Hyperfine Fields and Curie Temperatures of the Heusler Alloys ${\mathrm{Cu}}_2$MnAl, ${\mathrm{Cu}}_2$MnIn, and ${\mathrm{Cu}}_2$MnSn

The effective magnetic fields at all non-Mn sites, the nuclear-hyperfine contributions to the specific heat, and the paramagnetic Curie temperatures have been calculated for the Heusler alloys ${\mathrm{Cu}}_2$MnAl, ${\mathrm{Cu}}_2$MnIn, and ${\mathrm{Cu}}_2$MnSn, by an extension of the virtual-bound-state (resonance) model previously used by Caroli and Blandin. The required electronic $\xi$ factors are determined from paramagnetic-susceptibility and Knight-shift data on dilute Cu-base binary alloys; and a phenomenological procedure is used to estimate the reduction in $\xi$ factors appropriate for the corresponding ions in the Heusler alloys. The latter effect is important, and failure to take the reduced $s$-wave character into account yields hyperfine fields which are too large by a factor of 2-4 for the polyvalent ions. Our predictions for those saturation hyperfine fields which have not yet been determined are -355±45 KOe for In in ${\mathrm{Cu}}_2$MnIn, and -280±45 and -260±100 kOe for Cu and Sn, respectively, in ${\mathrm{Cu}}_2$MnSn. The nuclear-hyperfine contribution to the specific heat of ${\mathrm{Cu}}_2$MnIn is predicted to be $\frac{(5.94\mathrm{}\pm 1.11 \mathrm{mJ}°\mathrm{K}{\mathrm{mole}}^{-1\mathrm{}})}{T^2}$. We give a critical and comprehensive comparison of theoretical results and available experimental data.