The magnetic energy and the magnitudes of the magnetic moments are calculated for excited magnetic configurations with strong moment cantings. The calculations are performed by use of an exact constraining scheme for the moments via constraining fields, and by use of an approximate constraining scheme via the prescription of the local spin quantization axes in the spin atomic sphere approximation. It is shown that the latter constraining scheme becomes totally inadequate for systems with strong moment cantings. When increasing the degree of moment canting, the magnitudes of the moments remain rather stable for Fe but become completely unstable for Ni while for Co the situation is in between the two cases.
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