Anisotropic Superexchange for nearest and next nearest coppers in chain, ladder and lamellar cuprates

TL;DR

This paper provides detailed calculations of magnetic couplings in cuprates with edge-sharing geometry, highlighting anisotropic superexchange interactions for nearest and next-nearest neighbors, crucial for understanding their magnetic structures.

Contribution

It introduces a perturbation-based method to estimate magnetic energies and anisotropies in cuprates, accounting for bond angle deviations from 90 degrees.

Findings

Magnetic interactions depend on Cu-O-Cu bond angles.

Anisotropy energies vary with angular deviations.

Results aid in analyzing magnetic structures of cuprates.

Abstract

We present a detailed calculation of the magnetic couplings between nearest-neighbor and next-nearest-neighbor coppers in the edge-sharing geometry, ubiquitous in many cuprates. In this geometry, the interaction between nearest neighbor coppers is mediated via two oxygens, and the Cu-O-Cu angle is close to 90 degrees. The derivation is based on a perturbation expansion of a general Hubbard Hamiltonian, and produces numerical estimates for the various magnetic energies. In particular we find the dependence of the anisotropy energies on the angular deviation away from the 90 degrees geometry of the Cu-O-Cu bonds. Our results are required for the correct analysis of the magnetic structure of various chain, ladder and lamellar cuprates.