Figure 1

(a) Crystal structure of multiferroic ${\mathrm{Ba}}_2{\mathrm{CoGe}}_2{\mathrm{O}}_7$ within layers perpendicular to the tetragonal axis, $\mathbf{z}$. Magnetic ${\mathrm{Co}}^{2+}$ ions ($S=3/2$) form a square lattice. (b) Field dependence of the magnetization ($M_x$) and the polarization ($P_z$) at $T=3.4\mathrm{K}$. Note that the polarization is an even function of $H$. (c) For $\mathbf{H}\parallel \mathbf{x}$ a single domain with spin structure determined by Ref. 19 is formed and the polarization points to the $\mathbf{z}$ direction. (d) By $\pi$ rotation of the crystal around the $\mathbf{y}$ axis, the polarization is reversed in the frame of the observer while the magnetization is fixed by the external field.Reuse & Permissions

Figure 2

Selection rules and characteristics for the magnon modes. The spectra are shifted relative to each other with the corresponding baselines. (a) Light polarization dependence at $T=3.4\mathrm{K}$ in zero field when the $\mathbf{x}$ and $\mathbf{y}$ directions are equivalent. The 0.5 THz mode is excited by the ${\mathbf{H}}^{\omega }$ magnetic component of light but insensitive to the change of the ${\mathbf{E}}^{\omega }$ electric component. By contrast, the 1 THz mode is clearly affected by the variation of either ${\mathbf{H}}^{\omega }$ or ${\mathbf{E}}^{\omega }$. (b) Temperature dependence of the absorption spectrum. The conventional magnon disappears above the Néel temperature, while the electromagnon at 1 THz subsists well above $T_N$ with a considerable fraction of its oscillatory strength present even at $\sim 20\mathrm{K}$. (c) At $T=3.4\mathrm{K}$ both modes split into two excitations (the side peaks are indicated by arrows) with the $g$ factor $\sim 2$ in high fields.Reuse & Permissions

Figure 3

Directional dichroism, i.e., the change in the absorption upon reversal of the light propagation, can be equivalently induced by the switching of either the static magnetization ($\mathbf{M}$) or the polarization ($\mathbf{P}$) of the sample. (a) Because of the resonant absorption, the radiation decays while passing through the material. This loss can be controlled both by $\mathbf{M}$ ($\parallel {\mathbf{H}}^{\omega }$) and $\mathbf{P}$ ($\parallel {\mathbf{E}}^{\omega }$). (b) For example, the reversal of $\mathbf{P}$ by $\pi$ rotation of the sample around the $\mathbf{y}$ axis can reduce the absorption which is somewhat exaggerated for clarity. (c) and (d) Only the absorption of the electromagnon at 1 THz has a large odd component both in $\mathbf{M}$ and $\mathbf{P}$, and thus shows directional dichroism, $\Delta \alpha$. (e) With an increasing magnetic field $\Delta \alpha$ spectra grow gradually, (f) while it vanishes out of the multiferroic phase above $T_N=6.7\mathrm{K}$ even in $H=70\mathrm{kOe}$.Reuse & Permissions