Phonon Thermal Hall Effect in Mott Insulators via Skew Scattering by the Scalar Spin Chirality
Taekoo Oh, Naoto Nagaosa
Abstract
Thermal transport is a crucial probe for studying excitations in insulators. In Mott insulators, the primary candidates for heat carriers are spins and phonons; which of these candidates dominates the thermal conductivity is a persistent issue. Typically, phonons dominate the longitudinal thermal conductivity while the thermal Hall effect (THE) is primarily associated with spins, requiring time-reversal symmetry breaking. The coupling between phonons and spins usually depends on spin-orbit interactions and is relatively weak. Here, we propose a new mechanism for this coupling and the associated THE: the skew scattering of phonons via spin fluctuations by the scalar spin chirality. This coupling does not require spin-orbit interactions and is ubiquitous in Mott insulators, leading to a thermal Hall angle on the order of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msup> <a:mn>10</a:mn> <a:mrow> <a:mo>−</a:mo> <a:mn>3</a:mn> </a:mrow> </a:msup> </a:math> to <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msup> <c:mn>10</c:mn> <c:mrow> <c:mo>−</c:mo> <c:mn>2</c:mn> </c:mrow> </c:msup> </c:math> . Based on this mechanism, we investigate the THE in <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mrow> <e:msub> <e:mrow> <e:mi>YMnO</e:mi> </e:mrow> <e:mrow> <e:mn>3</e:mn> </e:mrow> </e:msub> </e:mrow> </e:math> with a trimerized triangular lattice where the THE beyond spins was recognized, and we predict the THE in the kagome and square lattices.