Distant-neighbor exchange constants in dilute magnetic semiconductors

Several exchange constants J(i) between Mn2+ ions which are not nearest neighbors were determined in Zn1-xMnxX (X = S, Se, 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.