Electronic Specific Heat and Saturation Magnetization of Cr-Fe and Fe-Co Alloys

The collective model of ferromagnetism is applied to various models for the upper third of the $3d$ band profile of bcc alloys of transition metals. In the first band profile, we consider a rectangular sub-band with rounded lower and upper edges, assuming an intra-atomic exchange integral just large enough to produce ferromagnetism. The low-temperature specific-heat coefficient $\gamma$ is found to have a sharp peak at the electron concentration where ferromagnetism starts (almost empty sub-band) and a deep minimum at the concentration with largest saturation magnetization (half-filled sub-band). This agrees qualitatively with the measurements by Cheng, Wei, and Beck in Cr-Fe and Fe-Co alloys. The agreement becomes quantitative if a second similar model of the band profile is used where the density of states inside the sub-band is not constant, but drops linearly with increasing energy. The calculated zero-temperature saturation magnetizations agree well with the Slater-Pauling curve for these alloys. In a third model, the sharp peak of $\gamma$ is not a simple consequence of the action of the collective model, but reflects the existence of a real peak in the assumed band profile. Then this peak of $\gamma$ is predicted to happen at an electron concentration slightly larger than the one at which ferromagnetism starts; this seems to be found experimentally in the Cr-Fe series. The calculated saturation magnetizations again agree with the Slater-Pauling curve.