Magnetoelectric Emission in a Magnetic Ferroelectric Er-doped (Ba,Sr)TiO$_3$

In the system where both space-inversion ($\mathcal{I}$) and time-reversal ($\mathcal{R}$) symmetries are broken simultaneously, a nonreciprocal optical phenomenon termed the optical magnetoelectric (OME) effect is expected to show up. As the crystal that has neither $\mathcal{I}$ nor $\mathcal{R}$ symmetry, we have investigated an Er$^{3+}$-doped ferroelectric (Ba,Sr)TiO$_3$ single crystal under magnetic field in which the luminescent magnetic Er$^{3+}$ ion occupies a noncentrosymmetric site. The ${\boldmath k}$-directional dichroism derived from the OME effect was verified in the $^{4}I_{13/2} {\rightarrow}^{4}I_{15/2}$ emission by the reversal of magnetic field and spontaneous polarization. The observed nonreciprocity $\Delta I/I \sim 0.5$ \% at 3000 Oe implies the possibility of the application of the OME effect to the function of an optical isolator.