Direct Exchange versus the indirect Exchange of the t-J Hamiltonian in HTSC Cuprates

TL;DR

This paper compares direct and indirect exchange interactions in HTSC cuprates, revealing that direct exchange is significantly stronger and predicts positive exchange energy, leading to a proposed modification of the t-J Hamiltonian.

Contribution

It introduces a modified t-J Hamiltonian based on calculated exchange integrals, challenging previous assumptions about exchange interactions in HTSC cuprates.

Findings

Direct exchange integral is three times larger than the indirect exchange.

Direct exchange predicts positive exchange energy for parallel spins.

Proposes a modified t-J Hamiltonian to better represent exchange interactions.

Abstract

The direct exchange integral and the transfer integral are calculated for the anti-bonding wave-function of the HTSC cuprates. The direct exchange integral yields a value three times larger than the indirect exchange of the t-J Hamiltonian. It also predicts positive exchange energy for neighboring parallel spins, contrary to the prediction of zero energy by the t-J Hamiltonian. A modified t-J Hamiltonian is proposed, and the implications of the results are discussed.