Relevance of the Heisenberg-Kitaev model for the honeycomb lattice iridates A_2IrO_3 (1106.0429v2)

Abstract: Combining thermodynamic measurements with theoretical density functional and thermodynamic calculations we demonstrate that the honeycomb lattice iridates A2IrO3 (A = Na, Li) are magnetically ordered Mott insulators where the magnetism of the effective spin-orbital S = 1/2 moments can be captured by a Heisenberg-Kitaev (HK) model with Heisenberg interactions beyond nearest-neighbor exchange. Experimentally, we observe an increase of the Curie-Weiss temperature from \theta = -125 K for Na2IrO3 to \theta = -33 K for Li2IrO3, while the antiferromagnetic ordering temperature remains roughly the same T_N = 15 K for both materials. Using finite-temperature functional renormalization group calculations we show that this evolution of \theta, T_N, the frustration parameter f = \theta/T_N, and the zig-zag magnetic ordering structure suggested for both materials by density functional theory can be captured within this extended HK model. Combining our experimental and theoretical results, we estimate that Na2IrO3 is deep in the magnetically ordered regime of the HK model (\alpha \approx 0.25), while Li2IrO3 appears to be close to a spin-liquid regime (0.6 < \alpha < 0.7).

• The paper demonstrates that Na2IrO3 and Li2IrO3 exhibit Mott insulating behavior with T_N around 15 K and distinct Curie-Weiss temperatures.
• The paper employs an extended Heisenberg-Kitaev model incorporating second- and third-neighbor exchanges, validated by FRG and DFT analyses.
• The paper highlights that Li2IrO3's proximity to a spin-liquid regime offers potential for tuning quantum states with implications for quantum computing.

Relevance of the Heisenberg-Kitaev Model for Honeycomb Lattice Iridates $A_2$IrO$_3$

The paper "Relevance of the Heisenberg-Kitaev model for the honeycomb lattice iridates $A_2$IrO$_3$" explores the magnetic properties of $A_2$IrO$_3$ compounds (where $A = \text{Na, Li}$), providing essential insights into the behavior of these materials as spin-orbit-coupled Mott insulators. Utilizing a combination of experimental thermodynamic measurements, density functional theory (DFT), and functional renormalization group (FRG) calculations, the paper aims to capture the magnetic interactions in these materials through an extended Heisenberg-Kitaev (HK) model.

Key Findings

1. Magnetic Characterization: The research provides robust thermodynamic evidence supporting that both Na$_2$IrO$_3$ and Li$_2$IrO$_3$ exhibit Mott insulating behavior with antiferromagnetic ordering temperatures ($T_N$) of approximately 15 K. Curie-Weiss temperature ($\theta$) values indicate effective spin-$\frac{1}{2}$ moments, with $\theta$ swinging from $-125$ K for Na$_2$IrO$_3$ to $-33$ K for Li$_2$IrO$_3$.
2. Theoretical Modeling: The extended HK model implemented accounts for Heisenberg interactions beyond nearest-neighbor exchanges (next-nearest ($J_2$) and next-to-next-nearest ($J_3$) neighbor interactions). Functional renormalization group calculations show that Na$_2$IrO$_3$ is located in the magnetically ordered regime of the HK model ($\alpha \approx 0.25$), while Li$_2$IrO$_3$ is adjacent to a spin-liquid regime ($0.6 \leq \alpha \leq 0.7$).
3. Experimental-Model Agreement: The evolution of thermodynamic properties in both compounds is well-captured by the extended HK model, revealing consistency in the ordering nature and thermodynamic scales such as $\theta$, $T_N$, and the frustration parameter $f$, leading to a comprehensive perspective of the magnetic phase space in these iridates.

Implications

The research suggests pivotal implications for understanding the magnetic properties of iridates, highlighting the significance of the spin-orbital interaction and the presence of extended Heisenberg exchanges. The articulation of the Na and Li variants against the backdrop of the HK model provides a contextual framework that highlights how specific model parameters correlate with observable magnetic ordering and potential states. Furthermore, the strong computational insights affirm that the observed zig-zag order in these materials, which appears inconsistent in a simplistic HK model, finds explanation upon considering further neighbor interactions.

Future Directions

The proximity of Li$_2$IrO$_3$ to the spin-liquid regime is particularly intriguing as it suggests possible avenues for experimental manipulations, such as applied pressure or chemical tuning, to transition the material into a non-magnetic spin-liquid state. Such states are of great interest for the realization of quantum computing applications through the exploitation of emergent quantum spin phenomena like Majorana fermions.

In conclusion, the integration of experimental observations with advanced theoretical models in this work establishes a comprehensive understanding of the magnetic properties and underlying physics of $A_2$IrO$_3$ compounds, providing a rich platform for exploration within the field of spin-orbit coupled systems.