# Critical properties of the Kitaev-Heisenberg model

A prominent example of anisotropic spin-orbital models is the Kitaev-Heisenberg (KH) model on

the honeycomb lattice [1,2]. This model was proposed as the minimal model to describe the low-

energy physics of the quasi two-dimensional compounds, Na2IrO3 and Li2IrO3. In these compounds,

Ir4+ ions are in a low spin 5d5 conguration and form weakly coupled hexagonal layers. Due to

strong SOC, the atomic ground state is a doublet where the spin and orbital angular momenta of Ir4+

ions are coupled into Je

= 1=2. The KH model describing the interactions between Je

moments

contains two competing nearest neighbor interactions: an isotropic antiferromagnetic Heisenberg

exchange interaction originated mainly from direct direct overlap of Ir t2g orbitals and a highly

anisotropic Kitaev exchange interaction [3] which originates from hopping between Ir t2g and O 2p

orbitals via the charge-transfer gap.

We study critical properties of the KH model on the honeycomb lattice at nite temperatures [4,5].

The model undergoes two phase transitions as a function of temperature. At low temperature,

thermal uctuations induce magnetic long-range order by order-by-disorder mechanism. This mag-

netically ordered state with a spontaneously broken Z6 symmetry persists up to a certain critical

temperature. We nd that there is an intermediate phase between the low-temperature, ordered

phase and the high-temperature, disordered phase. Finite-size scaling analysis suggests that the

intermediate phase is a critical Kosterlitz-Thouless phase with continuously variable exponents. We

argue that the intermediate phase has been likely observed above the magnetically ordered phase

in A2IrO3 compounds.

[1] G. Jackeli and G. Khaliullin, Phys. Rev. Lett. 102, 017205 (2009).

[2] J. Chaloupka, G. Jackeli, and G. Khaliullin, Phys. Rev. Lett. 105, 027204 (2010).

[3] A. Kitaev, Ann. Phys. 321, 2 (2006).

[4] C. Price and N. B. Perkins, Phys. Rev. Lett. 109, 187201 (2012).

[5] C. Price and N. B. Perkins, Phys. Rev. B 88, 024410 (2013).

- Last modified: 30/04/2014