Slave-boson study of the t-t'-J model: Phase diagram, spin susceptibility, and Hall resistivity.

Abstract

We investigate the normal-state properties of high-${\mathit{T}}_{\mathit{c}}$ cuprates in terms of the t-t'-J model using a spin-rotation-invariant slave-boson technique. The second-neighbor hopping t'0 is included in order to reproduce the Fermi surfaces of LSCO (${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Sr}}_{\mathit{x}}$${\mathrm{CuO}}_{4}$) and YBCO (${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{6+\mathit{x}}$) type. The magnetic phase diagram of the t-t'-J model is derived within the saddle-point approximation, by taking into account also incommensurate spiral order. Compared to the pure t-J model, N\'eel order is stabilized in the low-doping region. In particular, for the case t'>0, which corresponds to the electron-doped systems, e.g., ${\mathrm{Nd}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Ce}}_{\mathit{x}}$${\mathrm{CuO}}_{4}$ (NCCO), the antiferromagnetic correlations are strongly enhanced near half-filling. We include fluctuation corrections and calculate the dynamic (paramagnetic) spin susceptibility \ensuremath{\chi}(q,\ensuremath{\omega}) going beyond the random-phase approximation. The instability line of the paraphase obtained from \ensuremath{\chi}(q) is in agreement with the saddle-point phase diagram. The wave-vector dependence of \ensuremath{\chi}(q) reveals the commensurate (incommensurate) nature of spin fluctuations in YBCO (LSCO). Finally, the doping dependence of the Hall resistivity ${\mathit{R}}_{\mathit{H}}$(\ensuremath{\delta}) is calculated, where the results agree surprisingly well with experiments on LSCO. For YBCO and NCCO, the t' term suffices to give the correct dependence for ${\mathit{R}}_{\mathit{H}}$(\ensuremath{\delta}).