The Hall effect usually occurs in conductors when the Lorentz force acts on a charge current in the presence of a perpendicular magnetic field. Neutral quasi-particles such as phonons and spins can, however, carry heat current and potentially exhibit the thermal Hall effect without resorting to the Lorentz force. We report experimental evidence for the anomalous thermal Hall effect caused by spin excitations (magnons) in an insulating ferromagnet with a pyrochlore lattice structure. Our theoretical analysis indicates that the propagation of the spin waves is influenced by the Dzyaloshinskii-Moriya spin-orbit interaction, which plays the role of the vector potential, much as in the intrinsic anomalous Hall effect in metallic ferromagnets.

Noncentrosymmetric conductors are an interesting material platform, with rich spintronic functionalities 1,2 and exotic superconducting properties 3,4 typically produced in polar systems with Rashba-type spin-orbit interactions 5 . Polar conductors should also exhibit inherent nonreciprocal transport [6][7][8] , in which the rightward and leftward currents di er from each other. But such a rectification is di cult to achieve in bulk materials because, unlike the translationally asymmetric p-n junctions, bulk materials are translationally symmetric, making this phenomenon highly nontrivial. Here we report a bulk rectification e ect in a three-dimensional Rashba-type polar semiconductor BiTeBr. Experimentally observed nonreciprocal electric signals are quantitatively explained by theoretical calculations based on the Boltzmann equation considering the giant Rashba spin-orbit coupling. The present result o ers a microscopic understanding of the bulk rectification e ect intrinsic to polar conductors as well as a simple electrical means to estimate the spin-orbit parameter in a variety of noncentrosymmetric systems.The effect of the lattice symmetry on the electronic states is a fundamental issue in condensed matter physics. In particular, broken inversion symmetry in the crystal structure generally causes spin band splitting which modifies the electronic ground state, affecting transport properties represented by the superconductivity in noncentrosymmetric systems 3,4 or spin-related transport in nonmagnetic materials 1,2 . Among them, Rashba-5 and Dresselhaus 9 -type spin-orbit interactions are two well-known textbook models which have succeeded in explaining a variety of exotic phenomena in systems without inversion symmetry.Although the Rashba effect has been conventionally studied at surfaces or interfaces [10][11][12][13][14] , the recent discovery of three-dimensional (3D) materials which host a large Rashba-type band splitting [15][16][17][18] pave the way towards exploring novel transport originating from the 3D chiral spin-texture of the electronic band. BiTeX (X = I, Br) is one such bulk polar semiconductor, in which Bi, Te and X layers are stacked alternately so that the mirror symmetry along the c axis is broken (Fig. 1a). The resultant Rashba-type spin splitting of the electronic bands has been confirmed by angle-resolved photoemission spectroscopy (ARPES) 15,16 and the transport signatures of the split Fermi surface have been reported by quantum oscillations in resistance 19 or thermoelectric coefficients 20 . However, characteristic magneto-transport reflecting the spin polarization in the electronic band or polarity of the crystal has been elusive, except for photocurrent experiments on BiTeBr 21 . One of the manifestations of lattice symmetry breaking in electric transport is the rectification effect. In the presence of an in-plane magnetic field, the Rashba-type spin band splitting is modulated to become asymmetric along a direction perpendicular to both the polar axis and the magnetic field (Fig. ...

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The longitudinal spin Seebeck effect has been investigated for a uniaxial antiferromagnetic insulator Cr(2)O(3), characterized by a spin-flop transition under magnetic field along the c axis. We have found that a temperature gradient applied normal to the Cr(2)O(3)/Pt interface induces inverse spin Hall voltage of spin-current origin in Pt, whose magnitude turns out to be always proportional to magnetization in Cr(2)O(3). The possible contribution of the anomalous Nernst effect is confirmed to be negligibly small. The above results establish that an antiferromagnetic spin wave can be an effective carrier of spin current.

Giant nonreciprocal transport effect in noncentrosymmetric superconductors is studied both theoretically and experimentally.

We have investigated the thermal Hall effect of magnons for various ferromagnetic insulators. For pyrochlore ferromagnetic insulators Lu 2 V 2 O 7 , Ho 2 V 2 O 7 , and In 2 Mn 2 O 7 , finite thermal Hall conductivities have been observed below the Curie temperature T C . From the temperature and magnetic field dependences, it is concluded that magnons are responsible for the thermal Hall effect. The Hall effect of magnons can be well explained by the theory based on the Berry curvature in momentum space induced by the Dzyaloshinskii-Moriya (DM) interaction. The analysis has been extended to the transition metal (TM) oxides with perovskite structure. The thermal Hall signal was absent or far smaller in La 2 NiMnO 6 and YTiO 3 , which have the distorted perovskite structure with four TM ions in the unit cell. On the other hand, a finite thermal Hall response is discernible below T C in another ferromagentic perovskite oxide BiMnO 3 , which shows orbital ordering with a larger unit cell. The presence or absence of the thermal Hall effect in insulating pyrochlore and perovskite systems reflect the geometric and topological aspect of DM-induced magnon Hall effect. PACS numbers: 72.20.-i, 75.47.-m, 75.76.+j 1 arXiv:1201.3002v2 [cond-mat.mtrl-sci]

The spontaneous Hall effect driven by the quantum Berry phase (which serves as an internal magnetic flux in momentum space) manifests the topological nature of quasiparticles and can be used to control the information flow, such as spin and valley. We report a Hall effect of excitons (fundamental composite particles of electrons and holes that dominate optical responses in semiconductors). By polarization-resolved photoluminescence mapping, we directly observed the Hall effect of excitons in monolayer MoS and valley-selective spatial transport of excitons on a micrometre scale. The Hall angle of excitons is found to be much larger than that of single electrons in monolayer MoS (ref. ), implying that the quantum transport of the composite particles is significantly affected by their internal structures. The present result not only poses a fundamental problem of the Hall effect in composite particles, but also offers a route to explore exciton-based valleytronics in two-dimensional materials.

Chirality of materials are known to affect optical, magnetic and electric properties, causing a variety of nontrivial phenomena such as circular dichiroism for chiral molecules, magnetic Skyrmions in chiral magnets and nonreciprocal carrier transport in chiral conductors. On the other hand, effect of chirality on superconducting transport has not been known. Here we report the nonreciprocity of superconductivity—unambiguous evidence of superconductivity reflecting chiral structure in which the forward and backward supercurrent flows are not equivalent because of inversion symmetry breaking. Such superconductivity is realized via ionic gating in individual chiral nanotubes of tungsten disulfide. The nonreciprocal signal is significantly enhanced in the superconducting state, being associated with unprecedented quantum Little-Parks oscillations originating from the interference of supercurrent along the circumference of the nanotube. The present results indicate that the nonreciprocity is a viable approach toward the superconductors with chiral or noncentrosymmetric structures.