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The inverse spinel ferrimagnetic NiCo$_2$O$_4$ possesses high magnetic Curietemperature $T_C$, high spin polarization, and strain-tunable magneticanisotropy. Understanding the thickness scaling limit of these intriguingmagnetic properties in NiCo$_2$O$_4$ thin films is critical for theirimplementation in nanoscale spintronic applications. In this work, we reportthe unconventional magnetotransport properties of epitaxial (001) NiCo$_2$O$_4$films on MgAl$_2$O$_4$ substrates in the ultrathin limit. Anomalous Hall effectmeasurements reveal strong perpendicular magnetic anisotropy for films down to1.5 unit cell (1.2 nm), while $T_C$ for 3 unit cell and thicker films remainsabove 300 K. The sign change in the anomalous Hall conductivity ($\sigma_{xy}$)and its scaling relation with the longitudinal conductivity ($\sigma_{xx}$) canbe attributed to the competing effects between impurity scattering and bandintrinsic Berry curvature, with the latter vanishing upon the thickness drivenmetal-insulator transition. Our study reveals the critical role of filmthickness in tuning the relative strength of charge correlation, Berry phaseeffect, spin orbit interaction, and impurity scattering, providing importantmaterial information for designing scalable epitaxial magnetic tunnel junctionsand sensing devices using NiCo$_2$O$_4$.

Anomalous Hall Effect and Perpendicular Magnetic Anisotropy in Ultrathin Ferrimagnetic NiCo$_2$O$_4$ Films