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

Abstract: The inverse spinel ferrimagnetic NiCo$2$O$_4$ possesses high magnetic Curie temperature $T_C$, high spin polarization, and strain-tunable magnetic anisotropy. Understanding the thickness scaling limit of these intriguing magnetic properties in NiCo$_2$O$_4$ thin films is critical for their implementation in nanoscale spintronic applications. In this work, we report the unconventional magnetotransport properties of epitaxial (001) NiCo$_2$O$_4$ films on MgAl$_2$O$_4$ substrates in the ultrathin limit. Anomalous Hall effect measurements reveal strong perpendicular magnetic anisotropy for films down to 1.5 unit cell (1.2 nm), while $T_C$ for 3 unit cell and thicker films remains above 300 K. The sign change in the anomalous Hall conductivity ($\sigma{xy}$) and its scaling relation with the longitudinal conductivity ($\sigma_{xx}$) can be attributed to the competing effects between impurity scattering and band intrinsic Berry curvature, with the latter vanishing upon the thickness driven metal-insulator transition. Our study reveals the critical role of film thickness in tuning the relative strength of charge correlation, Berry phase effect, spin orbit interaction, and impurity scattering, providing important material information for designing scalable epitaxial magnetic tunnel junctions and sensing devices using NiCo$_2$O$_4$.