| Augmented by electronic correlations, spin orbit coupling in certain geometries can generate unusual quantum frustration. One appealing possibility is the Kitaev-Heisenberg family of Hamiltonians, originally proposed for the layered honeycomb iridate Mott insulators. We identify a number of potential structures for iridates with edge-sharing IrO6 octahedra where such magnetic exchanges may arise, studying their phase diagrams within semiclassical and mean field approximations, supplemented by a duality transformation for which we expose a Z2xZ2 geometrical structure. Motivated by possible experimental realizations, we also investigate the zero and finite temperature properties of the spin liquid phase in certain such quantum Hamiltonians and solve for the full quantum phase diagram in an appropriate limit, capturing a rich variety of behaviors. |
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