Spin-flip Raman scattering, bound magnetic polaron, and fluctuations in (Cd,Mn)Se

Abstract

The spin-flip energy of donor-bound electrons is investigated in the semimagnetic semi-conductor ${\mathrm{Cd}}_{1-x}{\mathrm{Mn}}_x\mathrm{Se}$. Temperature and magnetic field dependences are measured with the use of Raman scattering and calculated theoretically from a statistical-mechanical model. Results of spin-flip Raman scattering are obtained for $x=0.01\mathrm{}$ and 0.1 at temperatures from 1.5 to 30 K and fields to 10 T. For $x=0.1\mathrm{}$, the spin-flip energy is large (≤26 meV), giving $g$ values approaching 200 at low temperatures. This enhancement is interpreted as an effective magnification of the field due to the exchange interaction between the carrier electron spin and the ${\mathrm{Mn}}^{2+}$ spins. The magnitude and temperature dependence of $g$ are explained with the use of the mean-field approximation. At zero magnetic field the spin-flip energy is finite due to thermal fluctuations in the local magnetization and the bound magnetic polaron. These processes are incorporated in the theory which is used to derive simple formulas for the spin-flip energy and line shape. Good agreement is found between theory and experiment. The scattering strength and selection rules are also studied. The absolute cross section exceeds ${10}^{-20\mathrm{}}$ ${\mathrm{cm}}^2$/sr and is resonantly enhanced as the absorption edge is approached from lower energy.