  The intriguing nano-structural properties of a ZnMnGaO4 film epitaxially
grown on MgO (001) substrate have been investigated using synchrotron
radiation-based x-ray diffraction. The ZnMnGaO4 film consisted of a
self-assembled checkerboard (CB) structure with perfectly aligned and regularly
spaced vertical nanorods. The lattice parameters of the orthorhombic and
rotated tetragonal phases of the CB structure were analyzed using H-K, H-L, and
K-L cross sections of the reciprocal space maps measured around various
symmetric and asymmetric reflections of the spinel structure. We demonstrate
that the symmetry of atomic displacements at the phases boundaries provides the
means for coherent coexistence of two domains types within the volume of the
film.
