Related papers: Microscopic Description of Electric and Magnetic T…
In this short article, we overview a concept of electronic toroidal multipoles, and their ordering with associated physical properties in non-magnetic and magnetic materials. The toroidal multipoles are introduced as microscopic electronic…
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, and orbital of electrons. We here present…
Magnetic toroidal dipole (MTD) is one of a fundamental constituent to induce magneto-electric effects in the absence of both spatial inversion and time-reversal symmetries. We report on a microscopic investigation of the atomic-scale MTD in…
A whole series of expressions for four species of multipoles (electric, magnetic, magnetic toroidal, and electric toroidal) is provided as a complete basis set to describe arbitrary single-centered spinful electron systems. A compact…
We overview recent developments of electronic orderings and associated cross correlations in condensed matter physics based on a complete set of multipole representations (electric, magnetic, electric toroidal, and magnetic toroidal…
Orbital angular momentum and torque transfer play central roles in a wide range of magnetic textures and devices including skyrmions and spin-torque electronics(1-4). Analogous topological structures are now also being explored in…
We discuss predominant order parameters for structural chirality, and demonstrate that time-reversal-even axial-quadrupole plays a key role in stabilizing a chiral structure. Using the symmetry-adapted closest Wannier model of the trigonal…
The pairing interactions between electrons play an essential role in determining the properties in superconducting states. Recently, a plethora of unconventional superconducting states has been extensively explored, which often emerge owing…
Toroidal order, given by a composite of electric and magnetic orders, manifests itself not only in the peculiar magnetism but also in anomalous transport and magnetoelectric effect. We report our theoretical results on the influence and…
In solid state physics, any phase transition is commonly observed as a change in the microscopic distribution of charge, spin, or current. Here we report the nature of an exotic order parameter inherent in the localized electron orbitals…
It is commonly believed that electromagnetic spectra of atoms and molecules can be fully described by interactions of electric and magnetic multipoles. However, it has recently become clear that interactions between light and matter also…
Mutual interplay between the electronic degrees of freedom in solids, such as charge, spin, orbital, sublattice, and bond degrees of freedom, is a source of cross-correlated phenomena with unconventional electronic ordered states. Such…
One-body multipole operators are defined as irreducible representations of rotational symmetry together with spatial-inversion and time-reversal symmetries, providing a systematic framework for classifying electronic internal degrees of…
An electric toroidal dipole (ETD) moment is one of the fundamental dipole moments as well as electric and magnetic ones. Although it directly couples to neither an electric nor magnetic field due to its spatial inversion and time-reversal…
Higher-rank electric/magnetic multipole moments are attracting attention these days as candidate order parameters for exotic material phases. However, quantum-mechanical formulation of those multipole moments is still an ongoing issue. In…
Magnetic-ferroic ordering and magnetic-toroidal moments are essential concepts in molecular electronics and magnetics. The magnetic toroidal moment is critical in understanding new electronic states and their possible uses. This paper…
Multipolar order in bulk crystalline solids is characterized by multipole densities -- denoted as polarizations in this work -- that cannot be cleanly defined using the concepts of classical electromagnetism. Here we use group theory to…
We propose a consistent approach to the definition of electric, magnetic, and toroidal multipole moments. Electric and magnetic fields are split into potential, vortex, and radiative terms, with the latter ones dropped off in the…
Magnetic toroidal order features a loop-like arrangement of magnetic dipole moments, thus breaking both spatial inversion (P) and time-reversal (T) symmetries while preserving their combined PT sym-metry. This PT symmetry enables a linear…
We analyze the dynamic toroidal multipoles and prove that they do not have an independent physical meaning with respect to their interaction with electromagnetic waves. We analytically show how the split into electric and toroidal parts…