Related papers: Toroidal order in metals without local inversion s…
Magneto-toroidal order, also called ferrotoroidicity, is the most recently established type of ferroic state. It is based on a spontaneous and uniform alignment of unit-cell-sized magnetic whirls, called magneto-toroidal moments, associated…
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 partial disorder on a layered triangular lattice is theoretically investigated from a viewpoint of toroidal ordering and magnetoelectric effects. We consider an extended periodic Anderson model including a site-dependent antisymmetric…
This article is dedicated to the 60-th anniversary of the Landau Institute for Theoretical Physics and presents a review of normal and superconducting properties of toroidal, altermagnetic, and noncentrosymmetric metals. Metals with…
A ferroaxial ordering, which appears without mirror symmetry parallel to an electric axial moment, is described by a ferroic alignment of the electric toroidal (ET) dipole rather than the conventional electric and magnetic dipoles. Although…
Effects of spontaneous toroidal ordering on magnetic excitation are theoretically investigated for a localized spin model that includes a staggered Dzyaloshinsky-Moriya interaction and anisotropic exchange interactions, which arise from 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 theoretically investigate an antiferromagnetic structure in a hexagonal zigzag-chain compound Ce$_3$TiBi$_5$, which shows a linear magnetoelectric effect in metals and an unfamiliar temperature dependence of magnetic susceptibility. We…
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 show that a simplified two-band model describing toroidal magnetic order in two-dimensional crystal is entirely equivalent to the well-known Haldane model of a honeycomb lattice in periodic internal magnetic field with zero total flux…
Ferroic multipole orders break some symmetry and often activate unique physical properties, such as nonreciprocal directional dichroism and linear magnetoelectric effects. Here, we demonstrate the control of magnetic toroidal orientation in…
Different types of order are discussed in the context of strongly correlated transition metal oxides, involving pure compounds and $3d^{3}-4d^{4}$ and $3d^{2}-4d^{4}$ hybrids. Apart from standard, long-range spin and orbital orders we…
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…
We present a general formalism of multipole descriptions under the space-time inversion group. We elucidate that two types of atomic toroidal multipoles, i.e., electric and magnetic, are fundamental pieces to express electronic order…
A two dimensional system of discs upon which a triangle of spins are mounted is shown to undergo a sequence of interesting phase transitions as the temperature is lowered. We are mainly concerned with the `solid' phase in which bond…
Motivated by recent experimental progress in transition metal oxides with the K$_2$NiF$_4$ structure, we investigate the magnetic and orbital ordering in $\alpha$-Sr$_2$CrO$_4$. Using first principles calculations, first we derive a…
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…
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…
Magnetization measurements under direct electric currents were performed for toroidal magnetic ordered state of UNi$_4$B to test a recent theoretical prediction of current-induced magnetization in a metallic system lacking local inversion…
Beyond conventional electric and magnetic monopoles, electric and magnetic toroidal monopoles, which are rank-0 multipoles distinguished by opposite parities under spatial inversion and time reversal, can exist in nature. The recent…