# Spin-orbit-controlled metal-insulator transition in Sr$_2$IrO$_4$

## TL;DR

This paper demonstrates that spin-orbit coupling (SOC) is the key factor controlling the metal-insulator transition in Sr$_2$IrO$_4$, providing direct evidence and quantifying the critical SOC strength needed for the transition.

## Contribution

The study offers the first direct evidence of SOC's role in stabilizing the insulating state and quantifies the critical SOC value for the transition in Sr$_2$IrO$_4$.

## Key findings

- SOC is essential for the insulating state in Sr$_2$IrO$_4
- Critical SOC value for MIT is 0.42 eV
- Methodology distinguishes relativistic and filling effects

## Abstract

In the context of correlated insulators, where electron-electron interactions (U) drive the localization of charge carriers, the metal-insulator transition (MIT) is described as either bandwidth (BC) or filling (FC) controlled. Motivated by the challenge of the insulating phase in Sr$_2$IrO$_4$, a new class of correlated insulators has been proposed, in which spin-orbit coupling (SOC) is believed to renormalize the bandwidth of the half-filled $j_{\mathrm{eff}} = 1/2$ doublet, allowing a modest U to induce a charge-localized phase. Although this framework has been tacitly assumed, a thorough characterization of the ground state has been elusive. Furthermore, direct evidence for the role of SOC in stabilizing the insulating state has not been established, since previous attempts at revealing the role of SOC have been hindered by concurrently occurring changes to the filling. We overcome this challenge by employing multiple substituents that introduce well defined changes to the signatures of SOC and carrier concentration in the electronic structure, as well as a new methodology that allows us to monitor SOC directly. Specifically, we study Sr$_2$Ir$_{1-x}$T$_x$O$_4$ (T = Ru, Rh) by angle-resolved photoemission spectroscopy (ARPES), combined with ab-initio and supercell tight-binding calculations. This allows us to distinguish relativistic and filling effects, thereby establishing conclusively the central role of SOC in stabilizing the insulating state of Sr$_2$IrO$_4$. Most importantly, we estimate the critical value for spin-orbit coupling in this system to be $\lambda_c = 0.42 \pm 0.01$ eV, and provide the first demonstration of a spin-orbit-controlled MIT.