Abstract
The authors have investigated the role of non-linear c-f exchange interaction effect on the magnetic properties of the rare-earth metals. Using a simple band model they obtained the magnetic phase diagram at zero temperature. The non-linear effect stabilised the cone structure without the crystal field and caused the ferromagnetic transition. The magnitude of the helical wavevector Q decreased as the helical component mod (S(Q)) mod increased. When (S) was regarded as the observed magnetisation, the temperature dependence of Q agreed with the experimental results. The magnetic properties of Gd and its alloys were considered on this phase diagram. The effective lifetimes of the c electrons were also important for the phase diagram. The crystal field made the phase diagram complicated. For the easy plane anisotropy, the fan appeared instead of the cone. For the easy axis anisotropy, the helix was squared by the higher harmonics and became the antiphase domain structure in infinitesimal c-f exchange.