Effect of External or Exchange Fields

As noted above the rare earth intermetallics exhibit reasonably strong crystal fields. The influence of external fields and exchange fields vary to a great extent — sometimes their effects are negligible while in other cases they have dramatic effects. Examples of this behavior will be given in a later part of this paper. The effect of exchange field may be expressed as follows  

In systems with uniaxial symmetry the field may be applied along any one of the two possible directions, namely, along the c-axis and along a direction lying in the basal plane. Under these conditions the above equation may be expressed as 

The total Hamiltonian of a system thus consists of a crystal field term and an exchange (with or without external) field and may be expressed as 

In cases where the higher multiplets have to be included, it is appropriate to write the above expressions as 

Having established the general principles involved in evaluating the eigenvalues and eigenfunctions of the rare earth ions under the influence of pure crystal fields and the additional terms such as exchange and external fields (33,34), we shall illustrate the calculation of magnetic, thermal and electrical properties in the next section. 

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