Spin susceptibility and magnetic short-range order in the Hubbard model.

Abstract

The uniform static spin susceptibility in the paraphase of the one-band Hubbard model is calculated within a theory of magnetic short-range order (SRO) which extends the four-field slave-boson functional-integral approach by the transformation to an effective Ising model and the self-consistent incorporation of SRO at the saddle point. This theory describes a transition from the paraphase without SRO for hole dopings \ensuremath{\delta}\ensuremath{\gtrsim}${\mathrm{\ensuremath{\delta}}}_{{\mathit{c}}_{2}}$ to a paraphase with antiferromagnetic SRO for ${\mathrm{\ensuremath{\delta}}}_{{\mathit{c}}_{1}}$${\mathrm{\ensuremath{\delta}}}_{{\mathit{c}}_{2}}$. In this region the susceptibility consists of interrelated ``itinerant'' and ``local'' parts and increases upon doping. The zero-temperature susceptibility exhibits a cusp at ${\mathrm{\ensuremath{\delta}}}_{{\mathit{c}}_{2}}$ and reduces to the usual slave-boson result for larger dopings. Using the realistic value of the on-site Coulomb repulsion U=8t for ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$${\mathrm{Sr}}_{\mathrm{\ensuremath{\delta}}}$${\mathrm{CuO}}_{4}$, the peak position (${\mathrm{\ensuremath{\delta}}}_{{\mathit{c}}_{2}}$=0.26) as well as the doping dependence reasonably agree with low-temperature susceptibility experiments showing a maximum at a hole doping of about 25%. \textcopyright{} 1996 The American Physical Society.