Heisenberg-Kitaev models on hyperhoneycomb and stripy-honeycomb lattices: 3D-2D equivalence of ordered states and phase diagrams

@article{Krger2019HeisenbergKitaevMO,
  title={Heisenberg-Kitaev models on hyperhoneycomb and stripy-honeycomb lattices: 3D-2D equivalence of ordered states and phase diagrams},
  author={Wilhelm G. F. Kr{\"u}ger and Matthias Vojta and Lukas Janssen},
  journal={Physical Review Research},
  year={2019}
}
We discuss magnetically ordered states, arising in Heisenberg-Kitaev and related spin models, on three-dimensional (3D) harmonic honeycomb lattices. For large classes of ordered states, we show that they can be mapped onto two-dimensional (2D) counterparts on the honeycomb lattice, with the classical energetics being identical in the 2D and 3D cases. As an example, we determine the phase diagram of the classical nearest-neighbor Heisenberg-Kitaev model on the hyperhoneycomb lattice in a… 

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References

SHOWING 1-10 OF 56 REFERENCES

Heisenberg-Kitaev model on the hyperhoneycomb lattice

Motivated by recent experiments on $\beta-$Li$_2$IrO$_3$, we study the phase diagram of the Heisenberg-Kitaev model on a three dimensional lattice of tri-coordinated Ir$^{4+}$, dubbed the

Theory of magnetic phase diagrams in hyperhoneycomb and harmonic-honeycomb iridates

Motivated by recent experiments, we consider a generic spin model in the $j_{\text{eff}}=1/2$ basis for the hyperhoneycomb and harmonic-honeycomb iridates. Based on microscopic considerations, the

Hidden symmetries of the extended Kitaev-Heisenberg model:Implications for the honeycomb-lattice iridates A2IrO3

We have explored the hidden symmetries of a generic four-parameter nearest-neighbor spin model, allowed in honeycomb-lattice compounds under trigonal compression. Our method utilizes a systematic

Unconventional magnetic order on the hyperhoneycomb Kitaev lattice inβ−Li2IrO3: Full solution via magnetic resonant x-ray diffraction

The recently-synthesized iridate $\beta$-Li$_2$IrO$_3$ has been proposed as a candidate to display novel magnetic behavior stabilized by frustration effects from bond-dependent, anisotropic

Honeycomb-Lattice Heisenberg-Kitaev Model in a Magnetic Field: Spin Canting, Metamagnetism, and Vortex Crystals.

This work maps out the classical phase diagram for different directions of the magnetic field using a combination of Monte Carlo simulations and spin-wave theory, and finds various large-unit-cell and multi-Q phases including a vortex-crystal phase for a field in the [111] direction.

Magnetization processes of zigzag states on the honeycomb lattice: Identifying spin models for α − RuCl 3 and Na 2 IrO 3

We study the field-induced magnetization processes of extended Heisenberg-Kitaev models on the honeycomb lattice, taking into account off-diagonal and longer-range exchange interactions, using a

Unified theory of spiral magnetism in the harmonic-honeycomb iridates α ,β , and γ Li 2 IrO 3

A family of insulating iridates with chemical formula Li$_2$IrO$_3$ has recently been discovered, featuring three distinct crystal structures $\alpha,\beta,\gamma$ (honeycomb, hyperhoneycomb,

Order-by-disorder and magnetic field response in the Heisenberg-Kitaev model on a hyperhoneycomb lattice

We study the finite-temperature phase diagram of the Heisenberg-Kitaev model on a three-dimensional hyperhoneycomb lattice. Using semiclassical analysis and classical Monte Carlo simulations, we

Kitaev-Heisenberg model in a magnetic field: Order-by-disorder and commensurate-incommensurate transitions

We present a theoretical study of field-induced magnetic phases in the honeycomb Kitaev-Heisenberg model, which is believed to describe the essential physics of Mott insulators with strong spin-orbit

Field-induced intertwined orders in 3D Mott-Kitaev honeycomb $β$-Li2IrO3

Honeycomb iridates are thought to have strongly spin-anisotropic exchange interactions that could lead to an extraordinary state of matter known as the Kitaev quantum spin liquid. The realization of
...