Session F2: Invited Session: Low Energy Excitations in Iridates

Correlated phases and excitations in the iridates

The iridium oxides form an intriguing set of materials controlled by a delicate balance of kinetic, spin-orbit, and Coulomb interaction energies. Many possible exotic phases and phenomena have been suggested for them in the literature. I will review the theoretical context for these compounds, emphasizing effects arising from the combination of strong spin-orbit coupling and electron-electron correlations. Finally, I will discuss our group's on-going efforts to understand the excitations and magnetic phases in these materials.   

RIXS Studies of Magnetic Excitations in Layered Iridates

5$d$ Transition metal oxides lie at the intersection of strong spin-orbit coupling and electron correlation, and open a new playground for novel electronic phases with unconventional magnetic, superconducting, magneto-electric, and band-topological properties. In particular, a rich variety of magnetic phases are predicted from the magnetic interactions that take various forms ranging from Heisenberg to bond-directional dipolar-like couplings in the strong spin-orbit coupling limit. In this talk, I will review on these novel aspects of magnetism in iridates studied using resonant x-ray scattering techniques. Specifically, following topics will be discussed: (i) Heisenberg-like nature of magnetic coupling in Sr$_{2}$IrO$_{4}$ that sharply contrast with the unusually large spin-wave gap in Sr$_{3}$Ir$_{2}$O$_{7}$, (ii) the origin of strong Ising anisotropy in Sr$_{3}$Ir$_{2}$O$_{7}$, and (iii) the contrasting dynamics of ``spin-orbit exciton'' modes in the Heisenberg and Ising magnets.   

Interplay of spin-orbit coupling, correlations, and crystal anisotropy in 5d oxides

We investigate the correlated $d$-level electronic structure of $5d$ Ir and Os oxide compounds by fully {\it ab initio} quantum-chemical many-body calculations on finite embedded clusters. The wave-function quantum-chemical methods provide a promising alternative to density-functional-based approaches to the electronic structure of solids. The computed $d$-$d$ excitations in square-lattice, honeycomb, pyrochlore, and chain-like iridates compare well with recent RIXS (resonant inelastic x-ray scattering) data. We also perform a detailed analysis of the relativistic spin-orbit wave functions and compute observables such as the $\langle \mathbf{L}\!\cdot\!\mathbf{S} \rangle $ ground-state expectation value of the spin-orbit operator. The latter is in principle accessible from x-ray absorption and provides information on the role of $t_{2g}$--\,$e_g$ couplings in the ground-state wave function and on the strength of non-cubic fields that lift the degeneracy of the $t_{2g}$ levels. As concerns the departure from cubic symmetry, interesting effects are found in $A_2$Ir$_2$O$_7$ pyrochlores, where the highly anisotropic, hexagonal configuration of the adjacent $A$-site ions breaks cubic symmetry even in the absence of O-ligand trigonal distortions and moreover competes with the latter. Our findings open new perspectives in pyrochlore oxides. In 227 iridates, the outcome of this competition is decisive for the actual realization of any type of non-trivial topological ground state. In 227 spin systems with $S\!>\!1/2$, e.g., Cd$_2$Os$_2$O$_7$, this interplay decides the sign of the single-ion anisotropy and the degree of magnetic frustration.   

Low energy excitations in iridates studied with Resonant Inelastic X-ray Scattering

In the iridium oxides, the strong spin-orbit coupling (SOC) of the 5d iridium electrons entangles the orbital and spin degrees of freedom, providing opportunities for exotic magnetic states with highly anisotropic exchange interactions. At the same time, the spatially extended 5d electrons are expected to have much stronger hybridization with the oxygen 2p orbitals, comparing with that in 3d transition element compounds. Both factors make crystal symmetry and local environment crucial in determining the electronic and magnetic properties of the iridates. We present here our resonant inelastic X-ray scattering (RIXS) studies of a number of octahedrally coordinated iridates with special structures, exploring these effects. In particular, for the 1-D spin 1/2 chain compound, Sr$_3$CuIrO$_6$, the wavefunction of the hole in the t2g manifold was reconstructed based on the RIXS spectra. Our results show that it is significantly modified from the isotropic shape expected for J$_{\mathrm{eff}} = 1/2$ states in the strong SOC limit, due to the distortion of the oxygen octahedral cage. This distortion is comparable to, or smaller than, that present in most iridates and thus this work emphasizes the importance of local symmetry for the iridate families. Further, the magnetic excitations of this material were also measured. A large gap of $\sim$30 meV, was found, comparable to the magnetic dispersion bandwidth. This is in contrast to the gapless dispersion expected for linear chain with isotropic Heisenberg exchange interaction. We also studied Na$_4$Ir$_3$O$_8$ which has a hyperkagome lattice, and is a candidate quantum spin liquid. Here, a low energy continuum is observed below the d-d excitations. Optical conductivity measurements performed on the same sample and polarization dependence of the RIXS signal suggest that these excitations are magnetic in origin, agreeing with the spin-liquid state prediction.   

Spin Dynamics in Na2IrO3 Probed by Inelastic Neutron Scattering: Implications for Kitaev Physics

We explore the spin dynamics in the layered antiferromagnet Na$_2$IrO$_3$, a candidate for the Kitaev spin model on the honeycomb lattice [1]. Using powder inelastic neutron scattering with an optimised setup to minimise neutron absorption by Ir we observed evidence for dispersive spin wave excitations of the Ir moments below a zone-boundary energy of 5 meV [2]. Results are compared quantitatively with predictions of a Kitaev-Heisenberg model, as well as a Heisenberg model with further neighbour couplings, both with a magnetic ground state of zig-zag ferromagnetic chains ordered antiferromagnetically. By combining single-crystal xray diffraction and ab initio calculations we propose a revised crystal structure model with significant departures from the ideal case of regular IrO6 octahedra and 90$^{\circ}$ Ir-O-Ir bonds required for large Kitaev exchanges.\\[4pt] [1] J. Chaloupka, G. Jackeli, and G. Khaliullin, Phys. Rev. Lett. 105, 027204 (2010); arXiv:1209.5100 (2012).\\[0pt] [2] S.K. Choi, R. Coldea, A.N. Kolmogorov, T. Lancaster, I.I. Mazin, S.J. Blundell, P.G. Radaelli, Yogesh Singh, P. Gegenwart, K.R. Choi, S.-W. Cheong, P.J. Baker, C. Stock and J. Taylor, Phys. Rev. Lett. 108, 127204 (2012).