  We address the cross effects between mechanical strains and magnetic fields
on the plastic response of magnetoelastic amorphous solids. It is well known
that plasticity in non-magnetic amorphous solids under external strain $\gamma$
is dominated by the co-dimension 1 saddle-node bifurcation in which an
eigenvalue of the Hessian matrix vanishes at $\gamma_P$ like
$\sqrt{\gamma_P-\gamma}$. This square-root singularity determines much of the
statistical physics of elasto-plasticity, and in particular that of the
stress-strain curves under athermal-quasistatic conditions. In this Letter we
discuss the much richer physics that can be expected in magnetic amorphous
solids. Firstly, magnetic amorphous solids exhibit co-dimension 2 plastic
instabilities, when an external strain and an external magnetic field are
applied simultaneously. Secondly, the phase diagrams promise a rich array of
new effects that have been barely studied; this opens up a novel and extremely
rich research program for magnetoplastic materials.
