We show that for Ni3V2O8 long-range ferroelectric and incommensurate magnetic order appear simultaneously in a single phase transition. The temperature and magnetic field dependence of the spontaneous polarization show a strong coupling between magnetic and ferroelectric orders. We determine the magnetic symmetry of this system by constraining the data to be consistent with Landau theory for continuous phase transitions. This phenomenological theory explains our observation the spontaneous polarization is restricted to lie along the crystal b axis and predicts that the magnitude should be proportional to a magnetic order parameter.
@article{arxiv.cond-mat/0503385,
title = {Magnetically driven ferroelectric order in Ni$_3$V$_2$O$_8$},
author = {G. Lawes and A. B. Harris and T. Kimura and N. Rogado and R. J. Cava and A. Aharony and O. Entin-Wohlman and T. Yildrim and M. Kenzelmann and C. Broholm and A. P. Ramirez},
journal= {arXiv preprint arXiv:cond-mat/0503385},
year = {2007}
}