• DOI:10.1103/PhysRevB.93.184420
• Corpus ID: 118612306

Two iridates, two models, and two approaches: A comparative study on magnetism in three-dimensional honeycomb materials

@article{Lee2016TwoIT,
  title={Two iridates, two models, and two approaches: A comparative study on magnetism in three-dimensional honeycomb materials},
  author={Eric Kin-Ho Lee and Jeffrey G. Rau and Yong Baek Kim},
  journal={Physical Review B},
  year={2016},
  volume={93},
  pages={184420}
}

• Eric Kin-Ho Lee, J. Rau, Yong Baek Kim
• Published 22 June 2015
• Materials Science
• Physical Review B

Two recent theoretical works studied the role of Kitaev interactions in the newly observed incommensurate magnetic order in the hyper-honeycomb ($\ensuremath{\beta}\ensuremath{-}{\mathrm{Li}}_{2}{\mathrm{IrO}}_{3}$) and stripy-honeycomb ($\ensuremath{\gamma}\ensuremath{-}{\mathrm{Li}}_{2}{\mathrm{IrO}}_{3}$) iridates. Each of these works analyzed a different model ($JK\mathrm{\ensuremath{\Gamma}}$ versus coupled zigzag chain model) using a contrasting method (classical versus soft-spin analysis). The lack of commonality between these works precludes meaningful comparisons and a proper understanding of these unusual orderings. In this study, we complete the unfinished picture initiated by these two works by solving both models with both approaches for both three-dimensional (3D) honeycomb iridates. Through comparisons between all combinations of models, techniques, and materials, we find that the bond-isotropic $JK\mathrm{\ensuremath{\Gamma}}$ model consistently predicts the experimental phase of $\ensuremath{\beta}\ensuremath{-}{\mathrm{Li}}_{2}{\mathrm{IrO}}_{3}$ regardless of the method used, while the experimental phase of $\ensuremath{\gamma}\ensuremath{-}{\mathrm{Li}}_{2}{\mathrm{IrO}}_{3}$ can be generated by the soft-spin approach with eigenmode mixing irrespective of the model used. To gain further insights, we solve a one-dimensional (1D) quantum spin-chain model related to both 3D models using the density matrix renormalization group method to form a benchmark. We discover that in the 1D model, incommensurate correlations in the classical and soft-spin analysis survive in the quantum limit only in the presence of the symmetric-off-diagonal exchange $\mathrm{\ensuremath{\Gamma}}$ found in the $JK\mathrm{\ensuremath{\Gamma}}$ model. The relevance of these results to the real materials is also discussed.