Theory of the Thermal Hall Effect in Quantum Magnets

An electron hopping on non-coplanar spin sites with spin chirality obtains a complex phase factor (Berry phase) in its quantum mechanical amplitude that acts as an internal magnetic field, and is predicted to manifest itself in the Hall effect when it is not cancelled. The present combined work of transport measurement, neutron scattering, and theoretical calculation provides evidence that the gigantic anomalous Hall effect observed in Nd2Mo2O7, a pyrochlore ferromagnet with geometrically frustrated lattice structure, is mostly due to the spin chirality and the associated Berry phase originating from the Mo spin tilting.

1H NMR and static susceptibility measurements have been performed in an organic Mott insulator with a nearly isotropic triangular lattice, kappa-(BEDT-TTF)2Cu2(CN)(3), which is a model system of frustrated quantum spins. The static susceptibility is described by the spin S=1/2 antiferromagnetic triangular-lattice Heisenberg model with the exchange constant J approximately 250 K. Regardless of the large magnetic interactions, the 1H NMR spectra show no indication of long-range magnetic ordering down to 32 mK, which is 4 orders of magnitude smaller than J. These results suggest that a quantum spin liquid state is realized in the close proximity of the superconducting state appearing under pressure.

We have performed thermodynamic and neutron scattering measurements on the S=1/2 kagomé lattice antiferromagnet ZnCu3(OH)6Cl2. The susceptibility indicates a Curie-Weiss temperature of theta CW approximately = -300 K; however, no magnetic order is observed down to 50 mK. Inelastic neutron scattering reveals a spectrum of low energy spin excitations with no observable gap down to 0.1 meV. The specific heat at low-T follows a power law temperature dependence. These results suggest that an unusual spin liquid state with essentially gapless excitations is realized in this kagomé lattice system.