BOB Acoustic-mode vibrational anharmonicity in Cr-Si alloy single crystals

Abstract

Measurements are reported of the hydrostatic-pressure dependences of the elastic constants of $\mathrm{C}\mathrm{r}+0.5\mathrm{}\mathrm{at}.\mathrm{}%$ Si and $\mathrm{C}\mathrm{r}+1.6\mathrm{}\mathrm{at}.\mathrm{}%$ Si alloy single crystals through the N\'eel transition. In the former crystal the N\'eel transition is a second-order incommensurate (I) spin-density-wave (SDW)-to-paramagnetic (P) transition, while it is a first-order commensurate (C) SDW-to-P transition in the latter crystal. The pressure derivatives of the elastic constants at different constant temperatures are used to calculate the acoustic-mode Gr\"uneisen parameters, which quantify the vibrational anharmonicity, as a function of temperature through the N\'eel transition of each crystal. For the $\mathrm{C}\mathrm{r}+0.5\mathrm{}\mathrm{at}.\mathrm{}%$ Si crystal the mean long-wavelength acoustic mode Gr\"uneisen parameter, ${\overline{\ensuremath{\gamma}}}^{\mathrm{el}}\ensuremath{\approx}\ensuremath{-}5,$ jumps by $\ensuremath{\Delta}{\overline{\ensuremath{\gamma}}}^{\mathrm{el}}=30,$ from ${\overline{\ensuremath{\gamma}}}^{\mathrm{el}}\ensuremath{\approx}\ensuremath{-}5$ to ${\overline{\ensuremath{\gamma}}}^{\mathrm{el}}=+25,$ in going through the second-order ISDW-P N\'eel transition, and then decreases to a value of ${\overline{\ensuremath{\gamma}}}^{\mathrm{el}}\ensuremath{\approx}+5$ at temperatures well into the paramagnetic phase. This jump is much larger, $\ensuremath{\Delta}{\overline{\ensuremath{\gamma}}}^{\mathrm{el}}=170,$ from ${\overline{\ensuremath{\gamma}}}^{\mathrm{el}}=\ensuremath{-}50$ to ${\overline{\ensuremath{\gamma}}}^{\mathrm{el}}=+150,$ in going through the first-order CSDW-P N\'eel transition of $\mathrm{C}\mathrm{r}+1.6\mathrm{}\mathrm{at}.\mathrm{}%$ Si, after which ${\overline{\ensuremath{\gamma}}}^{\mathrm{el}}$ decreases to ${\overline{\ensuremath{\gamma}}}^{\mathrm{el}}\ensuremath{\approx}0$ at temperatures deep into the paramagnetic phase. The results show very strong coupling of the SDW to the long-wavelength longitudinal-acoustic phonons in both crystals. Coupling to the long-wavelength shear acoustic phonons is relatively weak. In both crystals there is also strong coupling of the longitudinal phonons with the spin fluctuations above ${T}_{N}.$ The present measurements are compared with anharmonic effects observed through the second-order CSDW-P N\'eel transitions of $\mathrm{C}\mathrm{r}+0.3\mathrm{}\mathrm{at}.\mathrm{}%$ Ru and $\mathrm{C}\mathrm{r}+3.5\mathrm{}\mathrm{at}.\mathrm{}%$ Al alloy single crystals.