Microwave Directional Dichroism Resonant with Spin Excitations in the Polar Ferromagnet ${\mathrm{GaV}}_4{\mathrm{S}}_8$

We have investigated the directional dichroism of magnetic resonance spectra in the polar ferromagnet ${\mathrm{GaV}}_4{\mathrm{S}}_8$. While four types of structural domains are energetically degenerated under a zero field, the magnetic resonance for each domain is well separated by applying magnetic fields due to uniaxial magnetic anisotropy. Consequently, a directional dichroism as large as 20% is clearly observed without domain cancellation. The present observation therefore demonstrates that not only magnetoelectric monodomain crystals but also magnetoelectric multidomain specimens can be used to realize microwave (optical) diodes owing to the lack of inversion domains.

Figure 1

(a) Crystal structure of ${\mathrm{GaV}}_4{\mathrm{S}}_8$ at room temperature. (b) The schematic illustration of ${\mathrm{V}}_4$ clusters. The V ion is displaced along four equivalent cubic $⟨111⟩$ axes below the structural phase transition temperature. [(c)–(e)] Three types of structural domains classified based on the relationship with respect to $H\parallel [11\overline{2}]$. $m^{\prime }$ represents a mirror plane combined with time reversal operation as indicated by the blue shaded region. (f) Schematic illustration of the coplanar wave guide (CPW). (g) Cross-sectional view of the CPW; the spatial distribution of microwave electric and magnetic fields is illustrated.

Figure 2

(a) The magnetic resonance spectra for each magnetic field when ${\mathit{k}}^{\omega }\parallel [1\overline{1}0]$ and $H\parallel [11\overline{2}]$. The spectra are shifted vertically for clarity. (b) Calculated angle of $\theta$, i.e., the angle between the magnetization direction and polar $⟨111⟩$ axis, numerically calculated based on Eq. (1). (c) The magnetic-field dependence of the resonance frequency (circles). The calculated resonance frequency of ferromagnetic states as a function of the magnetic field (solid lines).

Figure 3

The magnetic resonance spectra for $+{\mathit{k}}^{\omega }$ and $-{\mathit{k}}^{\omega }$ directions at $+700$ (a) and $-700\mathrm{mT}$ (b). (c) The $+{\mathit{k}}^{\omega }$ and $-{\mathit{k}}^{\omega }$ spectra for each magnetic field. The spectra are shifted vertically for clarity. (d) The magnetic-field dependence of the magnitude of the directional dichroism. The red, green, and blue circles correspond to the lower-, intermediate-, and higher-frequency modes, respectively.

Figure 4

(a) Schematic illustration of the DD and toroidal moment. [(b) and (c)] The experimental configurations for domain $A$ (b) and domain $C$ (c). [(d) and (e)] Instantaneous response of $\mathit{P}$ and $\mathit{M}$ for the $P_1$ domain (d) and $P_4$ domain (e). (f) The magnetic-field dependence of the dynamical polarization induced by the microwave magnetic field in domains $A$, $B$, and $C$.