Magnetization steps in ${\mathrm{Mn}}_{0.084}{\mathrm{Zn}}_{0.916}{\mathrm{F}}_2:$ Exchange constant and Mn distribution

The magnetization M of ${\mathrm{Mn}}_{0.084}{\mathrm{Zn}}_{0.916}{\mathrm{F}}_2$ was measured at 20 mK in magnetic fields H up to 115 kOe and at 0.65 K in fields up to 175 kOe. The magnetization was independent of magnetic field direction and showed no hysteresis. After a fast rise of M at low H, several magnetization steps (MS’s) were observed. These MS’s arose from ${\mathrm{Mn}}^{2+}$ pairs and triplets in which the spins are coupled by the dominant antiferromagnetic exchange constant, $J_2$ between next-nearest neighbors. The magnetic fields at the steps gave $J_2=-1.94\pm 0.01\hspace{0.5em}\mathrm{K}$ in this diluted magnetic material. The observed magnetization curves are in very good agreement with computer simulations which assume a random Mn distribution. However, at 20 mK the widths of MS’s are much larger than expected from thermal broadening alone. Possible mechanisms for nonthermal broadening are discussed. Theoretical results for cluster statistics, for $J_2$ clusters up to quintets, and for the fields at the MS’s from the various quintet types are presented. These theoretical results also apply to nearest-neighbor ${(J}_1)$ clusters in a body-centered-cubic cation lattice.