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In a magnetic material, the nuclear spins are coupled via the exchange of virtual spin waves (Suhl-Nakamura interaction). This long range interaction is known to contribute to the nuclear transverse relaxation time. It also gives rise to a depression of the nuclear resonance frequency and in fact to a complete nuclear spin-wave spectrum. This spectrum is well defined even when the nuclear spins are far from saturation. In materials of sufficiently high concentrations of nuclear spins and at sufficiently low temperatures (helium range) nonlinear effects may occur in the nuclear resonance signal, as have been observed by Heeger, Portis, and Witt in KMnF3.
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Pincus et al. (1963) studied this question.
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