Crystal-field model for acceptor-associated bound magnetic polarons in wurtzite semiconductors

The effects of coupling between the A and B valence-band states in an acceptor-associated bound magnetic polaron ($A^0$-BMP) in hexagonal crystals such as ${\mathrm{Cd}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Mn}}_{\mathrm{x}}$Se are studied within a uniaxial model. The effect is found to be small for both the average BMP energy and the equilibrium hole polarization. However, the average excitation energy of the B-like hole states is reduced by an order of magnitude at low temperatures. The resulting spin-lattice relaxation time of the hole, within the Orbach framework, accounts for the time evolution of the hole polarization, inferred from time-resolved luminescence experiments.