Reentrant ferroelectric phase induced by a tilting high magnetic field in Ni3V2O8

The canonical multiferroic material ${\mathrm{Ni}}₃{\mathrm{V}}₂{\mathrm{O}}₈$ with a kagome staircase structure of $S=1\phantom{\rule{0.16em}{0ex}}{\mathrm{Ni}}²⁺$ spins has attracted much attention for its complex magnetic phase diagram, as well as the interplay between spin orders and ferroelectricity. In the present work, we report a comprehensive angular dependent ferroelectric polarization study on ${\mathrm{Ni}}₃{\mathrm{V}}₂{\mathrm{O}}₈$ with the field rotating within the $ac$ plane at low temperatures. The low field induced ferroelectric (LF) state along the crystallographic $b$ axis, which has been observed when the field is applied parallel to the easy axis ($a$ axis), is revealed to vanish suddenly as the field is rotating close to the $c$ axis. Of particular interest is the observation of the reentrant ferroelectric (HF) phase at high field for various orientations when the field is between the $a$ and $c$ axes within a small angle range. The field-angle phase diagrams are built based on the low-temperature angular dependent polarization results and composed of a continuous LF phase and a discontinuous HF phase both exhibiting symmetry with respect to the $a$ axis. The microscopic origins of the two phases are different due to the two decoupled sublattices in the kagome staircase structure, where the low-field polarization is proposed to originate from the spiral structure of the spine spins, while the high-field phase is ascribed to the ordering of the cross-ties under a tilting high magnetic field.