Elastic properties of single-crystal NiF2

The elastic properties of Ni${\mathrm{F}}_2$ were studied at $65<T<\mathrm{}300\mathrm{}$ K using the ultrasonic pulse superposition method. At 300 K, the measured adiabatic elastic stiffness moduli, in units of ${10}^{11}$ dyn/${\mathrm{cm}}^2$, are $C_{11}=14.50\mathrm{}$, $C_{12}=11.04\mathrm{}$, $C_{13}=9.09\mathrm{}$, $C_{33}=22.08\mathrm{}$, $C_{44}=4.65\mathrm{}$, and $C_{66}=9.94\mathrm{}$. The measured moduli are compared with the theoretical values calculated from Pandey's model by using published Raman frequencies. Near 300 K, each $\frac{d{C}_{\mathrm{ij}}}{\mathrm{dT}}$ has a negative value. But $\frac{d{C}_S}{\mathrm{dT}}$, where $C_S=\frac{1}{2}(C_{11}-C_{12})$, is positive between 300 K and the Néel temperature $T_N$. Other anomalous features are the following. There is a long precursor above $T_N$ in $C_{33}$ and $C_{44}$, $C_{33}$ exhibits critical exponents near $T_N$, whereas the values of $C_{11}$, $C_{66}$, $C_S$, etc. show sharp "cut-off" anomalies below $T_N$. These can be eliminated by a 4-kOe magnetic field along suitable directions. These properties of the elastic moduli are discussed in terms of a lattice instability or volume magnetostricitve coupling mechanism above $T_N$, linear magnetoelastic couplings, shear instability, and weak ferromagnetic domain effects, respectively. Possible existence of twin domains is proposed.