Anisotropic effects from spin split bands

In metallic rare earths the RKKY interaction between localized moments is mediated through the conduction electrons and depends on the band structure. In a magnetically ordered state the spatial polarization will produce different band structure for electrons in different spin states. The effect of this polarization has been estimated for the ferromagnetically ordered state of Gd. A simple model for the spin-split bands is used and shows that the isotropic interaction becomes anisotropic. The effect is not large, but it could alter predictions for the Curie temperature. The transition remains of second order.