Distant-Neighbor Exchange Constants in Dilute Magnetic Semiconductors

Several exchange constants $J_i$ between ${\mathrm{Mn}}^{2+}$ ions which are not nearest neighbors were determined in ${\mathrm{Zn}}_{1-x}{\mathrm{Mn}}_{x}X$ ( $X=\mathrm{S},\mathrm{Se},\mathrm{Te}$) from magnetization steps at 20 mK. When the $J_i$'s are listed in order of decreasing size, ratios between successive $J_i$'s are material dependent, and differ from all predictions. The measured $J_i$'s were identified by comparing the magnetization curves with simulations which assumed a random Mn distribution. Contrary to existing theories the second-largest exchange constant is not $J_2$ between next-nearest neighbors. The most likely alternative is $J_4$, between fourth neighbors.