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Direct measurements of several exchange constants J;, for several neighbors located at different distances r;, are possible via the magnetization-steps method. Predictions for the distance dependence of the exchange constant can then be tested. The theory of the magnetization steps (MS's) caused by distant neighbors is presented. This theory is based on a sequence of cluster models. The problem of identifying the particular exchange constant J; that is responsible for an observed series of MS s is also discussed. The magnetization of Zn& "Co Te, with x =0. 007, was measured at 0.6 K in magnetic fields up to 27 T, and at 0.08 K in fields up to 20 T. Two series of MS's were observed. These series were identified as being due to pairs of next-nearest neighbors (J& pairs), and pairs of third neighbors (J3 pairs).The exchange constants deduced from the data are J2/k& = -(5.7+0.6) K and J3/k& = -(2.7+0.3) K. These values, and the earlier result J&/kz = -38 K for the nearest-neighbor exchange constant, are compared with several proposed dependences of J; on distance.

In the wurtzite structure the twelve nearest-neighbor (NN) cations surrounding a given cation belong to two groups: six "in" NN's that are in the same c plane, and six "out" NN's that are out of the c plane.These two groups are inequivalent, by symmetry, and the NN exchange constants J', " and J&"' are unequal. The difference hJ& = J& J] ' gives rise to a splitting of the magnetization steps (MST's) associated with pairs of NN magnetic ions. Each MST splits into two "half-steps, " one due to in pairs, and the other due to out pairs. The average J~, and the absolute value of the difference hJ& between the two J&'s, are obtained from the fields at the half steps. Analysis of the line shape of the split MST's yields the sign of AJ& and an estimate for the Dzyaloshinski-Moriya interaction constant D. These procedures were implemented for Cd& "Mn, Se with x =0.010 and 0.025. The first two MST's were observed at 0.5-0.6 K in experiments that used magnetic fields up to 30 T. At these temperatures only the splitting of the second MST was resolved. The splitting of the first MST was observed at 0.08 K, in experiments up to 20 T. The average NN exchange constant J& = --, '(J] +J& ') is J~/k& = -7.55+0. 1 K, and the magnitude of the difference is~hJ,~/J, =0.15+0.01. The latter value is in good agreement with a theoretical estimate by Larson. Line-shape analysis indicates that J', " is larger in magnitude than J &"', as predicted by Larson, and it places D in the range 0. 10 & D/kz &0.24 K. An alternative analysis of the line shape of the second MST gives the estimate D/k& -=0.21 K. These results for D compare well with the value D/kz =0.16 K predicted by Larson and Ehrenreich.

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