The quantum Hall effect in two-dimensional electron gases involves the flow of topologically protected dissipationless charge currents along the edges of a sample. Integer or fractional electrical conductance is associated with edge currents of electrons or quasiparticles with fractional charges, respectively. It has been predicted that quantum Hall phenomena can also be created by edge currents with a fundamentally different origin: the fractionalization of quantum spins. However, such quantization has not yet been observed. Here we report the observation of this type of quantization of the Hall effect in an insulating two-dimensional quantum magnet, α-RuCl, with a dominant Kitaev interaction (a bond-dependent Ising-type interaction) on a two-dimensional honeycomb lattice. We find that the application of a magnetic field parallel to the sample destroys long-range magnetic order, leading to a field-induced quantum-spin-liquid ground state with substantial entanglement of local spins. In the low-temperature regime of this state, the two-dimensional thermal Hall conductance reaches a quantum plateau as a function of the applied magnetic field and has a quantization value that is exactly half of the two-dimensional thermal Hall conductance of the integer quantum Hall effect. This half-integer quantization of the thermal Hall conductance in a bulk material is a signature of topologically protected chiral edge currents of charge-neutral Majorana fermions (particles that are their own antiparticles), which have half the degrees of freedom of conventional fermions. These results demonstrate the fractionalization of spins into itinerant Majorana fermions and Z fluxes, which is predicted to occur in Kitaev quantum spin liquids. Above a critical magnetic field, the quantization disappears and the thermal Hall conductance goes to zero rapidly, indicating a topological quantum phase transition between the states with and without chiral Majorana edge modes. Emergent Majorana fermions in a quantum magnet are expected to have a great impact on strongly correlated quantum matter, opening up the possibility of topological quantum computing at relatively high temperatures.

We have performed high-field magnetization and ESR measurements on Ba3CoSb2O9 single crystals, which approximates the two-dimensional (2D) S = 1/2 triangular-lattice Heisenberg antiferromagnet. For an applied magnetic field H parallel to the ab-plane, the entire magnetization curve including the plateau at one-third of the saturation magnetization (Ms) is in excellent agreement with the results of theoretical calculations except a small step anomaly near (3/5)Ms, indicative of a theoretically undiscovered quantum phase transition. However, for H c, the magnetization curve exhibits a cusp near Ms/3 owing to the weak easy-plane anisotropy and the 2D quantum fluctuation. From a detailed analysis of the collective ESR modes observed in the ordered state, combined with the magnetization process, we have determined all the magnetic parameters including the interlayer and anisotropic exchange interactions.PACS numbers: 75.10. Jm, 75.45.+j, 75.60.Ej, Over the past decades, there has been considerable interest in frustrated quantum magnets, owing to a rich variety of exotic quantum phenomena [1][2][3]. For classical spins with an antiferromagnetic coupling, a geometric frustration suppresses the long-range ordering, leading to a degenerate ground state. The degeneracy can be destroyed by quantum fluctuations, which emerge not only through an interplay of strong geometric frustration, low dimensionality, and small spin, but also through the application of a magnetic field. Despite intensive research efforts, the detailed mechanism of the quantum effects, e.g., the ground state property [4,5], has still been highly controversial.One macroscopic manifestation of the quantum phenomena is the stabilization of the "up-up-down" spin structure under a magnetic field, predicted for a twodimensional (2D) triangular-lattice Heisenberg antiferromagnet (TLHAF) with a small spin [6,7]. In a magnetization process, the nonclassical anomaly appears as a plateau in a finite field range at one-third of the saturation magnetization M s , hereafter referred to as the M s /3 plateau. In a classical picture, a monotonic increase in the magnetization is expected up to M s . A number of theoretical approaches for explaining the quantum mechanism of the M s /3 plateau have been proposed [8][9][10][11][12][13][14]. Thus far, however, few numbers of definite experimental results reserved judgment on the issue. This is mainly due to the experimental difficulty in growing the model material, let alone in observing the M s /3 plateau purely driven by quantum fluctuations. In fact, most of the TLHAFs ever studied, such as Cs 2 CuBr 4 , [15,16] have a distorted triangular lattice, which induces an antisymmetric Dzyaloshinsky-Moriya (DM) interaction.It is believed that the spin state in the lower-field range above the higher edge field of the M s /3 plateau is the 2 : 1 canted coplanar state that is a continuous variant of the up-up-down state [7][8][9][10][11]. However, whether the 2 : 1 canted coplanar state is stable up to the saturation or a new quan...

We report the synthesis and physical properties of single crystals of stoichiometric BaNi2As2 that crystalizes in the ThCr2Si2 structure with lattice parameters a = 4.112(4)Å and c = 11.54(2)Å. Resistivity and heat capacity show a first order phase transition at T0 = 130 K with a thermal hysteresis of 7 K. The Hall coefficient is weakly temperature dependent from room temperature to 2 K where it has a value of -4x10 −10 Ω-cm/Oe. Resistivity, ac-susceptibility, and heat capacity find evidence for bulk superconductivity at Tc = 0.7 K. The Sommerfeld coefficient at Tc is 11.6 ± 0.9 mJ/molK 2 . The upper critical field is anisotropic with initial slopes of dH c c2 /dT = -0.19 T/K and dH ab c2 /dT = -0.40 T/K, as determined by resistivity.

The Kitaev quantum spin liquid displays the fractionalization of quantum spins into Majorana fermions. The emergent Majorana edge current is predicted to manifest itself in the form of a finite thermal Hall effect, a feature commonly discussed in topological superconductors. Here we report on thermal Hall conductivity κ_{xy} measurements in α-RuCl_{3}, a candidate Kitaev magnet with the two-dimensional honeycomb lattice. In a spin-liquid (Kitaev paramagnetic) state below the temperature characterized by the Kitaev interaction J_{K}/k_{B}∼80  K, positive κ_{xy} develops gradually upon cooling, demonstrating the presence of highly unusual itinerant excitations. Although the zero-temperature property is masked by the magnetic ordering at T_{N}=7  K, the sign, magnitude, and T dependence of κ_{xy}/T at intermediate temperatures follows the predicted trend of the itinerant Majorana excitations.

We report on a band structure calculation and de Haas-van Alphen measurements of KFe 2 As 2 . Three cylindrical Fermi surfaces are found. Effective masses of electrons range from 6 to 18m e , m e being the free electron mass. Remarkable discrepancies between the calculated and observed Fermi surface areas and the large mass enhancement (&3) highlight the importance of electronic correlations in determining the electronic structures of iron pnicitide superconductors. The discovery of superconductivity at T c ¼ 26 K in LaFeAs (O,F) 1) has given rise to intense experimental and theoretical efforts to elucidate the superconducting pairing mechanism and symmetry in iron pnictide superconductors (see ref. 2 for a recent review). Since the development of realistic theories of the mechanism requires detailed knowledge of the Fermi surface (FS), experimental determination of the FS is highly desirable.Accordingly, many angle-resolved photoemission spectroscopy (ARPES) studies have been performed.2) Their results show some level of agreement in the FS and band dispersion with conventional band structure calculations and moderate mass renormalization due to many-body effects. On the other hand, measurements of de Haas-van Alphen (dHvA) or other quantum oscillations, which are bulk probes and allow accurate determination of the FS cross sections and effective masses m à , are rather limited. dHvA measurements performed on the FeP compounds LaFePO 3,4) and SrFe 2 P 2 5) have shown that band shifts of up to $0:1 eV are necessary to bring band structure calculations into agreement with experiments and that the enhancement of effective masses over band ones is about two. Since high T c 's are found only in FeAs compounds, dHvA studies of FeAs compounds are more desired. However, because of the structural/magnetic phase transitions, measurements on the alkaline-earth 122 parent compounds AFe 2 As 2 (A ¼ Ca, Sr, and Ba) [6][7][8] have observed only small FS pockets, which makes it difficult to draw an overall picture of the electronic structures of these compounds. Very recently, dHvA measurements have been performed on BaFe 2 (As 1Àx P x ) 2 for 0:41 x 1. 9) As one goes from x ¼ 1 to 0.41, where T c $ 25 K, the electron FS's shrink and the mass enhancement factor increases from $2 to $4.KFe 2 As 2 is an end member of the high-T c binary alloy (Ba 1Àx K x )Fe 2 As 2 with the ThCr 2 Si 2 structure and has T c $ 3 K.10,11) The low-temperature resistivity exhibits a clear T 2 dependence with a large coefficient of A ¼ 0:026 m cm/K 2 , 12) and specific heat measurements have found correspondingly large Sommerfeld coefficients: exp ¼ 69 or 93 mJ/(K 2 Ámol-f.u.) (f.u. = formula unit) for poly or single crystals, respectively. 13,14) These indicate the existence of moderately large electron correlations.75 As nuclear quadrupole resonance measurements have shown that spin fluctuations (SF's) are much suppressed (compared with the optimally doped compound).13) The first ARPES measurement 15) found and hole FS's at the À point in the Bri...