Spin-density-wave effects on the elasticity of Cr-Ga alloy single crystals

Measurements are reported of the temperature dependence of the elastic constants, ultrasonic attenuation and thermal expansion of dilute Cr-Ga alloy single crystals containing 0.16, 0.42 and 0.88 at.% Ga. Well defined magnetic anomalies were observed in all of these physical properties at the Néel temperature (T_N), at the incommensurate-commensurate (I-C) spin-density-wave (SDW) transition temperature (T_IC) and at the spin-flip transition temperature (T_sf). The complete magnetic phase diagram of the Cr_1-xGa_x alloy system has been determined for x < 1 at.% Ga from the temperatures of these anomalies. The magnetovolume (Δω) and the magnetic component (ΔB) to the bulk modulus were both found to vary as a + bT² + cT⁴, as predicted by theory, in the ISDW phases of all three of the crystals. Values of the pressure derivatives of T_N for the crystals containing 0.16 at.% Ga and 0.42 at.% Ga were calculated from the results for ΔB and Δω. DT_N/dω = (0.09 ± 0.02) × 10⁵ K calculated for the Cr + 0.16 at.% Ga crystal compares very well with the value dT_N/dω = (0.108 ± 0.006) × 10⁵ K obtained from direct high-pressure measurements. High-pressure measurements have not been made on the Cr + 0.42 at.% Ga crystal for a comparison. The value dT_IC/dω = (0.59 ± 0.03) × 10⁵ K calculated from Δω and ΔB for Cr + 0.88 at.% Ga does not compare well with dT_IC/dω = (0.17 ± 0.07) × 10⁵ K obtained from direct high-pressure measurements. This may point to inadequacies in the thermodynamic model used for the calculations. Predictions of microscopic theories for the temperature dependence of the ultrasonic attenuation, magnetovolume and the magnetic components of the elastic constants close to T_N do not fit the present measurements.