Strongly correlated materials with strong spin-orbit coupling hold promise for realizing topological phases with fractionalized excitations. Here we propose a chiral spin-orbital liquid as a stable phase of a realistic model for heavy-element double perovskites. This spin liquid state has Majorana fermion excitations with a gapless spectrum characterized by nodal lines along the edges of the Brillouin zone. We show that the nodal lines are topological defects of a non-Abelian Berry connection and that the system exhibits dispersing surface states. We discuss some experimental signatures of this state and compare them with properties of the spin liquid candidate Ba2YMoO6.PACS numbers: 71.70. Ej, 75.10.Jm, 75.10.Kt Quantum spin liquids (QSLs) are Mott insulators in which quantum fluctuations prevent long-range magnetic order down to zero temperature [1]. They have received both experimental and theoretical attention due to predictions of unusual phenomena such as spin-gapped phases with topological order or gapless phases without spontaneous breaking of continuous symmetries [2]. In recent years the evidence for QSLs in nature has started to look more auspicious thanks to the discovery of new compounds that realize the Heisenberg model on frustrated lattices [3]. While frustration is a desirable ingredient, seminal work by Kitaev [4] has demonstrated that bond-dependent exchange interactions may provide another route towards QSL ground states. The key idea is that a spin-1/2 model on the (bipartite) honeycomb lattice with judiciously chosen anisotropic interactions can be rewritten in terms of free Majorana fermions hopping in the background of a static Z 2 gauge field. The result is a QSL with exotic fractional excitations. The same idea has been applied to construct other exactly solvable models, including cases of higher spins [5][6][7][8][9].From a broader perspective, Kitaev's model is an instance of a quantum compass model [10][11][12]. Although Kitaev-type exactly solvable models are artificial, the kind of anisotropic interactions they presuppose arises naturally in Mott insulators with orbital degeneracy and strong spin-orbit coupling [13,14]. There is recent evidence that bond-dependent interactions are dominant in Na 2 IrO 3 [15]. While this compound is in a zigzag-ordered phase at low temperatures, the prospect of finding QSLs in compass models suggests inspecting other families of heavy-element transition metal oxides [16][17][18].All the conditions leading to quantum compass models can be found in Mott-insulating rock-salt-ordered double perovskites [19]. Given the chemical formula A 2 BB O 6 , particularly interesting properties are found in compounds where the B magnetic ions have a 4d 1 or 5d1 configuration. These ions are arranged in a facecentered-cubic (fcc) lattice, which, unlike the honeycomb lattice, is geometrically frustrated. The magnetic properties within this family are diverse [20][21][22][23], but the material that stands out is Ba 2 YMoO 6 [24-27]. Despite a Curie-Weiss temperatu...

We study a spin-orbital model for 4d 1 or 5d 1 Mott insulators in ordered double perovskites with strong spin-orbit coupling. This model is conveniently written in terms of pseudospin and pseudoorbital operators representing multipoles of the effective j = 3/2 angular momentum. Similarities between this model and the effective theories of Kitaev materials motivate the proposal of a chiral spin-orbital liquid with Majorana fermion excitations. The thermodynamic and spectroscopic properties of this quantum spin liquid are characterized using parton mean-field theory. The heat capacity, spin-lattice relaxation rate, and dynamic structure factor for inelastic neutron scattering are calculated and compared with the experimental data for the spin liquid candidate Ba2YMoO6. Moreover, based on a symmetry analysis, we discuss the operators involved in resonant inelastic X-ray scattering (RIXS) amplitudes for double perovskite compounds. In general, the RIXS cross sections allow one to selectively probe pseudospin and pseudo-orbital degrees of freedom. For the chiral spin-orbital liquid in particular, these cross sections provide information about the spectrum for different flavors of Majorana fermions. arXiv:1704.06134v3 [cond-mat.str-el]

The SU(4)-symmetric spin-orbital model on the honeycomb lattice was recently studied in connection to correlated insulators such as the eg Mott insulator Ba3CuSb2O9 and the insulating phase of magic-angle twisted bilayer graphene at quarter filling. Here we provide a unified discussion of these systems by investigating an extended model that includes the effects of Hund's coupling and anisotropic, orbital-dependent exchange interactions. Using a combination of mean-field theory, linear flavor-wave theory, and variational Monte Carlo, we show that this model harbors a quantum spin-orbital liquid over a wide parameter regime around the SU(4)-symmetric point. For large Hund's coupling, a ferromagnetic antiferro-orbital ordered state appears, while a valence-bond crystal combined with a vortex orbital state is stabilized by dominant orbital-dependent exchange interactions.