Spin Spiral and Topological Hall Effect in a Metamagnet Fe${}_3$Ga${}_4$

A new mechanism for Topological Hall Effect (THE) was recently proposed for the spiral magnet YMn${}_6$Sn${}_6,$ which requires transverse conical spiral (TCS) magnetism, induced by external magnetic field, combined with thermally excite helical spiral magnons. In principle, this mechanism should be applicable to other itinerant spiral magnets as well. In this paper, we show that another metamagnetic compound, Fe${}_3$Ga${}_4$, where THE was observed experimentally before, in one of its phases satisfies this condition, and the proposed theory of thermal-fluctuation driven THE is quantitatively consistent with the experiment. This finding suggests that this mechanism is indeed rather universal, and the effect may have been observed in other compounds before, but overlooked.