Magnetic Phase-Dependent Nonlinear Hall Transport in Ca₃Ru₂O₇

Non-linear Hall effect in non-centrosymmetric materials offers a unique lens into band topology, particularly in relation to symmetry and quantum geometry. While prior research has primarily centered around weakly correlated systems, recent theoretical insight suggests that strong electronic correlations can significantly enhance nonlinear transport signals [1]. In this talk, we present our findings on nonlinear response in the correlated bilayer ruthenate Ca₃Ru₂O₇. This material is well studied due to its strong electronic correlations, spin-orbit coupling, and rich magnetic phase diagram [2]. It undergoes antiferromagnetic ordering below T_N = 56K, with moments along the a-axis, followed by a spin reorientation transition at T_S = 48K, where the moments switch to the b-axis. Below T_S = 48K, the material also transitions into a canted antiferromagnetic state under an applied field along the b-axis [2]. The spin reorientation transition coincides with an electronic transition that opens a pseudogap and introduces Dirac nodes at the M point [3]. Our transport measurements reveal a significant enhancement of nonlinear response below T_S, coinciding with the emergence of Dirac fermions. Furthermore, we find that the nonlinear signal is suppressed in the canted antiferromagnetic phase, highlighting the intricate interplay between magnetic ordering and band topology in this material. Our theoretical studies suggest that the NLHE seen in Ca₃Ru₂O₇ has intrinsic origin, with contributions from both Berry curvature dipole and quantum geometry. This study underscores the potential of nonlinear Hall effect as a sensitive probe of band topology across multiple magnetic phases.