Photonics of topological magnetic textures

TL;DR

The paper addresses how electromagnetic waves interact with topological magnetic textures, focusing on Bloch points as paradigms for non-collinear spin order. It develops a self-consistent, classical framework that couples Maxwell's equations to magnetization dynamics, deriving a frequency- and position-dependent magnetic permeability tensor and solving the scattering problem with a spherical rigorous coupled-wave analysis across onion-like shells. Key contributions include explicit forms for the local magnetic permeability, demonstration of texture-induced resonances, and numerical demonstrations showing emergent photonic features such as orbital angular momentum, chirality density, and magnetoelectric density around hedgehog and twisted Bloch points. The approach enables photonic molding by magnetic textures and provides fingerprints to identify texture type and dynamics, with potential applications in nanoscale sensing, data processing, and metamaterial design built on topological spin textures.

Abstract

Topological textures in magnetically ordered materials are important case studies for fundamental research with promising applications in data science. They can also serve as photonic elements to mold electromagnetic fields endowing them with features inherent to the spin order, as demonstrated analytically and numerically in this work. A self-consistent theory is developed for the interaction of spatially structured electromagnetic fields with non-collinear, topologically non-trivial spin textures. A tractable numerical method is designed and implemented for the calculation of the formed magnetic/photonic textures in the entire simulation space. Numerical illustrations are presented for scattering from point-like singularities, i.e. Bloch points, in the magnetization vector fields, evidencing that the geometry and topology of the magnetic order results in photonic fields that embody orbital angular momentum, chirality as well as magnetoelectric densities. Features of the scattered fields can serve as a fingerprint for the underlying magnetic texture and its dynamics. The findings point to the potential of topological magnetic textures as a route to molding photonic fields.

Figures (7)

• Figure 1: Curve showing the normalized magnetization $M_0$ as a function of $k_0x$, where $k_0$ is the free-space wavenumber. Inset shows a schematic cross-sectional view of the BP, where the magnetic order is spherically surrounding the BP. The outer-radius of the sphere is $a$ and the inner-radius is denoted as $b$. The anisotropic region (see Appendix A) is marked by the gray color. It is divided into thin shell layers, each of which is characterized by the local magnetic permeability matrix $\mu_{ij}(\theta,r_l)$. Outside the anisotropic structure the medium is assumed to be free space. The relative dielectric permittivity of the spherical BP is $\epsilon_r$. The wavefront of the incident field is also depicted by thick red arrows. The direction of the associated magnetic field $\mathbf{H}_{ext}$ is indicated by dotted circles. Such a field can be realized by a radially directed elementary electric dipole which is marked by a blue arrow and is located on and parallel to the $z$-axis at a distance $h$ from the global origin (i.e., the center of the BP).
• Figure 2: (a) The hedgehog Bloch point ($\gamma = 0^0$); (b) the incident electric fields $|S^{inc}_\theta|$; (c), (d) the reflected electric fields $|S_\theta^{r}|$ and $|S_\varphi^{r}|$, respectively; (e),(f) the reflected magnetic fields $|U_\theta^{r}|$ and $|U_\varphi^{r}|$, respectively. Here $k_0 a = 0.06$, $k_0 b = 0.005$, $\epsilon_r = 12$ and $k_0 h = 4$.
• Figure 3: (a) The twisted BP; (b) its projection on the equatorial cut ($\theta = 90^0$); (c),(d) the spatial distributions of the reflected electric $|S_\varphi^{r}|$ and magnetic $|U_\theta^{r}|$ fields, respectively. The other parameters are the same as those in Fig. \ref{['fig::2']}.
• Figure 4: The reflected electric field components $|S_\theta^{r}|$ (left figure) and $|S_\varphi^{r}|$ (right figure) versus $k_0x$ at a fixed polar angle $\theta = 90^0$ for different azimuthal rotation angles $\gamma$: $\gamma = 0^0$ (solid line); $\gamma = 20^0$ (circles); $\gamma = 40^0$ (asterisk). The other parameters are the same as those in Fig. \ref{['fig::2']}.
• Figure 5: (a), (b): Time-averaged gauge-invariant optical chiral density and (c),(d): the magnetoelectric density for the hedgehog Bloch point (left figures) and the twisted Bloch point $\gamma = 60^0$ (right figures). The other parameters are the same as in Fig. \ref{['fig::2']}.