Unusual anomalous Hall effect in SrRuO₃ films with linear out-of-plane Ru vacancies gradient

The manipulation of magnetic transport properties has been one of the central problems in spintronics. However, the modulation of Hall signals in thin films has stringent requirements on their thickness and means of growth. Here, a series of inhomogeneous SrRuO3 thin films with different paths of linear out-of-plane Ru vacancies gradient was designed to generate an unusual anomalous Hall effect (UAHE) under broad growth conditions. Combining x-ray diffraction and magnetic data, it was concluded that the appearance of UAHE was not a simple superposition of AHE caused by multiple magnetic phases. The interaction between these magnetic phases in the linear-vacancies-gradient SrRuO3 films was analyzed by the first-order reversal curve (FORC) method, and it was found that the change trend of FORC was the same as that of UAHE. Such out-of-plane linear-vacancies-gradient thin film provides a way to regulate the different phases by introducing the cation vacancies distribution in an orderly way to control their magnetic and transport properties in oxide films. Furthermore, a distinctive perspective on the origin of UAHE was obtained by combining FORC with UAHE.