Spin-orbit physics ofj=12Mott insulators on the triangular lattice

Abstract

The physics of spin-orbital entanglement in effective j = 1/2 Mott insulators, which have been experimentally observed for various 5d transition metal oxides, has sparked an interest in Heisenberg-Kitaev (HK) models thought to capture their essential microscopic interactions. Here we argue that the recently synthesized Ba3IrTi2O9 is a prime candidate for a microscopic realization of the triangular HK model -a conceptually interesting model for its interplay of geometric and exchange frustration. We establish that an infinitesimal Kitaev exchange destabilizes the 120 • order of the quantum Heisenberg model. This results in the formation of an extended Z2-vortex crystal phase in the parameter regime most likely relevant to the real material, which can be experimentally identified with spherical neutron polarimetry. Moreover, using a combination of analytical and numerical techniques we map out the entire phase diagram of the model, which further includes various ordered phases as well as an extended nematic phase around the antiferromagnetic Kitaev point.

Kitaev anisotropy induces mesoscopicZ2vortex crystals in frustrated hexagonal antiferromagnets

“…This means that the stability region of the Z 2 VC phase should shrink by fluctuations, provided the corresponding effect of fluctuations of the Z 2 VC phases themselves is weak enough (close to the boundaries). This scenario is confirmed by the numerical results of Becker et al 57 , for the boundary with the AF Kitaev phase and for S = 1/2 spins. Let us now turn to possible realizations.…”

Semiclassical ground-state phase diagram andmulti-Qphase of a spin-orbit-coupled model on triangular lattice

“…For example, in the Kitaev-Heisenberg model on the triangular lattice, once a finite Kitaev exchange coupling is added to the antiferromagnetic Heisenberg interaction, the Néel AFM ground state immediately becomes unstable to an incommensurate Z 2 vortex crystal. 22,23 This is clearly seen in the spin-wave spectrum of the Néel AFM state, which is destabilized around M point of the Brilluion zone as soon as the system goes away from the Heisenberg point. Interestingly, the nature of the incommensurate state is closely connected to the properties of its parent state.…”

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

“…[39], we have uncovered intriguing discontinuous commensurate-incommensurate transitions and novel triple-Q incommensurate zigzag states at high magnetic field. We show that while our findings are reminiscent of the Z 2 vortex crystal one encounters in looking at the tri-angular KH model, 44,45 which arises from the commensurate 120 • state through a kind of a nucleation transition, in our case the origin of the incommensurate zigzag state is different and is driven partly by entropic selection.…”