$^{51}$V single-crystal NMR Study on multiferroic FeVO$_4$

The multiferroicity in FeVO$_4$ is so far not well understood because its spin-orbit coupling is probably very weak. In this talk, we report our $^{51}$V single crystal NMR study on FeVO$_4$ under zero field and a finite field. The double magnetic transitions with $T_{SDW}\approx$ 19 K and $T_{helical}\approx$ 13 K are clearly shown by NMR spectra and the spin-lattice relaxation rate $1/T_1$. Two noneqivalent $^{51}$V sites are identified with different hyperfine couplings. Just below $T_{helical}$, a large RF enhancement is seen, which indicates rich magnetic domain walls formed in the helical state and not in the SDW state. Based on our results, we discuss the coupling between the magnetism and the ferro-electricity in FeVO$_4$.