Planar thermal Hall effect from phonons in a Kitaev candidate material.

Chen, Lu; Lefrançois, Étienne; Vallipuram, Ashvini; Barthélemy, Quentin; Ataei, Amirreza; Yao, Weiliang; Li, Yuan; Taillefer, Louis · Nat Commun · 2024

basic_science · Level V

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Abstract

The thermal Hall effect has emerged as a potential probe of exotic excitations in spin liquids. In the Kitaev magnet <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>α</mi></math> -RuCl<sub>3</sub>, the thermal Hall conductivity <math xmlns="http://www.w3.org/1998/Math/MathML"> <msub><mrow><mi>κ</mi></mrow> <mrow><mi>x</mi> <mi>y</mi></mrow> </msub> </math> has been attributed to Majorana fermions, chiral magnons, or phonons. Theoretically, the former two types of heat carriers can generate a "planar" <math xmlns="http://www.w3.org/1998/Math/MathML"> <msub><mrow><mi>κ</mi></mrow> <mrow><mi>x</mi> <mi>y</mi></mrow> </msub> </math> , whereby the magnetic field is parallel to the heat current, but it is unknown whether phonons also could. Here we show that a planar <math xmlns="http://www.w3.org/1998/Math/MathML"> <msub><mrow><mi>κ</mi></mrow> <mrow><mi>x</mi> <mi>y</mi></mrow> </msub> </math> is present in another Kitaev candidate material, Na<sub>2</sub>Co<sub>2</sub>TeO<sub>6</sub>. Based on the striking similarity between <math xmlns="http://www.w3.org/1998/Math/MathML"> <msub><mrow><mi>κ</mi></mrow> <mrow><mi>x</mi> <mi>y</mi></mrow> </msub> </math> and the phonon-dominated thermal conductivity <math xmlns="http://www.w3.org/1998/Math/MathML"> <msub><mrow><mi>κ</mi></mrow> <mrow><mi>x</mi> <mi>x</mi></mrow> </msub> </math> , we attribute the effect to phonons. We observe a large difference in <math xmlns="http://www.w3.org/1998/Math/MathML"> <msub><mrow><mi>κ</mi></mrow> <mrow><mi>x</mi> <mi>y</mi></mrow> </msub> </math> between different configurations of heat current and magnetic field, which reveals that the direction of heat current matters in determining the planar <math xmlns="http://www.w3.org/1998/Math/MathML"> <msub><mrow><mi>κ</mi></mrow> <mrow><mi>x</mi> <mi>y</mi></mrow> </msub> </math> . Our observation calls for a re-evaluation of the planar <math xmlns="http://www.w3.org/1998/Math/MathML"> <msub><mrow><mi>κ</mi></mrow> <mrow><mi>x</mi> <mi>y</mi></mrow> </msub> </math> observed in <math xmlns="http://www.w3.org/1998/Math/MathML"><mspace></mspace> <mi>α</mi></math> -RuCl<sub>3</sub>.