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Broken symmetries in solids involving higher order multipolar degrees of freedom are historically referred to as "hidden orders" due to the formidable task of detecting them with conventional probes. Examples of such hidden orders include…
Detecting symmetry-breaking hidden orders with conventional probes has been a long-standing challenge in the field of magnetism. Higher-rank multipolar ordering $-$ anisotropic charge and magnetization distributions arising from a…
Motivated by the recent development in strong spin-orbit-coupled materials, we consider the dipole-octupole doublets on the triangular lattice. We propose the most general interaction between these unusual local moments. Due to the…
The concepts of topology have a profound impact on physics research spanning the fields of condensed matter, photonics and acoustics and predicting topological states that provide unprecedented versatility in routing and control of waves of…
In the electromagnetic multipole expansion, magnetic octupoles are the subsequent order of magnetic multipoles allowed in centrosymmetric systems, following the more commonly observed magnetic dipoles. As order parameters in condensed…
We present ab initio calculations of hidden magnetoelectric multipolar order in Cr$_2$O$_3$ and its iron-based analogue, $\alpha$-Fe$_2$O$_3$. First, we discuss the connection between the order of such hidden multipoles and the linear…
The formalism of composite and intertwined orders has been remarkably successful in discussing the complex phase diagrams of strongly correlated materials and high-$T_c$ superconductors. Here, we propose that composite orders are also…
A model for a monolayer of two types of particles spontaneously forming ordered patterns is studied by a mesoscopic theory and by MC simulations. We assume hard-cores of the same size for both components, short-range attraction long-range…
An antiferro ordering of an electric hexadecapole moment is discussed as a promising candidate for the long standing mystery of the hidden order phase in URu$_{2}$Si$_{2}$. Based on localized $f$-electron picture, we discuss the rationale…
Possible ways of identification are discussed of an electronic order of higher multipoles such as octupoles and hexadecapoles. A particularly powerful method is resonant X-ray scattering (RXS) using quadrupolar resonance processes called…
In many materials, ordered phases and their order parameters are easily characterized by standard experimental methods. "Hidden order" refers to a phase transition in which an ordered state emerges without such an easily detectable order…
"Hidden"-order phases with high-rank multipolar order parameters have been recently detected in several cubic double perovskites of 5$d$ transition metals. Here, by constructing and solving an ab initio low-energy Hamiltonian, we show that…
Motivated by recent studies of odd-parity multipole order in condensed matter physics, we theoretically study magnetoelectric responses in an electric octupole state. Investigating the Edelstein effect and spin Hall effect in a locally…
On the basis of group theory and the first-principles calculations, we investigate high-rank multipole orderings in URu2Si2, which have been proposed as a genuine primary order parameter in the hidden order phase below 17.5K. We apply…
Resonant elastic X-ray scattering is a powerful technique for measuring multipolar order parameters. In this paper, we theoretically and experimentally study the possibility of using this technique to detect the proposed multipolar order…
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 multipole order is a ubiquitous phenomenon in…
Possibility of a novel pseudo-scalar (octupole) order is studied theoretically for orbitally degenerate systems with strong spin-orbit coupling such as Ce$_x$La$_{1-x}$B$_6$. It is discussed that coexistence of an octupole order parameter…
The ground-state phase diagrams of the three-orbital t2g Hubbard model are studied using a Hartree-Fock approximation. First, a complete set of multipolar order parameters for t2g models defined in terms of the effective total angular…
We study quasi-one-dimensional strongly correlated materials using a multi-step approach based on density functional theory, downfolding techniques, and tensor-network simulations. The downfolding procedure yields effective multiband…
We study f-electron lattice models which are capable of supporting octupolar, as well dipolar and quadrupolar, order. Analyzing the properties of the Gamma8 ground state quartet, we find that (111)-type combinations of the Gamma5 octupoles…