Magnetism

We investigate a ferrimagnetic/ferroelectric bilayer in which a mixed-spin Heisenberg ferrimagnet is coupled to a three-state ferroelectric layer allowing for a nonpolar state. Using Monte Carlo simulations, we analyze how magnetic and electric single-ion anisotropies, together with interfacial magnetoelectric coupling, control phase transitions and hysteresis properties. We show that electric anisotropy, by tuning the population of nonpolar ferroelectric sites, strongly shifts the ferrimagnetic critical temperature, while magnetic anisotropy reciprocally affects the ferroelectric transition. Increasing the magnetoelectric coupling enhances both ordering temperatures and may induce a common transition. At fixed temperature, magnetic and electric hysteresis loops evolve from square to slim and nearly reversible shapes as anisotropies are varied. These results highlight the relevance of three-state ferroelectricity for describing polarization suppression and tunable magnetoelectric response in hybrid bilayers.

We investigate the role of single-ion anisotropy in stabilizing higher-order skyrmion crystal phases in centrosymmetric magnets under D_3d symmetry. Using a classical spin model that incorporates both a local single-ion anisotropy arising from the two-dimensional crystal symmetry and a D_3d-type magnetic anisotropy originating from the D_3d point-group symmetry, we perform simulated annealing calculations to explore the ground-state spin configurations. We find that a skyrmion crystal with a skyrmion number of two is stabilized over a wide range of parameters of single-ion anisotropy and D_3d-type anisotropy. We also show that the skyrmion core position shifts from an interstitial site to an on-site location as the magnitude of the easy-axis single-ion anisotropy increases. Furthermore, we demonstrate that the magnetic field drives a variety of topological phase transitions depending on the sign and magnitude of the single-ion and D_3d-type anisotropies. These results provide a possible microscopic understanding of how complex topological spin textures can be stabilized in centrosymmetric D_3d magnets, suggesting that multiple phases with topological spin textures could emerge even in the absence of the Dzyaloshinskii–Moriya interaction.

A magnetic vortex, characterized by curling in-plane magnetization, is generally unstable in two-dimensional (2D) ferromagnetic thin films. Here, we demonstrated that this vortex could be stable in three-dimensional (3D) pyramid-shaped Fe thin films and elucidated mechanistic origin of the stable vortex. Magnetization measurements reveal characteristic $M-H$ hysteresis loops with a pronounced bending and a gradual slope near zero magnetization, contrasting strongly with the abrupt switching seen in 2D films. By decomposing the magnetization processes on each facet in pyramid, we identify the sequence of vortex formation, stabilization, and annihilation. The key factor is the 3D geometry: non-coplanar facet junctions at the ridge lines act as structural singularities that naturally pin domain walls (DWs). These ridge lines restrict DW motion, confine local magnetic structures, and mediate inter-facet interactions, creating geometrical constraints enhancing vortex stability. Vortex formation is driven by magnetostatic energy minimization, as in 2D films. However, ridge-induced weakening of inter-facet exchange becomes the dominant factor in the 3D pyramidal structure. Overall, the interplay of shape anisotropy, magnetostatic, exchange, and Zeeman energies under 3D constraints provides a clear framework for vortex stability, offering the first mechanistic insight into stable vortices in 3D ferromagnetic films and supporting future 3D magnetic devices.