Paramagnetoelectric Effects in NiSO4·6H2O

Piezoelectric paramagnetic crystals can show a linear dependence of the paramagnetic susceptibility on an applied electric field. This effect has been detected in NiS${\mathrm{O}}_4$·6${\mathrm{H}}_2$O at low temperatures. The thermodynamic inverse effect, the creation of an electric polarization by applied magnetic fields, has also been observed. Both effects are derived from a free energy which for the tetragonal 422 symmetry takes the form $\xi (H_a{E}_b-H_b{E}_a)H_c$, where $c$ denotes the tetragonal axis. The quantity $\xi$ has been measured as a function of temperature. It has a pronounced maximum at 3°K, where $\xi =2.6\mathrm{}\times {10}^{-9\mathrm{}}$ esu. It passes through zero at 1.38°K. Between 10 and 70°K it decreases approximately as $T^{-2\mathrm{}}$. These features are explained by a microscopic theory which considers the linear variation in an applied electric field of all parameters in the spin Hamiltonian of the four ${\mathrm{Ni}}^{++}$ ions in the unit cell. The dominant contribution comes from the change in the crystal-field splitting $D$.