Spin nematic liquid crystal and scalar spin chirality in tetragonal lattice YbMnBi$_2$
A spin nematic order, analogous to the nematic liquid crystal, characterizes the spontaneous breaking of spin-space rotational symmetry while preserving time-reversal ($T$) symmetry. In contrast, scalar spin chirality (SSC), a composite three-spin order, breaks $T$ symmetry and is known to induce an anomalous Hall effect (AHE). Although a spin nematic phase has been suggested in frustrated magnets and the square-lattice iridate, how it might affect magnetotransport properties is unknown. Here we use polarized neutron scattering to show that tetragonal $A$MnBi$_2$ ($A$ = Ca, Yb) is a strictly $c$-axis-aligned collinear antiferromagnet (C-type), with $T_N \approx 270$ K and 290 K, respectively. On cooling from 450 K to $T_N$, low-energy spin excitations in YbMnBi$_2$ spontaneously change from isotropic to anisotropic in spin space within the tetragonal plane, forming a dynamic spin nematic phase around 400 K due to heavy Yb-induced spin-orbit coupling, before gapping out below $T_N$. Similar measurements on CaMnBi$_2$ reveal isotropic paramagnetic scattering without a spin nematic phase above $T_N$. Under an in-plane magnetic field, the Yb$^{3+}$ moments may interact with the dynamic spin nematic phase to induce nonzero SSC, giving rise to AHE and an anomalous Nernst effect (ANE) in YbMnBi$_2$ that are absent in CaMnBi$_2$ above $T_N$. A symmetry-based Ginzburg-Landau analysis shows that coupling terms between the nematic order and SSC are allowed under an external magnetic field, which could explain the rapid increase of AHE with field in YbMnBi$_2$. Our results provide compelling evidence for dynamic SSC-induced AHE and ANE in the paramagnetic phase of a compensated collinear antiferromagnet, opening a new avenue for the physics of composite spin orders and room-temperature spintronics without magnetic order.