Laser-Controlled Real- and Reciprocal-Space Topology in Multiferroic Insulators

Magnetic materials in which it is possible to control the topology of their magnetic order in real space or the topology of their magnetic excitations in reciprocal space are highly sought after as platforms for alternative data storage and computing architectures. Here we show that multiferroic insulators, owing to their magnetoelectric coupling, offer a natural and advantageous way to address these two different topologies using laser fields. We demonstrate that via a delicate balance between the energy injection from a high-frequency laser and dissipation, single skyrmions—archetypical topological magnetic textures—can be set into motion with a velocity and propagation direction that can be tuned by the laser field amplitude and polarization, respectively. Moreover, we uncover an ultrafast Floquet magnonic topological phase transition in a laser-driven skyrmion crystal and we propose a new diagnostic tool to reveal it using the magnonic thermal Hall conductivity.

Figure 1

Real- and reciprocal-space topology can be controlled by lasers. (a) The topological spin structure of a skyrmion carrying in-plane electric polarization $\mathbf{P}$ undergoes translational motion under a circularly polarized laser. (b) An ultrafast topological phase transition occurs in the Floquet magnon band structure of skyrmion crystals due to the effective magnetic field induced by circularly polarized laser irradiation.

Figure 2

Skyrmion motion under a circularly polarized laser. (a),(b) Displacement of the center of skyrmions (a) $R_x$ and (b) $R_y$ under LCP light as a function of time, defined in the text. The result for ${\mathbf{B}}_0\parallel [001]$, ${\mathbf{B}}_0\parallel [110]$, and ${\mathbf{B}}_0\parallel [111]$ is respectively depicted in solid magenta, solid cyan, and dashed lime lines. The nonlinear effect of damping and asymmetric magnetoelectric coupling drive skyrmions without exciting internal magnon modes. The parameters are fixed as $D/J=0.09$, ${\overline{B}}_0=0.9$, ${\tilde{B}}_d=2.0$, ${\tilde{\omega }}_0=10$, ${\mathcal{E}}_d=0.1$, and $\alpha =0.04$ (see Table 1). The inset in (b) shows the initial configuration of a single skyrmion prepared by Monte Carlo annealing for $150\times 150$ spins [73].

Figure 3

Floquet magnonic topological phase transition in skyrmion crystals. (a) Imaginary parts of in-plane (out-of-plane) dynamical susceptibilities shown in blue (red), obtained at $D/J=1.0$, ${\overline{B}}_0=0.4$, ${\tilde{B}}_d=1.0$, ${\tilde{\omega }}_0=10$, ${\mathcal{E}}_d=0.1$, and $\alpha =0.04$ under RCP light. The resonance peaks of the ($A$) counterclockwise (CCW), ($B$) breathing, and ($C$) clockwise (CW) modes are indicated. The inset shows the result near the driving frequency ${\tilde{\omega }}_0=10$. (b) Resonance frequencies of the CCW (blue) and breathing (red) modes as functions of the laser field amplitude ${\tilde{B}}_d$. (c) Floquet magnon band structures in the vicinity of the topological phase transition with integers indicating the total Chern number for each group of bands. The CCW and breathing modes at the $\mathrm{\Gamma }$ points are highlighted in blue and red, respectively. Roman numerals in (b) mark the values of ${\tilde{B}}_d$ used in the panels in (c).

Figure 4

Diagnosing a Floquet magnonic topological phase transition via the magnonic thermal Hall effect. The magnonic thermal Hall conductivity of the CCW (blue) and breathing (red) modes plotted against the laser field amplitude. These two modes can be resonantly and selectively excited using ac magnetic fields. The opposite sign enhancement at the critical value, due to the divergence of the Berry curvature, can be used as a topological phase transition diagnostic tool. The parameters are the same as in Fig 3.