The polarized-light observation of magnetic domain structures at early stages of disorder (Al)-order (L1(0)) transformation in CoPt single crystals is analyzed. A mechanism of the origin of micromagnetic and cooperative hierarchic magnetic domain structures in CoPt crystals consisting of nanosized phases is proposed. The conclusion is based on the concepts of a complex stressed crystal state and a nonlinear nonlocal elastic continuum model of the cubic-to-tetragonal phase transformation.