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Multipole moments serve as order parameters for characterizing higher-order magnetic effects in momentum space, providing a framework to describe diverse magnetic responses by extending the concept of magnetism. In this letter, we introduce…

Mesoscale and Nanoscale Physics · Physics 2026-01-14 Chang Niu , Lulu Li , Yiqing Wang , Lei Wang , Ke Xia

The multipole concept, which characterizes the spacial distribution of scalar and vector objects by their angular dependence, has already become widely used in various areas of physics. In recent years it has become employed to…

Strongly Correlated Electrons · Physics 2018-04-04 Michi-To Suzuki , Hiroaki Ikeda , Peter M. Oppeneer

Emergent quasiparticles that arise from the fractionalization of the microscopic degrees of freedom have been one of the central themes in modern condensed matter physics. The notion of magnetic monopoles, freely moving quasiparticles…

Strongly Correlated Electrons · Physics 2016-06-10 Gia-Wei Chern , Paula Mellado

A method is presented which allows the exact construction of conserved (i.e. divergence-free) current vectors from appropriate sets of multipole moments. Physically, such objects may be taken to represent the flux of particles or electric…

General Relativity and Quantum Cosmology · Physics 2008-11-26 Abraham I. Harte

We investigate effects of multipole moments in f-electron systems both from phenomenological and microscopic viewpoints. First, we discuss significant effects of octupole moment on the magnetic susceptibility in a paramagnetic phase. It is…

Strongly Correlated Electrons · Physics 2015-06-25 Katsunori Kubo , Takashi Hotta

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…

Classical Physics · Physics 2019-01-10 Yuri Krynytskyi , Andrij Rovenchak

We consider the magnetostatic response to an external magnetic field of a crystal containing off-center ions, such as Li^+ in KCl and KBr or the apical oxygens O(A) in the LaSCO family of layered perovskites. Magnetic dipoles are deduced…

Materials Science · Physics 2007-05-23 Mladen Georgiev

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

Multipolar degrees of freedom and their hidden orders have been widely discussed in the context of heavy fermions, frustrated magnets and exotic Kondo effects. Although there has been extensive search for multipolar degrees of freedom in…

Strongly Correlated Electrons · Physics 2023-09-15 Junmo Jeon , SungBin Lee

Multiferroics are materials with coexisting electric and magnetic orders that are of central importance for fundamental research and technological applications. Unfortunately, intrinsic multiferroics that operate at room temperature remain…

Materials Science · Physics 2025-11-06 Ping Tang , Gerrit E. W. Bauer

We theoretically investigate the effect of external fields and currents on electronic nematic orderings based on the concept of augmented multipoles consisting of electric, magnetic, magnetic toroidal, and electric toroidal multipoles. We…

Strongly Correlated Electrons · Physics 2023-11-29 Satoru Hayami

We study integral expressions of electromagnetic multipole moments of arbitrary order in Cartesian coordinates. The volume and surface integrals of charge-induced and current-induced multipole moment tensors are formulated and the…

Classical Physics · Physics 2013-07-30 J. Niitsuma

Background: The coupling of the last nucleon with configurations in the ground state of the even-even core is known to augment the single quasiparticle fragmentation pattern. In a recent experimental study by Yordanov \emph{et al.} the…

Nuclear Theory · Physics 2015-11-11 S. Mishev , V. V. Voronov

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

Electrically charged particles, such as the electron, are ubiquitous. By contrast, no elementary particles with a net magnetic charge have ever been observed, despite intensive and prolonged searches. We pursue an alternative strategy,…

Strongly Correlated Electrons · Physics 2011-11-08 Claudio Castelnovo , Roderich Moessner , Shivaji L. Sondhi

Magnetic multipole moments beyond dipoles have emerged as key descriptors of unconventional electromagnetic responses in crystalline solids. However, a gauge-invariant bulk expression for orbital magnetic multipole moments has remained…

Mesoscale and Nanoscale Physics · Physics 2026-01-01 Takumi Sato , Satoru Hayami

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 charged wave packets with non-Gaussian spatial profiles are shown to possess intrinsic multipole moments. The magnetic dipole moment and the electric quadrupole moment are found for a wide class of the packets, including the vortex…

Quantum Physics · Physics 2019-02-05 Dmitry Karlovets , Alexey Zhevlakov

We introduce a mechanism in which coupling between fluctuating spin magnetic dipole moments and polar optical phonons leads to a non-zero ferroic ordering of quasi-static magnetoelectric multipoles. Using first-principles calculations…

Superconductivity · Physics 2016-05-25 M. Fechner , M. J. A. Fierz , F. Thöle , U. Staub , N. A. Spaldin

Electrons navigate more easily in a background of ordered magnetic moments than around randomly oriented ones. This fundamental quantum mechanical principle is due to their Bloch wave nature and also underlies ballistic electronic motion in…

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