“…Assuming that both matrices have no defects, then the couplings between the magnetic moments localized on the chromium ions can be realized via three following types of magnetic interactions: (i) the superexchange (the interaction paths: Cr 3+ -X 2− -Cr 3+ , Cr 3+ -X 2− -X 2− -Cr 3+ , Cr 3+ -X 2− -A 2+ -X 2− -Cr 3+ ); (ii) the Zener double exchange interaction in the Cr 3+ -Cr 4+ ion pairs; and (iii) RKKY interaction caused by the appearance in the matrices of the itinerant electrons coming from the existence in them of a few percent of the Cu 2+ ions [1,2,[10][11][12][13][14]. As the crystal field of the ligands splits Table 5 The magnetic coupling constants J 1 /k B (for the first coordination sphere) and J 2 /k B (for the second coordination sphere) of both the stoichiometric and nonstoichiometric spinel compounds under study (calculated from the experimental data in [3][4][5][6][7] Spinel compounds every 3d energy level of the cations into the triplet t 2g and the doublet e g the different overlaps are possible of the wave functions 3d with the p orbitals of anions. Therefore, the exchange chains are created via the so-called -, -and -bands, the latter making different overlaps mentioned above.…”