Temperature dependence of third-order elastic constants of potassium manganese fluoride

The nonlinearity parameters along the three principal symmetry directions have been measured for ${\mathrm{KMnF}}_{3}$ from 298 to 350 K by means of acoustic second-harmonic generation. In conjunction with our earlier data on the temperature dependence of the pressure derivatives of the elastic constants, the complete set of the six third-order elastic (TOE) constants has been determined in this temperature range. For ${c}_{111}$, ${c}_{123}$, and ${c}_{166}$ the temperature dependence is linear, suggesting that the effect of the improper ferroelastic transition at 186 K is no longer present above 300 K. This permits us to eliminate the effects of zero-point and thermal motion and of the structural phase transition by linear extrapolation of the data to absolute zero temperature. The bare TOE constants thus obtained differ significantly from the room-temperature values. The bare (and the room-temperature) values exhibit large deviations from the Cauchy relations, indicating significant contributions from many-body forces.