  The magnetization of Pb_{1-x}Eu_{x}Te 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/k_{B} = -0.264 \pm 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 J_{1} rather than the
next-nearest-neighbor exchange constant J_{2}. On this basis, J is tentatively
identified as J_{1}. 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
micrometer. The theoretical simulations in the present work improve on those
performed earlier by including clusters larger than three spins.
