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

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 δ≳${\mathrm{\delta }}_{{\mathit{c}}_2}$ to a paraphase with antiferromagnetic SRO for ${\mathrm{\delta }}_{{\mathit{c}}_1}$<δ<${\mathrm{\delta }}_{{\mathit{c}}_2}$. In this region the susceptibility consists of interrelated ‘‘itinerant’’ and ‘‘local’’ parts and increases upon doping. The zero-temperature susceptibility exhibits a cusp at ${\mathrm{\delta }}_{{\mathit{c}}_2}$ 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{-}\mathrm{\delta }}$${\mathrm{Sr}}_{\mathrm{\delta }}$${\mathrm{CuO}}_4$, the peak position (${\mathrm{\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%. © 1996 The American Physical Society.