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

Internal quantum structures of Mn²⁺ spin clusters in Cd_1-x{Mn}ₓTe are studied by Faraday-rotation measurements up to 60 T at T~4 K. For x=0.1 we observe the contribution of{Mn}²⁺$ triplet clusters, as well as the saturation of ${Mn}²⁺$ 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, J₂/kB=-1.1 K.