Spin chirality fluctuations and anomalous Hall effect in itinerant ferromagnets

The anomalous Hall effect due to the spin chirality order and fluctuation is studied theoretically in a Kondo lattice model without the relativistic spin-orbit interaction. Even without the correlations of the localized spins, sigma(xy) can emerge depending on the lattice structure and the spin anisotropy. We reveal the condition for this chirality-fluctuation driven mechanism for sigma(xy). Our semiquantitative estimates for a pyrochlore oxide Nd2Mo2O7 give a finite sigma(xy) approximately equal 10 Omega(-1) cm(-1) together with a high resistivity rho(xx) approximately equal 10(-4)-10(-3) Omega cm, in agreement with experiments.     

Temperature and magnetic-field-enhanced hall slope of a dilute 2D hole system in the ballistic regime

We report the temperature (T) and perpendicular magnetic-field (B) dependence of the Hall resistivity rho(xy)(B) of dilute metallic 2D holes in GaAs over a broad range of temperature (0.02-1.25 K). The low B Hall coefficient, R(H), is found to be enhanced when T decreases. Strong magnetic fields further enhance the slope of rho(xy)(B) at all temperatures studied. Coulomb interaction corrections of a Fermi liquid (FL) in the ballistic regime can not explain the enhancement of rho(xy) which occurs in the same regime as the anomalous metallic longitudinal conductivity. In particular, although the metallic conductivity in 2D systems has been attributed to electron interactions in a FL, these same interactions should reduce, not enhance, the slope of rho(xy)(B) as T decreases and/or B increases.     

Anomalous Hall effect in ferromagnetic semiconductors in the hopping transport regime

We present a theory of the anomalous Hall effect in ferromagnetic (Ga,Mn)As in the regime when conduction is due to phonon-assisted hopping of holes between localized states in the impurity band. We show that the microscopic origin of the anomalous Hall conductivity in this system can be attributed to a phase that a hole gains when hopping around closed-loop paths in the presence of spin-orbit interactions and background magnetization of the localized Mn moments. Mapping the problem to a random resistor network, we derive an analytic expression for the macroscopic anomalous Hall conductivity sigma(AH)(xy). We show that sigma(AH)(xy) is proportional to the first derivative of the density of states varrho(epsilon) and thus can be expected to change sign as a function of impurity band filling. We also show that sigma(AH)(xy) depends on temperature as the longitudinal conductivity sigma(xx) within logarithmic accuracy.     

Quantized anomalous Hall effect in two-dimensional ferromagnets: quantum Hall effect in metals

We study the effect of disorder on the anomalous Hall effect (AHE) in two-dimensional ferromagnets. The topological nature of the AHE leads to the integer quantum Hall effect from a metal, i.e., the quantization of sigma(xy) induced by the localization except for the few extended states carrying Chern numbers. Extensive numerical study on a model reveals that Pruisken's two-parameter scaling theory holds even when the system has no gap with the overlapping multibands and without the uniform magnetic field. Therefore, the condition for the quantized AHE is given only by the Hall conductivity sigma(xy) without the quantum correction, i.e., /sigma(xy)/>e(2)/(2h).     

Anomalous hall heat current and nernst effect in the CuCr2Se4-xBrx ferromagnet

In a ferromagnet, an anomalous Hall heat current, given by the off-diagonal Peltier term alpha(xy), accompanies the anomalous Hall current. By combining Nernst, thermopower, and Hall experiments, we have measured how alpha(xy) varies with hole density and lifetime tau in CuCr2Se4-xBrx. At low temperatures T, we find that alpha(xy) is independent of tau, consistent with anomalous-velocity theories. Its magnitude is fixed by a microscopic geometric area A approximately 34 A(2). Our results are incompatible with some models of the Nernst effect in ferromagnets.     

Quantum Hall effect of massless dirac fermions in a vanishing magnetic field

The effect of strong long-range disorder on the quantization of the Hall conductivity sigma{xy} in graphene is studied numerically. It is shown that increasing Landau-level mixing progressively destroys all plateaus in sigma{xy} except the plateaus at sigma{xy}=-/+e{2}/2h (per valley and per spin). The critical state at the Dirac point is robust to strong disorder and belongs to the universality class of the conventional plateau transitions in the integer quantum Hall effect. We propose that the breaking of time-reversal symmetry by ripples in graphene can realize this quantum critical point in a vanishing magnetic field.     

Intrinsic optical dichroism in the chiral superconducting state of Sr2RuO4

We present an analysis of the Hall conductivity σ(xy)(ω,T) in time reversal symmetry breaking states of exotic superconductors. We find that the dichroic signal is nonzero in systems with interband order parameters. This new intrinsic mechanism may explain the Kerr effect observed in strontium ruthenate and possibly other superconductors. We predict coherence factor effects in the temperature dependence of the imaginary part of the ac Hall conductivity Imσ(xy)(ω,T), which can be tested experimentally.     

Unconventional integer quantum Hall effect in graphene

Monolayer graphite films, or graphene, have quasiparticle excitations that can be described by (2+1)-dimensional Dirac theory. We demonstrate that this produces an unconventional form of the quantized Hall conductivity sigma(xy) = -(2e2/h)(2n+1) with n = 0, 1, ..., which notably distinguishes graphene from other materials where the integer quantum Hall effect was observed. This unconventional quantization is caused by the quantum anomaly of the n=0 Landau level and was discovered in recent experiments on ultrathin graphite films.     

Fermionic Magnons, non-Abelian spinons, and the spin quantum Hall effect from an exactly solvable spin-1/2 Kitaev model with SU(2) symmetry

We introduce an exactly solvable SU(2)-invariant spin-1/2 model with exotic spin excitations. With time reversal symmetry (TRS), the ground state is a spin liquid with gapless or gapped spin-1 but fermionic excitations. When TRS is broken, the resulting spin liquid exhibits deconfined vortex excitations which carry spin-1/2 and obey non-Abelian statistics. We show that this SU(2) invariant non-Abelian spin liquid exhibits the spin quantum Hall effect with quantized spin Hall conductivity σ(xy)(s)=?/2π, and that the spin response is effectively described by the SO(3) level-1 Chern-Simons theory at low energy. We further propose that a SU(2) level-2 Chern-Simons theory is the effective field theory describing the topological structure of the non-Abelian SU(2) invariant spin liquid.     

Quantization of the diagonal resistance: density gradients and the empirical resistance rule in a 2D system

We have observed quantization of the diagonal resistance, R(xx), at the edges of several quantum Hall states. Each quantized R(xx) value is close to the difference between the two adjacent Hall plateaus in the off-diagonal resistance, R(xy). Peaks in R(xx) occur at different positions in positive and negative magnetic fields. Practically all R(xx) features can be explained quantitatively by a 1%/cm electron density gradient. Therefore, R(xx) is determined by R(xy) and unrelated to the diagonal resistivity rho(xx). Our findings throw an unexpected light on the empirical resistivity rule for 2D systems.     

Spin Hall effect in doped semiconductor structures

In this Letter we present a microscopic theory of the extrinsic spin Hall effect based on the diagrammatic perturbation theory. Side-jump and skew-scattering contributions are explicitly taken into account to calculate the spin Hall conductivity, and we show that their effects scale as sigma(xy)SJ/sigma(xy)SS approximately (h/tau)/epsilonF, with tau being the transport relaxation time. Motivated by recent experimental work we apply our theory to n- and p-doped 3D and 2D GaAs structures, obtaining sigma(s)/sigma(c) approximately 10(-3)-10(-4), where sigma(s(c)) is the spin Hall (charge) conductivity, which is in reasonable agreement with the recent experimental results of Kato et al. [Science 306, 1910 (2004)] in n-doped 3D GaAs system.     

Two-dimensional transport and strong spin-orbit interaction in SrMnSb_2

We have carried out magneto-transport measurements for single crystal SrMnSb_2. Clear Shubnikov-de Haas oscillations were resolved at relatively low magnetic field around 4 T, revealing a quasi-2D Fermi surface. We observed a development of quantized plateaus in Hall resistance(R_(xy)) at high pulsed fields up to 60 T. Due to the strong 2D confinement and layered properties of the samples, we interpreted the observation as bulk quantum Hall effect that is contributed by the parallel 2D conduction channels. Moreover, the spin degeneracy was lifted leading to Landau level splitting. The presence of anisotropic g factor and the formation of the oscillation beating pattern reveal a strong spin-orbit interaction in the SrMnSb_2 system.     

Hall resistivity of granular metals

We calculate the Hall conductivity sigma(xy) and resistivity rho(xy) of a granular system at large tunneling conductance g(T)>1. We show that in the absence of Coulomb interaction the Hall resistivity depends neither on the tunneling conductance nor on the intragrain disorder and is given by the classical formula rho(xy)=H/(n*ec), where n* differs from the carrier density n inside the grains by a numerical coefficient determined by the shape of the grains. The Coulomb interaction gives rise to logarithmic in temperature T correction to rho(xy) in the range Gamma less or similar T less or similar min(g(T)E(c), E(Th)), where Gamma is the tunneling escape rate, E(c) is the charging energy, and E(Th) is the Thouless energy of the grain.     

Extrinsic spin Hall effect induced by iridium impurities in copper

We study the extrinsic spin Hall effect induced by Ir impurities in Cu by injecting a pure spin current into a CuIr wire from a lateral spin valve structure. While no spin Hall effect is observed without Ir impurity, the spin Hall resistivity of CuIr increases linearly with the impurity concentration. The spin Hall angle of CuIr, (2.1±0.6)% throughout the concentration range between 1% and 12%, is practically independent of temperature. These results represent a clear example of predominant skew scattering extrinsic contribution to the spin Hall effect in a nonmagnetic alloy.     

Strong magnetic instability in correlated metallic Bi(2)Ir(2)O(7)

We report an experimental/theoretical study of single-crystal Bi(2)Ir(2)O(7) that possesses a metallic state with strongly exchange-enhanced paramagnetism. The ground state of Bi(2)Ir(2)O(7) is characterized by the following features: (1) a divergent low-temperature magnetic susceptibility that indicates no long-range order down to 50?mK; (2) strongly field-dependent coefficients of the low-temperature T and T(3) terms of the specific heat; (3) a conspicuously large Wilson ratio R(W)?≈?53.5; and (4) unusual temperature and field dependences of the Hall resistivity that abruptly change below 80?K, without any clear correlation with the magnetic behavior. All these unconventional properties suggest the existence of an exotic ground state in Bi(2)Ir(2)O(7).     

Dissipative quantum hall effect in graphene near the Dirac point

We report on the unusual nature of the nu=0 state in the integer quantum Hall effect (QHE) in graphene and show that electron transport in this regime is dominated by counterpropagating edge states. Such states, intrinsic to massless Dirac quasiparticles, manifest themselves in a large longitudinal resistivity rho(xx) > or approximately h/e(2), in striking contrast to rho(xx) behavior in the standard QHE. The nu=0 state in graphene is also predicted to exhibit pronounced fluctuations in rho(xy) and rho(xx) and a smeared zero Hall plateau in sigma(xy), in agreement with experiment. The existence of gapless edge states puts stringent constraints on possible theoretical models of the nu=0 state.     

Topological insulators in magnetic fields: quantum Hall effect and edge channels with a nonquantized θ term

We investigate how a magnetic field induces one-dimensional edge channels when the two-dimensional surface states of three-dimensional topological insulators become gapped. The Hall effect, measured by contacting those channels, remains quantized even in situations where the θ term in the bulk and the associated surface Hall conductivities, σ(xy)(S), are not quantized due to the breaking of time-reversal symmetry. The quantization arises as the θ term changes by ±2πn along a loop around n edge channels. Model calculations show how an interplay of orbital and Zeeman effects leads to quantum Hall transitions, where channels get redistributed along the edges of the crystal. The network of edges opens new possibilities to investigate the coupling of edge channels.     

Anomalous nernst effects in pyrochlore molybdates with spin chirality

The transverse thermoelectric (Nernst) effect on pyrochlore molybdates is investigated experimentally. In Nd(2)Mo(2)O(7) and Sm(2)Mo(2)O(7) with the spin chirality, the Nernst signal, which mostly arises from the transverse heat current (or equivalently the transverse Peltier coefficient alpha(xy)), shows a low-temperature (20-30 K) positive extremum, whereas it is absent in (Gd(0.95)Ca(0.05))(2)Mo(2)O(7) with no single-spin anisotropy of the rare-earth ion and hence with no spin chirality. The correlation between the Hall conductivity sigma(xy) and alpha(xy) in Nd(2)Mo(2)O(7) also indicates the spin chirality plays a significant role in the spontaneous (anomalous) Nernst effect.     

Giant enhancement of the thermal Hall conductivity kappa(xy) in the superconductor YBa(2)Cu(3)O(7)

In high-purity YBa(2)Cu(3)O(7), the (weak-field) thermal Hall conductivity kappa(xy) is observed to increase a thousand-fold between 90 and 30 K. The inferred quasiparticle lifetime tau increases a hundred-fold starting below 90 K, in disagreement with a recent photoemission experiment. We show that kappa(xy) exhibits a specific scaling behavior below approximately 30 K. This scaling may bear on the issue of whether Landau quantization of the quasiparticle states occurs.