NMR in an electric field: a bulk probe of the hidden spin and orbital polarizations

Recent theoretical work has established the existence of hidden spin and orbital textures in non-magnetic materials with inversion symmetry. Here, we propose that these textures can be detected by nuclear magnetic resonance (NMR) measurements carried out in the presence of an electric field. In crystals with hidden polarizations, a uniform electric field produces a staggered magnetic field that points to opposite directions at atomic sites related by spatial inversion. As a result, the NMR resonance peak corresponding to inversion partner nuclei is split into two peaks. The magnitude of the splitting is proportional to the electric field and depends on the orientation of the electric field with respect to the crystallographic axes and the external magnetic field. As a case study, we will present the theory of electric-field-induced splitting of ²⁰⁹Bi peaks in Bi₂Se₃. We will also mention other potentially more promising candidate materials, whose crystal symmetry enables strategies to suppress the linewidth produced by the Oersted field.