We reveal the unexpected role of the material inhomogeneity in unifying the formulation of intrinsic thermal and thermoelectric transport as well as magnetization currents. The smooth inhomogeneity leads to the position dependent local band dispersion and phase-space Berry curvature, enabling a general and rapid access to transport and magnetization currents displaying the momentum-space Berry curvature physics. Our theory does not invoke the boundary current, the thermodynamic approach to magnetization or any mechanical counterpart of statistical forces. By introducing a fictitious inhomogeneity, it applies to homogeneous samples as well, promoting the inhomogeneity to be a basic trick in semiclassical transport theories. Such a trick works regardless of the driving force of transport, e.g., temperature gradient, in contrast to the trick of fictitious gravitational field in quantum transport theories. We thus include more general mechanical driving forces and establish the Mott relation between the resulting transport thermal and electric currents, whereas this relation for these two currents was previously only known when an electric field is the driving force.
The magnetization and the de Haas-van Alphen oscillations of Bloch electrons are calculated near commensurate magnetic fluxes. Two phases that appear in the quantization of mixed systems--the Berry's phase and a phase first discovered by Wilkinson--play a key role in the theory.
A space-time crystal is defined as a quantum mechanical system with both spatial and temporal periodicity. Such a system can be described by the Floquet-Bloch (FB) theory. We first formulate a semiclassical theory by constructing a wave-packet through the superposition of the FB wave functions and derive the equations of motion of FB electrons subjected to slowly varying external fields (not to be confused with the fast-changing Floquet drive), revealing behaviors similar to ordinary Bloch electrons but with quantities modified in the Floquet context. Specifically, we study local magnetic mome…
The linear intrinsic anomalous Hall effect (IAHE) and second-order IAHE have been intensively investigated in time-reversal broken systems. However, as one of the important members of the nonlinear Hall family, the investigation of third-order IAHE remains absent due to the lack of an appropriate theoretical approach, although the third-order extrinsic AHE has been studied within the framework of first- and second-order semiclassical theory. Herein, we generalize the semiclassical theory for Bloch electrons under the uniform electric field up to the third-order using wavepacket method and base…
We consider a microscopic model of itinerant electrons coupled via ferromagnetic exchange to a local magnetization whose direction vector n(r,t) varies in space and time. We assume that to first order in the spatial gradient and time derivative of n(r,t) the magnetization distribution function f(p,r,t) of itinerant electrons has the Ansatz form: f(p,r,t)=f_{parallel}(p)n(r,t)+ f_{1 r}(p) n ^ nabla_{r} n+f_{2 r}(p) nabla_{r} n+ f_{1 t}(p) n ^ partial_t n+f_{2 t}(p) partial_t n. Using then the Landau-Sillin equations of motion approach we derive explicit forms for the components f_{parallel}(p),…
Antiferromagnets (AFMs) exhibit intrinsic magnetization when the order parameter spatially varies. This intrinsic spin is present even at equilibrium and can be interpreted as a twisting of the homogeneous AFM into a state with a finite spin. Because magnetic moments couple directly to external magnetic fields, the intrinsic magnetization can alter the dynamics of antiferromagnetic textures under such influence. Starting from the discrete Heisenberg model, we derive the continuum limit of the free energy of AFMs in the exchange approximation and explicitly rederive that the spatial variation o…
Recent measurements in current-driven spin valves demonstrate magnetization fluctuations that deviate from semiclassical predictions. We posit that the origin of this deviation is spin shot noise. On this basis, our theory predicts that magnetization fluctuations asymmetrically increase in biased junctions irrespective of the current direction. At low temperatures, the fluctuations are proportional to the bias, but at different rates for opposite current directions. Quantum effects control fluctuations even at higher temperatures. Our results are in semiquantitative agreement with recent exper…
A semiclassical theory for the orbital magnetization due to adiabatic evolutions of Bloch electronic states is proposed. It renders a unified theory for the periodic-evolution pumped orbital magnetization and the orbital magnetoelectric response in insulators by revealing that these two phenomena are the only instances where the induced magnetization is gauge invariant. This theory also accounts for the electric-field induced intrinsic orbital magnetization in two-dimensional metals and Chern insulators. We illustrate the orbital magnetization pumped by microscopic local rotations of atoms, wh…
To give a general description of the influences of electric fields or currents on magnetization dynamics, we developed a semiclassical theory for the magnetization implicitly coupled to electronic degrees of freedom. In the absence of electric fields the Bloch electron Hamiltonian changes the Berry curvature, the effective magnetic field, and the damping in the dynamical equation of the magnetization, which we classify into intrinsic and extrinsic effects. Static electric fields modify these as first-order perturbations, using which we were able to give a physically clear interpretation of the…
First principles calculations show that electric fields applied to ferromagnets generate spin currents flowing perpendicularly to the electric field. Reduced symmetry in these ferromagnets enables a wide variety of such spin currents. However, the total spin current is approximately the sum of a magnetization-independent spin Hall current and an anisotropic spin anomalous Hall current. Intrinsic spin currents are not subject to dephasing, enabling their spin polarizations to be misaligned with the magnetization, which enables the magnetization-independent spin Hall effect. The spin Hall conduc…
We study the effect of the ferromagnetic (FM) contacts on the spin accumulation in the lateral spin valve system for the collinear magnetization configurations. When an additional FM electrode is introduced in the all-metallic lateral spin-valve system, we find that the transresistance can be fractionally suppressed or very weakly influenced depending on the position of the additional FM electrode, and relative magnitudes of contact resistance and the bulk resistance defined over the spin diffusion length. Nonlocal spin signals such as nonlocal voltage drop and leakage spin currents are indepe…
We propose an orbital magnetothermal effect wherein a temperature gradient generates an orbital magnetization (OM) for Bloch electrons, and we present a unified theory for electrically and thermally induced OM, valid for both metals and insulators. We reveal that there exists an intrinsic response of OM, for which the susceptibilities are completely determined by the band geometric quantities such as interband Berry connections, interband orbital moments, and the quantum metric. The theory can be readily combined with first-principles calculations to study real materials. As an example, we cal…
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…
In this paper, we study the driven-dissipative p-spin models for $p\geq 2$. In thermodynamics limit, the equation of motion is derived by using a semiclassical approach. The long-time asymptotic states are obtained analytically, which exhibit multi-stability in some regions of the parameter space. The steady state is unique as the number of spins is finite. But the thermodynamic limit of the steady-state magnetization displays nonanalytic behavior somewhere inside the semiclassical multi-stable region. We find both the first-order and continuous dissipative phase transitions. As the number of …
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…
Motivated by recent interest in novel spintronics effects, we develop a semiclassical theory of spin transport that is valid for spin-orbit coupled bands. Aside from the obvious convective term in which the average spin is transported at the wavepacket group velocity, the spin current has additional contributions from the wavepacket's spin and torque dipole moments. Electric field corrections to the group velocity and carrier spin contribute to the convective term. Summing all terms we obtain an expression for the intrinsic spin-Hall conductivity of a hole-doped semiconductor, which agrees wit…
The interplay between band topology and magnetic order could generate a variety of time-reversal-breaking gapped topological phases with exotic topological quantization phenomena, such as quantum anomalous Hall (QAH) insulators and axion insulators (AxI). Here by combining analytic models and first-principles calculations, we predict QAH and AxI phases can be realized in thin film of an intrinsic antiferromagnetic van der Waal material Mn$_2$Bi$_2$Te$_5$. The phase transition between QAH and AxI is tuned by the layer magnetization, which would provide a promising platform for chiral supercondu…
Magnetization dynamics are strongly influenced by damping. An effective damping constant αeff is often determined experimentally from the spectral linewidth of the free induction decay of the magnetization after the system is excited to its non-equilibrium state. Such an αeff, however, reflects both intrinsic damping as well as inhomogeneous broadening. In this paper we compare measurements of the magnetization dynamics in ultrathin non-epitaxial films having perpendicular magnetic anisotropy using two different techniques, time-resolved magneto optical Kerr effect (TRMOKE) and hybrid optical-…
Micron-sized Hall bars and micro-SQUIDs are now used routinely to measure the local static and dynamic magnetic response with micron-scale spatial resolution. While this provides a powerful new tool, determining the intrinsic magnetization presents new challenges, as it requires correcting for demagnetization fields that vary widely with position on a sample. In this paper we develop a method to correct for the demagnetization effect at local points of a rectangular prism shaped sample using a finite element analysis of Maxwell's equation applied to local Hall sensor measurements calibrated by…
We study the intrinsic orbital magnetization (OM) in antiferromagnets on the distorted face-centered-cubic lattice. The combined lattice distortion and spin frustration induce nontrivial $k$-space Chern invariant, which turns to result in profound effects on the OM properties. We derive a specific relation between the OM and the Hall conductivity, according to which it is found that the intrinsic OM vanishes when the electron chemical potential lies in the Mott gap. The distinct behavior of the intrinsic OM in the metallic and insulating regions is shown. The Berry phase effects on the thermoe…
We present a theory of magnetization dynamics driven by spin-polarized current in terms of the quantum master equation. In the spin coherent state representation, the master equation becomes a Fokker-Planck equation, which naturally includes the spin transfer and quantum fluctuation. The current electron scattering state is correlated to the magnet quantum states, giving rise to quantum correction to the electron transport properties in the usual semiclassical theory. In the large spin limit, the magnetization dynamics is shown to obey the Hamilton-Jacobi equation or the Hamiltonian canonical …
The intrinsic orbital magnetization of a TMD monolayer is usually calculated for a plane unbounded system without mentioning the geometrical shape of samples and boundary conditions (BCs) for electron wave functions. The method of calculations includes allowing for the Berry curvature contribution also in the case when the system is described by the two-band minimal model [9]. In the present paper, we show that the geometrical and topological properties of the specimen, as well as the BCs, play an important role in the problem of magnetization even for a macroscopic specimen.
We study how the intrinsic anomalous Hall conductivity is modified in two-dimensional crystals with broken time-reversal symmetry due to weak inhomogeneity of the applied electric field. Focusing on a clean noninteracting two-band system without band crossings, we derive the general expression for the Hall conductivity at small finite wave vector $q$ to order $q^2$, which governs the Hall response to the second gradient of the electric field. Using the Kubo formula, we show that the answer can be expressed through the Berry curvature, Fubini-Study quantum metric, and the rank-3 symmetric tenso…
We present a theory of magnetotransport through a system of two coupled electronic orbitals, where the electron spin interacts with a (large) local magnetic moment via an exchange interaction. For the physical realization of such a set-up we have in mind, for example, semiconductor quantum dots coupled to an ensemble of nuclear spins in the host material or molecular orbitals coupled to a local magnetic moment. Using a semiclassical approximation, we derive a set of Ehrenfest equations of motion for the electron density matrix and the mean value of the external spin (Landau equations): Due to …
When electron spins are injected uniformly into a paramagnetic disc, they can precess along the demagnetizing field induced by the resulting magnetic moment. Normally this precession damps out by virtue of the spin relaxation which is present in paramagnetic materials. We propose a new mechanism to excite a steady-state form of this dynamics by injecting a constant spin current into this paramagnetic disc. We show that the rotating magnetic field generated by the eddy currents provide a torque which makes this possible. Unlike the ferromagnetic equivalent, the spin-torque-oscillator, the oscil…
The establishment of chiral coupling in thin magnetic films with inhomogeneous anisotropy has led to the development of artificial systems of fundamental and technological interest. The chiral coupling itself is enabled by the Dzyaloshinskii-Moriya interaction (DMI) enforced by the patterned noncollinear magnetization. Here, we create a domain wall track with out-of-plane magnetization coupled on each side to a narrow parallel strip with in-plane magnetization. With this we show that the chiral torques emerging from the DMI at the boundary between the regions of noncollinear magnetization in a…
Spin electronic structure of graphene pi-states and Pt 5d-states for the Graphene/Pt interface has been investigated. Here, we report a large induced spin-orbit splitting (~70-100 meV) of graphene pi-states with formation of non-degenerated Dirac-cone spin states at the K-point of the BZ crossed with spin-polarized Pt 5d-states at Fermi level that opens up a possibility for creation of new spintronics devices. We propose to use this spin structure for formation of spin current with spin locked perpendicular to the momentum for induced remagnetization of the (Ni-Fe)-nanodots arranged atop the i…
Thermal Hall conductivity from semiclassical spin dynamics simulations: implementation and applications to chiral ferromagnets and Kitaev magnets
Technical University of Munich（慕尼黑工业大学）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；University of Münster（明斯特大学）；Imperial College London（帝国理工学院）
Intrinsic magnetization of the superconducting condensate in Fe(Te,Se)
State University of New York, Albany（纽约州立大学奥尔巴尼分校）；City College of the City University of New York（纽约市立学院）；Brookhaven National Laboratory（布鲁克海文国家实验室）；Stony Brook University（石溪大学）；National Institute for Materials Science（国立材料研究所）
In bilayer nanowires consisting of a ferromagnetic layer and a non-magnetic layer with strong spin-orbit coupling, currents create torques on the magnetization beyond those found in simple ferromagnetic nanowires. The resulting magnetic dynamics appear to require torques that can be separated into two terms, damping-like and field-like. The damping-like torque is typically derived from models describing the bulk spin Hall effect and the spin transfer torque, and the field-like torque is typically derived from a Rashba model describing interfacial spin-orbit coupling. We derive a model based on…
The electron transport properties of hybrid ferromagnetic|normal metal structures such as multilayers and spin valves depend on the relative orientation of the magnetization direction of the ferromagnetic elements. Whereas the contrast in the resistance for parallel and antiparallel magnetizations, the so-called Giant Magnetoresistance, is relatively well understood for quite some time, a coherent picture for non-collinear magnetoelectronic circuits and devices has evolved only recently. We review here such a theory for electron charge and spin transport with general magnetization directions t…
By performing first principles calculations we investigate the intrinsic anomalous Hall conductivity (AHC) and its anisotropy in ordered L1o FePt, CoPt and NiPt ferromagnets, and their intermediate alloys. We demonstrate that the AHC in this family of compounds depends strongly on the direction of the magnetization in the crystal. We predict that such pronounced orientational dependence in combination with the general decreasing trend of the AHC when going from FePt to NiPt leads to a sign change of the AHC upon rotating the magnetization direction in the crystal of CoPt alloy. We also suggest…
We discuss the effects of thermal noise on the magnetic response of a lateral ferromagnetic Josephson junction with spin-orbit coupling and out-of-plane magnetization. The direction of the magnetic moment in the ferromagnetic layer can be inverted by using controlled current pulses. This phenomenon is due to the magnetoelectric effect that couples the flowing charge current and the magnetization of the ferromagnet. We investigate the magnetization reversal effect versus intrinsic parameters of the ferromagnet, such as the Gilbert damping and strength of the spin-orbit coupling. We estimate the…
