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A theoretical discussion of some of the effects resulting from the interplay between strong crystalline-field torques and weaker exchange torques acting on rare-earth ions is given. The crystalline field is supposed to have cubic symmetry. A semiclassical discussion of the effect of the crystalline field in determining easy directions, anisotropy, and the depression of ground-state ordered moment values for the rare-earth series is given and used to interpret the results of the exact calculations. It is shown that for some of the rare earths the crystalline field may be so large that no long-range magnetic order is possible at low temperatures. The theory is applied to the case of the rare-earth phosphides. Adjusting the exchange and crystalline-field parameters to yield the observed ordered moment values (and moment directions) of TbP and ErP, one predicts the HoP moment in agreement with the experimental value, and predicts that TmP will not order at all. The "holmium flopside" moment pattern is explained as being due to magnetic dipole forces. The ratio of the sixth-order component of the crystalline potential to the fourth-order component must be increased some five times over the naively computed value in order to reach agreement with experiment; however, an experimental indication of a possibly important noncubic component of the crystalline potential may change this value appreciably.
G. T. Trammell (Thu,) studied this question.