Probing multiferroic order parameters and domain population via nuclear spins

Quantifying domain population in multiferroics is required to understand domain nucleation/switching processes and achieve on-demand domain control. We report an approach based on nuclear magnetic resonance spectroscopy for the accurate measurement of volume fractions of multiferroic domains in bulk crystals. We demonstrate on a benchmarking system, GaV₄Se₈, that the electric quadrupole interaction of the ⁷¹Ga and the hyperfine field at the ⁵¹V nuclei are proper microscopic probes of the ferroelectric polarization and the ferromagnetic moment, respectively. We use the anisotropy of these local quantities to determine the multiferroic domain population, controlled here by both electric and magnetic fields. The sensitivity of this local-probe technique to site symmetries facilitates domain quantification in a wide range of anisotropic magnets, ferroelectrics, and multiferroics.