The zero temperature direction of spontaneous magnetisation of lanthanide ions at a site of cubic symmetry is investigated as a function of the electrostatic and magnetic interactions. For all the values of J between J = 3 and J = 8, two-dimensional diagrams giving the orientation of spontaneous magnetisation are obtained as a function of the parameters R representing the relative strength of the magnetic to electrostatic interaction and the parameter x representing the relative strength of the fourth to the sixth order terms in the crystal field. The boundaries between regions of the parameter space with different directions of spontaneous magnetisation are investigated. It is found that at some boundaries there is a gradual rotation of the direction of spontaneous magnetisation and that at other boundaries there is a sudden change of orientation of spontaneous magnetisation at a critical value of the (R,x) parameters. Two types of behaviour are observed when there is a critical value of (R,x). There are boundaries where there is at the critical value a degenerate plane in which all the orientations can be direction of spontaneous magnetisation and some boundaries where two different principal crystallographic axes can be direction of spontaneous magnetisation at the critical value. In the latter case there is a region near the boundary where an unstable equilibrium orientation for the magnetisation can be found.

The zero temperature direction of spontaneous magnetisation of lanthanide ions at a site of cubic symmetry is investigated as a function of the electrostatic and magnetic interactions. For all the values of J between J = 3 and J = 8, two-dimensional diagrams giving the orientation of spontaneous mag...