Possible role of toroidal moments and Dzyaloshinskii-Moriya interaction in the magnetoelectric effect of the hyperkagome compound Mn3Al2Ge3O12

The magnetoelectric (ME) effects originating from exotic magnetic states provide opportunities to explore novel topics such as topology and intriguing excitation. Herein, we report the ME effect in a cubic garnet Mn3Al2Ge3O12 with comprehensive magnetic and ferroelectric measurements. Our results reveal the dominant ME coefficient alpha with magnetic field perpendicular to electric field, in which electric polarization along the [110] axis is the strongest. We also observed a transition of coefficient alpha from negative to positive value upon switching of magnetic field. It is suggested that the ME effect of Mn3Al2Ge3O12 originates from the combination of special hyperkagome lattice and 120 degrees magnetic configuration, which leads to a -3' magnetic point group. The microscopic mechanism of the ME effect is discussed from viewpoints of toroidal moments and inverse Dzyaloshinskii-Moriya interaction. This work provides a scenario for understanding ME effect and further exploring the exotic state of Mn3Al2Ge3O12 and other garnets.