Thermal fluctuations induced scalar spin chirality in spin-trimer ferromagnet probed by Hall and Nernst effects

The scalar spin chirality (SSC) is defined as a mixed product of three neighbouring, non-coplanarly oriented spins: $\chi_{ijk} = S_i \cdot (S_j \times S_k)$. When SSC becomes non-zero, it affects the motion of conduction electrons causing them to accumulate the Berry phase and thus experience the presence of emergent, fictitious magnetic field. This gives a rise to the geometrical responses in off-diagonal transport properties such as Hall and Nernst effects, and thus provides a direct link between the magnetic structure topology and measurable experimental observables. The finite SSC has been found to arise from the long range magnetic ordering with non-coplanarly arranged spins [1] or from spin textures such as skyrmions [2]. Next to the static spin arrangements, it has been previously been found that the scalar spin chirality can also originate from an average structure of thermally canted spins [3,4]. The experimental reports on this scenario were however rare, and limited to the materials with conduction electrons strongly Hund's-rule coupled to the local magnetic moments.

We demonstrate that the mechanism of scalar spin chirality induced by thermal fluctuations is not an unique property of strongly coupled magnets, but is relevant also for the highly conducting magnetic material with weak coupling scheme of the itinerant electrons. Our experimental evidence is based on the observation of the geometrical features in both Hall and Nernst responses near the Curie temperature of Nd3Ru4Al12 [5], a ferromagnet with magnetic structure constructed of spin trimers [6]. Additional support to the experiment is delivered by Monte Carlo simulations of a classical spin model.

We find that the responses caused by the emergence of SSC created by thermal fluctuation in the vicinity of the Curie temperature are large, and even exceed the spin-coupling driven anomalous transport contributions [5]. Further analysis of the geometrical counterparts of Hall and Nernst effects, including the comparison of their sign and magnitude in fundamental units, we find the arguments for the necessity to employ the momentum space Berry curvature approach [7,8] to model the link between scalar spin chirality and transport responses.

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[4] W. Wang et al., Nature Materials 18, 1054-1059 (2019)
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[6] D. I. Gorbunov et al., Physical Review B 93, 024407 (2016)
[7] L. Xu et al., Physical Review B 101, 180404(R) (2020)
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