Quantitative estimation of the spin-wave features supported by a spin-torque-driven magnetic waveguide

The main features of the spin-waves excited at the threshold via spin-polarized currents in a one-dimensional normally-to-plane magnetized waveguide are quantitatively determined both analytically and numerically. In particular, the dependence of the threshold current, frequency, wavenumber and decay length is investigated as a function of the size of the nanocontact area through which the electric current is injected. From the analytical viewpoint, such a goal has required to solve the linearized Landau-Lifshitz-Gilbert-Slonczewski equation together with boundary and matching conditions associated to the waveguide geometry. Owing to the complexity of the resulting transcendent system, particular solutions have been obtained in the cases of elongated and contracted nanocontacts. These results have been successfully compared with those arising from numerical integration of the abovementioned transcendent system and with micromagnetic simulations. This quantitative agreement has been achieved thanks to the model here considered which takes explicitly into account the diagonal demagnetizing factors of a rectangular prism as well as the dependence of the relaxation rate on the wavenumber. Our analysis confirmed that the spin-wave features supported by such a waveguide geometry are significantly different from the ones observed in classical two-dimensional nanocontact devices. Moreover, it has been proved that the characteristic parameters depend strongly on the material properties and on the modulus of external field, but they could be independent of the nanocontact length. Finally, it is shown that spin-transfer oscillators based on contracted nanocontacts have a better capability to transmit spin-waves over large distances.