Distinguishing Hump-shape Hall Effects withKarplus-Luttinger and Topological Origins*

Using SrRuO₃-based thin film heterostructures, we aim to resolve the two debated interpretations that distinguish between the artefactual humps produced from overlapping double Karplus-Luttinger Anomalous Hall Effects (KL-AHE)[1] and the Geometrical/Topological Hall Effect (THE)[2], without magnetic imaging. Firstly, we prepared two heterostructures with similar hump-shape Hall features which have similar structures to earlier publications with magnetic force microscopy imaging[3,4]. Next, we performed θ-rotation of magnetic field from out-of-plane to in-plane in Hall measurement (R_xy(θ, H)) as the critical differentiation tool. The first heterostructure showing field-position of Hall hump (H_hump) diverging with ~1/cos(θ) can be correctly simulated using double Langevin loops, thus agrees with the expected behaviour of KL-AHE for topological-trivial magnetic domains. Yet, the second one showing constant Hhump with increasing θ agrees with a micromagnetic simulation with Néel-Skyrmions[5,6], thus can be convincingly assigned as Skyrmion-induced THE. The behaviour in the latter case can be explained by the Ginzburg-Landau framework of 3q spin-waves superposition for Skyrmion-lattice[7]. We further extended our investigation scope by R_xy(θ, H) to other reported heterostructures with Hall-humps such as the SrRuO₃/ferroelectric in (001)-orientation showing 2q spin-waves[8] and Pt/Tm₃Fe₅O₁₂(111)[9], and summarize the trends. We will provide magnetic imaging evidence as a strong support. We envision such R_xy(θ, H) scheme could establish as a protocol for identifying Skyrmions. Finally, in the continuous R_xy(θ) curves measured at H_peak for the second heterostructure, we discuss the finding of several periodic step-functions at θ=(n+1/2)*π/3 as a possible signature of “mirror anomaly”[10,11] arising from massive Dirac Fermions in the k-space band structure of a Skyrmion-lattice[12].