Absorption at multiple resonance frequencies is observed in magnetic nanoparticles in strong similarity with forbidden multiple quantum transitions known for paramagnetic ions. Temperature and concentration dependences have been studied to reveal the origin of the signals. The results are discussed using a "quantization" approach, considering resonance transitions between energy levels of a giant spin corresponding to the total magnetic moment of a nanoparticle. The multiple quantum transitions are ascribed to both the effects of anisotropy and dipole-dipole interactions between nanoparticles.

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