A model for doping-dependent magnetic frustration and ordering in a triangular lattice

The family of cobaltates A_xC_oO₂ (A = Na, Li, K), with a crystal structure consisting of a layered triangular lattice of Co ions, exhibits a fascinating range of coupled spin, charge and ion ordering phenomena as a function of electron doping content x. Based on these experimental observations, we investigate an extended Ising model for suppression of magnetic frustration caused by electron doping in a quasi-2-dimensional nearest-neighbour antiferromagnetic triangular lattice. As determined by geometry and bond-counting, it is found that magnetic frustration can be quantified by a frustration index f_ub and its magnitude is a non-monotonic function of x. A mean-field calculation is carried out to determine the temperature-dependent magnetization, spin-entropy and heat capacity for the obtained structures with the lowest energy (≡ lowest f_ub) for each x. The calculations reveal that the magnetic-ordering temperature T_C exhibits an anti-correlation with f_ub as a function of x. In addition, as seen in thermopower experiments, an anomalous spin-entropy is obtained for the high-doping cases when . The results indicate the importance of doping-dependent magnetic frustration in the layered cobaltates.