Ferromagnetic resonance in very thin films

Abstract

Ferromagnetic resonance absorption (FMR) is often used to measure the effective fields that exert torques on the magnetization in thin films. One such effective field, H s , is related to the front and rear two-fold surface anisotropy parameters K 1 , K 2 . We have investigated three models that can be used to extract information about the surface energy parameters from FMR data. These models are (1) the rigid magnetization model in which the magnetization is assumed to be uniform across the film; (2) the continuum model in which the atomic structure of the film is completely ignored; and (3) the discrete atomic layer model in which the film is composed of layers of uniform magnetization each one monolayer thick. In the latter two models exchange and surface pinning are explicitly taken into account. It is shown that for all three models the shift H s is model dependent and is given by H s = 2 M s D K 1 m ( 0 ) 〈 m 〉 + K 2 m ( D ) 〈 m 〉 , where D is the film thickness, M s is the saturation magnetization, m ( 0 ) and m ( D ) are radio frequency amplitudes at the front and rear film surfaces, and 〈 m 〉 is the spatial average of the amplitude over the film thickness. It is shown that values of H s deduced from the FMR data may differ between models by values of the order of ( K 1 ± K 2 ) 2 / AM s , where A is the exchange stiffness, i.e., by 1 2 kG or more for antisymmetric pinning, K 1 = - K 2 = K , for the case of iron with K = 1 erg / cm 2 . Despite the model dependence of the surface effective fields it turns out that the slope of a plot of 4 π M eff = ( 4 π M s - H s ) vs. ( 1 / D ) is very insensitive to the model used to analyze the FMR data. We have also used a model BCC lattice of atomic point dipoles to calculate 4 π M eff for iron. It is shown that the results are in very good agreement with the discrete atomic layer model if one takes into account a surface energy contribution due to the dipolar magnetic fields.