Session M53: Invited Session: Iridium-Based Kitaev Materials

Importance of anisotropic exchange interactions in honeycomb iridates. New phenomena due to Kitaev interactions.

We investigate the microscopic nature of the magnetism in honeycomb iridium-based systems. We show that the minimal model describing the magnetism in A$_2$IrO$_3$ includes both isotropic and anisotropic Kitaev-type spin-exchange interactions between nearest and next-nearest neighbor Ir ions, and that the magnitude of the Kitaev interaction between next-nearest neighbor Ir magnetic moments is comparable with nearest neighbor interactions. We computed the low temperature phase diagram of the effective model with classical Monte Carlo simulations. Due to the presence of the anisotropic Kitaev interactions and the frustration introduced by the competition of the spin couplings between nearest and next-nearest neighbors, the resulting phase diagram is very rich. It contains both various commensurate states and incommensurate single-Q and multi-Q phases, whose regions of stability are controlled by the ratios between competing exchange constants. We showed that the second neighbor Kitaev term plays an important role in the stabilization of the commensurate antiferromagnetic zigzag phase which has been experimentally observed in Na$_2$IrO$_3$. In our simulations, we found this phase to be the ground state for parameters of the model of both the correct signs and magnitudes.   

Magnetic and Orbital Excitations in $\alpha $-A$_{2}$IrO$_{3}$ (A $=$ Li, Na) Probed by Resonant Inelastic X-ray Scattering

The honeycomb lattice iridates Na$_{2}$IrO$_{3}$ and Li$_{2}$IrO$_{3}$ are two of the most promising candidates for the experimental realization of Kitaev-like physics. Although the formation of long-range magnetic order (T$_{N} $ $\sim $ 15 K) excludes a pure Kitaev model, there are many extended Kitaev models (which include contributions such as isotropic Heisenberg exchange, further-neighbor interactions, symmetric off-diagonal exchange, and structural distortions) that may be relevant to these materials. We have performed high-resolution Ir L$_{3}$-edge resonant inelastic x-ray scattering (RIXS) measurements to investigate the excitation spectra of Na$_{2}$IrO$_{3}$ and Li$_{2}$IrO$_{3}$. In Na$_{2}$IrO$_{3}$, we observe a new branch of dispersive magnetic excitations, which reaches a maximum energy of $\sim $35 meV at the $\Gamma $ point [1]. This mode is distinct from the low energy ($\sim $6 meV) magnon mode observed in previous inelastic neutron scattering measurements [2], and implies the presence of a significant bond-dependent Kitaev interaction. The d-d excitations in Na$_{2}$IrO$_{3}$ and Li$_{2}$IrO$_{3}$ reveal important information about crystal electric field effects, and the potential impact of trigonal and monoclinic structural distortions [3]. New developments in high pressure RIXS allow us to study the evolution of these excitations up to 6 GPa, providing insight into future prospects for tuning Kitaev interactions via applied pressure.\\[4pt] Work performed in collaboration with H. Gretarsson, J.A. Sears, Y.-J. Kim (University of Toronto), M.H. Upton, J. Kim, Y. Ding, A.H. Said, D. Casa, T. Gog (Argonne National Laboratory), S. Desgreniers (University of Ottawa), Y. Singh (IISER Mohali), S. Manni, P. Gegenwart (University of Gottingen), X. Liu, J.P. Hill (Brookhaven National Laboratory), V.M. Katukuri, L. Hozoi, J. van den Brink (IFW Dresden).\\[4pt] [1] H. Gretarsson et al, Phys. Rev. B 87, 220407(R) (2013).\\[0pt] [2] S.K. Choi et al, Phys. Rev. Lett. 108, 127204 (2012).\\[0pt] [3] H. Gretarsson et al, Phys. Rev. Lett. 110, 076402 (2013).   

Generic spin model for the honeycomb iridates with trigonal distortion

Recently, realizations of Kitaev physics have been sought in the A$_2$IrO$_3$ family of honeycomb iridates, originating from oxygen-mediated exchange through edge-shared octahedra. However, for the j = 1/2 Mott insulator in these materials exchange from direct d-orbital overlap is relevant, and it was proposed that a Heisenberg term should be added to the Kitaev model. Here we provide the generic nearest-neighbour spin Hamiltonian when both oxygen-mediated and direct overlap are present, containing a bond dependent off-diagonal exchanges in addition to Heisenberg and Kitaev terms. We analyze this complete model using a combination of classical techniques and exact diagonalization. Near the Kitaev limit, we find new magnetic phases, 120 degree and incommensurate spiral order, as well as extended regions of zigzag and stripy order. By including a small amount of trigonal distortion, as found in Na$_2$IrO$_3$, we show that such a zigzag phase can be stabilized near the ferromagnetic Kitaev limit. Decreasing the distortion destabilizes the zigzag phase toward a spiral phase that may be relevant for Li$_2$IrO$_3$. Using semi-classical spin-wave calculations we show that this regime is qualitatively consistent with experimentally known features of the dynamical structure factor in Na$_2$IrO$_3$ and speculate on implications for Li$_2$IrO$_3$.   

Magnetic properties of hexagonal iridates

Hexagonal iridates A$_{\mathrm{2}}$IrO$_{\mathrm{3}}$ (A$=$Na, Li) are discussed in the context of realizing magnetic Kitaev exchange between j$=$1/2 moments. This talk reports experimental investigation of magnetic properties of Na$_{\mathrm{2}}$IrO$_{\mathrm{3}}$ and $\alpha $-Li$_{\mathrm{2}}$IrO$_{\mathrm{3}}$, crystallizing in a layered honeycomb structure, as well as, the related ``hyper-honeycomb'' $\beta $-Li$_{\mathrm{2}}$IrO$_{\mathrm{3}}$. For the latter material, very recent magnetic resonant X-ray diffraction experiments allowed a complete solution of the magnetic structure. Incommensurate magnetic order with non-coplanar and counter-rotating Ir moments are found, similar as also realized in another polytype, the ``stripyhoneycomb'' $\gamma $-Li$_{\mathrm{2}}$IrO$_{\mathrm{3}}$. Theoretically, such structure is stabilized by dominant Kitaev interactions. The similarities between the two materials which share similar local connectivity between the Ir neighbors suggest dominating Kitaev magnetic exchange in both materials. Work in collaboration with F. Freund, S. Manni, Y. Singh, S. Choi and R. Coldea.