GENERAL SCIENTIFIC SUMMARY
Introduction and background. The phonon Hall effect (PHE) was discovered experimentally by Strohm et al in 2005; the authors found a temperature difference in the direction perpendicular to both the heat flow and the magnetic field in paramagnetic dielectrics. Few theoretical models for the PHE have been proposed by treating the spin–phonon interaction perturbatively. In this work, we use an exact nonperturbative theory – the nonequilibrium Green function (NEGF) approach – to study the ballistic PHE in nanosystems

Main results. An exact theory to study the ballistic PHE via the NEGF formulation is proposed in this work. We find that there is a PHE in nanoscale paramagnetic dielectrics, the magnitude of which is comparable to millimeter scale experiments. We find that there is no PHE if the lattice dynamic matrix satisfies mirror reflection symmetry, which is the key for the existence of PHE. The Hall temperature difference changes sign if the magnetic field is sufficiently large or if it increases in size.

Wider implications. The theory proposed in this work can be applied to the study of the ballistic PHE in different paramagnetic materials. Our results can be verified by experiments on nanoscale paramagnetic dielectrics, which have potential applications for controlling nanoscale phonon transport. For most paramagnetic dielectric materials, the dynamic matrix does not satisfy mirror reflection symmetry, and so the PHE can be present.

Figure. Variation of Hall temperature with magnetic field at a temperature of 5.45 K. The hexagons and squares correspond to the central regions for honeycomb and square lattices with nearest-neighbor coupling. The red dotted line corresponds to a linear fit from 0 to 40 T. Inset: the four-terminal PHE setup used for calculating the thermal conductance and the temperature difference: (a) the central area can be either a square lattice (b) or a honeycomb lattice (c).

72.20.My Galvanomagnetic and other magnetotransport effects

75.20.-g Diamagnetism, paramagnetism, and superparamagnetism

77.84.-s Dielectric, piezoelectric, ferroelectric, and antiferroelectric materials

73.63.Rt Nanoscale contacts

63.20.-e Phonons in crystal lattices

85.35.-p Nanoelectronic devices

Electronics and devices

Condensed matter: electrical, magnetic and optical

Semiconductors

Condensed matter: structural, mechanical & thermal

Nanoscale science and low-D systems

Issue 11 (November 2009)

Received 24 July 2009

Published 20 November 2009