Determination of the exchange anisotropy and the one-ion anisotropy in Tb, Dy, Ho, Er, and Tm

The contributions of the exchange anisotropy and of the one-ion anisotropy to the total anisotropy are determined in Tb, Dy, Ho, Er, and Tm. The contribution of the one-ion anisotropy is deduced from that of rare-earth-doped gadolinium single crystals. The exchange anisotropy is then obtained from the difference from the anisotropy of pure-rare-earth metals. The exchange anisotropy is about -1/2 of the one-ion anisotropy. The variation of the one-ion anisotropy from one rare earth to another has been calculated using a screened-point-charge model. The variation of the exchange anisotropy has been calculated from a theoretical Hamiltonian using an exact expression of the paramagnetic susceptibility given in a previous paper. The theoretical and experimental variations of the two anisotropies are in good agreement for most of the rare earths.