  We investigate the problem of dimension reduction for plates in nonlinear
magnetoelasticity. The model features a mixed Eulerian-Lagrangian formulation,
as magnetizations are defined on the deformed set in the actual space. We
consider low-energy configurations by rescaling the elastic energy according to
the linearized von K\'{a}rm\'{a}n regime. First, we identify a reduced model by
computing the $\Gamma$-limit of the magnetoelastic energy, as the thickness of
the plate goes to zero. This extends a previous result obtained by the first
author in the incompressible case to the compressible one. Then, we introduce
applied loads given by mechanical forces and external magnetic fields and we
prove that, under clamped boundary conditions, sequences of almost minimizes of
the total energy converge to minimizers of the corresponding energy in the
reduced model. Subsequently, we study quasistatic evolutions driven by
time-dependent applied loads and a rate-independent dissipation. We prove that
solutions to the approximate incremental minimization problem at the bulk
converge to energetic solutions to the reduced model. This result provides a
further justification of the latter in the spirit of evolutionary
$\Gamma$-convergence.
