# Hopping induced ground-state magnetism in 6H perovskite iridates

## TL;DR

This study reveals that in 6H perovskite iridates, substantial intra-dimer hopping modifies spin-orbit states, leading to unexpected magnetism despite strong SOC, and suggests tuning Ir-Ir distances could enable quantum criticality.

## Contribution

It demonstrates that hopping significantly influences low-energy physics in iridates, challenging the assumption that strong SOC dominates and highlighting the importance of intra-dimer interactions.

## Key findings

- Hopping reduces spin-orbit excitation energies in 6H iridates.
- Magnetism observed contrary to expected non-magnetic ground state.
- SOC is effectively scaled down to ~0.26 eV, enabling potential quantum criticality.

## Abstract

Investigation of elementary excitations has advanced our understanding of many-body physics governing most physical properties of matter. Recently spin-orbit excitons have drawn much attention, whose condensates near phase transitions exhibit Higgs mode oscillations, a long-sought physical phenomenon [Nat. Phys. {\bf 13}, 633 (2017)]. These critical transition points resulting from competing spin-orbit coupling (SOC), local crystalline symmetry and exchange interactions, are not obvious in Iridium based materials, where SOC prevails in general. Here, we present results of resonant inelastic x-ray scattering on a spin-orbital liquid Ba$_3$ZnIr$_2$O$_9$ and three other 6H-hexagonal perovskite iridates which show magnetism, contrary to non-magnetic singlet ground state expected due to strong SOC. Our results show that substantial hopping between closely placed Ir$^{5+}$ ions within Ir$_2$O$_9$ dimers in these 6H-iridates, modifies spin-orbit coupled states and reduces spin-orbit excitation energies. Here, we are forced to use at least a two-site model, to match the excitation spectrum going in line with the strong intra-dimer hopping. Apart from SOC, low energy physics of iridates is thus critically dependent on hopping, and may not be ignored even for systems having moderate hopping, where the excitation spectra can be explained using an atomic model. SOC which is generally found to be 0.4-0.5~eV in iridates, is scaled in effect down to $\sim$0.26~eV for the 6H-systems, sustaining the hope to achieve quantum criticality by tuning Ir-Ir separation.