Magnetization steps inPb1−xEuxSe: Determination and identification of the dominant antiferromagnetic exchange constant

The magnetization of three ${\mathrm{Pb}}_{1-x}{\mathrm{Eu}}_x\mathrm{Se}$ samples, with $x=1.3, 3.0, \mathrm{and} 4.1\%$, was measured at 30 and 50 mK in magnetic fields $H$ up to 50 kOe, and at 0.6 K in fields up to 180 kOe. For $x=1.3\%$ and with H∥[100], a magnetization step (MST) due to an energy-level crossing for isolated ${\mathrm{Eu}}^{2+}$ ions was observed at 30 and 50 mK. The magnetic field at this MST, 1.76±0.2 kOe, was close to the predicted value $H_c=1.98\mathrm{}$ kOe. At the same low temperatures (30 and 50 mK) but at higher fields, a magnetization "ramp" due to pairs was observed in all samples. For $x=3.0\mathrm{} \mathrm{and} 4.1\%$ this ramp consisted of well-resolved MST's arising from pairs. A ramp due to open triplets was also observed in these two samples. The MST's due to pairs were used to obtain the value $\frac{J}{k_B}=-0.24\mathrm{}\pm 0.03$ K for the dominant antiferromagnetic exchange constant. Comparisons between the measured magnetization curves at 30 or 50 mK and theoretical simulations indicates that this $J$ is the nearest-neighbor (NN) exchange constant $J_1$. At 0.62 K the magnetization of each of the three samples rose rapidly with $H$ in fields below several kOe. At higher fields a rounded ramp due to pairs and triplets was present. This ramp ended near 40 kOe, and complete saturation was achieved near 50 kOe. A model which includes only the NN exchange constant $J_1$ gave a reasonably good account for all the data at 0.62 K. Calculated magnetization curves for pairs, and for open and closed triplets, at various values of $\frac{k_{B}T}{\mathrm{}\left|J\right|\mathrm{}}$ are presented. The effects of the single-ion and dipole-dipole anisotropies on the MST's due to pairs are also discussed.