${}^{63,65}$Cu and ${}^{53}$Cr nuclear magnetic resonance spectra for CuCr${}_2$O${}_4$ were measured at various magnetic fields and temperatures. The microscopic evidence of orbital ordering in CuCr${}_2$O${}_4$ was obtained from a dipolar hyperfine field, NQR, and magnetic anisotropy analysis of the linewidth broadening of the Cu and Cr NMR spectra measured in the external magnetic field. The energy gap in the dispersion relation of the spin wave excitation was measured from the temperature dependence of the resonance frequency of Cu and Cr ions in CuCr${}_2$O${}_4$. The energy gap of the Cu ions is about 10 K ($\pm$ 5 K), and that of the Cr ions is about 40 K ($\pm$ 5 K). These values imply that the spin-orbit coupling of Cr ions is stronger than that of Cu ions related to the orbital ordering in CuCr${}_2$O${}_4$. The magnetic field dependence of the Cr NMR frequency shows that the angle between the Cr${}^{3+}$ magnetic moment and the Cu${}^{2+}$ magnetic moment is about 98${}^{\circ }$ ($\pm$ 2${}^{\circ }$).

• Received 20 June 2013

DOI:https://doi.org/10.1103/PhysRevB.88.094417