Magnetization steps in Pb 1 − x Eu x S : Exchange and anisotropic interactions

Magnetization measurements were performed on five ${\mathrm{Pb}}_{1\ensuremath{-}x}{\mathrm{Eu}}_{x}\mathrm{S}$ samples, with $0.0092l~xl~0.059$. Two of the samples were measured at 20 mK in magnetic fields $\mathbf{H}$ up to 50 kOe parallel to the $[111]$ and $[100]$ directions. The other three samples were measured at 0.6 K in fields up to 180 kOe. The 20 mK data exhibit magnetization steps (MST's) arising from pairs. These MST's depend on the direction of H, so that anisotropic interactions must be included in the data analysis. The MST's lead to a value ${J/k}_{B}=\ensuremath{-}0.228\ifmmode\pm\else\textpm\fi{}0.007$ K for the dominant antiferromagnetic exchange constant. Computer simulations identify this $J$ as the nearest-neighbor exchange constant ${J}_{1}$, and show that the Eu distribution over the cation sites is random or very nearly random. The MST's from pairs exhibit a splitting when $\mathbf{H}$ is parallel to $[100]$. The splitting is tentatively attributed to exchange anisotropy, in which case the above value for $J$ refers to the average exchange constant $\overline{J}$. The 20 mK data for $\mathbf{H}||[100]$ also show a MST from isolated Eu ions. This MST occurs because such ``singles'' are subjected to a cubic crystal-field anisotropy.