  The Landau-Lifshitz equation governing magnetization dynamics is written in
terms of the amplitudes of normal modes associated with the micromagnetic
system's appropriate ground state. This results in a system of nonlinear
ordinary differential equations (ODEs), the right-hand side of which can be
expressed as the sum of a linear term and nonlinear terms with increasing order
of nonlinearity (quadratic, cubic, etc.). The application of the method to
nanostructured magnetic systems demonstrates that the accurate description of
magnetization dynamics requires a limited number of normal modes, which results
in a considerable improvement in computational speed. The proposed method can
be used to obtain a reduced-order dynamical description of magnetic
nanostructures which allows to adjust the accuracy between low-dimensional
models, such as macrospin, and micromagnetic models with full spatial
discretization. This new paradigm for micromagnetic simulations is tested for
three problems relevant to the areas of spintronics and magnonics: directional
spin-wave coupling in magnonic waveguides, high power ferromagnetic resonance
in a magnetic nanodot, and injection-locking in spin-torque nano-oscillators.
The case studies considered demonstrate the validity of the proposed approach
to systematically obtain an intermediate order dynamical model based on normal
modes for the analysis of magnetic nanosystems. The time-consuming calculation
of the normal modes has to be done only one time for the system. These modes
can be used to optimize and predict the system response for all possible
time-varying external excitations (magnetic fields, spin currents). This is of
utmost importance for applications where fast and accurate system simulations
are required, such as in electronic circuits including magnetic devices.
