The iron sulphide ${\mathrm{Fe}}_3{\mathrm{S}}_4$ (greigite) is similar to its oxide counterpart ${\mathrm{Fe}}_3{\mathrm{O}}_4$ (magnetite) as to the crystal structure and ferrimagnetic order, but differs in electronic states. The ab initio calculations have evidenced $p$-type carriers at three spin-minority and three spin-majority Fermi surfaces, which is in contrast to the half-metallic character of magnetite with $n$-type carriers at three spin-minority Fermi surfaces. The transport properties including Hall and Nernst effects have been studied over the range 2–300 K by using nanogranular ceramics prepared by cold isostatic pressing of ${\mathrm{Fe}}_3{\mathrm{S}}_4$ particles with the mean crystallite size of $d_{\mathrm{XRD}}\approx 80$ and 30 nm, respectively. The samples show metalliclike electrical resistivity with large residual value at $T$ → 0 K. The $p$-type character of the charge carriers is reflected by the positive sign of both the thermopower and Hall effect. Temperature dependencies of the electrical resistivity, thermal conductivity, and thermopower are analyzed by considering processes of the grain boundary and defect intragrain scattering; simultaneously the role of magnons and their dynamics in electronic and heat transport is revealed. The Nernst and Hall effects show dominant contributions of anomalous type (ANE and AHE) with signs exactly opposite to those of ${\mathrm{Fe}}_3{\mathrm{O}}_4$, i.e., positive AHE and negative ANE in ${\mathrm{Fe}}_3{\mathrm{S}}_4$. The results are interpreted by evoking the original Callen treatment of thermoelectric and thermomagnetic phenomena using Onsager equations. Scaling between the longitudinal and transverse components of the electrical resistivity and thermoelectric conductivity tensors is checked. The analysis of the temperature dependent AHE using the relation between transverse and longitudinal resistivity ${\rho }_{yx}^A\left(T\right)\sim {\rho }_{xx}{\left(T\right)}^n$ gives the characteristic exponent $n=1.15$, which is close to the $n=1$ predicted by the skew-scattering mechanism.

• Received 18 January 2021
• Revised 2 June 2021
• Accepted 3 June 2021
• Corrected 13 April 2022

DOI:https://doi.org/10.1103/PhysRevB.103.245129