Direct Observation of Orbital Reorientation in MnV$_{2}$O$_{4}$ by NMR

The effect of magnetostriction on the orbital states in MnV$_{2} $O$_{4}$ was investigated by rotating the direction of magnetic field. The microscopic evidence of the orbital reorientation process, induced by the rotation, was found from the variation of V$^{3+}$ NMR spectrum. Despite the magnetic field is rotated from z axis to y axis, NMR spectrum of $0\,^{\circ}$ is almost identical to that of $90\,^{\circ}$, which reveals the reorientation of the orbital states of V$^{3+}$ ions following deformation of lattice. It was also observed that the reorientation process takes place suddenly when the magnetic field made $45\,^{\circ}$ with respect to the z axis. Such a sudden behavior implies that the orbital-lattice coupling is much stronger than the spin-orbital coupling in MnV$_{2}$O$_{4} $.