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The electric field effect on magnetism was examined in the multiferroicconical magnet Mn$_2$GeO$_4$, which shows a strong coupling betweenferromagnetic and ferroelectric order parameters. The systematic evaluation ofthe electric polarization in the multiferroic phase below 5.5 K under variousfield cooling conditions reveals that small magnetic fields of 0.1 Tsignificantly reduce the required electric fields needed to reach saturation.By applying electric fields during magnetic field dependent hysteresismeasurements of magnetization M and polarization P an electrically controllableexchange bias was observed, a phenomenon exceedingly rare in single phasemultiferroics. Furthermore, non-reversible electric switching of P and Mdomains was achieved under specific magnetic field conditions.

Domain switching and exchange bias control by electric field in multiferroic conical magnet Mn$_2$GeO$_4$