Eu-Eu exchange interaction and Eu distribution in Pb 1-x Eu x Te from magnetization steps

The magnetization of ${\mathrm{Pb}}_{1\ensuremath{-}x}{\mathrm{Eu}}_{x}\mathrm{Te}$ samples with $x=0.019$, 0.026, and 0.060 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 (MST's) arising from pairs and from triplets. The pair MST's are used to obtain the dominant Eu-Eu antiferromagnetic exchange constant, ${J/k}_{B}=\ensuremath{-}0.264\ifmmode\pm\else\textpm\fi{}0.018$ 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 ${J}_{1}$. However, the possibility that ${J=J}_{2}$ 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 $\ensuremath{\mu}$m. The theoretical simulations in the present work improve on those performed earlier by including clusters larger than three spins.