We are interested in how to achieve much higher thermoelectric conversion efficiency by effectively manipulating electron-spin degree of freedom. As one possibility, we have been studying Berry-phase-mediated thermoelectric effects, namely the contribution of the anomalous Hall conductivity (AHC) to thermoelectric power. What we target here is the anomalous Nernst effect (ANE), which is a heat-to-electricity conversion observed in magnetic materials and directly related to AHC. We discussed AHC mainly driven by an effective magnetic field, Berry curvature, induced by spin-orbit coupling and/or spin chirality.

Fig. 1. (a) Calculated spin structures for skyrmion of EuO monolayer model. (b) Calculated band structure, (c) chemical potential dependence of anomalous Nernst coefficients and (d) power factors. Results are shown for different values of temperature 100K and 300K. We assumed the constant relaxation time τ = 10 fs.

We have so far found from computations on some models that, in the so-called 2D Skyrmion crystal (SkX) phase, where skyrmions are crystallized in two dimensions, the crystal-momentum component of effective magnetic field gives rise to the band structure that could generate large ANE when chemical potential μ is properly tuned [1]. Although this behavior was most clearly confirmed in the simplest model of square SkX with single s-orbital per site, our subsequent computations on more realistic models of transition-metal oxides also showed possible large ANE [2]. A sizable transverse thermoelectric coefficient is predicted to arise, by means of first-principles calculations, in a SkX assumed on EuO monolayer (Fig. 1(a)) where carrier electrons are introduced upon a quantum anomalous Hall insulating phase of Chern number C = 2. This encourages future experiments to pursue such an effect.

Figure 1 (b) shows the band structure of electron-doped EuO monolayer. There is a narrow band gap of ~20 meV between the valence band top and conduction band bottom. The Chern number was calculated by integrating Berry curvatures of Brillouin zone. The occupied two bands with Chern number C = 2 are mainly composed of Eu 5d and 6s characters. We have calculated anomalous Nernst coefficients N and pure Nernst coefficients N₀ ≡ α_xy/σ_xy [2] by using semiclassical Boltzmann transport theory with constant relaxation time, τ = 10 fs. The calculated chemical potential dependence of Nernst coefficients N, pure Nernst coefficients and power factor are plotted in Fig 1(c) and (d). The large anomalous Nernst coefficients up to 60 μV/K and power factor up to 70 μW/mK² can be obtained.

Such N arises from the coexistence of large longitudinal thermoelectric coefficient and large Hall angle ratio, realized in the vicinity of a narrow band gap with Chern number C = 2. This demonstrates a prototype of novel class of new thermoelectric materials utilizing the nanoscale topological spin textures, motivating further studies including relevant experiments. We concluded that the SkX and narrow-gap Chern insulators could be candidate materials for thermoelectric applications.

References

• [1] Y. P. Mizuta and F. Ishii, Sci. Rep. 6, 28076 (2016).
• [2] Y. P. Mizuta, H. Sawahata, and F. Ishii, Phys. Rev. B 98, 205125 (2018).

Authors

• F. Ishii^a, Y.P. Mizuta^b, and H. Sawahata^a
• ^aKanazawa University
• ^bOsaka University