Dynamic hysteresis in thin and ultra-thin films

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The physics of thin and ultra-thin magnetic films has been extensively studied in the recent past, because of its important implications for applications to high frequency devices. Power losses in ferromagnetic materials generally depend on the frequency of the applied field, a phenomenon referred to as dynamic hysteresis. The problem has great importance from a purely theoretical point of view, for the understanding of the dynamics of disordered magnetic systems, which represents a central issue in non–equilibrium statistical mechanics. While dynamic hysteresis in metallic bulk three dimensional systems is well understood in terms of eddy current dissipation, a satisfying theory for thin films, where the effect of eddy current is expected to become negligible, is still lacking. Hence, in recent years a great attention, both experimental and theoretical has been devoted to magnetic reversal in thin and ultra-thin ferromagnetic films.

 

An accurate interpretation of the experimental data requires a detailed understanding of the magnetization reversal properties on a microscopic scale. Based on the analogy with Ising type models, experimental data are often analyzed in terms of universal scaling laws, such as the one relating the dynamical hysteresis loop area to external parameters such temperature, amplitude, and frequency of the applied magnetic field. The experimental estimates of these exponents, often based on a very limited scaling regime, display a huge variability, so that the validity of a simple universal scaling law is still under question. Some authors also interpret the lack of good scaling of A as a cross–over between two distinct dynamical regimes, at low frequencies dominated by domain wall propagation, at high frequencies by the nucleation of new domains.

Domain wall depinning: We analyzed the magnetization reversal dynamics in two-dimensional structures. In particular, we focused on recent experimental measurements on Finemet thin films obtained by magneto-optical Kerr effect, and by a fluxometric inductive method. In these materials the dynamic hysteresis loop area A behave as a power law of the amplitude and frequency of the applied field, once the static hysteresis contribution has been subtracted. The identification of a non-zero static hysteresis is crucial in the analysis of the frequency and amplitude dependence, and was often neglected in previous studies. Under the assumption that hysteresis is mainly due to domain wall motion, we proposed a domain wall depinning model that we could solve analytically, and which is able to reproduce the observed hysteretic behavior.

Theory of loss separation: We developed a theory for dynamic hysteresis in ferromagnetic thin films, on the basis of the phenomenological principle of loss separation. Remarkably, although the theory of loss separation was originally derived for bulk metallic materials, is applicable to disordered magnetic systems under fairly general conditions regardless of the particular damping mechanism. This theory is confirmed both by numerical simulations of a driven random–field Ising model, and by re–examining several experimental data reported in the literature on dynamic hysteresis in thin films. All the experiments examined and the simulations find a natural interpretation in terms of loss separation. The power losses dependence on the driving field rate predicted by our theory, unlike the simple scaling law hypothesis, fits satisfactorily all the data in the entire frequency range, thus reconciling the apparent lack of universality observed in different materials. This also seriously puts in doubt the existence of a dynamic transition between a regime dominated by propagation and one dominated by nucleation of new domains.