Toroidic phase transitions in a direct-kagome artificial spin ice

Wen-Cheng Yue; Zixiong Yuan; Peiyuan Huang; Yizhe Sun; Tan Gao; Yang-Yang Lyu; Xuecou Tu; Sining Dong; Liang He; Ying Dong; Xun Cao; Lin Kang; Huabing Wang; Peiheng Wu; Cristiano Nisoli; Yong-Lei Wang

doi:10.1038/s41565-024-01666-6

Toroidic phase transitions in a direct-kagome artificial spin ice

Nat Nanotechnol. 2024 Apr 29. doi: 10.1038/s41565-024-01666-6. Online ahead of print.

Authors

Wen-Cheng Yue^#^{1

2

3}, Zixiong Yuan^#^{1

2

3}, Peiyuan Huang^{1

2

3}, Yizhe Sun^{1

4}, Tan Gao^{1

2

3}, Yang-Yang Lyu^{1

2

3}, Xuecou Tu^{1

2

3}, Sining Dong^{5

6

7}, Liang He^{1

4}, Ying Dong⁸, Xun Cao¹, Lin Kang^{1

3}, Huabing Wang^{9

10

11}, Peiheng Wu^{1

2

3}, Cristiano Nisoli¹², Yong-Lei Wang^{13

14

15

16}

Affiliations

¹ School of Electronic Science and Engineering, Nanjing University, Nanjing, China.
² Purple Mountain Laboratories, Nanjing, China.
³ Research Institute of Superconductor Electronics, Nanjing University, Nanjing, China.
⁴ National Key Laboratory of Spintronics, Nanjing University, Suzhou, China.
⁵ School of Electronic Science and Engineering, Nanjing University, Nanjing, China. sndong@nju.edu.cn.
⁶ Research Institute of Superconductor Electronics, Nanjing University, Nanjing, China. sndong@nju.edu.cn.
⁷ National Key Laboratory of Spintronics, Nanjing University, Suzhou, China. sndong@nju.edu.cn.
⁸ College of Metrology Measurement and Instrument, China Jiliang University, Hangzhou, China.
⁹ School of Electronic Science and Engineering, Nanjing University, Nanjing, China. hbwang@nju.edu.cn.
¹⁰ Purple Mountain Laboratories, Nanjing, China. hbwang@nju.edu.cn.
¹¹ Research Institute of Superconductor Electronics, Nanjing University, Nanjing, China. hbwang@nju.edu.cn.
¹² Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM, USA. cristiano@lanl.gov.
¹³ School of Electronic Science and Engineering, Nanjing University, Nanjing, China. yongleiwang@nju.edu.cn.
¹⁴ Purple Mountain Laboratories, Nanjing, China. yongleiwang@nju.edu.cn.
¹⁵ Research Institute of Superconductor Electronics, Nanjing University, Nanjing, China. yongleiwang@nju.edu.cn.
¹⁶ National Key Laboratory of Spintronics, Nanjing University, Suzhou, China. yongleiwang@nju.edu.cn.

^# Contributed equally.

PMID: 38684808
DOI: 10.1038/s41565-024-01666-6

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.

Grants and funding

62274086/National Natural Science Foundation of China (National Science Foundation of China)