We additionally find that applying an external magnetic field whilst the system is in the long-range ordered zigzag ground state can induce a phase transition into a quantum SL. While a SL state does show up in this phase diagram, it arises in a setting different from Kitaev’s original SL regime, as it emerges from an interplay of Kitaev physics and geometrically frustrated magnetism. The resulting magnetic phase diagram that we compute as function of longer-range second- and third-neighbor magnetic couplings is very rich, due to the comparable size of the various residual interactions. It is however significantly weaker than in 5 d 5 Ir oxides and even than in 4 d 5 Li 2RhO 3, which points at a rather different balance between the various superexchange processes in the halide and in the oxides. Calculating the magnetic interactions between two adjacent 1/2-pseudospins, we find that the nearest-neighbor (NN) Kitaev exchange K is ferromagnetic (FM), in any of the α-RuCl 3 crystalline structures reported so far. The trigonally distorted environment further gives rise to strong anisotropy of the computed g factors, consistent with experimental observations 20, 27. Our results for the Ru 3+ 4 d-shell electronic structure show sizable trigonal splitting of the 4 d t 2 g levels and therefore a spin-orbit ground state that significantly deviates from the j eff = 1/2 picture 7. Here we present results of combined quantum chemistry electronic-structure computations and exact-diagonalization (ED) calculations for extended Kitaev-Heisenberg spin Hamiltonians using as starting point for the ED study the magnetic couplings derived at the quantum chemistry level. But also this material orders antiferromagnetically at low temperatures, as the 5 d 5 iridium oxides do, and precisely how close to the idealized Kitaev model α-RuCl 3 is, remains a question to be clarified. Very recent Raman and neutron scattering measurements suggest that the 4 d 5 halide honeycomb system is closer to the Kitaev limit 22, 23. The SL regime is most likely preempted in the iridates by the presence of significant residual Heisenberg-type J couplings, by longer-range spin interactions, or by having crystallographically distinct Ir-Ir bonds with dominant J’s on some of those, if not a combination of these factors 14, 15, 16, 17.Īlso of interest in this context is ruthenium trichloride, RuCl 3, in its honeycomb ( α) crystalline phase 18, 19, 20, 21, 22, 23, 24, 25, 26. In these systems though long-range magnetic order develops at low temperatures, for all known different crystallographic phases 9, 10, 11, 12, 13. The search to realize the Kitaev model of effectively spin-1/2 particles on the honeycomb lattice was centered until recently mainly on honeycomb iridate materials 7, 8 of the type A 2IrO 3, where A is either Na or Li. Its remarkable properties include protection of quantum information and the emergence of Majorana fermions 5, 6. Of particular interest is the Kitaev Hamiltonian on the honeycomb lattice 5, which is a mathematically well-understood two-dimensional model exhibiting various topological SL states. Whereas there is a rich variety of mathematical models that exhibit SL behavior, finding materials in which a quantum SL state is realized is an intensely pursued goal in present day experimental condensed-matter physics 2, 3, 4. Quantum spin liquids (SL’s) are states of matter that cannot be described by the broken symmetries associated with conventional magnetic ground states 1. Our results offer a unified picture on recent magnetic and spectroscopic measurements on this material and open new perspectives on the prospect of realizing quantum spin liquids in d 5 halides and oxides in general. Using exact diagonalization and density-matrix renormalization group techniques for extended Kitaev-Heisenberg spin Hamiltonians, we find indications for a transition from zigzag order to a gapped spin liquid when applying magnetic field. A ferromagnetic Kitaev coupling is also supported by a detailed analysis of the field-dependent magnetization. From advanced electronic-structure calculations, we find that the Kitaev interaction is ferromagnetic, as in 5 d 5 iridium honeycomb oxides, and indeed defines the largest superexchange energy scale. Here we discuss the promise for spin-liquid behavior in the 4 d 5 honeycomb halide α-RuCl 3. A prominent case is the Kitaev spin liquid, host of remarkable properties such as protection of quantum information and the emergence of Majorana fermions. Large anisotropic exchange in 5 d and 4 d oxides and halides open the door to new types of magnetic ground states and excitations, inconceivable a decade ago.
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