**1. Introduction**

This chapter is dedicated to the analysis of the spin resonance response (ESR) of different magnetic phases, in nanoparticles (NPs) of magnetic oxides, or ferrites. Evidence of the correlations between resonance spectrum and magnetic structure has been published, of course, in many works; however, to our knowledge, it is somewhat scattered and not easily accessible. We have chosen to carry out this analysis mainly on ferrite NPs because these magnetic materials exhibit a wide variety of magnetic properties, and as a consequence, a large diversity of classic and novel applications in technological fields ranging from electronics to biomedics.

Ferrites can also be easily tailored, and in the nanometric range and at the appropriate temperatures, they exhibit one of the main magnetic structures: ordered ferrimagnetic, superparamagnetic, or paramagnetic. The latter structure is less complex, and electron

paramagnetic resonance (EPR) has been known for ~50 years, so in some way, this is a situation both classic and new. Ferrimagnetic and superparamagnetic NPs are more complex, and their resonance response is currently an active research subject.

We first describe the general basis of the classic resonance technique, where a microwave signal of constant frequency is applied on the sample, which is simultaneously subjected to a sweeping magnetic field, in order to achieve the resonance conditions. We tried to establish the main differences between the response of classic and metallic paramagnetic phases and the shapes of magnetically ordered (ferro- or ferrimagnetic) phases in the bulk state.

We then briefly review the novel properties associated with the nanometric size, followed by a short account of crystal structure and magnetic interactions in ferrites. EPR is briefly described, illustrated with some recent results. A basic description of the superparamagnetic phase is then given, with a review of some of the theoretical models proposed, as well as some of the most representative experimental results. The ferrimagnetic phase is then described with an accent on the differences originated by the exchange interactions, magnetocrystalline anisotropy, demagnetization fields, etc., and their effects on the response signal. The general response of magnetic nanoparticles in the ordered state is discussed. In the conclusion, finally, an attempt is made to establish a correlation between these phases and their resonance signals.
