  We investigate the irreversible growth of $(2+1)-$dimensional magnetic thin
films under the influence of a transverse temperature gradient, which is
maintained by thermal baths across a direction perpendicular to the direction
of growth. Therefore, different longitudinal layers grow at different
temperatures between $T_1$ and $T_2$, where $T_1<T_c^{hom}<T_2$ and
$T_c^{hom}=0.69(1)$ is the critical temperature of films grown in homogeneous
thermal baths. We find a far-from-equilibrium continuous order-disorder phase
transition driven by the thermal bath gradient. We characterize this
gradient-induced critical behavior by means of standard finite-size scaling
procedures, which lead to the critical temperature $T_c=0.84(2)$ and a new
universality class consistent with the set of critical exponents $\nu=3/2$,
$\gamma=5/2$, and $\beta=1/4$. In order to gain further insight into the
effects of the temperature gradient, we also develop a bond model that captures
the magnetic film's growth dynamics. Our findings show that the interplay of
geometry and thermal bath asymmetries leads to growth bond flux asymmetries and
the onset of transverse ordering effects that explain qualitatively the shift
observed in the critical temperature. The relevance of these mechanisms is
further confirmed by a finite-size scaling analysis of the interface width,
which shows that the growing sites of the system define a self-affine
interface.
