Nonlinear characterization and modeling of magnetic tunnel junction (MTJ)-based magnetic sensors

Abstract

As magnetic nanodevices (e.g., magnetic sensors) continue to shrink in size, the inherent nonlinear nature of magnetization dynamics may emerge during device operation. Firstly, the energy barrier separating the two possible magnetic states is directly proportional to the nanomagnets volume. Thus, thermal fluctuations in these nanomagnets might cause thermally-induced transitions from one state to another. Secondly, for a smaller ferro-magnetic sample, the same bias voltage corresponds to a larger current density. The latter may result in large-angle magnetization precession where the nonlinear nature of the Landau-Lifshitz-Gilbert (LLG) equation is especially pronounced. To optimize these devices and/or choose the most favorable operating point, one must first develop a charac-terization protocol tailored to nonlinear measurements in the presence of dynamic effects. As these effects occur in the gigahertz range, i.e., ferromagnetic resonance (FMR) in nanoelements, their characterization would greatly benefit from advances in microwave measurement techniques. In particular, a comprehensive nonlinear analysis of magnetic sensors can be accomplished using a nonlinear vector network analyzer, which measures the incident and reflected waves (A1 and B1, respectively) magnitudes and phases at the excitation frequency and harmonic components to which energy may be transferred due to the devices nonlinear characteristics. The problem studied in this thesis is the identification of the new resonances at fractional frequencies of the free layer (FL) FMR mode resulting from the nonlinear nature of the spin-torque (ST)-induced magnetization dynamics. We discovered that all characterized magnetic sensors DC responses reveal peaks at frequencies that are the integer fractions (1/2, 1/3, 1/4, and 1/6) of the devices natural FL FMR frequency. These peaks, in turn, generate the second and third harmonics of B1. New spectral lines at fractional frequencies of the devices FMR modes were observed using an alternative measurement technique, and the results of this study are also reported in this work. A complimentary micromagnetic study showed that the experimentally observed DC re-sponse at frequencies that are the integer fractions of the FLs resonant precession fre-quency can be defined by a low-order nonlinearity and strong magnetodipolar feedback between the magnetic layers adjacent to an MgO barrier. Additionally, the harmonic response is enhanced by the mutual ST effect between these layers. Most importantly, strong magnetodipolar feedback permitted sub-harmonic injection lock-ing within a wide range of integer fractions, which can be used in the development of a new generation of frequency multipliers.