High-pressure ultrasonic properties of spin-density-wave Cr–Re alloy single crystals

Abstract

The pressure dependence of the elastic constants ( c ij ) of Cr–Re alloy single crystals, containing 0.3 and 0.5 at.% Re, are reported. For 0.3 at.% Re the concentration ( c) is below the triple point concentration ( c t) on the ( c– T) magnetic phase diagram. This crystal therefore remains in the incommensurate (I) spin-density-wave (SDW) antiferromagnetic phase at all temperatures below the ISDW–paramagnetic (P) Néel transition temperature ( T N). The pressure derivatives of the elastic constants, d c ij /d p, were measured for the Cr+0.3 at.% Re crystal as a function of temperature through T N. The Cr+0.5 at.% Re crystal has c> c t and exhibits an incommensurate–commensurate (I–C) SDW phase transition at a temperature T IC< T N on heating. In the case of this crystal d c ij /d p was studied at temperatures close to and above T IC. The acoustic mode Grüneisen parameters ( γ n ), which quantify the lattice vibrational anharmonicity, were calculated as a function of temperature from the d c ij /d p data for each crystal. These calculations indicate much larger coupling of the SDW to the long-wavelength longitudinal phonons than to the shear modes for both Cr–Re crystals. Longitudinal mode softening under applied pressure, due to strong magnetoelastic interactions between the SDW and the longitudinal acoustic phonons, in Cr+0.3 at.% Re at T< T N, gives nearly discontinuously way to extremely large mode stiffening as the crystal is heated through T N. γ n in the CSDW and pressure-induced ISDW phases of the Cr+0.5 at.% Re crystal shows unusual behaviour with temperature. This is particularly so for the shear mode Grüneisen parameters which are relatively large and negative just above T IC, implying significant shear mode softening under applied pressure. γ n (shear) then increases on further increasing the temperature of this crystal. In comparison, γ n (shear) for both the CSDW and pressure-induced ISDW phases of other Cr alloys, with c> c t, for instance Cr–Ru and Cr–Ir alloys, is near zero, slightly positive, and remains constant with temperature. The measurements on the Cr+0.5 at.% Re crystal suggest the existence of a new phase line, separating the ISDW phase present at atmospheric pressure from that induced from the CSDW phase by applying high pressure, on the pressure–temperature magnetic phase diagrams of dilute Cr alloys with c> c t. More experimentation, particularly high pressure neutron diffraction studies, are needed to verify this point.