Linear and non-linear dynamics of the free and reference layers in a sub-40 nm magnetic tunnel junction: A micromagnetic study

Micromagnetic simulations are exploited to analyse the spectrum of dynamical spin eigenmodes in a rectangular MgO-based magnetic tunnel junction (MTJ), with sub-40 nm lateral size, as those exploited in current read heads. It is found that, in spite of the reduced lateral dimensions of this structure, there are several eigenmodes in the range between 0 and 20 GHz, whose frequency and spatial character are markedly dependent on the non-uniformity of the internal field, as well as on the characteristics of the external bias field that is provided by an integrated permanent magnet. The frequency evolution of the modes with the intensity of an additional external field is such that it exists a range of values where the two main eigenmodes of the stack get very close to each other and interchange their preferential localization in the free and reference layers. If one moves from analysis of the small-amplitude magnetization precession to larger amplitude dynamics (precession angles exceeding a few degrees, as it occurs in current MTJ sensors), significant non-linear effects appear in the spectra, such as second harmonics and extra-peaks due to mode mixing. In addition, a sizeable low-frequency tail, that can negatively impact the signal-to-noise ratio of read heads and MTJ sensors, is found in the sub GHz range. These results suggest that a detailed understanding of the dynamical properties of these devices is crucial in order to tailor and optimize their performance.