  A thermodynamically consistent model for soft deformable viscoelastic magnets
is formulated in actual space (Eulerian) coordinates. The possibility of a
ferro-paramagnetic-type (or ferri-antiferromagnetic) transition exploiting
Landau phase transition theory as well as mechanical melting or solidification
is considered, being motivated and applicable to paleomagnetism (involving both
thermo- and isothermal and viscous remanent magnetization) in rocks in Earth's
crust and to rock-magma transition. The temperature-dependent Jeffreys rheology
in the deviatoric part combined with the Kelvin-Voigt rheology in the spherical
(volumetric) part is used. The energy balance and the entropy imbalance behind
the model are demonstrated, and its analysis is performed by time
discretization, proving existence of weak solutions.
