The exactly solvable Kitaev model on the honeycomb lattice has recently received enormous attention linked to the hope of achieving novel spin-liquid states with fractionalized Majorana-like excitations.In this review, we analyze the mechanism proposed by G. Jackeli and G. Khaliullin to identify Kitaev materials based on spin-orbital dependent bond interactions and provide a comprehensive overview of its implications in real materials. We set the focus on experimental results and current theoretical understanding of planar honeycomb systems (Na2IrO3, α-Li2IrO3, and α-RuCl3), three-dimensional Kitaev materials (β-and γ-Li2IrO3), and other potential candidates, completing the review with the list of open questions awaiting new insights.

Hexagonal α-Ru trichloride single crystals exhibit a strong magnetic anisotropy and we show that upon applying fields up to 14 T in the honeycomb plane the successive magnetic order at T1 = 14 K and T2 = 8 K could be completely suppressed whereas in the perpendicular direction the magnetic order is robust. Furthermore the field dependence of χ(T) implies coexisting ferro-and antiferromagnetic exchange between in-plane components of Ru 3+ -spins, whereas for out-of-plane components a strong antiferromagnetic exchange becomes evident. 101 Ru zero-field nuclear magnetic resonance in the ordered state evidence a complex (probably non coplanar chiral) long-range magnetic structure. The large orbital moment on Ru 3+ is found in density-functional calculations. PACS numbers: 75.30.Gw, 75.40.Cx, Low dimensional 4d-and 5d-magnets show a wide variety of magnetic ground states due to crystal electric field (CEF) splitting in combination with a strong spin-orbit coupling (SOC). Especially the 5d 5 -iridate compounds earned great attention because of the predicted topological Mott insulating state due to the strong SOC and the Coulomb correlation [1]. Furthermore the strong SOC favors the asymmetric Dzyaloshinskii-Moriya (DM) interaction that often results in chiral spin arrangements in the ordered phases [2,3]. In addition, for spin-1/2 systems geometrical frustration of the magnetic exchange interactions frequently leads to a quantum spin-liquid ground state[4]. Among 4d-and 5d-systems, the Heisenberg-Kitaev model (HKM) was established to describe the competing bond-dependent magnetic exchange interactions in the honeycomb type of lattice structures [5]. Prominent examples are the 2-1-3 iridates (Li 2 IrO 3 , Na 2 IrO 3 ) where the magnetism is associated to the 5d 5 electrons on the Ir 4+ ions. According to the HKM, the phase diagram provides a transition from a conventional Neel-type of antiferromagnetic (AFM) order to a AFM stripy-(or zigzag-) type of order towards a pure quantum spin liquid (QSL) phase as a function of control parameter [6]. Indeed Na 2 IrO 3 shows an AFM order of zigzag-type at T = 15 K, whereas the Li 2 IrO 3 system is more close to the QSL regime and a non coplanar spiral order is discussed [7].In order to search for new 4d-or 5d-model system with the honeycomb lattice arrangement as a platform of HKM α-RuCl 3 turns out to be an excellent candidate because the low spin 3+ state of Ru (4d 5 ) is equivalent to the low spin 4+ state of Ir (5d 5 ). However, lowtemperature magnetic properties of α-RuCl 3 were not studied in detail and, so far, on powders only. Recently, Plumb and co-workers have shown in a spectroscopic experiment that α-RuCl 3 is a magnetic insulator due to sizable Coulomb correlations accompanied by the spinorbit coupling [8].In this Rapid Communication, we report detailed studies on the magnetic anisotropy by magnetization and specific heat on single crystals over a wide temperature and field range. Furthermore, we applied 99,101 Ru zero-field nuclear magnetic resonance as a local and ...

We apply moderate-high-energy inelastic neutron scattering (INS) measurements to investigate Yb 3+ crystalline electric field (CEF) levels in the triangular spin-liquid candidate YbMgGaO4. Three CEF excitations from the ground-state Kramers doublet are centered at the energies~! = 39, 61, and 97 meV in agreement with the e↵ective spin-1/2 g-factors and experimental heat capacity, but reveal sizable broadening. We argue that this broadening originates from the site mixing between Mg 2+ and Ga 3+ giving rise to a distribution of Yb-O distances and orientations and, thus, of CEF parameters that account for the peculiar energy profile of the CEF excitations. The CEF randomness gives rise to a distribution of the e↵ective spin-1/2 g-factors and explains the unprecedented broadening of low-energy magnetic excitations in the fully polarized ferromagnetic phase of YbMgGaO4, although a distribution of magnetic couplings due to the Mg/Ga disorder may be important as well.PACS numbers: 75.10. Dg, 75.10.Kt, 78.70.Nx Introduction.-Quantum spin liquid (QSL) is a novel state of matter with zero entropy and without conventional symmetry breaking even at zero temperature. Such states were proposed to host 'spinons', exotic spin excitations with fractional quantum numbers [1][2][3]. Although many candidate QSL materials with two-dimensional or three-dimensional interaction topologies on the triangular, kagome, and pyrochlore lattices were reported [4][5][6][7][8][9][10][11][12][13][14][15][16][17], they typically suffer from magnetic or non-magnetic defects [18][19][20][21][22], spatial anisotropy [4,7,15], antisymmetric DzyaloshinskyMoriya anisotropy [23][24][25], and (or) interlayer magnetic couplings [25][26][27] that reduce or even completely release magnetic frustration [25,[27][28][29][30].Many of the aforementioned shortcomings can be remedied in a new triangular antiferromagnet YbMgGaO 4 that was recently reported by our group [31][32][33]. No spin freezing was detected down to at least 0.048 K, which is about 3% of the nearest-neighbor interaction J 0 ⇠ 1.5 K [33]. Residual spin entropy is nearly zero at 0.06 K, excluding any magnetic transitions at lower temperatures [31]. Below 0.4 K, thermodynamic properties evidence the putative QSL regime with temperature-independent magnetic susceptibility = const [33] and power-law behavior of the magnetic heat capacity, C m ⇠ T 2/3 [31], the observations that are consistent with theoretical predictions for the U(1) QSL ground state (GS) on the triangular lattice [34][35][36].Very recently, two inelastic neutron scattering (INS) studies of YbMgGaO 4 [37, 38] reported continuous excitations at transfer energies of 0.1 2.5 meV extending well above the energy scale of the magnetic coupling J 0 ⇠ 0.13 meV. These spectral features were identified as fractionalized excitations ('spinons') from the QSL GS [37]. Surprisingly, though, magnetic excitations remain very broad in both energy and wave-vector (Q) even in the almost fully polarized state at 7.8 T, where only narrow spin-wave e...

Muon spin relaxation (μSR) experiments on single crystals of the structurally perfect triangular antiferromagnet YbMgGaO_{4} indicate the absence of both static long-range magnetic order and spin freezing down to 0.048 K in a zero field. Below 0.4 K, the μ^{+} spin relaxation rates, which are proportional to the dynamic correlation function of the Yb^{3+} spins, exhibit temperature-independent plateaus. All these μSR results unequivocally support the formation of a gapless U(1) quantum spin liquid ground state in the triangular antiferromagnet YbMgGaO_{4}.