Ground state properties of $\mathrm{N}{\mathrm{a}}_2\mathrm{Ir}{\mathrm{O}}_3$ determined from $\text{ab initio}$ Hamiltonian and its extensions containing Kitaev and extended Heisenberg interactions

Abstract

We investigate the ground state properties of $\mathrm{N}{\mathrm{a}}_2\mathrm{Ir}{\mathrm{O}}_3$ based on numerical calculations of the recently proposed {\it ab initio} Hamiltonian represented by Kitaev and extended Heisenberg interactions. To overcome the limitation posed by small tractable system sizes in the exact diagonalization study employed in a previous study (Yamaji $\text{et al.}$, Phys. Rev. Lett. $\text{113}$, 107201 (2014)), we apply two-dimensional density matrix renomalization group, and infinite-size tensor-network method. By calculating at much larger system sizes, we critically test the validity of the exact diagonalization results. The results consistently indicate that the ground state of $\mathrm{N}{\mathrm{a}}_2\mathrm{Ir}{\mathrm{O}}_3$ is a magnetically ordered state with zigzag configuration in agreement with experimental observations and the previous diagonalization study. Applications of the two independent methods in addition to the exact diagonalization study further uncover a consistent and rich phase diagram near the zigzag phase beyond the accessibility of the exact diagonalization. For example, in the parameter space away from the $\text{ab initio}$ value of $\mathrm{N}{\mathrm{a}}_2\mathrm{Ir}{\mathrm{O}}_3$ controlled by the trigonal distortion, we find three phases: (i) an ordered phase with the magnetic moment aligned mutually in $120$ degrees orientation on every third hexagon, (ii) a magnetically ordered phase with a $16$-site unit-cell, and (iii) an ordered phase with presumably incommensurate periodicity of the moment. It suggests that potentially rich magnetic structures may appear in $A_2\mathrm{Ir}{\mathrm{O}}_3$ compounds for $A$ other than Na. The present results also serve to establish the accuracy of the first-principles approach in reproducing the available experimental results thereby further contribute to find a route to realize the Kitaev spin liquid.

14 pages, 11 figures

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• Theory of a quantum spin liquid in hydrogen-intercalated honeycomb iridate, H3LiIr2O6
• Interlayer Coupling Effect on a Bilayer Kitaev Model
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• Topological phase transition to Abelian anyon phases due to off-diagonal exchange interaction in the Kitaev spin liquid state
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• TeNeS: Tensor Network Solver for Quantum Lattice Systems
• Ground state phase diagram of Kitaev-Heisenberg model on honeycomb-triangular lattice
• First-principles Study on the Magnetic Interactions in Honeycomb Na2IrO3
• Thermal Hall conductivity with sign change in the Heisenberg-Kitaev kagome magnet
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