Transition-metal dihalide $MX_2$ as magnetoelectric multiferroics

Magnetoelectric properties were investigated for transition-metal dihalide $MX_2$, which turns out to be the first example of non-chalcogen based spiral-spin induced multiferroics. We discovered the emergence of ferroelectric polarization ($P$) in helimagnetic state for several compounds such as CuCl$_2$ with edge-shared $S=1/2$ chain and MnI$_2$ with stacked triangular lattice. In the latter material, in-plane magnetic field ($H$) was found to induce the rearrangement of six possible multiferroic domains. With every $60^{\circ}$-rotation of $H$ around the $c$-axis, discontinuous $120^{\circ}$-flop of $P$-vector is observed as a result of the flop of magnetic modulation vector ($q$). In-plane $H$ also alters the stable direction of $q$-vector from original $q \parallel \langle 1\bar{1}0 \rangle$ to $q \parallel \langle 110 \rangle$ above 3 T, which leads to significant change of $P$-flop patterns under rotating $H$. At the critical field region ($\sim$ 3T), due to the enhanced $q$-flexibility, $P$-vector smoothly rotates clockwisely twice while $H$ rotates counter-clockwisely only once.