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Skyrmions are topologically nontrivial, magnetic quasi-particles, that are characterized by a topological charge. A regular array of skyrmions - a skyrmion crystal (SkX) - features the topological Hall effect (THE) of electrons, that, in…

Strongly Correlated Electrons · Physics 2017-08-16 Börge Göbel , Alexander Mook , Jürgen Henk , Ingrid Mertig

Topological Hall effect (THE) caused by a noncoplanar spin texture characterized by a scalar spin chirality is often described by the Berry phase, or the associated effective magnetic field. This picture is appropriate when the coupling,…

Mesoscale and Nanoscale Physics · Physics 2019-05-28 Kazuki Nakazawa , Hiroshi Kohno

Topological Hall effect (THE) of electrons coupled to a noncoplanar spin texture has been studied so far for the strong- and weak-coupling regimes separately; the former in terms of the Berry phase and the latter by perturbation theory. In…

Mesoscale and Nanoscale Physics · Physics 2019-05-29 Kazuki Nakazawa , Manuel Bibes , Hiroshi Kohno

The phonon thermal Hall effect (THE) is a ubiquitous yet poorly understood phenomenon in insulators. Its microscopic origin remains debated, partly due to significant sample-dependent variations that hint at uncontrolled experimental…

Strongly Correlated Electrons · Physics 2025-11-13 Qiaochao Xiang , Xiaokang Li , Xiaodong Guo , Kamran Behnia , Zengwei Zhu

The quantum anomalous Hall effect has been theoretically predicted and experimentally verified in magnetic topological insulators. In addition, the surface states of these materials exhibit a hedgehog-like "spin" texture in momentum space.…

Mesoscale and Nanoscale Physics · Physics 2017-04-07 Narayan Mohanta , Arno P. Kampf , Thilo Kopp

Magneto-transport properties have been investigated for epitaxial thin films of B20-type MnSi grown on Si(111) substrates. Both Lorentz transmission electron microscopy (TEM) images and topological Hall effect (THE) clearly point to the…

Materials Science · Physics 2013-03-19 Yufan Li , N. Kanazawa , X. Z. Yu , A. Tsukazaki , M. Kawasaki , M. Ichikawa , X. F. Jin , F. Kagawa , Y. Tokura

Discoveries of interfacial topological Hall effect (THE) provide an ideal platform for exploring physics arising from the interplay between topology and magnetism. The interfacial topological Hall effect is closely related to the…

We demonstrate the emergence of an anomalous Hall effect in chiral magnetic textures which is neither proportional to the net magnetization nor to the well-known emergent magnetic field that is responsible for the topological Hall effect.…

Mesoscale and Nanoscale Physics · Physics 2020-03-11 Fabian R. Lux , Frank Freimuth , Stefan Blügel , Yuriy Mokrousov

We show that the two dimensional spatial inversion-symmetry (SIS) broken square lattice antiferromagnet with easy-plane spin anisotropy exhibits a thermal Hall effect and the edge modes characterized by the Z 2 topological invariant. These…

Materials Science · Physics 2019-02-22 Masataka Kawano , Chisa Hotta

The well-known Hall effect describes the transverse deflection of charged particles (electrons or holes) in an electric-current carrying conductor under the influence of perpendicular magnetic fields, as a result of the Lorentz force.…

The topological Hall effect, driven by the exchange interaction between conduction electrons and topological magnetic textures such as skyrmions, is a powerful probe for investigating the topological properties of magnetic materials.…

Materials Science · Physics 2026-03-31 Hyuncheol Kim , Kai-Xuan Zhang , Yu-Hang Li , Giung Park , Ran Cheng , Je-Geun Park

Magnetic skyrmions have attracted enormous research interest since their discovery a decade ago. The non-trivial real-space topology of these nano-whirls leads to fundamentally interesting and technologically relevant consequences - the…

Mesoscale and Nanoscale Physics · Physics 2021-01-18 Börge Göbel , Ingrid Mertig , Oleg A. Tretiakov

The 'magnetoelectric effect' arises from the coupling between magnetic and electric properties in materials. The Z2 invariant of topological insulators (TIs) leads to a quantized version of this phenomenon, known as the topological…

Mesoscale and Nanoscale Physics · Physics 2018-02-07 Di Xiao , Jue Jiang , Jae-Ho Shin , Wenbo Wang , Fei Wang , Yi-Fan Zhao , Chaoxing Liu , Weida Wu , Moses H. W. Chan , Nitin Samarth , Cui-Zu Chang

The anomalous Hall {\color{black} e}ffect (AHE) has emerged as a key indicator of time-reversal symmetry breaking (TRSB) and topological features in electronic band structures. Absent of a magnetic field, the AHE requires spontaneous TRSB…

Over a long period of exploration, the successful observation of quantized version of anomalous Hall effect (AHE) in thin film of magnetically-doped topological insulator completed a quantum Hall trio---quantum Hall effect (QHE), quantum…

Mesoscale and Nanoscale Physics · Physics 2015-08-18 Hongming Weng , Rui Yu , Xiao Hu , Xi Dai , Zhong Fang

The topological Hall effect (THE) has been discovered in ultrathin SrRuO3 (SRO) films, where the interface between the SRO layer and another oxide layer breaks the inversion symmetry resulting in the appearance of THE. Thus, THE only occurs…

The effects of spin-orbit coupling and symmetry breaking at the interface between a ferromagnet and heavy metal are particularly important for spin-based information storage and computation. Recent discoveries suggest they can create chiral…

We report an experimental and computational study of the Hall effect in Mn$_{\rm 1-x}$Fe$_{\rm x}$Si, as complemented by measurements in Mn$_{\rm 1-x}$Co$_{\rm x}$Si, when helimagnetic order is suppressed under substitutional doping. For…

Strongly Correlated Electrons · Physics 2015-06-19 C. Franz , F. Freimuth , A. Bauer , R. Ritz , C. Schnarr , C. Duvinage , T. Adams , S. Blügel , A. Rosch , Y. Mokrousov , C. Pfleiderer

The Berry phase picture provides important insights into the electronic properties of condensed matter systems. The intrinsic anomalous Hall (AH) effect can be understood as a consequence of non-zero Berry curvature in momentum space. The…

In quantum matters hosting electron-electron correlation and spin-orbit coupling, spatial inhomogeneities, arising from competing ground states, can be essential for determining and understanding topological properties. A prominent example…

Materials Science · Physics 2020-04-22 Lingfei Wang , Qiyuan Feng , Han Gyeol Lee , Eun Kyo Ko , Qingyou Lu , Tae Won Noh