Magnetoelasticity of dilute Cr-Si alloy single crystals

Abstract

Measurements are reported of the temperature dependence of the elastic constants and thermal expansion of dilute Cr-Si alloy single crystals containing 0.5, 1.2, 1.6 and 3.0 at.% Si. Well defined anomalies in all elastic constants, and in the thermal expansion, were observed at the Neel points (TN) and at the commensurate-incommensurate spin density wave transition temperatures (TIC) of the alloys. Elastic anomalies were also observed at the longitudinal-transverse incommensurate spin density wave transition temperature of the Cr+0.5 at.% Si crystal, but not in the thermal expansion thereof. The transition at the Neel point of the Cr+0.5 at.% Si crystal is continuous, that of the Cr+1.2 at.% Si and Cr+1.6 at.% Si crystals of first order, while the order of the transition in the Cr+3.0 at.% Si crystal could not be determined unambiguously. For the Cr+1.2 at.% Si and Cr+1.6 at.% Si crystals the discontinuous transitions at TN show hysteresis behaviour. In the 1.2 at.% Si crystal it is also accompanied by structure effects that were absent for 1.6 at.% Si. Hysteresis, accompanied by structure effects, was also observed at TIC for Cr+1.2 at.% Si. The structure effects are ascribed to the possibility of mixed incommensurate-commensurate spin density wave states in the dilute Cr-Si magnetic phase diagram. The magnetovolume and magnetic contributions to the bulk modulus have been found to fit the equation a+bT2+cT4, predicted by theory, rather well up to temperatures (T) close to the Neel points of Cr+0.5 at.% Si and Cr+1.6 at.% Si.

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

“…Previous measurements 8 show that the volume increase through the first-order CSDW-P transition of Crϩ1.6 at. % Si is much larger than that through the second-order ISDW-P transition of Crϩ0.5 at.…”

“…Here W is the natural velocity, defined 11 as the path length at zero pressure divided by the transit time at pressure P. Due to the large ultrasonic attenuation in the CSDW phase for the c 11 propagation mode, 8 we obtained ͓dc i j /dP͔ Pϭ0 for both crystals only from ͓110͔ wave propagation measurements. This means that the experimental error in ͓dc 11 /dP͔ Pϭ0 , calculated from the sums and differences between the measured values of ͓dc L /dP͔ Pϭ0 , ͓dc 44 /dP͔ Pϭ0 , and ͓dcЈ/dP͔ Pϭ0 , is larger than that in the last mentioned three quantities.…”

“…% Si it is 253 K on heating and 245 K on cooling. 8 The different T N values for the latter crystal stem from the first-order nature of its Néel transition. Highpressure ultrasonic wave velocity measurements were done at ten different constant temperatures for Crϩ0.5 at.…”

“…% Si is shown, respectively, in Figs. 8 6. The pressure dependences of ͑a͒ dc L /dP, ͑b͒ dc 11 /dP, ͑c͒ dB/dP, ͑d͒ dc 44 /dP, and ͑e͒ dcЈ/dP for Crϩ1.6 at.…”

Effect of pressure on the magnetic phase diagram of the antiferromagnetic spin density wave alloy Cr–1.6% Si

“…This crystal cut from the same single crystal as the sample used in the measurements of Lourens and Alberts [4] and Anderson et al [5]. The sample was cut down T=100K.…”