  Solid phase epitaxy is a crystallization technique used to produce high
quality thin films. Lateral solid phase epitaxy furthermore enables the
realization of non-planar structures, which are interesting, e.g., in the field
of spintronics. Here, we demonstrate lateral solid phase epitaxy of yttrium
iron garnet over an artificial edge, such that the crystallization direction is
perpendicular to the initial seed. We use single crystalline garnet seed
substrates partially covered by a SiOx film to study the lateral
crystallization over the SiOx mesa. The yttrium iron garnet layer retains the
crystal orientation of the substrate not only when in direct contact with the
substrate, but also across the edge on top of the SiOx mesa. By controlling the
crystallization dynamics it is possible to almost completely suppress the
formation of polycrystals and to enable epitaxial growth of single crystalline
yttrium iron garnet on top of mesas made from arbitrary materials. From a
series of annealing experiments, we extract an activation energy of 3.0 eV and
a velocity prefactor of $6.5 \times 10^{14}$ nm/s for the lateral epitaxial
crystallization along the <100> direction. Our results pave the way to engineer
single crystalline non-planar yttrium iron garnet structures with controlled
crystal orientation.
