Ferromagnetic Resonance as a Probe of Magnetization Dynamics : A Study of FeCo Thin Films and Trilayers

Abstract: The high frequency dynamic magnetic responses of FeCo thin films and structures have been investigated mainly using ferromagnetic resonance (FMR) technique.The FMR resonance condition and linewidth are first derived from the dynamic Landau- Lifshitz-Gilbert equation, followed by a study of the conversion between FMR field and frequency linewidths. It is found that the linewidth conversion relation based on the derivative of resonance condition is only valid for samples with negligible extrinsic linewidth contribution. The dynamic magnetic properties obtained by using FMR measurements of FeCo thin films grown on Si/SiO2 substrates with varying deposition temperatures is then presented. The effective Landé g-factor, extrinsic linewidth, and Gilbert relaxation rate are all found to decrease in magnitude with increasing sample growth temperature from 20oC to about 400–500oC and then on further increase of the growth temperature to increase in magnitude. Samples grown at about 400–450oC display the smallest coercivity, while the smallest value of the Gilbert relaxation rate of about 0.1 GHz is obtained for samples grown at 450–500oC. An almost linear relation between extrinsic linewidth and coercivity is observed, which suggests a positive correlation between magnetic inhomogeneity, coercivity and extrinsic linewidth. Another major discovery in this study is that the Gilbert relaxation decreases with increasing lattice constant, which is ascribed to the degree of structural order in the films.A micromagnetic model is established for an asymmetric trilayer system consisting of two different ferromagnetic (FM) layers separated by thin non-magnetic (NM) layer, treating the magnetization in each FM layer as a macrospin. Based on the model, numerical simulations of magnetization curves and FMR dispersion relations, of both the acoustic mode where magentizations in the two FM layers precess in phase and the optic mode where they precess out-of-phase, have been carried out. The most significant implication from the results is that the coupling strength can be extracted by detecting only the acoustic mode resonances at many different unsaturated magnetic states using broadband FMR technique.Finally, trilayer films of FeCo(100 Å)/NM/FeNi(100 Å) with NM=Ru or Cu were prepared and studied. The thickness of the Ru and Cu spacer was varied from 0 to 50 Å. For the Ru spacer series, the film with 10 Å Ru spacer shows antiferromagnetic coupling while all other films are ferromagnetically coupled. For the Cu spacer trilayers, it is found that all films are ferromagnetically coupled and that films with thin Cu spacer are surprisingly strongly coupled (the coupling constant is 3 erg/cm2 for the sample with 5 Å Cu spacer). The strong coupling strength is qualitatively understood within the framework of a combined effect of Ruderman-Kittel- Kasuya-Yosida interaction and pinhole coupling, which is evidenced by transmission electron microscopy analysis. The magnetic coupling constant decreases exponentially with increasing Cu spacer thickness, without showing an oscillatory thickness dependence. The results have implications for the design of multilayers for spintronic applications.