Theory of orbital magnetic quadrupole moment and magnetoelectric susceptibility

  title={Theory of orbital magnetic quadrupole moment and magnetoelectric susceptibility},
  author={Atsuo Shitade and Hikaru Watanabe and Youichi Yanase},
  journal={Physical Review B},
We derive a quantum-mechanical formula of the orbital magnetic quadrupole moment (MQM) in periodic systems by using the gauge-covariant gradient expansion. This formula is valid for insulators and metals at zero and finite temperature. We also prove a direct relation between the MQM and magnetoelectric (ME) susceptibility for insulators at zero temperature. It indicates that the MQM is a microscopic origin of the ME effect. Using the formula, we quantitatively estimate these quantities for room… Expand
13 Citations

Figures from this paper

Orbital magnetic quadrupole moment and nonlinear anomalous thermoelectric transport
We present a microscopic theory of the magnetic quadrupole moment density $\Qij$ in periodic crystals using the semiclassical framework of electron dynamics. We obtain a gauge-invariant expressionExpand
Theory of spin magnetic quadrupole moment and temperature-gradient-induced magnetization
We revisit a quantum-mechanical formula of the spin magnetic quadrupole moment (MQM) in periodic crystals. Two previous attempts were inconsistent with each other; one is gauge dependent and theExpand
Berry Phase Effects in Dipole Density and the Mott Relation.
The dipole density of a physical quantity emerges and plays a vital role, which contains not only the statistical sum of the dipole moment of θ[over ^] but also a Berry phase correction. Expand
Magnetoelectric Multipoles in Condensed-Matter Systems
Magnetoelectric multipoles describe inhomogeneities in the magnetization density of a material beyond the magnetic dipole and are formally defined as the second order term in a multipole expansion ofExpand
Geometric orbital magnetization in adiabatic processes
We consider periodic adiabatic processes of gapped many-body spinless electrons. We find an additional contribution to the orbital magnetization due to the adiabatic time evolution, dubbedExpand
Orbital magnetization and anomalous Hall effect in interacting Weyl semimetals
Ferromagnetic Weyl semi-metals exhibit an anomalous Hall effect, a consequence of their topological properties. In the non-interacting case, the derivative of the orbital magnetization with respectExpand
Charge density waves in multiple- Q spin states
Coupling between spin and charge degrees of freedom in electrons is a source of various electronic and magnetic properties of solids. We theoretically study charge density waves induced by theExpand
Higher-order topological insulators in a crisscross antiferromagnetic model
We present a $4'/m'$-respecting crisscross AFM model in 2D and 3D, both belonging to the $Z_2$ classification and exhibiting interesting magnetic high-order topological insulating (HOTI) phases. TheExpand
Classification of atomic-scale multipoles under crystallographic point groups and application to linear response tensors
Four types of atomic-scale multipoles, electric, magnetic, magnetic toroidal, and electric toroidal multipoles, give a complete set to describe arbitrary degrees of freedom for coupled charge, spin,Expand
Group-theoretical classification of multipole order: Emergent responses and candidate materials
The multipole moment is an established concept of electrons in solids. Entanglement of spin, orbital, and sublattice degrees of freedom is described by the multipole moment, and spontaneous multipoleExpand


Orbital magnetoelectric coupling in band insulators
Magnetoelectric responses are a fundamental characteristic of materials that break time-reversal and inversion symmetries (notably multiferroics) and, remarkably, of "topological insulators" in whichExpand
Magnetoelectric polarizability and axion electrodynamics in crystalline insulators.
The orbital motion of electrons in a three-dimensional solid can generate a pseudoscalar magnetoelectric coupling theta, a fact that can be generalized to the many-particle wave function and defines the 3D topological insulator in terms of a topological ground-state response function. Expand
First-principles calculation of the bulk magnetoelectric monopole density: Berry phase and Wannier function approaches
We present a formalism to calculate the macroscopic magnetoelectric monopolization from first principles within the density functional theory framework. An expression for the monopolization in theExpand
Orbital magnetization of correlated electrons with arbitrary band topology
Spin-orbit coupling introduces chirality into electronic structure. This can have profound effects on the magnetization induced by orbital motion of electrons. Here we derive a formula for theExpand
Monopole-based formalism for the diagonal magnetoelectric response
We develop the formalism of the macroscopic monopolization-that is, the magnetoelectric monopole moment per unit volume-in periodic solids, and discuss its relationship to the magnetoelectric effect.Expand
Theory of orbital magnetization in disordered systems
We present a general formula of the orbital magnetization of disordered systems based on the Keldysh Green's function theory in the gauge-covariant Wigner space. In our approach, the gauge invarianceExpand
Gyrotropic Magnetic Effect and the Magnetic Moment on the Fermi Surface.
The current density j^{B} induced in a clean metal by a slowly-varying magnetic field B is formulated as the low-frequency limit of natural optical activity, or natural gyrotropy. Working with aExpand
Quantum theory of orbital magnetization and its generalization to interacting systems.
The formula for the orbital magnetization in periodic systems is shown to be valid in the presence of electron-electrons interaction, provided the one-electron energies and wave functions are calculated self-consistently within the framework of the exact current and spin-density functional theory. Expand
Berry-phase effect in anomalous thermoelectric transport.
A finite-temperature formula for the orbital magnetization is derived, which enables to provide an explicit expression for the off-diagonal thermoelectric conductivity, to establish the Mott relation between the anomalous Nernst and Hall effects, and to reaffirm the Onsager relations between reciprocal thermoelectedric conductivities. Expand
Magneto-Electric Effect in Three-Dimensional Coupled Zigzag Chains
Stimulated by recent studies of quantum phases with broken local inversion symmetry, we study the magnetoelectric effect in locally noncentrosymmetric metals. We consider three-dimensional (3D)Expand