The study of curvature-induced effects on the properties of nanostructures has become a cornerstone of magnetism. However, several methodologies usually used for studying nanoscale magnetic systems present difficulties for adequately describing curvature. In this work, we present a method that allows studying, under specific conditions, curved dome/antidome surfaces using an equivalent system without curvature. From the described methodology we obtain the phase diagram between easy-normal and skyrmionic magnetization configurations, as a function of spin-orbit coupling, Dzyaloshinskii-Moriya interaction (DMI), and curvature. The effective DMI of the dome structure increases with the curvature. Nevertheless, the effective anisotropy presents the opposite behavior, decreasing with curvature. These results allow us to conclude that an increase in the skyrmion stability is observed in nanostructures having positive curvature. The presented results propose a route that could facilitate the study of curved nanofilms with intrinsic DMI from comparing them with their planar counterparts.

We investigate the dynamics of a transverse domain wall (DW) in a bent nanostripe under an external field and spin-polarized current. Besides the standard Walker breakdown phenomenon, we show the emergence of a second Walker-like critical field, which depends on both the curvature of the nanostripe and its cross section geometry. At this field, DW can change its phase, i.e., can be re-oriented along another direction with respect to the nanostripe face. Additionally, we show that the amplitude and frequency of the DW oscillations above the Walker breakdown field also depend on the nanostripe geometry and can be controlled by external stimuli. Our results evidence that the inclusion of local curvatures in nanostripes is an important component for applications that demand an adequate control of the DW phase by the proper choice of external stimuli.

Three dimensional magnetic textures are a cornerstone in magnetism research. In this work, we analyze the stabilization and dynamic response of a magnetic hopfion hosted in a toroidal nanoring with intrinsic Dzyaloshinskii–Moriya interaction simulating FeGe. Our results evidence that unlike their planar counterparts, where perpendicular magnetic anisotropies are necessary to stabilize hopfions, the shape anisotropy originated on the torus symmetry naturally yields the nucleation of these topological textures. We also analyze the magnetization dynamical response by applying a magnetic field pulse to differentiate among several magnetic patterns. Finally, to understand the nature of spin wave modes, we analyze the spatial distributions of the resonant mode amplitudes and phases and describe the differences among bulk and surface modes. Importantly, hopfions lying in toroidal nanorings present a non-circularly symmetric poloidal resonant mode, which is not observed in other systems hosting hopfions.

The search for magnetic hopfions has been the focus of intense research during the last years. In this direction, and using micromagnetic simulations, we studied the magnetization reversal mechanism in toroidal nanoparticles under the action of an Oersted magnetic field. Our results evidence the nucleation of four magnetic configurations as a function of geometry, two of them being hopfion-like textures. These mechanisms are preferred for large toroidal structures. The annihilation of such texture is indicated by strong changes in the energy, which characterizes a topological transition.

The recently introduced area of topological magnetism searches for equilibrium structures stabilized by a combination of interactions and specific boundary conditions. Until now, the internal energy of open magnetic chains has been explored. Here, we study the energy landscape of closed magnetic chains with on-site anisotropy coupled with antiferromagnetic exchange and dipolar interactions analytically and numerically. We show that there are many stable stationary states in closed geometries. These states correspond to the noncollinear spin spirals for vanishing anisotropy or to kink solitons for high magnetic anisotropy. Particularly, the noncollinear Möbius magnetic state can be stabilized at finite temperatures in nonfrustrated rings or other closed shapes with an even number of sites without the Dzyaloshinskii-Moriya interaction. We identify the described configurations with the stable stationary states, which appear due to the finite length of a ring.