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We report structural studies of the spin-orbit Mott insulator family K$_x$Ir$_y$O$_2$, with triangular layers of edge-sharing IrO$_6$ octahedra bonded by potassium ions. The potassium content acts as a chemical tuning parameter to control the amount of charge in the Ir-O layers. Unlike the isostructural families with Ir replaced by Co or Rh ($y=1$), which are metallic over a range of potassium compositions $x$, we instead find insulating behaviour with charge neutrality achieved via iridium vacancies, which order in a honeycomb supercell above a critical composition $x_c$. By performing density functional theory calculations we attribute the observed behaviour to a subtle interplay of crystal-field environment, local electronic correlations and strong spin-orbit interaction at the Ir$^{4+}$ sites, making this structural family a candidate to display Kitaev magnetism in the experimentally unexplored regime that interpolates between triangular and honeycomb structures.
We investigate topological transport in a spin-orbit coupled bosonic Mott insulator. We show that interactions can lead to anomalous quasi-particle dynamics even when the spin-orbit coupling is abelian. To illustrate the latter, we consider the spin-
Spin-orbit entangled magnetic dipoles, often referred to as pseudospins, provide a new avenue to explore novel magnetism inconceivable in the weak spin-orbit coupling limit, but the nature of their low-energy interactions remains to be understood. We
The concept of the entanglement between spin and orbital degrees of freedom plays a crucial role in understanding various phases and exotic ground states in a broad class of materials, including orbitally ordered materials and spin liquids. We invest
Using ab initio calculations, we have investigated an insulating tetragonally distorted perovskite BaCrO$_3$ with a formal $3d^2$ configuration, the volume of which is apparently substantially enhanced by a strain due to SrTiO$_3$ substrate. Inclusio
Complex oxides with $4d$ and $5d$ transition-metal ions recently emerged as a new paradigm in correlated electron physics, due to the interplay between spin-orbit coupling and electron interactions. For $4d$ and $5d$ ions, the spin-orbit coupling, $z