A study of cobalt-carrier exchange interactions is carried out in very
dilute Zn1-xCoxTe (x less than or equal to 1%) from correlated magnet
o-optical and magnetization measurements at T=1.8 K. The resonant magn
eto-optic Ken effect is used to complement magnetoreflectance experime
nts, and determine precisely the exciton Zeeman splittings on single c
rystals of various Co compositions. Correlated measurements of magneti
zation performed on the same samples provide a determination of exchan
ge integrals for Gamma(6) and Gamma(8) bands within the framework of t
he exchange model based on the mean-field approximation. In the invest
igated field and composition range, we find N-o alpha=0.31+/-0.03 eV;
N-o beta=-3.03+/-0.15 eV. This abnormally large value of the p-d excha
nge constant does not vary with Co concentration in the investigated r
egion. Low-temperature magnetization data obtained in fields up to 15
T are consistently interpreted in a model including the contributions
of isolated ions and Co2+-Co2+ pairs of second and third neighbors for
the values of exchange constants previously determined. Antiferromagn
etic interactions between more distant ions than third neighbors are a
lso taken into account. The long-range exchange parameters obtained by
using either a modified Brillouin function or a mean-field approach a
re in good agreement.