Several exchange constants J i between Mn 21 ions which are not nearest neighbors were determined in Zn 12x Mn x X (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. [S0031-9007 (98)06413-8] PACS numbers: 75.30.Et, 75.50.Ee, 75.50.Pp, 75.60.EjThe distance dependence of the d-d exchange constants J i in dilute magnetic semiconductors (DMS's) has been discussed for more than a decade [1][2][3][4][5][6][7][8][9]. The focus has been on Mn-based II-VI DMS's with the zinc-blende structure. It has been established that the largest J i is the nearest-neighbor (NN) exchange constant J 1 . This J 1 is antiferromagnetic (AF), and is of order 210 K [5,6]. It is generally accepted that the second-neighbor (next-nearestneighbor) exchange constant J 2 , third-neighbor constant J 3 , etc., are all AF. What is at issue are the ratios J 1 : J 2 : J 3 : J 4 , etc.All existing theories, conjectures, and reported data as interpreted by their authors maintain that J 2 is the secondlargest exchange constant, after J 1 . The theory of Larson et al. [1] predicts that J 2 : J 1 , J 3 : J 2 , and J 4 : J 3 are all about 0.08. In the modified version by Rusin [9], J 2 : J 1 Х 0.08, and both J 3 and J 4 are less than 0.1J 2 . According to Bruno and Lascaray (BL), J 3 : J 2 J 4 : J 3 1͞2 (no prediction for J 2 : J 1 ) [4]. A power law dependence of J i on distance, J i~r

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The magnetization of Sn1-x Eux Te, with x = 0.011 and 0.042, was measured at 20 mK in magnetic fields up to 90 kOe. Magnetization steps (MSTs) from pairs and triplets were observed. The MSTs give J /kB = -0.311±0.006 K for the dominant Eu-Eu exchange constant. Comparisons of the magnetization curves with numerical simulations indicate that, instead of being distributed randomly, the Eu ions tend to bunch together. A phenomenological approach which uses the concept of a local Eu concentration xL is quite successful in describing the data for these two samples.

The magnetization of Pb1−xEuxTe samples with x = 1.9, 2.6 and 6.0% was measured at 20 mK in fields up to 50 kOe, and at 0.6 K in fields up to 180 kOe. The 20 mK data show the magnetization steps (MSTs) arising from pairs and from triplets. The pair MSTs are used to obtain the dominant Eu-Eu antiferromagnetic exchange constant, J/kB = −0.264 ± 0.018 K. The exchange constant for triplets is the same. Comparison of the magnetization curves with theoretical simulations indicates that the Eu ions are not randomly distributed over all the cation sites. The deviation from a random distribution is much smaller if J is assumed to be the nearest-neighbor exchange constant J1 rather than the next-nearest-neighbor exchange constant J2. On this basis, J is tentatively identified as J1. However, the possibility that J = J2 cannot be excluded completely. To obtain agreement with the data, it must be assumed that the Eu ions tend to bunch together. Comparision with microprobe data indicates that the length scale for these concentration variations is smaller than a few µm. The theoretical simulations in the present work improve on those performed earlier by including clusters larger than three spins.75.50. Pp, 75.30.Et, 75.60.Ej