Nearest-neighbor exchange constant and Mn distribution in ${\mathrm{Zn}}_{1\mathrm{-}\mathrm{x}}$${\mathrm{Mn}}_{\mathrm{x}}$Te from high-field magnetization step and low-field susceptibility

Magnetization data in fields up to 210 kOe were obtained on ${\mathrm{Zn}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Mn}}_{\mathrm{x}}$Te samples with x=0.031 and 0.040. At Tapeq21.4 K, a magnetization step was observed near 150 kOe. This step is attributed to a level crossing for pairs of nearest-neighbor (NN) Mn spins. The magnetic field at the center of the step gives J/$k_B$=-10.0±0.8 K for the NN exchange constant. This value is slightly higher than that obtained from inelastic neutron scattering. The magnitude of the magnetization step agrees with calculations which assume a random Mn distribution. The technical saturation value for the magnetization at low temperatures also agrees with calculations which assume a random Mn distribution. Low-field susceptibility data, taken at 4≤T≤350 K, lead to Curie constants which agree with those calculated with S=(5/2) and g=2 for each Mn ion. Assuming NN interactions only, and a random Mn distribution, the Curie-Weiss temperatures give J/$k_B$apeq2-12 K. A detailed theoretical discussion of the NN cluster model, as it applies to the magnetization curve of a dilute magnetic semiconductor at low T, is given. Many of the theoretical results also should apply to a larger class of dilute magnetic materials.