First-Principle Investigations of Topological Solitons in Multiferroic Cu₂OSeO₃

Materials with topologically nontrivial spin textures promise technological advances and have attracted a huge surge of interest in recent years. Recently, an intriguing discovery of skyrmion phases at low temperature and in the presence of an applied magnetic field has been made in an insulating multiferroic Cu₂OSeO₃ [1,2]. Its phase diagram shows a variety of non-collinear spin states. At low magnetic fields, the ground state is an incommensurate helical spiral with a long period of about 50 nm. It was also found that the magnetic field - temperature phase diagram is similar to those reported for the metallic alloys that show skyrmions. Moreover, the system can become polar when the hexagonal skyrmion lattice is formed in Cu₂OSeO₃ with a small applied magnetic field. The local magnetoelectric coupling, in this case, leads to skyrmions carrying an electric dipole or quadrupole [3].<br/><br/>We developed an effective Hamiltonian scheme to study the finite-temperature properties of multiferroic Cu₂OSeO₃. Our approach reproduces very well the magnetic field – temperature phase diagram, namely (i) the long-range helical phase at low temperature and zero magnetic fields and (ii) the skyrmion lattice phase, in which skyrmions are arranged in a two-dimensional hexagonal lattice existing in a narrow pocket of magnetic field and temperature phase diagram near the paramagnetic-helical state phase transition temperature, and (iii) the vortex lattice phase that is characterized by two non-collinear propagation vectors. The scheme also elucidates the role of thermal fluctuations in destabilizing the helical state and stabilizing the skyrmion lattice phase.<br/><br/>[1]. Seki S, Yu X Z, Ishiwata S and Tokura Y (2012) - Observation of Skyrmions in a Multiferroic Material Science(80),336,198–201<br/>[2] Chacon A, Heinen L, Halder M, Bauer A, Simeth W, Mühlbauer S, Berger H, Garst M, Rosch A and Pfleiderer C (2018) -Observation of two independent skyrmion phases in a chiral magnetic material Nat. Phys. 14,936–41<br/>[3]. Seki S, Ishiwata S and Tokura Y (2012) - Magnetoelectric nature of skyrmions in a chiral magnetic insulator Cu₂OSeO₃ Phys. Rev. B 86