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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 $sim1.2mu_B$. 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 $sim2.3mu_B$ 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.
The topological property of SrRu$_2$O$_6$ and isostructural CaOs$_2$O$_6$ under various strain conditions is investigated using density functional theory. Based on an analysis of parity eigenvalues, we anticipate that a three-dimensional strong topol
The high temperature magnetic order in SrRu$_2$O$_6$ was studied by measuring magnetization and neutron powder diffraction with both polarized and unpolarized neutrons. SrRu$_2$O$_6$ crystallizes into the hexagonal lead antimonate (PbSb$_2$O$_6$, spa
We have explored the magnetism in the non-geometrically frustrated spin-chain system $gamma$-CoV$_{2}$O$_{6}$ which possesses a complex magnetic exchange network. Our neutron diffraction patterns at low temperatures ($T$ $leqslant$ $T_{mathrm{N}}$ =
The current family of experimentally realized two-dimensional magnetic materials consist of 3$d$ transition metals with very weak spin-orbit coupling. In contrast, we report a new platform in a chemically bonded and layered 4$d$ oxide, with strong el
The dimerized quantum magnet BaCuSi$_2$O$_6$ was proposed as an example of dimensional reduction arising near the magnetic-field-induced quantum critical point (QCP) due to perfect geometrical frustration of its inter-bilayer interactions. We demonst