  We present a comprehensive numerical study on the kinetics of phase
transition that is characterized by two non-conserved scalar order parameters
coupled by a special linear-quadratic interaction. This particular
Ginzburg-Landau theory has been proposed to describe the coupled charge- and
magnetic transition in nickelates and the collinear stripe phase in cuprates.
The inhomogeneous state of such systems at low temperatures consists of
magnetic domains separated by quasi-metallic domain-walls where the
charge-order is reduced. By performing large-scale cell dynamics simulations,
we find a two-stage phase-ordering process in which a short period of
independent evolution of the two order parameters is followed by a correlated
coarsening process. The long-time growth and coarsening of magnetic domains is
shown to follow the Allen-Cahn power law. We further show that the
nucleation-and-growth dynamics during phase transformation to the ordered
states is well described by the Kolmogorov-Johnson-Mehl-Avrami theory in two
dimensions. On the other hand, the presence of quasi-metallic magnetic domain
walls in the ordered states gives rise to a very different kinetics for phase
transition to the high temperature paramagnetic phase. In this new scenario,
the phase transformation is initiated by the decay of magnetic domain walls
into two insulator-metal boundaries, which subsequently move away from each
other. Implications of our findings to recent nano-imaging experiments on
nickelates are also discussed.
