Topological Nernst effect emerging from real-space gauge field and thermal fluctuations in a magnetic skyrmion lattice

Recent studies on quantum transport in metals have revealed that a gauge field acting on the electron wavefunction yields a peculiar Hall or Nernst effect. When topologically nontrivial spin textures are present, a gauge field appears in real space and affects the electron transport. However, the understanding of the Nernst effect emerging from a real-space gauge field (topological Nernst effect) remains qualitative, and moreover, the influence of thermal fluctuations has been elusive. Here, we report a pronounced temperature-dependent topological Nernst effect in the metastable skyrmion lattice in MnSi. Our density functional theory, assuming a temperature-independent gauge field, is successful in an order-of-magnitude estimate of the Nernst signal, whereas the experimental values decrease more significantly with increasing temperature. A similar tendency is observed for the topological Hall effect, thus indicating that pronounced suppression of the real-space gauge field is crucial for the quantitative understanding of the quantum transport induced by topological spin textures at finite temperatures.