Magnetization steps of spin quartets

Magnetization steps (MST's) arising from quartets consisting of four identical spins, each of magnitude $S$, are discussed. It is assumed that the only interactions are (1) antiferromagnetic exchange bonds between quartet members, with only one exchange constant $J$, and (2) the Zeeman interaction with the magnetic field H. There are six quartet types. Each type gives rise to steps in the magnetization curve at low temperatures, $k_{B}T<\mathrm{}\left|J\right|\mathrm{}$. For five quartet types analytical expressions for the magnetic fields $H_n$ at the MST's are given, for any $S$. These results are based on expressions for the quartets' energy levels. For the sixth quartet type (called "string"), numerical results for $H_n$ are given assuming $S=\frac{5}{2}$, which is appropriate for ${\mathrm{Mn}}^{2+}$ and ${\mathrm{Fe}}^{3+}$ ions. The probabilities that a magnetic ion is in any of the six quartet types are given for an fcc lattice. Magnetization curves for ${\mathrm{Zn}}_{1-x}{\mathrm{Mn}}_x\mathrm{S}$ ($x=2.5\mathrm{} \mathrm{and} 3.8\%$) and ${\mathrm{Zn}}_{1-x}{\mathrm{Mn}}_x\mathrm{Se}$ ($x=3.1\mathrm{} \mathrm{and} 5.3\%$) were measured at 0.6 K in dc magnetic fields up to 190 kOe. The data show an MST which is a superposition of the first MST from "string quartets" and the first MST from "funnel quartets" (two of the six quartet types). The predicted fields for these two MST's differ by only 5%, so that the two MST's overlap in the experiment. The magnetic field at the center of the observed MST is close to the predicted value in all cases. The size of the magnetization rise at the observed MST is consistent with the calculated probabilities of finding a spin in strings and funnels.