Fig. 4: Asymmetric anomalous Nernst conductivity.

a Anomalous Nernst conductivity as a function of temperature at zero magnetic field. b Temperature dependence of symmetric and antisymmetric components of the anomalous Nernst conductivity at zero magnetic field. c Comparison of S_ij and S_ij/M of SISO with other magnetic oxides with significant ANE, including Nd₂Mo₂O₇⁴⁰, Fe₃O₄⁴¹, SrRuO₃⁴², and La_0.7Sr_0.3CoO₃⁴³. d The schematic of possible mechanism for the time-reversal odd and symmetric component of the ANE. The red and blue shade represent the hot and cold end, respectively. J^s represents a magnon-driven longitudinal spin current between the hot and cold ends. E^sym represent the transverse electric field induced by J^s via the inverse spin Hall effect. The left and middle configurations are related by exchanging the roles of the two axes, illustrating the symmetric relation. The middle and right configurations are related by reversing the magnetic order parameter M, illustrating the time-reversal odd nature of the mechanism. The error bars arise from propagation of uncertainty.