Magnetic-ion triplet clusters and non-nearest-neighbor exchange effect in (Cd,Mn)Te

Internal quantum structures of ${\mathrm{Mn}}^{2+}$ spin clusters in ${\mathrm{Cd}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Mn}}_{\mathrm{x}}$Te are studied by Faraday-rotation measurements up to 60 T at T∼4 K. For x=0.1 we observe the contribution of ${\mathrm{Mn}}^{2+}$ triplet clusters, as well as the saturation of ${\mathrm{Mn}}^{2+}$ pairs. Overall good agreement between the experiments and a nearest-neighbor cluster model is obtained. By quantitative analysis of the data for pairs, we find a linear relation between bias field (average exchange field due to more-distant interactions) and total magnetization, independent of x (for x≤0.1). This relation allows us to determine the strength of next-nearest-neighbor interactions, $J_2$/$k_B$=-1.1 K.