Anisotropic nematic fluctuations above the ferroquadrupolar transition in TmVO4

Ferroquadrupole order of local atomic orbitals provides a specific realization of electronic nematic order. ${\mathrm{TmVO}}₄$ is an insulator and undergoes ferroquadrupolar order associated with the local Tm $4f$ orbitals at ${T}_Q=2.15$ K. The material is a model system to study nematic order and the roles played by nematic fluctuations. Here we present $⁵¹\mathrm{V}$ nuclear magnetic resonance data as a function of field orientation in a single crystal. Although the spectra are well understood in terms of direct dipolar hyperfine couplings, the spin-lattice relaxation rate exhibits strong anisotropy that cannot be understood in terms of magnetic fluctuations. We find that the spin-lattice relaxation rate scales with the shear elastic constant associated with the ferroquadrupole phase transition, suggesting that quadrupole (nematic) fluctuations dominate the spin-lattice relaxation for in-plane fields.