High-pressure ultrasonic study of the commensurate-incommensurate spin-density-wave transition in an antiferromagnetic Cr-0.3 at. % Ru alloy single crystal

A comprehensive experimental study has been made of the elastic and nonlinear acoustic behavior of a dilute Cr alloy as it undergoes a commensurate (C)-incommensurate (I) spin-density-wave transition. Simultaneous measurements of the temperature dependence of ultrasonic wave velocity and attenuation of longitudinal and shear 10-MHz ultrasonic waves propagated along both the [100] and the [110] direction of Cr-0.3 at. % Ru alloy single crystal have been made in the temperature range 200–300 K. The temperature dependence of ultrasonic attenuation for each mode is characterized by a spikelike peak centered at ${\mathit{T}}_{\mathit{C}\mathit{I}}$ (=238.6 K) (on cooling) and at ${\mathit{T}}_{\mathit{I}\mathit{C}}$ (=255.6 K) (on warming). The velocities of both longitudinal and shear ultrasonic waves exhibit a large and steep increase at ${\mathit{T}}_{\mathit{C}\mathit{I}}$ on cooling and a similar drop at ${\mathit{T}}_{\mathit{I}\mathit{C}}$ on warming with a pronounced hysteresis between ${\mathit{T}}_{\mathit{I}\mathit{C}}$ and ${\mathit{T}}_{\mathit{C}\mathit{I}}$. These observations show that the transition between the commensurate and incommensurate phases is first order. Measurements of the effects of hydrostatic pressure (up to 0.15 GPa) on the velocities of ultrasonic waves, which were made at several fixed temperatures between 248 and 297 K, show similar features: a steep increase at ${\mathit{P}}_{\mathit{C}\mathit{I}}$ (increasing pressure) and a similar drop at ${\mathit{P}}_{\mathit{I}\mathit{C}}$ (decreasing pressure) with a well-defined hysteresis. Both ${\mathit{T}}_{\mathit{C}\mathit{I}}$ and ${\mathit{T}}_{\mathit{I}\mathit{C}}$ increase strongly and approximately linearly with pressure, the mean values of ${\mathit{dT}}_{\mathit{C}\mathit{I}}$/dP and ${\mathit{dT}}_{\mathit{I}\mathit{C}}$/dP being (333±3) K/GPa and (277±5) K/GPa, respectively. The pressure and temperature dependencies of the anomalies in the ultrasonic wave velocity have been used to locate both the C-I and I-C boundaries on the magnetic P-T phase diagram. There is a triple point (at about 315 K and 0.22 GPa) where the paramagnetic, commensurate, and incommensurate spin-density-wave phases coexist.