Magnetic Coupling in CuCr$\text{}_{2}$X$\text{}_{4}$ (X = S, Se) Spinel Compounds Obtained via Substitution of the Chromium Ions by Nonmagnetic Sb or Al Ions

Taking into account both the dc magnetic susceptibility and the magnetization measurements as well as the high-temperature expansion of the magnetic susceptibility procedure the hopping integrals and superexchange integrals for the first and second coordination sphere were evaluated. The two hopping integrals are positive and many times greater than the superexchange ones. The obtained results testify to that in the stoichiometric compounds under study the double-exchange magnetic interaction is the main mechanism responsible for very strong, ferromagnetic coupling. Using the total hopping integral B the bandwidth of mixed valence band of chromium ions was determined.