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Altermagnets host an array of magnetic multipoles, which are often visualized and studied in the reciprocal space. In the real space, the relative phase of the multipoles of the spin-density around atoms determines whether a system is an…

Materials Science · Physics 2026-01-01 Luca Buiarelli , Rafael M. Fernandes , Turan Birol

Recently, spin splitting of non-relativistic origin in compensated antiferromagnets has drawn growing attention in condensed matter research. Although many materials, now known to exhibit such spin splitting, have been studied for decades,…

Materials Science · Physics 2025-10-24 Sayantika Bhowal , Arnab Bose

We propose a realization of an antisymmetric spin-split band structure through magnetic phase transitions without spin-orbit coupling. It enables us to utilize for a variety of magnetic-order-driven cross-correlated and nonreciprocal…

Strongly Correlated Electrons · Physics 2020-07-01 Satoru Hayami , Yuki Yanagi , Hiroaki Kusunose

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

We clarify the macroscopic symmetry and microscopic model-parameter conditions for emergence of spin-split electronic band structure in collinear antiferromagnets without atomic spin-orbit coupling. By using the microscopic multipole…

Strongly Correlated Electrons · Physics 2019-11-12 Satoru Hayami , Yuki Yanagi , Hiroaki Kusunose

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

Multipole representation is proposed for the anisotropic Coulomb interactions in solids. Any local interactions can be expressed as the product of two multipole operators, and the interaction parameters are systematically classified based…

Materials Science · Physics 2021-08-25 Shoma Iimura , Motoaki Hirayama , Shintaro Hoshino

In a collinear magnet, the predominant magnetic moments are collectively aligned along a specific spatial orientation, and this alignment may yield intriguing phenomena such as spin orientation driven polarization. It is well known that…

Materials Science · Physics 2025-12-12 Yixun Zhang , Longju Yu , Yizhou Tong , Ying Sun , Xu Li , Hong Jian Zhao , Yanming Ma

Characterizing the anisotropic structure in noncollinear antiferromagnets is essential for antiferromagnetic spintronics. In this work, we provide a microscopic theory linking the anisotropy effects induced by the rigid-body rotation of…

Materials Science · Physics 2025-07-15 Zheng Liu , Yang Gao , Qian Niu

A systematic framework to investigate spin dynamics in non-collinear antiferromagnet is proposed. Taking Mn$_3$Sn as a representative example, we derive an effective low energy model based on the multipole expansion of the magnetic…

Mesoscale and Nanoscale Physics · Physics 2020-03-04 Takuya Nomoto , Ryotaro Arita

Spintronics has advanced through discoveries of various electrically-driven spin dynamics in nanomagnets. Here, we report a novel switching dynamics of spin systems driven by spin-orbit torque, using a noncollinear antiferromagnetic…

Mesoscale and Nanoscale Physics · Physics 2026-05-19 Yuma Sato , Yutaro Takeuchi , Yuta Yamane , Shun Kanai , Shunsuke Fukami

The search for novel magnetic quantum phases, phenomena and functional materials has been guided by relativistic magnetic-symmetry groups in coupled spin and real space from the dawn of the field in 1950s to the modern era of topological…

Mesoscale and Nanoscale Physics · Physics 2022-09-27 Libor Šmejkal , Jairo Sinova , Tomas Jungwirth

Spin-dependent electric dipole operators are investigated group-theoretically for the emergence of an electric dipole induced by a single spin or by two spins, where the spin dependences are completely classified up to the quadratic order.…

Strongly Correlated Electrons · Physics 2017-02-09 Masashige Matsumoto , Kosuke Chimata , Mikito Koga

The non-relativistic spin-splitting (NRSS) of electronic bands in "altermagnets" has sparked renewed interest in antiferromagnets (AFMs) that have no net magnetization. However, altermagnets with collinear and compensated magnetism are not…

Materials Science · Physics 2024-12-31 Lin-Ding Yuan , Alexandru B. Georgescu , James M. Rondinelli

We show that the surface of a centrosymmetric, collinear, compensated antiferromagnet, which hosts bulk ferroically ordered magnetic octupoles, exhibits a linear magnetoelectric effect, a net magnetization, and a net electric dipole moment.…

Materials Science · Physics 2025-06-10 Sayantika Bhowal , Andrea Urru , Sophie F. Weber , Nicola A. Spaldin

Multipoles provide a systematic framework for describing the electronic structures of quantum materials from a symmetry perspective. Thermodynamic multipole moments in crystalline solids exhibit direct microscopic connections to certain…

Mesoscale and Nanoscale Physics · Physics 2026-04-01 Takumi Sato , 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

We revise existing group-theoretical approaches for a treatment of nonrelativistic collinear magnetic systems with perfect translation invariance. We show that full symmetry groups of these systems, which contain elements with independent…

Materials Science · Physics 2022-09-30 Ilja Turek

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
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