Theory of Magnetic Short--Range Order for High-T_c Superconductors

TL;DR

This paper develops a theoretical model for magnetic short-range order in high-temperature cuprate superconductors, explaining experimental observations of magnetic behavior and susceptibility changes with doping.

Contribution

It introduces a combined slave-boson and Bethe cluster approach to model magnetic short-range order, providing a self-consistent phase diagram aligned with experimental data.

Findings

Reproduces suppression of long-range magnetic order in cuprates.

Predicts doping-dependent spin susceptibility consistent with experiments.

Identifies the transition from antiferromagnetic short-range order to Pauli paramagnetism.

Abstract

A theory of magnetic short--range order for high--$T_c$ cuprates is presented on the basis of the one--band $t$--$t^{\prime}$--Hubbard model combining the four--field slave--boson functional integral technique with the Bethe cluster method. The ground--state phase diagram evaluated self--consistently at the saddle--point and pair--approximation levels shows the experimentally observed suppression of magnetic long--range order in the favour of a paraphase with antiferromagnetic short--range order. In this phase the uniform static spin susceptibility consists of interrelated itinerant and local parts and increases upon doping up to the transition to the Pauli paraphase. Using realistic values of the Hubbard interaction we obtain the cusp position and the doping dependence of the zero--temperature susceptibility in reasonable agreement with experiments on $\rm La_{2-\delta}Sr_{\delta}CuO_4$.