# Localized-itinerant dichotomy and unconventional magnetism in SrRu$_2$O$_6$

## TL;DR

This study combines DFT and DMFT to reveal that SrRu$_2$O$_6$ exhibits a coexistence of localized and itinerant electrons, with strong hybridization and orbital effects influencing its magnetic properties and high Neel temperature.

## Contribution

It provides a detailed theoretical analysis of SrRu$_2$O$_6$, highlighting the role of hybridization, orbital splitting, and correlation effects in its unconventional magnetism and electron behavior.

## Key findings

- Small ordered magnetic moment (~1.2 μB) due to hybridization and valence shift.
- Finite local moments (~2.3 μB) persist across temperatures.
- Theoretical Neel temperature (~700 K) aligns with experiments.

## Abstract

Electron correlations tend to generate local magnetic moments that usually order if the lattices are not too frustrated. The hexagonal compound SrRu$_2$O$_6$ has a relatively high Neel temperature but small local moments, which seem to be at odds with the nominal valence of Ru$^{5+}$ in the $t_{2g}^3$ configuration. Here, we investigate the electronic property of SrRu$_2$O$_6$ using density functional theory (DFT) combined with dynamical-mean-field theory (DMFT). We find that the strong hybridization between Ru $d$ and O $p$ states results in a Ru valence that is closer to $+4$, leading to the small ordered moment $\sim1.2\mu_B$. While this is consistent with a DFT prediction, correlation effects are found to play a significant role. The local moment per Ru site remains finite $\sim2.3\mu_B$ in the whole temperature range investigated. Due to the lower symmetry, the $t_{2g}$ manifold is split and the quasiparticle weight is renormalized significantly in the $a_{1g}$ state, while the renormalization in $e_g'$ states is about a factor of 2--3 weaker. Our theoretical Neel temperature $\sim700$~K is in reasonable agreement with experimental observations. SrRu$_2$O$_6$ is a unique system in which localized and itinerant electrons coexist with the proximity to an orbitally-selective Mott transition within the $t_{2g}$ sector.