  In this paper a detailed numerical study (in frames of the Slonczewski
formalism) of magnetization oscillations driven by a spin-polarized current
through a thin elliptical nanoelement is presented. We show that a
sophisticated micromagnetic model, where a polycrystalline structure of a
nanoelement is taken into account, can explain qualitatively all most important
features of the magnetization oscillation spectra recently observed
experimentally (S.I. Kiselev et al., Nature, vol. 425, p. 380 (2003), namely:
existence of several equidistant spectral bands, sharp onset and abrupt
disappearance of magnetization oscillations with increasing current, absence of
the out-of-plane regime predicted by a macrospin model and the relation between
frequencies of so called small-angle and quasichaotic oscillations. However, a
quantitative agreement with experimental results (especially concerning the
frequency of quasichaotic oscillations) could not be achieved in the region of
reasonable parameter values, indicating that further model refinement is
necessary for a complete understanding of the spin-driven magnetization
precession even in this relatively simple experimental situation.
