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A controversy arose over the interpretation of the recently observed humpfeatures in Hall resistivity $\rho_{xy}$ from ultra-thin SrRuO$_3$ (SRO) film;it was initially interpreted to be due to topological Hall effect but was laterproposed to be from existence of regions with different anomalous Hall effect(AHE). In order to settle down the issue, we performed Hall effect as well asmagneto-optic Kerr-effect measurements on 4 unit cell SRO films grown onSrTiO$_3$ (001) substrates. Clear hump features are observed in the measured$\rho_{xy}$, whereas neither hump feature nor double hysteresis loop is seen inthe Kerr rotation which should be proportional to the magnetization. Inaddition, magnetization measurement by superconducting quantum interferencedevice shows no sign of multiple coercive fields. These results show thatinhomogeneous AHE alone cannot explain the observed hump behavior in$\rho_{xy}$ data from our SRO ultra-thin films. We found that emergence of thehump structure in $\rho_{xy}$ is closely related to the growth condition, highquality films having clear sign of humps.

Hump-like structure in Hall signal from SrRuO$_3$ ultra-thin films without inhomogeneous anomalous Hall effect