Photonic Signatures of Spin-Driven Ferroelectricity in Multiferroic Dielectric Oxides

We study the dispersion and scattering properties of electromagnetic modes coupled to a helically ordered spin lattice hosted by a dielectric oxide with a ferroelectric polarization driven by vector spin chirality. Quasianalytical approaches and full-fledged numerics evidence the formation of a chiral magnonic photonic band gap and the presence of gate-voltage dependent circular dichroism in the scattering of electromagnetic waves from the lattice. Gating couples to the emergent ferroelectric polarization and hence, to the underlying vector-spin chirality. The theory relies on solving simultaneously Maxwell’s equations coupled to the driven localized spins taking into account their spatial topology and spatial anisotropic interactions. The developed approach is applicable to various settings involving noncollinear spins and multiferroic systems with potential applications in noncollinear magnetophotonics.

Figure 1

Schematic of the considered sample with a spin-current-driven helical spin order in the $y\text{−}z$ plane and an antiferromagnetic ordering along the $x$ axis. A spin-driven ferroelectric polarization along the $z$ axis couples to an applied static electric field $E_0^z$ (caused by a gate voltage). The lattice spacing in the $y\text{−}z$ planes is $a$, and $p$ is an interlayer spacing. The helical period $w=2\pi /Q$ is set by the helicity index $Q$ (or $y$ component of the spin chirality vector). Plane waves are impinging from free space with an angle of incidence ${\varphi }_i$.

Figure 2

Real (blue) and imaginary (red) parts of $k_y/Q$ for two Bloch modes (solid and dashed lines) versus the normalized frequency $\omega /(cQ)$ at ${\varphi }_i=30°$. The inset shows an enlarged view of the band gap region.

Figure 3

Dependence of the amplitudes of the reflected fields $R_{\mathrm{TE}}$ (for TE polarization) and $R_{\mathrm{TM}}$ (for TM polarization) versus $\omega /(cQ)$ at two angles of incidence for waves impinging on the helical lattice from free space: ${\varphi }_i=25°$ (blue line) and ${\varphi }_i=89°$ (red line). The thickness of the sample is $d_y=50w$, $a=2p$, and ${\omega }_M/(2cQ)=0.04$. The results are calculated using a full-wave numerical analysis based on RCWM.

Figure 4

Numerical results for the peak values of the reflection coefficients for both TE and TM polarizations versus the angle of incidence ${\varphi }_i$. Inset: the ratio $R_{\mathrm{TE}}^{\max }/R_{\mathrm{TM}}^{\max }$ (red circles) compared with Eq. (8) (black dotted line).