Exchange energy, magnetization, and Raman scattering of (Cd,Mn)Se

Abstract

The exchange-energy parameter $\ensuremath{\alpha}{N}_{0}$ for conduction-band electrons in ${\mathrm{Cd}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{Se}$ was determined at $T=1.9$ K for $0.05\ensuremath{\le}x\ensuremath{\le}0.2$. For this range of $x$, $\ensuremath{\alpha}{N}_{0}$ is independent of $x$ and has the value (258\ifmmode\pm\else\textpm\fi{}5) meV. These results were obtained by comparing Raman scattering data for the spin splitting of donor electrons with magnetization data on the same crystals. The Raman data were obtained for $0.01\ensuremath{\le}x\ensuremath{\le}0.2$, and the magnetization data were taken for $0.05\ensuremath{\le}x\ensuremath{\le}0.3$. The magnetization was measured at temperatures $T$ between 1.5 and 4.2 K in magnetic fields $H$ up to 83 kOe. These data were fit to a parametrized Brillouin function. One of the fitting parameters gave an effective concentration ${\overline{x}}_{s}$ of magnetically active ${\mathrm{Mn}}^{2+}$ ions. The second fitting parameter ${T}_{0}$ was a measure of the average antiferromagnetic interaction between the Mn spins. The low-field magnetic susceptibility ${\ensuremath{\chi}}_{0}$ was fit to a Curie-Weiss law, which yielded the analogous parameters ${\overline{x}}_{C}$ and ${T}_{\mathrm{AF}}$ for low fields. As $x$ increased from 0.05 to 0.3, the fraction of magnetically active ions, $\frac{{\overline{x}}_{s}}{x}$, decreased from 0.6 to 0.1, and ${T}_{0}$ increased from 1.5 to 7 K. These trends are caused by the increase in the average antiferromagnetic interaction between the Mn spins as the average distance between them decreases with increasing $x$. Results of spin-flip Raman scattering from donor-bound electrons show that the Zeeman splitting $\ensuremath{\Delta}E$ of the donor's energy is large ($\ensuremath{\Delta}E\ensuremath{\gtrsim}10$ meV) for fields above 40 kOe. The splitting $\ensuremath{\Delta}E$ is approximately proportional to the magnetization, except at low $H$ where there is an additional contribution due to the difference between the local magnetization within the donor's orbit and the average bulk magnetization. This effect decreases for both increasing $H$ and decreasing $x$.