A ferromagnet with spin anisotropies on the 2D Kagome lattice is theoretically studied. This is a typical example of the flat-band ferromagnet. The Berry phase induced by the tilting of the spins opens the band gap and quantized Hall conductance σxy = ±e 2 /h is realized without external magnetic field. This is the most realistic chiral spin state based on the ferromagnetism. We also discuss the implication of our results to anomalous Hall effect observed in the metallic pyrochlore ferromagnets R2Mo2O7 (R =Nd, Sm, Gd).75.10. Lp, 75.30.Gw, 72.15.Eb The spin Berry phase plays an important role in the quantum transport of strongly correlated electronic systems. Consider an electron hopping from site i to j coupled to a spin at each site with Hund's coupling J H [1]. When J H is strong enough the spin of the hopping electron is forced to align parallel to S i and S j at each site, with the spin wave function being |χ i > and |χ j >, respectively. The spin wavefunction is explicitly given bywhere we have introduced the polar coordinates asThe overall phase b i corresponds to the gauge degrees of freedom and does not appear in physical quantities. Therefore, the effective transfer integral t ij is given by [1]where θ ij is the angle between the two spins S i and S j . The phase a ij is the vector potential generated by the spin, and corresponds to the Berry phase felt by the hopping electron. Let us consider an electron hopping along a loop 1 → 2 → 3 → 1. The total phase that the electron obtains is the gauge flux by a ij , which corresponds to the solid angle subtended by the three spins S i (i = 1, 2, 3). This is called the spin chirality and is one of the key concept in the physics of strongly correlated electronic systems [2][3][4][5][6]. One can easily see that the spin chirality is absent for collinear spin alignment, and the spin chirality has been intensively discussed in the context of quantum spin liquid where the spins and hence a ij fluctuate quantum mechanically [2][3][4][5][6]. This a ij is the leading actor in the gauge theory of strongly correlated electronic systems [3,6]. Among them the proposal of chiral spin liquid with broken time-reversal symmetry in a triangular lattice [2], and later the anyon superconductivity [4] attracted great interests at the early stage of the high-T c research. Wen et al.[5] constructed a mean field theory for a chiral spin liquid on a square lattice. They start from the π-flux state, and break the time-reversal symmetry by introducing the next-nearest-neighbor hopping with a phase. However, it turned out to be rather difficult to find physical realization of the (chiral) spin liquid in real materials, even in frustrated lattices.The spin Berry phase has been discussed also in the context of anomalous Hall effect (AHE) in manganites [7]. It is proposed that the spin-orbit interaction H ′ leads to the coupling between the magnetization M and the spin chirality, i.e., the gauge flux, b as expressed by H ′ = λbM . At finite temperature T , Skyrmions are thermally excited...

We report results of 75 As nuclear magnetic resonance (NMR) experiments on a self-flux grown single crystal of BaFe2As2. A first-order antiferromagnetic (AF) transition near 135 K was detected by the splitting of NMR lines, which is accompanied by simultaneous structural transition as evidenced by a sudden large change of the electric field gradient tensor at the As site. The NMR results lead almost uniquely to the stripe spin structure in the AF phase. The data of spin-lattice relaxation rate indicate development of anisotropic spin fluctuations of the stripe-type with decreasing temperature in the paramagnetic phase.

All the iron-based superconductors identified to date share a square lattice composed of Fe atoms as a common feature, despite having different crystal structures. In copper-based materials, the superconducting phase emerges not only in square lattice structures but also in ladder structures. Yet iron-based superconductors without a square lattice motif have not been found despite being actively sought out. Here, we report the discovery of pressure-induced superconductivity in the iron-based spin-ladder material BaFe 2 S 3 , a Mott insulator with striped-type magnetic ordering below ~120 K. On the application of pressure this compound exhibits a metal-insulator transition at about 11 GPa, followed by the appearance of superconductivity below T c = 14 K, right after the onset of the metallic phase. Our findings indicate that iron-based ladder compounds represent promising material platforms, in particular for studying the fundamentals of iron-based superconductivity.The discovery of iron-based superconductors had a significant impact on condensed matter physics and led to extensive study of the interplay between crystal structure, magnetism and superconductivity 1 . All the iron-based superconducting materials discovered to date share the same structural motif: a two-dimensional square lattice formed by edge-shared FeX 4 tetrahedra (X = Se, P and As). The Fe atoms are nominally divalent in most of the parent materials. These parent compounds undergo a magnetic transition at low temperatures, typically exhibiting striped-type ordering.Superconductivity appears when the magnetic order is fully suppressed by the application of pressure or by the addition of doping carriers through chemical Purpose of this studyThe application of pressure is often a useful means of changing the electronic structure of a compound so as to induce a metallic state without simultaneously introducing any degree of disorder 17 . In this study, we investigated in detail the magnetic properties of a sulphur-analogue of the Fe-based ladder materials, BaFe 2 S 3 (space group: orthorhombic, Cmcm) 18,19 , and undertook experimental trials in which this compound was subjected to high pressures to obtain the metallic state. The electronic properties of this material depend on the manner in which the samples are synthesized, and thus we present data for sample 1 describing magnetic properties, and data for a range of samples 1 to 6 describing high-pressure effects. The details of the sample preparation process are given in the Method section. Electronic properties under ambient pressureFigure 2a displays the temperature dependence of the electrical resistivity (ρ) of BaFe 2 S 3 along the leg direction under ambient pressure. The observed insulating behaviour, which occurs despite the expected metallic behaviour in an unfilled 3d manifold, is caused by the Coulomb repulsion between Fe 3d electrons, which becomes prominent in a quasi-one-dimensional ladder structure. Figure 2b shows the magnetic susceptibility (χ) at 5 T along the three orthorhombic...