In EPR with linearly polarised microwaves if just the diagonal contributions chi ++( omega ) and chi --( omega ) of the dynamic susceptibility are considered then a discrepancy occurs between the experimentally observed signal and the predictions of theory. By means of the Mori formalism the authors have calculated the non-diagonal contributions chi +-( omega ) and chi -+( omega ) for insulators with dominating isotropic exchange. For rather small linewidth these terms result in a new kind of dynamic shift of the resonance field, whereas for broad lines they give rise to a drastic anomaly of lineshape. All these effects could be verified experimentally in both one- and three-dimensional spin lattices of axial symmetry in the following ways: the dynamic shift expected for narrow lines could be observed in TMMC; lineshape anomalies were studied in the very broad line of CsNiF3; and in MnF2 the critical increase of linewidth near TN allowed variation between the two extreme cases.
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