Frequency of the Spin-Transfer Nano-Oscillator Based on a Perpendicular Tunnel Nanoheterostructure with Nonzero Ellipticity

The free layer in a nanoheterostructure with the magnetic tunnel junction (MTJ) usually has the shape of a thin disk with a diameter of several tens of nanometers and a thickness of several nanometers. For certain values of the current passing through such an MTJ structure, the magnetization of the free layer experiences the stationary precession caused by the compensation of precession energy dissipation by the spin-transfer effect. An important property of such an oscillator is the linear dependence of the oscillation frequency on the applied voltage. If the shape of the MTJ structure acquires ellipticity during its preparation, the magnetization oscillations become nonsinusoidal, and the voltage dependence of the frequency becomes more complicated. In this article, we consider an approximate expression for calculating the frequency of a monodomain nano-oscillator in the MTJ structure with a nonzero ellipticity, which has been obtained using the asymptotic method of solution of the Landau-Lifshitz equation with additional phenomenological transport terms. This expression is also compared with the results of numerical calculations and shows good agreement for small deviations of the MTJ structure shape from a symmetric disk.