arXiv subjects

I. A. Ado

Publications and source records attributed to I. A. Ado.

16 recordsLinked to original sources

arXiv2026

Magnetic moment of electrons in systems with spin-orbit coupling

Magnetic effects originating from spin-orbit coupling (SOC) have been attracting major attention. However, SOC contributions to the electron magnetic moment operator are conventionally disregarded. In this work, we analyze relativistic contributions to the latter operator, including those of the SOC-type: in vacuum, for the semiconductor 8 band Kane model, and for an arbitrary system with two spectral branches. In this endeavor, we introduce a notion of relativistic corrections to the operation $\partial/\partial\boldsymbol B$, where $\boldsymbol B$ is an external magnetic field. We highlight the difference between the magnetic moment and $-\partial H/\partial\boldsymbol B$, where $H$ is the system Hamiltonian. We suggest to call this difference the abnormal magnetic moment. We demonstrate that the conventional decomposition of the total magnetic moment into the spin and orbital parts becomes ambiguous when relativistic corrections are taken into account. The latter also jeopardize the "modern theory of orbital magnetization" in its standard formulation. We derive a linear response Kubo formula for the kinetic magnetoelectric effect projected to individual branches of a two branch system. This allows us, in particular, to identify a source of this effect that stems from noncommutation of the position and $\partial/\partial\boldsymbol B$ operators' components. This is an analog of the contribution to the Hall conductivity from noncommuting components of the position operator. We comment on the relation between such contributions and the Berry curvature theory. We also report several additional observations related to the electron magnetic moment operator in systems with SOC and other relativistic corrections.

cond-mat.mes-hall↗

arXiv2025

Orbital magnetization from interface reflections in a conductor with charge current

We propose that a high-quality flat interface or boundary can serve as a long-range skew scatterer for charged quasiparticles in a metal. When an electric current flows parallel to the interface, the balance between clockwise and counterclockwise reflections is disrupted, leading to a net orbital magnetization. This magnetization is maximized at the interface and varies linearly in the direction perpendicular to it. We suggest that this effect can be detected using spatially resolved Kerr effect measurements at distances up to the electron phase coherence length from the interface. Unlike the orbital Hall and orbital Edelstein effects, the proposed phenomenon does not require inversion symmetry breaking in the bulk of the sample and is unrelated to Hall effect physics.

cond-mat.mes-hall↗

arXiv2024

Orbital Edelstein effect from the gradient of a scalar potential

We study the orbital Edelstein effect (OEE) that originates from a particular inversion symmetry breaking mechanism: an asymmetric scalar potential. We compute OEE of this kind with the help of the Kubo formula in the diffusive regime for a parabolic band Hamiltonian. We also present a qualitative derivation of the effect. Both approaches give the same result. This result does not rely on spin-orbit coupling (SOC) and scales as a cube of the momentum relaxation time. In sufficiently clean large systems with weak SOC, OEE of this nature should exceed the spin Edelstein effect by orders of magnitude. It may also provide an alternative interpretation for some experiments concerning the spin Hall effect.

cond-mat.mes-hall↗

arXiv2024

Position operators and interband matrix elements of scalar and vector potentials in the 8-band Kane model

We diagonalize the 8-band Kane Hamiltonian with a proper inclusion of the interband matrix elements of the scalar and vector potentials. This leads, among other results, to a modification of the conventional expression for the spin-orbit coupling (SOC) strength in narrow-gap semiconductors with the zinc blende symmetry. We find that in GaAs, at low temperatures, the correct expression for the SOC strength is actually twice as large as usually considered. In InSb it is $1.76$ times larger. We also provide a proper treatment of the interband matrix elements of the position operator. We show that the velocity operator in a crystal should be defined as a time-derivative of a fictitious position operator rather than the physical one. We compute the expressions for both these position operators projected to the conduction band of the 8-band Kane model. We also derive an expression for the projected velocity operator and demonstrate that the SOC strength in it differs from the SOC strength in the Hamiltonian. The ratio between them is not equal to $1$, as it is often assumed for the Rashba model. It does not equal $2$ either. The correct result for this ratio is given by a rational function of the parameters of the model. This function takes values between $4(23+3\sqrt{2})/73\approx 1.49$ and $2$. Our findings modify a vast number of research results obtained using the Rashba model and provide a path for a consistent treatment of the latter in future applications.

cond-mat.mes-hall↗

arXiv2024

Kubo formula for dc conductivity: generalization to systems with spin-orbit coupling

We revise the Kubo formula for the electric dc conductivity in the presence of spin-orbit coupling (SOC). We discover that each velocity operator that enters this formula differs from $\partial H/\partial \boldsymbol p$, where $H$ is the Hamiltonian and $\boldsymbol p$ is the canonical momentum. Moreover, we find an additional contribution to the Hall dc conductivity from noncommuting coordinates that is missing in the conventional Kubo-Streda formula. This contribution originates from the "electron-positron" matrix elements of the velocity and position operators. We argue that the widely used Rashba model does in fact provide a finite anomalous Hall dc conductivity in the metallic regime (in the noncrossing approximation) if SOC-corrections to the velocity and position operators are properly taken into account. While we focus on the response of the charge current to the electric field, linear response theories of other SOC-related effects should be modified similarly.

cond-mat.mes-hall↗

arXiv2022

Quartic asymmetric exchange for two-dimensional ferromagnets with trigonal prismatic symmetry

We suggest a possible origin of noncollinear magnetic textures in ferromagnets (FMs) with the $D_{3h}$ point group symmetry. The suggested mechanism is different from the Dzyaloshinskii-Moriya interaction (DMI) and its straightforward generalizations. The considered symmetry class is important because a large fraction of all single-layer intrinsic FMs should belong to it. In particular, so does a monolayer Fe$_3$GeTe$_2$. At the same time, DMI vanishes identically in materials described by this point group, in the continuous limit. We use symmetry analysis to identify the only possible contribution to the free energy density in two dimensions that is of the fourth order with respect to the local magnetization direction and linear with respect to its spatial derivatives. This contribution predicts long-range conical magnetic spirals with both the average magnetization and the average chirality dependent on the spiral propagation direction. We relate the predicted spirals to a recent experiment on Fe$_3$GeTe$_2$. Finally, we demonstrate that, for easy-plane materials, the same mechanism may stabilize bimerons.

cond-mat.mes-hall↗

arXiv2021

Signatures of quartic asymmetric exchange in a class of two dimensional magnets

Indirect quartic interaction of spins is suggested to play an important role in two dimensional magnets with trigonal prismatic symmetry such as Fe$_3$GeTe$_2$ monolayer. The proposed interaction is described by terms in micromagnetic energy that are linear in magnetization gradients. Such terms enable the stability of non-collinear magnetic textures. We investigate signatures of the quartic interaction in magnon spectra in the presence of anisotropy and external magnetic field. We also show how magnetic spirals, which are induced by the proposed interaction, can be manipulated by external field. Our analysis is based on symmetry considerations and can be used to quantify the quartic interaction strength in experiments with magnetic monolayers.

cond-mat.mtrl-sci↗

arXiv2020

Anomalous Hall effect with massive Dirac fermions

Anomalous Hall effect arises in systems with both spin-orbit coupling and magnetization. Generally, there are three mechanisms contributing to anomalous Hall conductivity: intrinsic, side jump, and skew scattering. The standard diagrammatic approach to the anomalous Hall effect is limited to computation of ladder diagrams. We demonstrate that this approach is insufficient. An important additional contribution comes from diagrams with a single pair of intersecting disorder lines. This contribution constitutes an inherent part of skew scattering on pairs of closely located defects and essentially modifies previously obtained results for anomalous Hall conductivity. We argue that this statement is general and applies to all models of anomalous Hall effect. We illustrate it by an explicit calculation for two-dimensional massive Dirac fermions with weak disorder. In this case, inclusion of the diagrams with crossed impurity lines reverses the sign of the skew scattering term and strongly suppresses the total Hall conductivity at high electron concentrations.

cond-mat.dis-nn↗

arXiv2020

Non-collinear ground state from a four-spin chiral exchange in a tetrahedral magnet

We propose a quartic chiral term $m_x m_y m_z \nabla \cdot \mathbf{m}$ for the energy density of a cubic ferromagnet with broken parity symmetry (point group $T_d$). We demonstrate that this interaction causes a phase transition from a collinear ferromagnetic state to a non-collinear magnetic cone ground state provided its strength exceeds the geometric mean of magnetic exchange and cubic anisotropy. The corresponding non-collinear ground state may also be additionally stabilized by an external magnetic field pointing along certain crystallographic directions. The four-spin chiral exchange does also manifest itself in peculiar magnon spectra and favors spin waves with the wave vector that is perpendicular to the average magnetization direction.

cond-mat.str-el↗

arXiv2020

Anisotropy of spin-transfer torques and Gilbert damping induced by Rashba coupling

Spin-transfer torques (STT), Gilbert damping (GD), and effective spin renormalization (ESR) are investigated microscopically in a 2D Rashba ferromagnet with spin-independent Gaussian white-noise disorder. Rashba spin-orbit coupling induced anisotropy of these phenomena is thoroughly analysed. For the case of two partly filled spin subbands, a remarkable relation between the anisotropic STT, GD, and ESR is established. In the absence of magnetic field and other torques on magnetization, this relation corresponds to a current-induced motion of a magnetic texture with the classical drift velocity of conduction electrons. Finally, we compute spin susceptibility of the system and generalize the notion of spin-polarized current.

cond-mat.mes-hall↗

arXiv2020

Anomalous Hall effect in 2D Rashba ferromagnet

Skew scattering on rare impurity configurations is shown to dominate the anomalous Hall effect in a 2D Rashba ferromagnet. The mechanism originates in scattering on rare impurity pairs separated by distances of the order of the Fermi wave length. Corresponding theoretical description goes beyond the conventional non-crossing approximation. The mechanism provides the only contribution to the anomalous Hall conductivity in the most relevant metallic regime and strongly modifies previously obtained results for lower energies in the leading order with respect to impurity strength.

cond-mat.mes-hall↗

arXiv2020

Chiral ferromagnetism beyond Lifshitz invariants

We consider a contribution $w_{\text{ch}}$ to the micromagnetic energy density that is linear with respect to the first spatial derivatives of the local magnetization direction. For a generalized 2D Rashba ferromagnet, we present a microscopic analysis of this contribution and, in particular, demonstrate that it cannot be expressed through Lifshitz invariants beyond the linear order in the spin-orbit coupling (SOC) strength. Terms in $w_{\text{ch}}$ beyond Lifshitz invariants emerge as a result of spin rotation symmetry breaking caused by SOC. Effects of these terms on the phase diagram of magnetic states and spin-wave dispersion are discussed. Finally, we present a classification of terms in $w_{\text{ch}}$, allowed by symmetry, for each crystallographic point group.

cond-mat.mes-hall↗

arXiv2019

Spin-torque resonance due to diffusive dynamics at a surface of topological insulator

We investigate spin-orbit torques on magnetization in an insulating ferromagnetic (FM) layer that is brought into a close proximity to a topological insulator (TI). In addition to the well-known field-like spin-orbit torque, we identify an anisotropic anti-damping-like spin-orbit torque that originates in a diffusive motion of conduction electrons. This diffusive torque is vanishing in the limit of zero momentum (i. e. for spatially homogeneous electric field or current), but may, nevertheless, have a strong effect on spin-torque resonance at finite frequency provided external field is neither parallel nor perpendicular to the TI surface. The required electric field configuration can be created by a grated top gate.

cond-mat.mes-hall↗

arXiv2019

Asymmetric and symmetric exchange in a generalized 2D Rashba ferromagnet

Dzyaloshinskii-Moriya interaction (DMI) is investigated in a 2D ferromagnet (FM) with spin-orbit interaction of Rashba type at finite temperatures. The FM is described in the continuum limit by an effective $s$-$d$ model with arbitrary dependence of spin-orbit coupling (SOC) and kinetic energy of itinerant electrons on the absolute value of momentum. In the limit of weak SOC, we derive a general expression for the DMI constant $D$ from a microscopic analysis of the electronic grand potential. We compare $D$ with the exchange stiffness $A$ and show that, to the leading order in small SOC strength $α_{\text{R}}$, the conventional relation $D=(4 mα_{\text{R}}/\hbar)A$, in general, does not hold beyond the Bychkov-Rashba model. Moreover, in this model, both $A$ and $D$ vanish at zero temperature in the metal regime (i.e., when two spin sub-bands are partly occupied). For nonparabolic bands or nonlinear Rashba coupling, these coefficients are finite and acquire a nontrivial dependence on the chemical potential that demonstrates the possibility to control the size and chirality of magnetic textures by adjusting a gate voltage.

cond-mat.mes-hall↗

arXiv2017

Sensitivity of anomalous Hall effect to disorder correlations

Both longitudinal and anomalous Hall conductivity are computed in the model of two-dimensional Dirac fermions with a mass in the presence of arbitrary correlated weak disorder. The anomalous Hall conductivity is shown to be highly sensitive to the correlation properties of the random potential, such as the correlation length, while it remains independent of the integral disorder strength. This property extends beyond the Dirac model making the anomalous Hall effect an interesting tool to probe disorder correlations.

cond-mat.dis-nn↗

arXiv2017

Microscopic theory of spin-orbit torques and skyrmion dynamics

We formulate a general microscopic approach to spin-orbit torques in thin ferromagnet/heavy-metal bilayers in linear response to electric current or electric field. The microscopic theory we develop avoids the notion of spin currents and spin-Hall effect. Instead, the torques are directly related to a local spin polarization of conduction electrons, which is computed from generalized Kubo-Středa formulas. A symmetry analysis provides a one-to-one correspondence between polarization susceptibility tensor components and different torque terms in the Landau-Lifshitz-Gilbert equation for magnetization dynamics. The spin-orbit torques arising from Rashba or Dresselhaus type of spin-orbit interaction are shown to have different symmetries. We analyze these spin-orbit torques microscopically for a generic electron model in the presence of an arbitrary smooth magnetic texture. For a model with spin-independent disorder we find a major cancelation of the torques. In this case the only remaining torque corresponds to the magnetization-independent Edelstein effect. Furthermore, our results are applied to analyze the dynamics of a Skyrmion under the action of electric current.

cond-mat.mes-hall↗