topological structural vortex in hexagonal manganites

In this talk, I will introduce hexagonal REMnO3 (RE= RE=Ho-Lu and Y), which is an improper ferroelectric where the size mismatch between RE and Mn induces a trimerization-type structural phase transition, and this structural transition leads to three structural domains and two ferroelectric polarization domains, which can be viewed as topological vortices and antivortices[1]. We reported that the network of vortices can be neatly analyzed by graph theory and the evolution in the presence of electric field is related to domain preferential attachment [2, 3]. The vortices network turns out to be three-dimensional vortex loops, which result from the emergent continuous U(1) symmetry near the critical temperature [4]. This spontaneous trapping of topological defects in the process of undergoing a continuous phase transition is related with so-called Kibble-Zurek mechanism, which is proposed to test the birth of cosmos. Meanwhile, the manipulation of topological defects also will be discussed in this talk [5].[1] Fei-Ting Huang, Xueyun Wang, Sinead Majella Griffin, Yu Kumagai, Ming-Wen Chu, Oliver Gindele, Yoichi Horibe, Nicola Spaldin, and Sang-Wook Cheong, Phys. Rev. Lett., 113, 267602 (2014)[2] Fei Xue, Xueyun Wang, Ion Socolenc, Yijia Gu, Long-Qing Chen and Sang-Wook Cheong Scientific Reports, 5, 17057 (2015)[3] Xueyun Wang, Fei-Ting Huang, Rongwei Hu, Fei Fan and Sang-Wook Cheong, Invited paper in Applied Physics Letters Material, 3, 041505 (2015)[4] Shi-Zeng Lin*, Xueyun Wang*, Yoshitomo Kamiya, Gia-Wei Chern, Fei Fan, David Fan, Brian Casas, Yue Liu, Valery Kiryukhin, Wojciech H. Zurek, Cristian D. Batista, and Sang-Wook Cheong, Nature Physics, 10, 970-977 (2014)[5] Xueyun Wang, M. Mostovoy, M. G. Han, Y. Horibe, T. Aoki, Y. Zhu and S.-W. Cheong, Phys. Rev. Lett., 112, 247201 (2014)