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Single-crystal permalloy films were grown epitaxially on (001) GaAs substrates by sputtering. The relationship between the crystal orientations of the permalloy and GaAs were (001) NiFe // (001) GaAs, ≪100≫ NiFe // ≪110≫ GaAs. The crystal structures of permalloy films were deformed from cubic to tetragonal; films with positive and negative tetragonal strain have small and large respective unit cell volumes. Films with a small lattice constant in the film plane have a large strain distribution. The magnetocrystalline anisotropy of films with a large strain distribution is small, and that of films with a negative tetragonal strain is large.