Abstract
We study the intrinsic scattering of phonons by a general quantum degree of freedom, i.e., a fluctuating “field” , which may have completely general correlations, restricted only by unitarity and translational invariance. From the induced scattering rates, generalizing the model studied in a companion paper [Mangeolle et al., Phys. Rev. X 12, 041031 (2022)], we obtain the consequences on the thermal conductivity tensor of the phonons. We confirm that, even within our generalized model, the off-diagonal scattering rates involve a minimum of three- to four-point correlation functions of the fields, and we discuss the “semiclassical” versus “quantum” nature of all contributions. We obtain general and explicit forms for these correlations which isolate the contributions to the Hall conductivity, and we provide a general discussion of the implications of symmetry and equilibrium; this elaborates on, and extends, the results of Mangeolle et al. [Phys. Rev. X 12, 041031 (2022)]. We also extend the discussion and evaluation of these two- (diagonal scattering) and four-point correlation functions, and hence the thermal transport, for the illustrative example of an ordered two-dimensional antiferromagnet, where the field is a composite of magnon operators arising from spin-lattice coupling, and confirm numerically that the results, while satisfying all the necessary symmetry restrictions, lead to nonvanishing scattering and Hall effects. In particular, we investigate, both analytically and numerically, the dependence of such intrinsic scattering on a crucial parameter—the magnon to phonon velocity ratio . We in particular confirm that within some range of of order 1 the skew-scattering mechanism leads to comparable thermal Hall conductivity for thermal currents within and normal to the plane of the antiferromagnetism, and we discover that the temperature scaling of the longitudinal conductivity displays a threshold effect and a nonuniversal, continuous variation of the scaling exponent with .
3 More- Received 13 June 2022
- Revised 26 October 2022
- Accepted 27 October 2022
DOI:https://doi.org/10.1103/PhysRevB.106.245139
©2022 American Physical Society
Physics Subject Headings (PhySH)
Viewpoint
Resolving the Achilles’ Heel of Thermal Hall Conductivity Measurements
Published 21 December 2022
For a long time, researchers assumed that phonons could not contribute to the thermal Hall effect because of their lack of charge and spin. New work challenges this assumption.
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