Magnetic susceptibility and phase transitions in LiNiPO4

Detailed studies of specific heat, magnetization, and magnetic torque of a single crystal of ${\mathrm{LiNiPO}}_{4}$ olivine are presented. Olivines attract attention as promising for application as cathodes in Li-ion batteries and exhibiting a unique set of properties. ${\mathrm{LiNiPO}}_{4}$ is the unique olivine, in which antiferromagnetic order develops in two steps, i.e., at 21.8 K, the second-order transition to an incommensurate phase and then, at 20.9 K, the first-order transition to a commensurate phase appears. Specific heat studies, supplemented by the ``slope analysis procedure,'' revealed a splitting of the specific heat anomaly accompanying the first-order transition, which suggests that actually, these are two coupled transitions, one of which can be the ferroelectric one. The specific heat was measured as a function of temperature for a series of fixed external magnetic field $B$ values. As the result, analytical equations describing the phase transition lines in the $T\text{\ensuremath{-}}B$ plane were determined and evolution of a shape of the specific heat anomalies accompanying the phase transitions, observed in the powder sample under influence of $B$, was modeled. Angular dependence of magnetic torque and of magnetization for $B$ rotating within the $a\text{\ensuremath{-}}c$ and $b\text{\ensuremath{-}}c$ crystalline planes was measured for several fixed temperature and $B$ values. Based on these results, we found a new effect, that we called ``off-diagonal nonlinear magnetic susceptibility,'' i.e., we found that for each main crystallographic axis $(a,b$, and $c)$, an additional component of magnetic susceptibility, proportional to the square of the perpendicular to this axis component of $B$, exists. A phenomenological model of this effect, describing the experimental results correctly, was proposed.