Two iridates, two models, two approaches: a comparative study on magnetism in 3D honeycomb materials

TL;DR

This study compares different models and methods to understand magnetism in 3D honeycomb iridates, revealing consistent predictions for one compound and method-dependent results for another, with insights from 1D quantum models.

Contribution

It systematically analyzes two models and two approaches across both materials, clarifying their predictive consistency and the role of specific interactions in magnetic ordering.

Findings

The $JK\Gamma$ model predicts the experimental phase of $eta$-Li$_2$IrO$_3$ reliably.

The phase of $\gamma$-Li$_2$IrO$_3$ can be reproduced by soft-spin analysis with eigenmode mixing.

In 1D models, incommensurate correlations survive quantum effects only with symmetric-off-diagonal exchange $\Gamma$.

Abstract

Two recent theoretical works studied the role of Kitaev interactions in the newly observed incommensurate magnetic order in the hyper-honeycomb ($\beta$-Li$_2$IrO$_3$) and stripy-honeycomb ($\gamma$-Li$_2$IrO$_3$) iridates. Each of these works analyzed a different model ($JK\Gamma$ 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 3D honeycomb iridates. Through comparisons between all combinations of models, techniques, and materials, we find that the bond-isotropic $JK\Gamma$ model consistently predicts the experimental phase of $\beta$-Li$_2$IrO$_3$ regardless of the method used, while the experimental phase of $\gamma$-Li$_2$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 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 $\Gamma$ found in the $JK\Gamma$ model. The relevance of these results to the real materials are also discussed.