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Yue WC, Yuan Z, Huang P, Sun Y, Gao T, Lyu YY, Tu X, Dong S, He L, Dong Y, Cao X, Kang L, Wang H, Wu P, Nisoli C, Wang YL. Toroidic phase transitions in a direct-kagome artificial spin ice. NATURE NANOTECHNOLOGY 2024; 19:1101-1107. [PMID: 38684808 DOI: 10.1038/s41565-024-01666-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/09/2023] [Accepted: 03/27/2024] [Indexed: 05/02/2024]
Abstract
Ferrotoroidicity-the fourth form of primary ferroic order-breaks both space and time-inversion symmetry. So far, direct observation of ferrotoroidicity in natural materials remains elusive, which impedes the exploration of ferrotoroidic phase transitions. Here we overcome the limitations of natural materials using an artificial nanomagnet system that can be characterized at the constituent level and at different effective temperatures. We design a nanomagnet array as to realize a direct-kagome spin ice. This artificial spin ice exhibits robust toroidal moments and a quasi-degenerate ground state with two distinct low-temperature toroidal phases: ferrotoroidicity and paratoroidicity. Using magnetic force microscopy and Monte Carlo simulation, we demonstrate a phase transition between ferrotoroidicity and paratoroidicity, along with a cross-over to a non-toroidal paramagnetic phase. Our quasi-degenerate artificial spin ice in a direct-kagome structure provides a model system for the investigation of magnetic states and phase transitions that are inaccessible in natural materials.
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Affiliation(s)
- Wen-Cheng Yue
- School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- Purple Mountain Laboratories, Nanjing, China
- Research Institute of Superconductor Electronics, Nanjing University, Nanjing, China
| | - Zixiong Yuan
- School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- Purple Mountain Laboratories, Nanjing, China
- Research Institute of Superconductor Electronics, Nanjing University, Nanjing, China
| | - Peiyuan Huang
- School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- Purple Mountain Laboratories, Nanjing, China
- Research Institute of Superconductor Electronics, Nanjing University, Nanjing, China
| | - Yizhe Sun
- School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- National Key Laboratory of Spintronics, Nanjing University, Suzhou, China
| | - Tan Gao
- School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- Purple Mountain Laboratories, Nanjing, China
- Research Institute of Superconductor Electronics, Nanjing University, Nanjing, China
| | - Yang-Yang Lyu
- School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- Purple Mountain Laboratories, Nanjing, China
- Research Institute of Superconductor Electronics, Nanjing University, Nanjing, China
| | - Xuecou Tu
- School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- Purple Mountain Laboratories, Nanjing, China
- Research Institute of Superconductor Electronics, Nanjing University, Nanjing, China
| | - Sining Dong
- School of Electronic Science and Engineering, Nanjing University, Nanjing, China.
- Research Institute of Superconductor Electronics, Nanjing University, Nanjing, China.
- National Key Laboratory of Spintronics, Nanjing University, Suzhou, China.
| | - Liang He
- School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- National Key Laboratory of Spintronics, Nanjing University, Suzhou, China
| | - Ying Dong
- College of Metrology Measurement and Instrument, China Jiliang University, Hangzhou, China
| | - Xun Cao
- School of Electronic Science and Engineering, Nanjing University, Nanjing, China
| | - Lin Kang
- School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- Research Institute of Superconductor Electronics, Nanjing University, Nanjing, China
| | - Huabing Wang
- School of Electronic Science and Engineering, Nanjing University, Nanjing, China.
- Purple Mountain Laboratories, Nanjing, China.
- Research Institute of Superconductor Electronics, Nanjing University, Nanjing, China.
| | - Peiheng Wu
- School of Electronic Science and Engineering, Nanjing University, Nanjing, China
- Purple Mountain Laboratories, Nanjing, China
- Research Institute of Superconductor Electronics, Nanjing University, Nanjing, China
| | - Cristiano Nisoli
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM, USA.
| | - Yong-Lei Wang
- School of Electronic Science and Engineering, Nanjing University, Nanjing, China.
- Purple Mountain Laboratories, Nanjing, China.
- Research Institute of Superconductor Electronics, Nanjing University, Nanjing, China.
- National Key Laboratory of Spintronics, Nanjing University, Suzhou, China.
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Neto JF, Silva CCDS. Mesoscale Phase Separation of Skyrmion-Vortex Matter in Chiral-Magnet-Superconductor Heterostructures. PHYSICAL REVIEW LETTERS 2022; 128:057001. [PMID: 35179935 DOI: 10.1103/physrevlett.128.057001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/17/2021] [Revised: 08/05/2021] [Accepted: 01/06/2022] [Indexed: 06/14/2023]
Abstract
We investigate theoretically the equilibrium configurations of many magnetic skyrmions interacting with many superconducting vortices in a superconductor-chiral-magnet bilayer. We show that miscible mixtures of vortices and skyrmions in this system break down at a particular wave number for sufficiently strong coupling, giving place to remarkably diverse mesoscale patterns: gel, stripes, clusters, intercalated stripes, and composite gel-cluster structures. We also demonstrate that, by appropriate choice of parameters, one can thermally tune between the homogeneous and density-modulated phases.
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Affiliation(s)
- José F Neto
- Departamento de Física, Universidade Federal de Pernambuco, Cidade Universitária, 50670-901 Recife-PE, Brazil
| | - Clécio C de Souza Silva
- Departamento de Física, Universidade Federal de Pernambuco, Cidade Universitária, 50670-901 Recife-PE, Brazil
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