Magnetic Interaction in Insulating Cuprates

TL;DR

This paper investigates magnetic interactions in insulating cuprates, revealing that cyclic four-spin interactions are significant and influence low-energy excitations, with implications for understanding magnetic properties.

Contribution

It quantitatively evaluates two-spin and four-spin interactions in cuprates, highlighting the importance of four-spin interactions in low-energy magnetic excitations.

Findings

Four-spin interaction is about 10% of nearest neighbor two-spin interaction.

Four-spin interaction is larger in ladder cuprates than in 2D cuprates.

Heisenberg ladder model with these interactions reproduces experimental magnetic susceptibility data.

Abstract

We examine two-spin (2S) and cyclic four-spin (4S) magnetic interactions in insulating ladder and two-dimensional (2D) cuprates. By a comparison of eigenstates between d-p and Heisenberg models, we evaluate magnitudes of these interactions. We find that the 4S interaction is $\sim$10% of nearest neighboring 2S interaction, and a diagonal 2S interaction is considerably small. The 4S interaction for a ladder cuprate is larger than that for 2D one, and plays an important role in the low-energy excitation. The Heisenberg ladder with the obtained 2S and 4S interactions reproduces very well the experimental result of the temperature dependence of the magnetic susceptibility.