Finite-temperature properties of the triangular lattice t-J model and applications to Na_xCoO₂

Abstract

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 Na_xCoO₂ (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 et al. [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=∞) 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 et al., 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.