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Non-van der Waals honeycomb antiferromagnet SrRu$_2$O$_6$ down to a few layers

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 Added by Ashna Bajpai
 Publication date 2019
  fields Physics
and research's language is English




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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 electron correlations and competing spin-orbit coupling. We synthesize ultra-thin sheets of SrRu$_2$O$_6$ using scalable liquid exfoliation. These exfoliated sheets are characterized by complementary experimental and theoretical techniques. The thickness of the nano-sheets varies between three to five monolayers, and within the first-principles calculations, we show that antiferromagnetism survives in these ultra-thin layers. Experimental data suggest that exfoliation occurs from the planes perpendicular to the $c$-axis as the intervening hexagonal Sr-lattice separates the two-dimensional magnetic honeycomb Ru-layers. The high-resolution transmission electron microscope images indicate that the average inter-atomic spacing between the Ru-layers is slightly reduced, which agrees with the present calculations. The signatures of rotational stacking of the nanosheets are also observed. Such new two-dimensional platform offers enormous possibilities to explore emergent properties that appear due to the interplay between magnetism, strong correlations and spin-orbit coupling. Moreover, these effects can be further tuned as a function of layer thickness.



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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$_6$, space group textit{P}$overline{3}$1textit{m}) structure with layers of edge-sharing RuO$_6$ octahedra separated by Sr$^{2+}$ ions. SrRu$_2$O$_6$ orders at $T_N$=565,K with Ru moments coupled antiferromagnetically both in-plane and out-of-plane. The magnetic moment is 1.30(2) $mu_mathrm{B}$/Ru at room temperature and is along the crystallographic textit{c}-axis in the G-type magnetic structure. We performed density functional calculations with constrained RPA to obtain the electronic structure and effective intra- and inter-orbital interaction parameters. The projected density of states show strong hybridization between Ru 4$d$ and O 2$p$. By downfolding to the target $t_{2g}$ bands we extracted the effective magnetic Hamiltonian. We performed Monte Carlo simulations to determine the transition temperature as a function of inter- and intra-plane couplings and find weak inter plane coupling, 3% of the intra-plane coupling, permits three dimensional magnetic order at $T_N$. As suggested by the magnetic susceptibility, two-dimensional correlations persist above $T_N$ due to the strong intra-plane coupling.
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The electronic structure in unconventional superconductors holds a key to understand the momentum-dependent pairing interactions and the resulting superconducting gap function. In superconducting Fe-based chalcogenides, there have been controversial results regarding the importance of the $k_z$ dependence of the electronic dispersion, the gap structure and the pairing mechanisms of iron-based superconductivity. Here, we present a detailed investigation of the van der Waals interaction in FeSe and its interplay with magnetic disorder and real space structural properties. Using density functional theory we show that they need to be taken into account upon investigation of the 3-dimensional effects, including non-trivial topology, of FeSe$_{1-x}$Te$_x$ and FeSe$_{1-x}$S$_x$ systems. In addition, the impact of paramagnetic (PM) disorder is considered within the spin-space average approach. Our calculations show that the PM relaxed structure supports the picture of different competing ordered magnetic states in the nematic regime, yielding magnetic frustration.
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 topological insulating state should be realized when band inversion is induced at the A point in the hexagonal Brillouin zone. For SrRu$_2$O$_6$, such a transition requires rather unrealistic tuning, where only the $c$ axis is reduced while other structural parameters are unchanged. However, given the larger spin-orbit coupling and smaller lattice constants in CaOs$_2$O$_6$, the desired topological transition does occur under uniform compressive strain. Our study paves a way to realize a topological insulating state in a complex oxide, which has not been experimentally demonstrated so far.
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