  We report on x-ray diffraction, magnetic susceptibility, electron- spin
resonance and heat- capacity studies of Co[Al_1-xCo_x]_2O_4 for Co
concentrations 0<x<1. In this spinel system only the A-site Co^2+ cation is
magnetic, while the non-magnetic B-site Al^3+ is substituted by the low-spin
non-magnetic Co^3+, and it is possible to investigate the complete phase
diagram from Co^2+Al^3+_2O_4 to Co^2+Co^3+_2O_4. All samples reveal large
negative Curie-Weiss temperatures Theta_CW of the order of -110 K independent
of concentration, which is attributed to a high multiplicity of the
superexchange interactions between the A-site Co^2+ cations. A pure
antiferromagnetic state is found for x = 1.0 and 0.9 with Neel temperatures T_N
= 29.5 K and 21.2 K, respectively, as evidenced by lambda-like anomalies in the
specific heat. Compositions with 0.3<x<0.75 show smeared out strongly reduced
magnetic ordering temperatures. At low temperatures, a T^2.5 dependence of the
specific heat is indicative of a spin-liquid state. For x < 0.2 a T^2
dependence of the specific heat and a spin-glass like behavior of the
susceptibility below T_f = 4.7 K are observed. The high value of the
frustration parameter f = |Theta_CW|/T_f > 10 indicates the presence of strong
spin frustration at least for x < 0.6. The frustration mechanism is attributed
to competing nearest neighbor and next-nearest neighbor superexchange
interactions between the A-site Co^2+ ions.
