Constraints on the two-dimensional pseudo-spin 1/2 Mott insulator description of Sr$_2$IrO$_4$

TL;DR

This study demonstrates that a realistic multi-band Hubbard model, rather than a simplified pseudo-spin 1/2 model, is necessary to accurately describe the electronic structure of Sr$_2$IrO$_4$, highlighting the importance of multi-orbital effects.

Contribution

The paper shows that a multi-band Hubbard Hamiltonian better captures the complex interplay of spin-orbital entanglement and electron interactions in Sr$_2$IrO$_4$ than a simplified pseudo-spin model.

Findings

A pseudo-spin 1/2 model fails to describe the system accurately.

Approximately 74% of the low-energy spectral weight involves $j_{3/2}$ states.

A multi-band approach aligns well with experimental data.

Abstract

Sr$_{2}$IrO$_{4}$ has often been described via a simple, one-band pseudo-spin 1/2 model, subject to electron-electron interactions, on a square lattice, fostering analogies with cuprate superconductors, believed to be well described by a similar model. In this work we argue - based on a detailed study of the low-energy electronic structure by circularly polarized spin and angle-resolved photoemission spectroscopy combined with dynamical mean-field theory calculations - that a pseudo-spin 1/2 model fails to capture the full complexity of the system. We show instead that a realistic multi-band Hubbard Hamiltonian, accounting for the full correlated $t_{2g}$ manifold, provides a detailed description of the interplay between spin-orbital entanglement and electron-electron interactions, and yields quantitative agreement with experiments. Our analysis establishes that the $j_{3/2}$ states make up a substantial percentage of the low energy spectral weight, i.e. approximately 74% as determined from the integration of the $j$-resolved spectral function in the $0$ to $-1.64$ eV energy range. The results in our work are not only of relevance to iridium based materials, but more generally to the study of multi-orbital materials with closely spaced energy scales.