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The intriguing nano-structural properties of a ZnMnGaO4 film epitaxiallygrown on MgO (001) substrate have been investigated using synchrotronradiation-based x-ray diffraction. The ZnMnGaO4 film consisted of aself-assembled checkerboard (CB) structure with perfectly aligned and regularlyspaced vertical nanorods. The lattice parameters of the orthorhombic androtated tetragonal phases of the CB structure were analyzed using H-K, H-L, andK-L cross sections of the reciprocal space maps measured around varioussymmetric and asymmetric reflections of the spinel structure. We demonstratethat the symmetry of atomic displacements at the phases boundaries provides themeans for coherent coexistence of two domains types within the volume of thefilm.

Epitaxial checkerboard arrangement of nanorods in ZnMnGaO4 films studied by x-ray diffraction