Topological phase transitions by time-dependent electromagnetic fields in frustrated magnets: Role of dynamical and static magnetic fields

TL;DR

This study shows that time-dependent electromagnetic fields can selectively stabilize and control skyrmion-crystal phases in frustrated magnets on a triangular lattice. Using a classical Heisenberg model and solving the Landau-Lifshitz-Gilbert dynamics, the authors reveal that circularly polarized fields and a combination of circularly polarized electric fields with static magnetic fields induce distinct SkX phases with topological charges $n_{ m sk}$ that depend on field balance and polarization. Floquet theory explains these results via emergent effective interactions, including DM and three-spin terms, and the Zeeman coupling, with the stability windows of SkXs strongly influenced by the timing of field application. Overall, the work broadens the toolkit for generating and controlling topological spin textures in frustrated magnets, with potential implications for dynamical spintronics and information storage.

Abstract

We theoretically investigate the effects of time-dependent electromagnetic fields on frustrated magnets with the spatial inversion symmetry. Two types of external-field setups are considered: One is a circularly polarized electromagnetic field and the other is a combination of a circularly polarized electric field and a static magnetic field. The system is modeled by a classical frustrated Heisenberg model on a triangular lattice, whose ground state is a single-$Q$ spiral spin configuration. The effects of irradiated electric and magnetic fields are taken into account by the inverse Dzyaloshinskii-Moriya (DM) interaction and the Zeeman coupling, respectively, without heating effects. By numerically solving the Landau-Lifshitz-Gilbert equation, we find that the two field configurations lead to distinct skyrmion crystal (SkX) phases and their associated topological phase transitions: in the former setup, SkXs composed of skyrmions with skyrmion numbers of one and two with opposite signs emerge, whereas in the latter setup, SkXs with the same sign appear. The stabilization mechanisms of these SkXs are accounted for by the competition among electromagnetic-field-induced chiral DM interactions, electric-field-induced three-spin interactions, and the Zeeman coupling based on the high-frequency expansion within the Floquet formalism. Furthermore, for the latter setup, we find that the stability region of the SkX phase varies significantly depending on the timing of the application of the circularly polarized electric field and the static magnetic field. Our findings would broaden the possible routes to generate and control SkXs by time-dependent electromagnetic fields, advancing both the theoretical comprehension and experimental control of topological spin crystals.

Figures (7)

• Figure 1: Averaged skyrmion number $N_{\rm sk}$ as functions of $E_{\rm d}$ and $B_{0}$ at $\omega/|E_{\rm gs}|=7.5$ in the NESSs under the RCP electromagnetic field.
• Figure 2: (a) $E_{\rm d}$ dependence of the absolute $N_{\rm sk}$ and averaged absolute out-of-plane magnetization $M^{z}$ at $B_0/E_{\mathrm{d}}=0.2$. (b) $B_{0}$ dependence of the absolute $N_{\rm sk}$ and the absolute $M^{z}$ at $B_0/E_{\mathrm{d}}=3.6$.
• Figure 3: Snapshots of the NESSs under the RCP electric field with $\omega/|E_{\rm gs}|=7.5$; (a) ($E_{\rm d}/|E_{\rm gs}|, B_{0}/|E_{\rm gs}|)=(1.25, 0.25)$ and (b) ($E_{\rm d}/|E_{\rm gs}|, B_{0}/|E_{\rm gs})=(0.5, 1.8)$. (Left panels) Real-space spin configurations; the arrows and color denote the spins $\bm{S}_i$ and the $z$ component $S^z_i$, respectively. (Middle panels) Local scalar spin chirality configurations; the arrows and color of the circles denote the spins $\bm{S}_i$ and the local scalar spin chirality $\chi_{\bm{r}}$, respectively. (Right panels) Reciprocal-space spins $S_{\bm{q}}$. The large hexagons represent the first Brillouin zone. The vertices of the small hexagons correspond to $\pm\boldsymbol{Q}^*_1$, $\pm\boldsymbol{Q}^*_2$, and $\pm\boldsymbol{Q}^*_3$.
• Figure 4: (a) Averaged skyrmion number $N_{\rm sk}$ as functions of $E_{\rm d}$ and $B_{\rm s}^z$ at $\omega/|E_{\rm gs}|=7.5$ in the NESSs under the RCP electric field and the static magnetic field. (b) $B_{\mathrm{s}}^z$ dependence of the absolute $N_{\rm sk}$ and the absolute $M^{z}$ at $E_{\mathrm{d}}/|E_{\rm gs}|=1.25$.
• Figure 5: Snapshots of the NESSs under the RCP electric field with $\omega/|E_{\rm gs}|=7.5$; (a) ($E_{\rm d}/|E_{\rm gs}|, B_{\mathrm{s}}^z)=(1.25, 0.3)$ and (b) ($E_{\rm d}/|E_{\rm gs}|, B_{\mathrm{s}}^z)=(1.25, -0.3)$. (Left panels) Real-space spin configurations; the arrows and color denote the spins $\bm{S}_i$ and the $z$ component $S^z_i$, respectively. (Middle panels) Local scalar spin chirality configurations; the arrows and color of the circles denote the spins $\bm{S}_i$ and the local scalar spin chirality $\chi_{\bm{r}}$, respectively. (Right panels) Reciprocal-space spins $S_{\bm{q}}$. The large hexagons represent the first Brillouin zone. The vertices of the small hexagons correspond to $\pm\boldsymbol{Q}^*_1$, $\pm\boldsymbol{Q}^*_2$, and $\pm\boldsymbol{Q}^*_3$.