Split magnetization steps in ${\mathrm{Cd}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Mn}}_{\mathit{x}}$Se: Inequivalent nearest neighbors and the Dzyaloshinski-Moriya interaction

In the wurtzite structure the twelve nearest-neighbor (NN) cations surrounding a given cation belong to two groups: six ‘‘in’’ NN’s that are in the same c plane, and six ‘‘out’’ NN’s that are out of the c plane. These two groups are inequivalent, by symmetry, and the NN exchange constants ${\mathit{J}}_1^{\mathrm{in}}$ and ${\mathit{J}}_1^{\mathrm{out}}$ are unequal. The difference Δ${\mathit{J}}_1$==${\mathit{J}}_1^{\mathrm{in}}$-${\mathit{J}}_1^{\mathrm{out}}$ gives rise to a splitting of the magnetization steps (MST’s) associated with pairs of NN magnetic ions. Each MST splits into two ‘‘half-steps,’’ one due to in pairs, and the other due to out pairs. The average ${\mathit{J}}_1$, and the absolute value of the difference Δ${\mathit{J}}_1$ between the two ${\mathit{J}}_1$’s, are obtained from the fields at the half steps. Analysis of the line shape of the split MST’s yields the sign of Δ${\mathit{J}}_1$ and an estimate for the Dzyaloshinski-Moriya interaction constant D. These procedures were implemented for ${\mathrm{Cd}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Mn}}_{\mathit{x}}$Se with x=0.010 and 0.025. The first two MST’s were observed at 0.5–0.6 K in experiments that used magnetic fields up to 30 T. At these temperatures only the splitting of the second MST was resolved. The splitting of the first MST was observed at 0.08 K, in experiments up to 20 T.