Ferromagnetic resonance in core-shell nanoparticles with multitype exchange anisotropy

A phenomenological model for magnetodynamics of core-shell nanoparticles is presented. The term core-shell implies, prima facie, that the spin structures (phases) of the particle components are different, no matter whether or not they are chemically identical. The model takes in two main assumptions. First, the interphase boundary is a thin (in comparison with the core and shell scales) transition layer with strongly inhomogeneous spin arrangement. Second, the shell is a granular structure consisting of spin-ordered crystallites with a wide spread of internal anisotropy, including a fraction of ones with extremely high coercivity. The framework developed on that basis, despite its simplicity, provides a unified explanation for the major specific properties of magnetic core-shell particles. Namely, (i) the growth of observed anisotropy field with reduction of the particle size, (ii) the presence of fixed unidirectional anisotropy, and (iii) the existence of rotatable anisotropy that emerges in a threshold manner under an external field. For a nanoparticle with the above-described core-shell architecture, a theory of ferromagnetic resonance with allowance for the superparamagnetic effect is worked out, and the ferromagnetic resonance absorption lines of noninteracting ensembles of such particles are presented. It is demonstrated that all the qualitatively different contributions to the core-shell-induced anisotropy could be evaluated from the data on a temperature sweep of the resonance field. Moreover, to do that, it suffices to use just the samples with random orientation of the particle axes. Preliminary assessment shows that a set of measurements for complete evaluation of the exchange-mediated anisotropies is feasible with the aid of a standard X-band spectrometer.