A method of Koster and Statz is used to analyze an electron spin resonance spectrum for theShyphen;state Gd3plus;ion in CeO2, when the ion occupies a crystalline site of cubic symmetry. It is found that six ``gvalues'' are required, and the valuesg1equals;g2equals;2.0,thinsp;g3equals;5sol;3,thinsp;g4equals;g5equals;1.0, andg6equals;2.1 give an approximate fit to the spectrum. It is shown that the method can qualitatively explain the existence of low field resonances which are not easily accounted for using a conventional spin Hamiltonian.
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