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With large spin-orbit coupling, the $t_{2g}^5$ electron configuration in$d$-metal oxides is prone to highly anisotropic exchange interactions andexotic magnetic properties. In $5d^5$ iridates, given the existing variety ofcrystal structures, the magnetic anisotropy can be tuned from antisymmetric tosymmetric Kitaev-type, with interaction strengths that outsize the isotropicterms. By many-body electronic-structure calculations we here address thenature of the magnetic exchange and the intriguing spin-glass behavior ofLi$_2$RhO$_3$, a $4d^5$ honeycomb oxide. For pristine crystals without Rh-Lisite inversion, we predict a dimerized ground state as in the isostructural$5d^5$ iridate Li$_2$IrO$_3$, with triplet spin dimers effectively placed on afrustrated triangular lattice. With Rh-Li anti-site disorder, we explain theobserved spin-glass phase as a superposition of different, nearly degeneratesymmetry-broken configurations.

Strong magnetic frustration and anti-site disorder causing spin-glass behavior in honeycomb Li2RhO3