Optical determination of the antiferromagnetic exchange constant between nearest-neighbor ${\mathrm{Mn}}^{2+}$ ions in ${\mathrm{Cd}}_{0.95}$${\mathrm{Mn}}_{0.05}$Te

Optical splittings of the band-edge exciton in ${\mathrm{Cd}}_{0.95}$ ${\mathrm{Mn}}_{0.05}$Te have been measured at 1.45 K with dc magnetic fields B up to 20 T, using magnetoreflectance in the Faraday configuration. The splitting Δ$E_{3/2}$ between the highest- and lowest-energy components, involving ±(3/2) hole states, follows a modified Brillouin function at low values of B. At higher values of B, Δ$E_{3/2}$ exhibits temperature-broadened, steplike increases due to the magnetic-field-induced alignment of the antiferromagnetically coupled nearest-neighbor (NN) ${\mathrm{Mn}}^{2+}$-ion pairs. The first of the expected five steps was observed at $B_1$=11.5±0.5 T, which yields a value $J_{\mathrm{NN}=\mathrm{-}7.7\pm 0.3}$ K for the ${\mathrm{Mn}}^{2+}$ nearest-neighbor antiferromagnetic exchange constant. The presence of a second step is indicated at $B_2$=19.5±1.0 T, somewhat below the predicted value of 2$B_1$.