Abstract
Spins often prefer to anti-align with their neighbors in antiferromagnetic correlation. Materials with triangle lattices exhibit energetic degeneracy among the possible rearrangements of anti-aligned spins, which is denoted geometric frustration that is associated with strongly depressed transitions to magnetic order. Honeycomb iridates and ruthenates, pyrochlore systems, and double-perovskite iridates all feature triangular lattices as primary building blocks of their structures. Another frustration mechanism evolves from the Kitaev’s exact solution of a spin-liquid model on a honeycomb lattice with strong spin-orbit interactions. The protracted search for a Kitaev spin liquid has recently focused on the honeycomb itidates Na2IrO3 and Li2IrO3. A newer kind of quantum liquid has been identified in the magnetic insulator Ba4Ir3O10, where Ir3O12 trimers form an unfrustrated square lattice.
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