In Situ Electric-Field Control of THz Nonreciprocal Directional Dichroism in the Multiferroic ${\mathrm{Ba}}_2{\mathrm{CoGe}}_2{\mathrm{O}}_7$

Nonreciprocal directional dichroism, also called the optical-diode effect, is an appealing functional property inherent to the large class of noncentrosymmetric magnets. However, the in situ electric control of this phenomenon is challenging as it requires a set of conditions to be fulfilled: Special symmetries of the magnetic ground state, spin excitations with comparable magnetic- and electric-dipole activity, and switchable electric polarization. We demonstrate the isothermal electric switch between domains of ${\mathrm{Ba}}_2{\mathrm{CoGe}}_2{\mathrm{O}}_7$ possessing opposite magnetoelectric susceptibilities. Combining THz spectroscopy and multiboson spin-wave analysis, we show that unbalancing the population of antiferromagnetic domains generates the nonreciprocal light absorption of spin excitations.

Figure 1

(a) The canted antiferromagnetic order of ${\mathrm{Ba}}_2{\mathrm{CoGe}}_2{\mathrm{O}}_7$ in domain I in zero fields. Cyan circles denote the ${\mathrm{Co}}^{2+}$ ions with $S=3/2$ (dark red arrows) in the center of the ${\mathrm{O}}^{2-}$ tetrahedra (grey). The symmetry operations are the $2_1$ screw axis, (black half-arrow) and the orthogonal $2_1^{\prime }$ screw axis followed by the time reversal (red half-arrow). $\mathbf{M}$ and $\mathbf{L}$ correspond to the uniform and staggered sublattice magnetizations, respectively. (b) The four antiferromagnetic domains. A magnetic field applied along the [001] axis induces a polarization $\delta \mathbf{P}$ (light blue arrows) via linear magnetoelectric effect.

Figure 2

(a) Magnetic field dependence of the THz absorption spectra averaged for the measurements performed in electric fields with opposite signs, $E=\pm 3\mathrm{kV}/\mathrm{cm}$ at $T=3.5\mathrm{K}$. The light polarization is ${\mathbf{E}}^{\omega }\parallel [001]$ and ${\mathbf{H}}^{\omega }\parallel [100]$. The spectra measured in positive (red) or negative (blue) magnetic fields $\mathbf{H}\parallel [001]$ are shifted in proportion with the absolute value of the field. Grey lines indicate the magnetic field dependence of the resonance energies (peak Nos. 1–4). (b) shows the electric field-induced change in the absorption spectra as the difference of the absorption spectra recorded in $E=\pm 3\mathrm{kV}/\mathrm{cm}$. (c) The magnetic susceptibility calculated from the spin-wave theory in domains I and III (purple) and in domains II and IV (green). (d) The ME susceptibility in domain I (red) and domain III (blue).

Figure 3

(a) The electric field induced change in the absorption spectra measured with respect to the zero field cooled state at 3.5 K and in fixed magnetic field 12 T. (b) The hysteresis of the electric field dependence of the peak absorption. The horizontal arrows connect corresponding points of panels (a) and (b). (c) Temperature dependence of the electric field induced change in the absorption spectra measured in 12 T.