Session D19: Invited Session: Novel Phases in Strongly Correlated Iridates

Spin orbit coupling, electron correlations and exotic magnetism in 5d complex Ir oxides

In 5d Iridium oxides, a large spin-orbit coupling of $\sim $ 0.5 eV, inherent to heavy 5d elements, is not small as compared with the width of d bands and often modifies the landscape of the electronic structure substantially. This is distinct from those of 3d transition metal oxides and gives rise to a variety of novel electronic phases. Layered Ir$^{4+}$ perovskite Sr$_{2}$IrO$_{4}$ is recently revealed to be a novel J$_{eff}$=1/2 Mott insulator [1,2], where even a moderate Coulomb U can open up a correlation gap because of the large spin-orbit coupling. In the three dimensional analogue of Sr$_{2}$IrO$_{4}$, SrIrO$_{3, }$ the large spin-orbit coupling manifests itself in a contrasted way, where the interplay of strong spin-orbit coupling and lattice distortions brings the system almost to a band insulator. SrIrO$_{3}$ is in fact a very low carrier density semimetal with unusual transport and magnetic properties. If J$_{eff}$=1/2 Ir$^{4+}$ is placed on a honeycomb lattice or a geometrically frustrated lattice such as pyrochlore lattice, even more exotic states might be anticipated, including a correlated topological insulator [3] and a Kiteav magnet [4]. Our attempt to explore such spin-orbit coupling induced states will be reported.\\[4pt] Work done in collaboration with T. Takayama, B.J.Kim, S.Fujiyama, K.Ohashi, J.Matsuno, H.Osumi and T.Arima. \\[4pt] [1] B.J.Kim et al., Phys Rev Lett 101, 076402 (2008). \\[0pt] [2] B. J. Kim, H. Ohsumi, T. Komesu, S. Sakai, T. Morita, H. Takagi, and T. Arima, Science 323, 1329 (2009). \\[0pt] [3] Shitade et al., Phys. Rev. Lett. 102, 256403 (2009). \\[0pt] [4] J. Chaloupka, G.Jackeli, and G.Khaliullin, Phys. Rev. Lett. 105, 027204 (2010)   

Topological and spin-liquid phases in strongly correlated iridates

Recently, the emergence of topological phases in interacting electron systems such as topological insulators and spin liquid phases, has been a subject of intensive research. In particular, much attention has been given to 5d transition metal oxides where the strong spin-orbit coupling and intermediate strength of the electron interaction provide an ideal playground for the emergence of a number of interesting topological phases. We summarize recent theoretical efforts in this direction in the context of Iridates, or iridium oxides. We make connections to the existing and future experiments on a variety of iridates materials including pyrochlore iridates, honeycomb-lattice iridates, and hyperkagome-lattice systems.   

Possible proximity of the Iridates (Na,Li)$_2$IrO$_3$ to a topologically ordered Mott insulator: Phase diagram of the Heisenberg-Kitaev model

Motivated by the recent experimental observation of a Mott insulating state for the layered Iridates (Na,Li)$_2$IrO$_3$, we discuss possible ordering states of the effective Iridium moments taking into account the extreme sensitivity of these 5d transition metal oxides to crystal field effects and strong spin-orbit coupling. The microscopic exchange has been argued [1,2] to be a combination of isotropic Heisenberg and highly anisotropic Kitaev exchange, which can be tracked back to the spin and orbital components of the effective momenta. Depending on the relative strength of these two couplings, the system exhibits either various types of conventional magnetic order or a more exotic gapless spin-liquid ground state. Carefully studying [3] the stability of these phases at finite-temperatures -- and the role of frustration, i.e. a considerable suppression of the ordering temperature from the Curie-Weiss temperature -- allows us to connect back to thermodynamic experiments [4] on the Iridates (Na,Li)$_2$IrO$_3$ and possibly estimate microscopic coupling parameters. Finally, we discuss the effects of a magnetic field applied in the [111] direction -- perpendicular to the hexagonal lattice formed by the Iridium moments -- and show that a topologically ordered ground state is found over a small range of coupling parameters [5], also indicating the existence of an exotic critical point whose location might not be far from actual material parameters.\\[4pt] Work done in collaboration with H.C. Jiang, Z.C. Gu, X.L. Qi, J. Reuther, and R. Thomale.\\[4pt] [1] G. Jackeli and G. Khaliullin, Phys. Rev. Lett. 102, 017205 (2009). \\[0pt] [2] J. Chaloupka, G. Jackeli, and G. Khaliullin, Phys. Rev. Lett. 105, 027204 (2010). \\[0pt] [3] J. Reuther, R. Thomale, and S. Trebst, Phys. Rev. B 84, 100406(R) (2011).\\[0pt] [4] Y. Singh, S. Manni, and P. Gegenwart, arXiv:1106.0429\\[0pt] [5] H.C. Jiang, Z.C. Gu, X.L. Qi, and S. Trebst, Phys. Rev. B 83, 245104 (2011).   

Honeycomb lattice spin-orbit Mott insulators

Iridates displaying a Mott insulating state caused by the interplay of electronic correlations and strong spin-orbit coupling have recently attracted considerable attention. We focus on the honeycomb material A$_{2}$IrO$_{3}$ (A=Na, Li), in which the topology of the underlying lattice leads to interesting magnetic properties [1]. The strong spin-orbit coupling in this 5d transition metal system is expected to result in orbital-dependent highly anisotropic magnetic in-plane exchange [2]. The combination of J$_{eff}$ = 1/2 and the underlying honeycomb lattice makes A$_{2}$IrO$_{3}$ a promising candidate for the Kitaev model, which is exactly solvable and has a spin-liquid ground state. Our experimental data on Na$_{2}$IrO$_{3}$ prove a Mott insulating state of effective J=1/2 moments with predominant antiferromagnetic coupling, indicated by a Weiss temperature of $\theta =-$120 K. A bulk antiferromagnetic transition occurs at a much reduced temperature of T$_{N}$ = 15 K and the reduced magnetic entropy suggests strong magnetic frustration and/or low-dimensional magnetic interactions. The nature of the ordered phase has also been studied by resonant x-ray spectroscopy near the Ir-L3 edge, providing evidence for an unconventional, most-likely zig-zag-type spin ordering [3]. The latter may be related to next-nearest neighbour exchange and/or a substantial Kitaev contribution in the Heisenberg-Kitaev model [2]. Upon replacing Na with the smaller Li, one may enhance the relative importance of the Kitaev contribution. For Mott insulating Li$_{2}$IrO$_{3}$ we observe a similar ordering temperature of 15 K, while the negative Weiss temperature is drastically reduced. These observations are compatible with an enhancement of the Kitaev contribution compared to the Na-system, suggesting that Li$_{2}$IrO$_{3}$ could be located close to the Kitaev limit [5]. \\[4pt] [1] Yogesh Singh and P. Gegenwart, Phys. Rev. B. 82, 064412 (2010). \\[0pt] [2] G. Jackeli and G. Khaliullin, Phys. Rev. Lett. 102, 017205, (2009). \\[0pt] [3] X. Liu et al., Phys. Rev. B 83, 220403(R) (2011). \\[0pt] [4] Yogesh Singh, S. Manni, P. Gegenwart, arXiv:1106.0429v1. \\[0pt] [5] J. Reuther, R. Thomale, S. Trebst, Phys. Rev. B 84, 100406 (2011).