Topological thermal Hall effect and nondissipative transport of the nanometric skyrmion lattice in Gd2PdSi3

We report the first observation of a topological thermal Hall effect (tTHE) of electrons moving through a magnetic skyrmion lattice (SkL) of short period, where the skyrmion diameter is only a few nanometers. In the hexagonal intermetallic Gd₂PdSi₃, we observe a characteristic anomaly in the magnetic field dependence of the thermal Hall conductivity <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>κ</mml:mi> <mml:mrow><mml:mi>x</mml:mi> <mml:mi>y</mml:mi></mml:mrow> </mml:msub> </mml:math> , which scales well with the anomaly in the electrical Hall conductivity <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>σ</mml:mi> <mml:mrow><mml:mi>x</mml:mi> <mml:mi>y</mml:mi></mml:mrow> </mml:msub> </mml:math> and is closely related to the topological winding number of the SkL ground state. The relative magnitude of entropy and charge currents, defined as the Lorenz ratio <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>∼</mml:mo> <mml:msub><mml:mi>κ</mml:mi> <mml:mrow><mml:mi>x</mml:mi> <mml:mi>y</mml:mi></mml:mrow> </mml:msub> <mml:mo>/</mml:mo> <mml:mo>(</mml:mo> <mml:msub><mml:mi>σ</mml:mi> <mml:mrow><mml:mi>x</mml:mi> <mml:mi>y</mml:mi></mml:mrow> </mml:msub> <mml:mi>T</mml:mi> <mml:mo>)</mml:mo></mml:math> , is consistent with a nondissipative, or intrinsic, mechanism for the topological Hall effect. We stress that the Berry phase in momentum space ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>k</mml:mi></mml:math> -space) causes such a nondissipative Hall transport, independent of the carrier relaxation time.