Finite-temperature properties of the triangular lattice t-J model and applications to NaxCoO2

We present a finite temperature (T) study of the t-J model on the two-dimensional triangular lattice for the negative hopping t, as relevant for the electron-doped NaxCoO2 (NCO). We study several thermodynamic and transport properties in this study: the T-dependent chemical potential, specific heat, magnetic susceptibility, and the dynamic Hall coefficient across the entire doping range. We show systematically how this simplest model for strongly correlated electrons describes a crossover as function of doping (x) from a Pauli-like weakly spin-correlated metal close to the band limit (density n=2) to the Curie-Weiss metallic phase (1.5 < n < 1.75) with pronounced antiferromagnetic (AFM) correlations at low temperatures and Curie-Weiss-type behavior in the high-temperature regime. Upon further reduction of the doping, a different energy scale, dominated by spin-interactions (J) emerges. It is apparent both in specific heat and susceptibility, and we identify an effective interaction J(eff)(x), valid across the entire doping range. This is in contrast to the formula by Anderson [J. Phys.: Condens. Matter 16, R755 (2004)] for the square lattice. NCO has t < 0, hence the opposite sign of the Nagaoka-ferromagnetic situation, this expression includes the subtle effect of weak kinetic AFM [Haerter and Shastry, Phys. Rev. Lett. 95, 087202 (2005)], as encountered in the infinitely correlated situation (U=infinity) for electronic frustration. By explicit computation of the Kubo formulas, we address the question of practical relevance of the high-frequency expression for the Hall coefficient R-H(*) [Shastry , Phys. Rev. Lett. 70, 2004 (1993)]. We hope to clarify some open questions concerning the applicability of the t-J model to real experimental situations through this study.