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 (± 5 K), and that of the Cr ions is about 40 K (± 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 • (± 2 •).

The magnetoelectric properties of hexaferrite Ba0.5Sr1.5Zn2Fe12O22 are significantly improved by Al substitution and thermal annealing. Measuring the enhancement factor of 57Fe NMR, we found direct microscopic evidence that the magnetic moments of the L and S blocks are rotated by a magnetic field in such a way as to increase the net magnetic moment of a magnetic unit, even after the field is removed. Al substitution makes magnetoelectric property arise easily by suppressing the easy-plane anisotropy. The effect of thermal annealing is to stabilize the multiferroic state by reducing the number of pinning sites and the electron spin fluctuation. The transverse conic structure gradually changes to the alternating longitudinal conic structure where spins fluctuate more severely.

The simultaneous occurrence of the structural and magnetic phase transitions observed in MnV2O4 is one clear example of strong interplay among the spin, orbital and lattice degrees of freedom. The structure of MnV2O4 is switched by the magnetic field and the linear magnetostriction is very high. The orbital order mediates the interaction between the spin and the lattice generating these phenomena. In this work, we present experimental evidence of an orbital order in MnV2O4 and its reorientation under a rotating magnetic field as obtained by nuclear magnetic resonance(NMR). The shift in the resonance frequency of the V NMR spectrum is symmetrical with respect to 45° as an external magnetic field of 7 T rotates from the c-axis to the b-axis, indicating that the initial easy axis flips to the orthogonal direction most parallel to the field direction. The spectrum of V3+ ions splits into four peaks with a maximum shift of 40 MHz. Our analysis revealed that this is the combined effect of the anisotropic hyperfine field due to an ordered orbital and the dipolar hyperfine field. Reorientation of the orbital order in response to an external magnetic field accompanies the macroscopically observed magnetostriction in MnV2O4.