Intensive studies of the interplay between spin-orbit coupling (SOC) and electronic correlations in transition metal compounds have recently been undertaken. In particular, j eff = 1/2 bands on a honeycomb lattice provide a pathway to realize Kitaev's exactly solvable spin model. However, since current wisdom requires strong atomic SOC to make j eff = 1/2 bands, studies have been limited to iridium oxides. Contrary to this expectation, we demonstrate how Kitaev interactions arise in 4d-orbital honeycomb α-RuCl3, despite having significantly weaker SOC than the iridium oxides, via assistance from electron correlations. A strong coupling spin model for these correlation-assisted j eff = 1/2 bands is derived, in which large antiferromagnetic Kitaev interactions emerge along with ferromagnetic Heisenberg interactions. Our analyses suggest that the ground state is a zigzagordered phase lying close to the antiferromagnetic Kitaev spin liquid. Experimental implications for angle resolved photoemission spectroscopy, neutron scattering, and optical conductivities are discussed.arXiv:1411.6623v3 [cond-mat.str-el]

The electronic structure of the honeycomb lattice iridates Na(2)IrO(3) and Li(2)IrO(3) has been investigated using resonant inelastic x-ray scattering (RIXS). Crystal-field-split d-d excitations are resolved in the high-resolution RIXS spectra. In particular, the splitting due to noncubic crystal fields, derived from the splitting of j(eff)=3/2 states, is much smaller than the typical spin-orbit energy scale in iridates, validating the applicability of j(eff) physics in A(2)IrO(3). We also find excitonic enhancement of the particle-hole excitation gap around 0.4 eV, indicating that the nearest-neighbor Coulomb interaction could be large. These findings suggest that both Na(2)IrO(3) and Li(2)IrO(3) can be described as spin-orbit Mott insulators, similar to the square lattice iridate Sr(2)IrO(4).

α-RuCl3 has been proposed recently as an excellent playground for exploring Kitaev physics on a twodimensional (2D) honeycomb lattice. However, structural clarification of the compound has not been completed, which is crucial in understanding the physics of this system. Here, using ab-initio electronic structure calculations, we study a full three dimensional (3D) structure of α-RuCl3 including the effects of spin-orbit coupling (SOC) and electronic correlations. Three major results are as follows; i) SOC suppresses dimerization of Ru atoms, which exists in other Ru compounds such as isostructural Li2RuO3, and making the honeycomb closer to an ideal one. ii) The nearest-neighbor Kitaev exchange interaction between the j eff =1/2 pseudospin depends strongly on the Ru-Ru distance and the Cl position, originating from the nature of the edge-sharing geometry.iii) The optimized 3D structure without electronic correlations has P31m space group symmetry independent of SOC, but including electronic correlation changes the optimized 3D structure to either C2/m or Cmc21 within 0.1 meV per formula unit (f.u.) energy difference. The reported P 3112 structure is also close in energy. The interlayer spin exchange coupling is a few percent of in-plane spin exchange terms, confirming α-RuCl3 is close to a 2D system. We further suggest how to increase the Kitaev term via tensile strain, which sheds new light in realizing Kitaev spin liquid phase in this system.

Mott insulators with strong spin-orbit coupling have been proposed to host unconventional magnetic states, including the Kitaev quantum spin liquid. The 4d system α-RuCl3 has recently come into view as a candidate Kitaev system, with evidence for unusual spin excitations in magnetic scattering experiments. We apply a combination of optical spectroscopy and Raman scattering to study the electronic structure of this material. Our measurements reveal a series of orbital excitations involving localized total angular momentum states of the Ru ion, implying that strong spin-orbit coupling and electron-electron interactions coexist in this material. Analysis of these features allows us to estimate the spin-orbit coupling strength as well as other parameters describing the local electronic structure, revealing a well-defined hierarchy of energy scales within the Ru d states. By comparing our experimental results with density functional theory calculations, we also clarify the overall features of the optical response. Our results demonstrate that α-RuCl3 is an ideal material system to study spin-orbit coupled magnetism on the honeycomb lattice.Introduction.-A variety of novel electronic phases are predicted to emerge in the solid state due to the cooperative action of spin-orbit coupling and electron correlation [1]. One prominent example is the proposed realization of the Heisenberg-Kitaev model in a strongly spin-orbit coupled Mott insulator on the honeycomb lattice [2,3]. In this scenario, the combination of spin-orbit coupling and orbital degeneracy leads to the formation of j ef f = 1/2 pseudospins. The spatial anisotropy inherent to these pseudospins in turn yields bond-dependent, anisotropic exchange interactions that can be mapped onto a generalized Heisenberg-Kitaev model [4], which hosts a variety of unusual magnetic states, including the Kitaev quantum spin liquid [5]. Experimental work in this direction has focussed on honeycomb lattice iridates [6,7], although the electronic structure of these materials is complicated by structural distortions and electron itinerancy [8].

Numerous efforts have been devoted to reveal exotic semimetallic phases with topologically non-trivial bulk and/or surface states in materials with strong spin-orbit coupling. In particular, semimetals with nodal line Fermi surface (FS) exhibit novel properties, and searching for candidate materials becomes an interesting research direction. Here we provide a generic condition for a four-fold degenerate nodal line FS in non-symmorphic crystals with inversion and time-reversal symmetry (TRS). When there are two glide planes or screw axes perpendicular to each other, a pair of Bloch bands related by non-symmorphic symmetry become degenerate on a Brillouin Zone (BZ) boundary. There are two pairs of such bands, and they disperse in a way that the partners of two pairs are exchanged on other BZ boundaries. This enforces a nodal line FS on a BZ boundary plane protected by non-symmorphic symmetries. When TRS is broken, four-fold degenerate Dirac points or Weyl ring FS could occur depending on a direction of the magnetic field. On a certain surface double helical surface states exist, which become double Ferm arcs as TRS is broken. arXiv:1512.08865v3 [cond-mat.str-el]