ABSTRACT
When magnetic elements are reduced to a submicrometer size
the spin-wave (SW) spectra of these elements are modified
substantially. This modification affects not only the linear, but also
the nonlinear properties of magnetic elements. In particular, in a
flat cylindrical magnetic dot of a radius R the long-wavelength SWs having the wave number k < 1/R are excluded from the SW spectrum and the frequency degeneracy between the quasi-uniform
mode of the ferromagnetic resonance (FMR) and higher SW modes
could be removed. This spectral modification qualitatively changes
all the nonlinear dynamic properties of the dots, as they would not
be susceptible to the second-order (four-wave) nonlinear processes
that limit the FMR precession amplitude and, consequently, limit
the efficiency of all the other nonlinear processes involving a quasi-
uniform FMR mode. This effect is demonstrated experimentally
in the example of parametric generation of a subharmonic of an
external microwave signal in a two-dimensional array of Permalloy
nanodots. Due to the reduction of the dot sizes the characteristic
lifetime of the electromagnetic radiation at the subharmonic
frequency originated from the parametrically excited FMR mode
is increased by 2 orders of magnitude, compared to the case of a continuous magnetic film, where this lifetime is limited by the four-
wave relaxation processes involving SWs degenerate in frequency
with the quasi-uniform FMRmode.
