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

Measurements are reported of the hydrostatic-pressure dependences of the elastic constants of (Formula presented) Si and (Formula presented) Si alloy single crystals through the Néel transition. In the former crystal the Néel 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 Grüneisen parameters, which quantify the vibrational anharmonicity, as a function of temperature through the Néel transition of each crystal. For the (Formula presented) Si crystal the mean long-wavelength acoustic mode Grüneisen parameter, (Formula presented) jumps by (Formula presented) from (Formula presented) to (Formula presented) in going through the second-order ISDW-P Néel transition, and then decreases to a value of (Formula presented) at temperatures well into the paramagnetic phase. This jump is much larger, (Formula presented) from (Formula presented) to (Formula presented) in going through the first-order CSDW-P Néel transition of (Formula presented) Si, after which (Formula presented) decreases to (Formula presented) 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 (Formula presented) The present measurements are compared with anharmonic effects observed through the second-order CSDW-P Néel transitions of (Formula presented) Ru and (Formula presented) Al alloy single crystals.