On the Origin of the Metallic and Anisotropic Magnetic Properties of Na_xCoO_2 (x~~0.75)
Non-stoichiometric NaxCoO2 (0.5 < x < 1) consists of CoO2 layers made up of edge-sharing CoO6 octahedra, and exhibits strongly anisotropic magnetic susceptibilities as well as metallic properties. A modified Curie-Weiss law was proposed for systems containing anisotropic magnetic ions to analyze the magnetic susceptibilities of NaxCoO2 (x ~~ 0.75), and implications of this analysis were explored. Our study shows that the lowspin Co4+ (S = 1/2) ions of NaxCoO2 generated by the Na vacancies cause the anisotropic magnetic properties of NaxCoO2, and suggests that the six nearest-neighbor Co3+ ions of each Co4+ ion adopt the intermediate-spin electron configuration thereby behaving magnetically like low-spin Co4+ ions. The Weiss temperature of NaxCoO2 is more negative along the direction of the lower g-factor (i.e., Theta_parallel < Theta_perp < 0, and g_parallel < g_perp). The occurrence of intermediate-spin Co3+ ions surrounding each Co4+ ion account for the apparently puzzling magnetic properties of NaxCoO2 (x ~~ 0.75), i.e., the large negative Weiss temperature, the three-dimensional antiferromagnetic ordering below ~22 K, and the metallic properties. The picture of the magnetic structure derived from neutron scattering studies below ~22 K are in apparent conflict with that deduced from magnetic susceptibility measurements between ~50 - 300 K. These conflicting pictures are resolved by noting that the spin exchange between Co3+ ions is more strongly antiferromagnetic than that between Co4+ and Co3+ ions.