the two-dimensional massive Dirac equation to find the exact universal total current flowing along a potential step of arbitrary shape. For a spatially slowly varying potential we find the current density $\mathbf{j}(\vec r)$ and the energy distribution of the current de…
We theoretically demonstrate that the in-plane magnetization induced quantum anomalous Hall effect (QAHE) can be realized in atomic crystal layers of group-V elements with buckled honeycomb lattice. We first construct a general tight-binding Hamiltonian with $sp^3$ orbitals via Slater-Koster two-center approximation, and then numerically show that for weak and strong spin-orbit couplings the systems harbor QAHEs with Chern numbers of $\mathcal{C}=\pm1$ and $\pm2$ , respectively. For the $\mathcal{C}=\pm1$ phases, we find the critical phase-transition magnetization from a trivial insulator to Q…
In this paper, we establish existence of solutions to an indefinite coupled non-linear system. We use partial coercivity to establish existence of a critical point to an indefinite functional and thus the existence of solutions on both bounded domains and doubly-periodic domains. We then take the limit of the bounded domain to extend solutions on a bounded domain to the full-plane. We also provide asymptotic decay analysis for solutions over the full-plane. Necessary and sufficient conditions are also provided for the doubly periodic domain.
The magneto-transport and magnetization measurements of Sb1.90Cu0.10Te3 were performed at different temperatures and different fields. Magneto-transport measurement at high field indicates the coexistence of both bulk and surface states. The magnetization shows the induced antiferromagnetic ordering with Cu doping and the observed quantum oscillation in it indicates that magnetization in Sb1.90Cu0.10Te3 is the bulk property. The non linearity in Hall data suggests the existence of anomalous and topological Hall effect. The anomalous and topological Hall effect (THE) from measured hall data of …
An array of spin torque oscillators (STOs) for practical applications such as pattern recognition was recently proposed, where several STOs are connected by a common nonmagnet. In this structure, in addition to the electric and/or magnetic interactions proposed in previous works, the STOs are spontaneously coupled to each other through the nonmagnetic connector, due to the injection of spin current. Solving the Landau-Lifshitz-Gilbert equation numerically for such system consisting of three STOs driven by the spin Hall effect, it is found that both in-phase and antiphase synchronization of the…
We study deterministic magnetic reversal of a perpendicularly magnetized Co layer in a Co/MgO/Ta nano-square driven by spin Hall torque from an in-plane current flowing in an underlying Pt layer. The rate-limiting step of the switching process is domain-wall (DW) depinning by spin Hall torque via a thermally-assisted mechanism that eventually produces full reversal by domain expansion. An in-plane applied magnetic field collinear with the current is required, with the necessary field scale set by the need to overcome DW chirality imposed by the Dzyaloshinskii-Moriya interaction. Once Joule hea…
We investigate the possibility of exciting self-oscillation in a perpendicular ferromagnet by the spin Hall effect on the basis of a nonlinear analysis of the Landau-Lifshitz-Gilbert (LLG) equation. In the self-oscillation state, the energy supplied by the spin torque during a precession on a constant energy curve should equal the dissipation due to damping. Also, the current to balance the spin torque and the damping torque in the self-oscillation state should be larger than the critical current to destabilize the initial state. We find that the second condition in the spin Hall system is not…
The occurrence of Spin-Hall Magnetoresistance (SMR) in platinum (Pt) on top of yttrium iron garnet (YIG) has been investigated, for both in-plane and out-of-plane applied magnetic fields and for different Pt thicknesses [3, 4, 8 and 35nm]. Our experiments show that the SMR signal directly depends on the in-plane and out-of-plane magnetization directions of the YIG. This confirms the theoretical description, where the SMR occurs due to the interplay of spin-orbit interaction in the Pt and spin-mixing at the YIG/Pt interface. Additionally, the sensitivity of the SMR and spin pumping signals on t…
Near-zero effective magnetization enabling ultra-low threshold currents in spin Hall micro-oscillators
Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau（莱茵兰-普法尔茨技术大学凯泽斯劳滕-兰道）；University College London（伦敦大学学院）；Tohoku University（东北大学）；Japan Atomic Energy Agency（日本原子能机构）；CNRS, Université Paris-Saclay（法国国家科学研究中心，巴黎萨克雷大学）
We investigate the interplay between ferromagnetic and superconducting order at the edge of a quantum spin Hall insulator. Using complementary analytical and self-consistent numerical approaches, we study a ferromagnetic Josephson junction and show how the direct coupling between magnetism and the superconducting U(1) phase gives rise to several unusual phenomena which distinguishes the present system from its non-topological equivalent. In particular, we demonstrate how the anomalous current-phase relation triggers supercurrent-induced magnetization dynamics and also study the spatial localiz…
We study the spin Hall magnetoresistance (SMR) in Pt grown $\textit{in situ}$ on CoFe$_2$O$_4$ (CFO) ferrimagnetic insulating (FMI) films. A careful analysis of the angle-dependent and field-dependent longitudinal magnetoresistance indicates that the SMR contains a contribution that does not follow the bulk magnetization of CFO but it is a fingerprint of the complex magnetism at the surface of the CFO layer, thus signaling SMR as a tool for mapping surface magnetization. A systematic study of the SMR for different temperatures and CFO thicknesses gives us information impossible to obtain with …
The intrinsic spin-Hall effect on spin accumulation and electric conductance in a diffusive regime of a 2D electron gas has been studied for a 2D strip of a finite width. It is shown that the spin polarization near the flanks of the strip, as well as the electric current in the longitudinal direction exhibit damped oscillations as a function of the width and strength of the Dresselhaus spin-orbit interaction. Cubic terms of this interaction are crucial for spin accumulation near the edges. As expected, no effect on the spin accumulation and electric conductance have been found in case of Rashb…
