Excitation of spin waves by a current-driven magnetic nanocontact in a perpendicularly magnetized waveguide

It is demonstrated both analytically and numerically that the properties of spin wave modes excited by a current-driven nanocontact of length $L$ in a quasi-one-dimensional magnetic waveguide magnetized by a perpendicular bias magnetic field ${H}_{e}$ are qualitatively different from the properties of spin waves excited by a similar nanocontact in a two-dimensional unrestricted magnetic film (``free layer''). In particular, there is an optimum nanocontact length ${L}_{\mathrm{opt}}$ corresponding to the minimum critical current of the spin wave excitation. This optimum length is determined by the magnitude of ${H}_{e}$, the exchange length, and the Gilbert dissipation constant of the waveguide material. Also, for $Ll{L}_{\mathrm{opt}}$ the wavelength \ensuremath{\lambda} (and the wave number $k$) of the excited spin wave can be controlled by the variation of ${H}_{e}$ (\ensuremath{\lambda} decreases with the increase of ${H}_{e}$), while for $Lg{L}_{\mathrm{opt}}$ the wave number $k$ is fully determined by the contact length $L$ ($k\ensuremath{\sim}1/L$), similar to the case of an unrestricted two-dimensional free layer.