Theory of photoinduced ferromagnetism in dilute magnetic semiconductors

Abstract

We study the photoinduced ferromagnetism in the dilute magnetic semiconductors by solving a Hamiltonian model that consists of localized magnetic moments interacting with the photoexcited itinerant carriers. The spin states of the itinerant carriers are split due to the interaction with the localized magnetic moments, which are assumed to be in thermal equilibrium in the local magnetic field due to the carriers. The time dependence of the light-matter interaction term is eliminated by a unitary transformation and the resulting Hamiltonian is solved by making a Bogoliubov-Valatin transformation or by a variational approach using a Bardeen-Cooper-Schrieffer-type wave function. Without incident light, there are no carriers present to mediate magnetic interaction between the localized spins, so that the system is nonmagnetic. When light is present, the photoexcited carriers mediate a ferromagnetic interaction between the localized moments resulting in a ferromagnetic state, with a transition to a paramagnetic state as temperature is increased beyond ${T}_{c}$. The magnitude of ${T}_{c}$ is determined by the parameters of the system such as the strength of the light-matter coupling, the frequency of light, interaction strength of the carriers with the localized moments, etc. Even for a sub-band-gap light frequency, there are induced carriers, primarily due to the Rabi oscillations, leading to a small but nonzero ${T}_{c}$. We find that for typical parameters, ${T}_{c}$ is about a fraction of a Kelvin or so, which is sizable. In systems which are already ferromagnetic such as GaAs(Mn), the incident light would enhance the ${T}_{c}$ by this amount, an effect which has been recently observed.