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 Crϩ0.5 at. % Si and Crϩ1.6 at. % Si alloy single crystals through the Néel transition. In the former crystal the Néel transition is a second-order incommensurate ͑I͒ spin-density-wave ͑SDW͒-to-paramagnetic ͑P͒ transition, while it is a first-order commensurate ͑C͒ 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 Crϩ0.5 at. % Si crystal the mean long-wavelength acoustic mode Grüneisen parameter, ␥ el ϷϪ5, jumps by ⌬␥ el ϭ30, from ␥ el ϷϪ5 to ␥ el ϭϩ25, in going through the second-order ISDW-P Néel transition, and then decreases to a value of ␥ el Ϸϩ5 at temperatures well into the paramagnetic phase. This jump is much larger, ⌬␥ el ϭ170, from ␥ el ϭϪ50 to ␥ el ϭϩ150, in going through the first-order CSDW-P Néel transition of Crϩ1.6 at. % Si, after which ␥ el decreases to ␥ el Ϸ0 at temperatures deep into the paramagnetic phase. The results show very strong coupling of the SDW to the long-wavelength longitudinalacoustic 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 Néel transitions of Crϩ0.3 at. % Ru and Crϩ3.5 at. % Al alloy single crystals.

Spin-density-wave effects on the vibrational anharmonicity of acoustic phonons in Cr-Ir alloy single crystals

“…(1) The longitudinal mode ultrasonic wave velocity of Cr + 0.07 at.% Ir behaves hysteretically under increasing and decreasing applied hydrostatic pressures in the ISDW phase at temperatures T < T N . Similar behaviour was recently [9] also observed in an ISDW Cr + 0.5 at.% Si single crystal. The concentrations of both of these crystals are below the triple-point concentration on the magnetic phase diagram.…”

“…The third feature of interest in figure 5 is the large negative (∂c 11 /∂p) p=0 and (∂B/∂p) p=0 in the SDW phases of Cr + 0.20 at.% Ir. Negative (∂c 11 /∂p) p=0 and (∂B/∂p) p=0 were previously also observed in the SDW phases of Cr + 0.3 at.% Ru [3], Cr-Si alloys [9] and in Cr + 3.5 at.% Al [8]. The negative values are unusual as they indicate that c 11 and B soften under pressure, which is anomalous when compared with the case for normal metals.…”

“…It is usual [3,8,9] to present the pressure dependence of the ultrasonic wave velocities for the different propagation modes in terms of the relative change in natural velocity, W/W 0 .…”

A Time- and Position-Sensitive Detector using a Resistive Film Anode Combined with a “Modified Backgammon with Weighted Capacitors” Readout Pad

“…The Cr-Ga [14] and Cr-Si [15,16] single crystals used in the present study are the same crystals as were previously used for measurements of the temperature dependence of the elastic constants and thermal expansion. The single crystals were grown by a floatingzone technique using radio-frequency heating as previously described [16].…”

“…We [14][15][16] recently succeeded in growing good quality Cr-Si and Cr-Ga alloy single crystals and ρ-T measurements up to about 1000 K on these crystals are reported here. Three Cr-Si and three Cr-Ga alloy single crystals were studied.…”