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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…

Materials Science · Physics 2024-09-12 Hiroaki Kusunose , Satoru Hayami

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…

Materials Science · Physics 2018-12-20 Hikaru Watanabe , Youichi Yanase

Cluster magnetic multipoles are order parameters that describe the symmetry of spin arrangements in magnetic materials. High-order multipoles are particularly important in non-collinear antiferromagnets, where they determine key physical…

Mesoscale and Nanoscale Physics · Physics 2025-01-14 Myoung-Woo Yoo , Axel Hoffmann

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…

Strongly Correlated Electrons · Physics 2018-10-24 Satoru Hayami , Megumi Yatsushiro , Yuki Yanagi , Hiroaki Kusunose

Natural optical activity is the paradigmatic example of an effect originating in the weak spatial inhomogeneity of the electromagnetic field on the atomic scale. In molecules, such effects are well described by the multipole theory of…

Materials Science · Physics 2023-05-31 Óscar Pozo , Ivo Souza

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…

Strongly Correlated Electrons · Physics 2021-08-18 Megumi Yatsushiro , Hiroaki Kusunose , Satoru Hayami

Antiferromagnets with vanishing net magnetization are naturally expected to host higher-order magnetic multipole moments. Understanding and utilizing the multipole degrees of freedom are imperative for novel conceptual designs and…

Materials Science · Physics 2026-04-07 Hua Chen , Guang-Yu Guo , Di Xiao

We provide a first-principle, materials-specific theory of multipolar order and superexchange in NpO$_2$ by means of a non-collinear local-density approximation +$U$ (LDA+$U$) method. Our calculations offer a precise microscopic description…

Strongly Correlated Electrons · Physics 2010-12-22 Michi-To Suzuki , Nicola Magnani , Peter M. Oppeneer

Magnetic multipoles have been recognized as order parameters characterizing magnetic structure in solids. Recently, magnetic octupoles have been proposed as the order parameters of time-reversal-symmetry breaking centrosymmetric…

Mesoscale and Nanoscale Physics · Physics 2026-02-06 Takumi Sato , Satoru Hayami

Multiferroics are materials where two or more ferroic orders coexist owing to the interplay between spin, charge, lattice and orbital degrees of freedom. The explosive expansion of multiferroics literature in recent years demon-strates the…

Multiferroics, materials where spontaneous long-range magnetic and dipolar orders coexist, represent an attractive class of compounds, which combine rich and fascinating fundamental physics with a technologically appealing potential for…

Materials Science · Physics 2015-05-13 Silvia Picozzi , Claude Ederer

Achieving and exceeding the diversity of colloidal analogs of chemical elements and molecules as building blocks of matter has been the central goal and challenge of colloidal science ever since Einstein introduced the colloidal atom…

Soft Condensed Matter · Physics 2019-06-19 Bohdan Senyuk , Jure Aplinc , Miha Ravnik , Ivan I. Smalyukh

Electric and magnetic multipole densities in crystalline solids, including the familiar electric dipole density in ferroelectrics and the magnetic dipole density in ferromagnets, are of central importance for our understanding of ordered…

Materials Science · Physics 2025-10-03 R. Winkler , U. Zülicke

Magnetic ordering beyond the standard dipolar order has attracted significant attention in recent years, but it remains an open question how to effectively manipulate such nontrivial order parameters using external perturbations. In this…

Materials Science · Physics 2023-09-08 Muhammad Tahir , Hua Chen

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…

Strongly Correlated Electrons · Physics 2024-11-13 R. Matthias Geilhufe

Materials that combine magnetic and ferroelectric properties have generated increasing interest over the last few years, due to both their diverse properties and their potential utility in new types of magnetoelectric device applications.…

Materials Science · Physics 2014-11-17 Claude Ederer , Nicola A. Spaldin

We demonstrate computationally the existence of magnetoelectric multipoles, arising from the second order term in the multipole expansion of a magnetization density in a magnetic field, in noncentrosymmetric magnetic metals. While…

Materials Science · Physics 2021-03-09 Florian Thöle , Nicola A. Spaldin

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…

We establish a quantitative relation between the altermagnetic spin-splitting and different higher order multipoles of the charge and magnetization density around the magnetic atoms. Magnetic multipoles such as octupoles or triakontadipoles…

Materials Science · Physics 2025-12-22 Francesco Martinelli , Anouk Droux , Claude Ederer

This chapter reviews the basic physics and thermodynamics that govern magnetocaloric materials. The thermodynamics of magnetic materials is discussed by introducing relevant free energy terms together with their microscopic origin leading…

Materials Science · Physics 2017-02-28 Vittorio Basso
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