Magnesium oxide (MgO) films were prepared on a Si(001) substrate by the rf sputtering method at low ambient pressure using a metal target. The X-ray diffraction verified the epitaxial growth of MgO( 001) with a cubic-on-cubic arrangement despite the large lattice mismatch between MgO(100) and Si(100), and contractions of the unit cell along both the out-of-plane and in-plane directions. Epitaxial growth is described as a domain epitaxial relation with a domain mismatch consisting of (k × ) lattice units of the Si substrate and (m × n) ones of the MgO film. To visualize the domain mismatch with combinations of k, , m and n, coherent strains were depicted on polar coordinates. The domain mismatch was estimated as a small value, which was further decreased by the contraction of the unit cell in the epitaxial MgO film.

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110)-oriented epitaxial Fe 3 Si films were grown on (100) and ( 111) Si substrates with an epitaxial yttria-stabilized zirconia (YSZ) buffer layer by rf-magnetron sputtering. The epitaxial Fe 3 Si films contained a two-domain structure on the (100) substrate with a YSZ buffer layer, and a three-domain structure on the (111) substrate with a YSZ buffer layer. The coercive forces (H c ) of both epitaxial films were each approximately 40 Oe, and the saturation magnetizations (M s ) were each 850 emu/ cm 3 , which are almost at the same level as those of bulk Fe 3 Si.