  We study the dynamics of topological defects in the magnetic texture of
rectangular Permalloy thin film elements during relaxation from random
magnetization initial states. Our full micromagnetic simulations reveal complex
defect dynamics during relaxation towards the stable Landau closure domain
pattern, manifested as temporal power-law decay, with a system-size dependent
cut-off time, of various quantities. These include the energy density of the
system, and the number densities of the different kinds of topological defects
present in the system. The related power-law exponents assume non-trivial
values, and are found to be different for the different defect types. The
exponents are robust against a moderate increase in the Gilbert damping
constant and introduction of quenched structural disorder. We discuss details
of the processes allowed by conservation of the winding number of the defects,
underlying their complex coarsening dynamics.
