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We show that in cubic crystals with anisotropic impurity centers the sum ofsquares of the magnetic resonance (EPR) frequencies is invariant with respectto the magnetic field direction. The connection between such an invariant andthe g-tensor components of the impurity is derived for different types ofcenters. The established regularity is confirmed experimentally for thespin-noise spectra of a CaF2-Nd3+ crystal. We show how this property of the EPRspectra can be efficiently used for the assignment of paramagnetic centers incubic crystals.

Invariants in the paramagnetic resonance spectra of impurity crystals