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In the early 2000s, low dimensional systems were predicted to have topologically nontrivial polar structures, such as vortices or skyrmions, depending on mechanical or electrical boundary conditions. A few variants of these structures have…

Magnetic spin topological textures recently found their electrical counterparts in polar topologies emerging from the condensation of inhomogeneous polar atomic distortions. Here, we further extend the concept to other non-polar atomic…

Materials Science · Physics 2025-10-10 Fernando Gómez-Ortiz , Louis Bastogne , Philippe Ghosez

Topological textures like vortices, labyrinths and skyrmions formed in ferroic materials have attracted extensive interests during the past decade for their fundamental physics, intriguing topology, and technological prospects. So far,…

Polar topologies, such as vortex and skyrmion, have attracted significant interest due to their unique physical properties and promising applications in high-density memory devices. Currently, most polar vortices are observed in…

Applied Physics · Physics 2024-04-15 Haozhi Sha , Yixuan Zhang , Yunpeng Ma , Wei Li , Wenfeng Yang , Jizhe Cui , Qian Li , Houbing Huang , Rong Yu

Discovery of topological polarization textures has put ferroelectrics at the frontier of topological matter science. High-symmetry ferroelectric oxide materials allowing for freedom of the polarization vector rotation offer a fertile ground…

Polar topology, an analogue of the magnetic topology, serves as a large playground for exotic physical phenomena with a wide range of multifunctional applications. Polar vortices and skyrmions are representative polar topologies that have…

Polar skyrmions are topologically stable, swirling polarization textures with particle-like characteristics, which hold promise for next-generation, nanoscale logic and memory. While understanding of how to create ordered polar skyrmion…

Magnetic skyrmions are mesmerizing spin textures with peculiar topological and dynamical properties, typically the product of competing interactions in ferromagnets, and with great technological potential [1-5]. Researchers have long…

The generation of topologically non-trivial magnetic configurations has been a pivotal topic in both basic and applied nanomagnetism research. Localized non-coplanar magnetic defects such as skyrmions or merons were found to interact…

Mesoscale and Nanoscale Physics · Physics 2025-06-13 Reiner Brüning , Levente Rózsa , Roberto Lo Conte , André Kubetzka , Roland Wiesendanger , Kirsten von Bergmann

Particle-like topological structures such as skyrmions and vortices have garnered ever-increasing interests due to the rich physical insights and potential broad applications. Here we discover the reversible switching between polar skyrmion…

Mesoscale and Nanoscale Physics · Physics 2018-05-01 Zijian Hong , Long-Qing Chen

Polar topological structures in ferroelectric thin films have recently drawn significant interest due to their fascinating physical behaviors and promising applications in high-density nonvolatile memories. However, most polar topological…

Materials Science · Physics 2024-02-26 Bo Xu , Zhanpeng Gong , Jingran Liu , Yunfei Hong , Yang Yang , Lou Li , Yilun Liu , Junkai Deng , Jefferson Zhe Liu

Magnetic vortices and skyrmions represent two fundamental classes of topological spin textures in ferromagnetic systems, distinguished by their unique stabilization mechanisms and degrees of freedom. Vortices, characterized by circular…

Computational Physics · Physics 2025-03-21 Haobing Zhang , Xintao Fan , Weiwei Wang

The collective dynamics of topological structures have been of great interest from both fundamental and applied perspectives. For example, the studies of dynamical properties of magnetic vortices and skyrmions not only deepened the…

Polar topological textures in low-dimensional ferroelectrics have emerged as a versatile platform for high-density information storage and neuromorphic computing. While low-order topological states, such as vortices and skyrmions, have been…

Materials Science · Physics 2026-01-12 Kefan Liu , Yuhui Huang , Xiangwei Guo , Yongjun Wu , Juan Li , Zijian Hong

The research on topological phenomena in ferroelectric materials has revolutionized the way we understand polar order. Intriguing examples are polar skyrmions, vortex/anti-vortex structures and ferroelectric incommensurabilties, which…

The ability to controllably manipulate the complex topological polar configurations, such as polar flux-closure via external stimuli, enables many applications in electromechanical devices and nanoelectronics including high-density…

Magnetic skyrmions can be considered as topologically protected localized vortex-like spin textures. Due to their stability, their small size, and the possibility to move them by low electric currents they are promising candidates for…

Mesoscale and Nanoscale Physics · Physics 2017-07-05 Martin Stier , Wolfgang Häusler , Thore Posske , Gregor Gurski , Michael Thorwart

In ferroelectrics, complex interactions among various degrees of freedom enable the condensation of topologically protected polarization textures. Known as ferroelectric solitons, these particle-like structures represent a new class of…

Materials Science · Physics 2023-08-02 V. Govinden , P. R. Tong , X. Guo , Q. Zhang , S. Mantri , S. Prokhorenko , Y. Nahas , Y. Wu , L. Bellaiche , H. Tian , Z. Hong , D. Sando , V. Nagarajan

Topological materials, including topological insulators, magnets with Skyrmions and ferroelectrics with topological vortices, have recently attracted phenomenal attention in the materials science community. Complex patterns of ferroelectric…

Materials Science · Physics 2015-06-15 S. C. Chae , Y. Horibe , D. Y. Jeong , N. Lee , K. Iida , M. Tanimura , S. -W. Cheong

The wealth of complex polar topologies recently found in nanoscale ferroelectrics result from a delicate balance between the materials intrinsic tendency to develop a homogeneous polarization and the electric and mechanic boundary…

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