High-field magnetization steps and the nearest-neighbor exchange constant in ${\mathrm{Cd}}_{1\mathrm{-}\mathrm{x}}$${\mathrm{Mn}}_{\mathrm{x}}$S, ${\mathrm{Cd}}_{1\mathrm{-}\mathrm{x}}$${\mathrm{Mn}}_{\mathrm{x}}$Te, and ${\mathrm{Zn}}_{1\mathrm{-}\mathrm{x}}$${\mathrm{Mn}}_{\mathrm{x}}$Se

High-field magnetization steps due to energy-level crossings for pairs of nearest-neighbor Mn spins were observed in ${\mathrm{Cd}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Mn}}_{\mathrm{x}}$S, ${\mathrm{Cd}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Mn}}_{\mathrm{x}}$Te, and ${\mathrm{Zn}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Mn}}_{\mathrm{x}}$Se. For ${\mathrm{Cd}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Mn}}_{\mathrm{x}}$Te, two steps were observed. The difference $H_2$-$H_1$ between the magnetic fields at the centers of these steps gives $J_{\mathrm{NN}/k_B=\mathrm{-}6.1\pm 0.3}$ K for the exchange constant between nearest-neighbor Mn spins. For ${\mathrm{Cd}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Mn}}_{\mathrm{x}}$S and ${\mathrm{Zn}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Mn}}_{\mathrm{x}}$Se, only the first step at $H_1$ was observed. The values of $H_1$ give the estimates $J_{\mathrm{NN}/k_B\mathrm{\simeq }\mathrm{-}10.5}$ K for ${\mathrm{Cd}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Mn}}_{\mathrm{x}}$S, and $J_{\mathrm{NN}/k_B\mathrm{\simeq }\mathrm{-}12.6}$ K for ${\mathrm{Zn}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Mn}}_{\mathrm{x}}$Se. Our results for $J_{\mathrm{NN}}$ in the three materials are in good agreement with other recent determinations. The magnitudes of the magnetization steps in all three materials are consistent with those expected from a random distribution of Mn ions over the cation sites in the crystals.