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Altermagnetism has been proposed as a new type of magnetism, simultaneously exhibiting compensated spin moments in real space and spin-split electronic bands in reciprocal space. Alternating chiral magnon splitting is considered a unique…

Materials Science · Physics 2025-03-18 Yi-Fan Zhang , Xiao-Sheng Ni , Ke Chen , Kun Cao

In semiconductor heterostructures, bulk and structural inversion asymmetry and spin-orbit coupling induce a k-dependent spin splitting of valence and conduction subbands, which can be viewed as being caused by momentum-dependent crystal…

Mesoscale and Nanoscale Physics · Physics 2009-11-10 C. A. Ullrich , M. E. Flatte

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 present a phenomenological model for magnetoelectricity in multiferroic materials. The distinctive feature of the model is a two-component complex order parameter that encodes the electric polarization, along with a direct coupling…

Materials Science · Physics 2024-04-11 Pei Wang , You-Quan Li

Multiferroics, showing simultaneous ordering of electrical and magnetic degrees of freedom, are remarkable materials as seen from both the academic and technological points of view. A prominent mechanism of multiferroicity is the…

Strongly Correlated Electrons · Physics 2012-08-31 P. Lunkenheimer , J. Müller , S. Krohns , F. Schrettle , A. Loidl , B. Hartmann , R. Rommel , M. de Souza , C. Hotta , J. A. Schlueter , M. Lang

Bringing magnetic metals into superconducting states represents an important approach for realizing unconventional superconductors and potentially even topological superconductors. Altermagnetism, classified as a third basic collinear…

Superconductivity · Physics 2023-11-07 Di Zhu , Zheng-Yang Zhuang , Zhigang Wu , Zhongbo Yan

We analyze the pairing instability of an altermagnetic metal on a square lattice driven by an attractive nearest-neighbor interaction. This interaction enables multiple pairing channels, including even-parity extended $s$-wave and $d$-wave…

Superconductivity · Physics 2026-03-16 Hui Hu , Zhao Liu , Jia Wang , Xia-Ji Liu , Yoji Ohashi

Altermagnetism, known for its non-relativistic spin-split band structures with yet compensated moments, is being intensively investigated. Discovering new altermagnetic materials with characteristics suitable for practical use remains an…

We propose many-body order parameters for bulk multipoles in crystalline systems, which originate from the non-trivial topology of the nested Wilson loop spectrum. The many-body order parameters are designed to measure multipolar charge…

Strongly Correlated Electrons · Physics 2019-12-25 Byungmin Kang , Ken Shiozaki , Gil Young Cho

Gaining growing attention in spintronics is a class of magnets displaying zero net magnetization and spin-split electronic bands called altermagnets. Here, by combining density functional theory and symmetry analysis, we show that RuF$_4$…

Materials Science · Physics 2024-06-19 Marko Milivojević , Marko Orozović , Silvia Picozzi , Martin Gmitra , Srdjan Stavrić

Altermagnetism has recently emerged as a new class of spin compensated magnetic materials that exhibit momentum dependent spin splitting despite having zero net magnetization. The origin of these electronic signatures lies in symmetry…

Materials Science · Physics 2026-03-06 Diego López-Alcalá , Andrei Shumilin , José J. Baldoví

Altermagnetism stands as a third type of collinear magnetic order, whose band structure combines a net zero magnetization with a non-relativistic spin-splitting caused by a broken time reversal symmetry. So far, the strategy to design…

Mesoscale and Nanoscale Physics · Physics 2025-08-06 Ricardo Ortiz , Karol Strutyński , Manuel Melle-Franco

We introduce the concept of \emph{orbital altermagnetism}, a symmetry-protected magnetic order of pure orbital degrees of freedom. It is characterized with ordered anti-parallel orbital magnetic moments in real space but momentum-dependent…

Materials Science · Physics 2026-05-22 Mingxiang Pan , Feng Liu , Huaqing Huang

We report the emergence of altermagnetism, a magnetic phase characterized by the coexistence of compensated spin ordering and momentum-dependent spin splitting, in graphite intercalation compounds (GICs), a prototypical material system long…

Materials Science · Physics 2025-11-21 Weida Fu , Guo-Dong Zhao , Tao Hu , Wencai Yi , Hui Zhang , Alessandro Stroppa , Wei Ren , Zhongming Ren

The Pauli exclusion principle combined with interactions between fermions is a basic mechanism across condensed-matter systems giving rise to a spontaneous breaking of the spin-space rotation symmetry of spin-ordered phases. Ferromagnetism…

Materials Science · Physics 2025-03-13 T. Jungwirth , R. M. Fernandes , E. Fradkin , A. H. MacDonald , J. Sinova , L. Smejkal

Organic charge transfer salts show a variety of complex phases ranging from antiferromagnetic long-range order, spin liquid, bad metal or even superconductivity. A powerful method to investigate magnetism is spin-polarized inelastic neutron…

Materials Science · Physics 2014-07-29 Francesc Salvat-Pujol , Harald O. Jeschke , Roser Valenti

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

The development of altermagnets is fundamentally important for advancing spintronic device technology, but remains unpractical for the weak spin splitting in most cases, especially in two-dimensional materials. Based on spin group symmetry…

Materials Science · Physics 2026-02-03 Xinyu Yang , Shan-Shan Wang , Shuai Dong

Ferroelectric and ferromagnetic materials possess spontaneous electric and magnetic order, respectively, which can be switched by the corresponding applied electric and magnetic fields. Multiferroics combine these properties in a single…

Strongly Correlated Electrons · Physics 2012-11-27 J. Lee , S. A. Trugman , C. D. Batista , C. L. Zhang , D. Talbayev , X. S. Xu , S. --W. Cheong , D. A. Yarotski , A. J. Taylor , R. P. Prasankumar

At high densities fluids of strongly dipolar spherical particles exhibit spontaneous long-ranged orientational order. Typically, due to demagnetization effects induced by the long range of the dipolar interactions, the magnetization…

Soft Condensed Matter · Physics 2009-10-30 B. Groh , S. Dietrich
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