Planar thermal Hall effect from phonons in a Kitaev candidate material

Abstract

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

Topics & Concepts