On the theory of domain structure in ferromagnetic phase of diluted magnetic semiconductors

We present a comprehensive analysis of domain structure formation in ferromagnetic phase of diluted magnetic semiconductors (DMS) of p-type. Our analysis is carried out on the base of effective magnetic free energy of DMS calculated by us earlier [Yu.G. Semenov, V.A. Stephanovich, Phys. Rev. B 67 (2003) 195203]. This free energy, substituting DMS (a disordered magnet) by effective ordered substance, permits to apply the standard phenomenological approach to domain structure calculation. Using coupled system of Maxwell equations with those obtained by minimization of above free energy functional, we show the existence of critical ratio νcr of concentration of charge carriers and magnetic ions such that sample critical thickness Lcr (such that at Lνcr the sample is monodomain. This feature makes DMS different from conventional ordered magnets as it gives a possibility to control the sample critical thickness and emerging domain structure period by variation of ν. As concentration of magnetic impurities grows, νcr→∞ restoring conventional behavior of ordered magnets. Above facts have been revealed by examination of the temperature of transition to inhomogeneous magnetic state (stripe domain structure) in a slab of finite thickness L of p-type DMS. Our theory can be easily generalized for arbitrary temperature and DMS shape.