Nonreciprocal Directional Dichroism in Magnetoelectric Spin Glass

Optical absorption spectra in the visible and near-infrared light were measured for magnetoelectric spin glass Ni_{0.4}Mn_{0.6}TiO_{3} under various field-cooled conditions. Despite the absence of long-range magnetic-dipole order, this spin-glass system exhibits nonreciprocal directional dichroism (NDD) at zero external field after a magnetoelectric field-cooled procedure. This result is distinct from previous studies on NDD in systems with magnetic toroidal moments induced either by long-range magnetic-dipole order or by applying crossed electric and magnetic fields. The present Letter conclusively demonstrates that the observed NDD originates from magnetoelectrically induced ferroic order of magnetic toroidal moments without conventional magnetic-dipole order.