Between ferro- and para- magnetism. Electron magnetic resonance and quantal effects in superparamagnetic nanoparticles

Nanometer-scale magnetic objects are at the interface between quantum dynamics of several interacting spins and classical thermodynamics of multi-particle systems. We present results of electron magnetic resonance (EMR) studies in suspensions of two different systems with superparamagnetic iron oxide nanoparticles with average size of 5 nm and 9 nm correspondingly. It is shown that both types of particles demonstrate common EMR behavior, including the broad spectral component, temperature-dependent narrow component with g-factor of $\sim $ 2, and additional low-field signals observed at the fields B$_{0k}$ = B$_{0}$/k, where B$_{0}$ is the resonance field of the main resonance, and k = 2, 3, and 4. These lines correspond to the transitions at the double, triple, etc., resonance frequencies and can be described in terms of the non-secular spin operators arising from the single-particle magnetic anisotropy or/and inter-particle dipole-dipole interactions. These features are common for small quantum systems and not expected in classical case. The relative intensity of the narrow component and low-field signals rapidly decreases with cooling or increase of particle size, marking gradual transition to classical FMR behavior.