Anisotropic superexchange of a 90 degree Cu-O-Cu bond

TL;DR

This paper investigates the magnetic anisotropy of a specific Cu-O-Cu bond in cuprates, revealing an easy axis perpendicular to the plaquettes and deriving a pseudo-dipolar interaction, with implications for materials like Li_2CuO_2.

Contribution

It provides a second-order spin-orbit interaction analysis of anisotropic superexchange in 90-degree Cu-O-Cu bonds, including the derivation of pseudo-dipolar interactions.

Findings

Easy axis perpendicular to CuO_2 plaquettes in ferromagnetic coupling

Pseudo-dipolar interaction is much smaller than dipole-dipole interaction

Results agree with experimental spin structure of Li_2CuO_2

Abstract

The magnetic anisotropy af a rectangular Cu-O-Cu bond is investigated in second order of the spin-orbit interaction. Such a bond is characteristic for cuprates having edge sharing CuO_2 chains, and exists also in the Cu_3O_4 plane or in ladder compounds. For a ferromagnetic coupling between the copper spins an easy axis is found perpendicular to the copper oxygen plaquettes in agreement with the experimental spin structure of Li_2CuO_2. In addition, a pseudo-dipolar interaction is derived. Its estimation in the case of the Cu_3O_4 plane (which is present for instance in Ba_2Cu_3O_4Cl_2 or Sr_2Cu_3O_4Cl_2) gives a value which is however two orders of magnitude smaller than the usual dipole-dipole interaction.