Partially disordered antiferromagnetism and multiferroic behavior in a frustrated Ising system, CoCl$_{2}$-2SC(NH$_{2}$)$_{2}$

We investigate partially disordered antiferromagnetism in CoCl$_2$-2SC(NH$_2$)$_2$, in which a-b plane hexagonal layers are staggered along the c-axis, rather than stacked. A robust 1/3 state forms in applied magnetic fields which the spins are locked, varying neither as a function of temperature nor field. By contrast, in zero field, partial antiferromagnetic order occurs, in which free spins are available to create a Curie-like magnetic susceptibility. We report measurements of the crystallographic structure, and the specific heat, magnetization, and electric polarization down to $T$ = 50 mK and up to $μ_{0}H$ = 60 T. The Co$^{2+}$ $S = 3/2$ spins are Ising-like and form distorted hexagonal layers. The Ising energy scale is well separated from the magnetic exchange, and both energy scales are accessible to the measurements allowing us to cleanly parameterize them. In transverse fields, a quantum Ising phase transition can be observed at 2 T. Finally we find that magnetic exchange striction induces changes in the electric polarization up to 3 $μ$C/m$^2$ and single-ion magnetic anisotropy effects induce a much a larger electric polarization change of 300 $μ$C/m$^2$.