In this letter, we study the origin of the anomalous Hall effect (AHE) in ferrimagnetic insulator ${\mathrm{Tm}}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12}$ (TmIG)/Pt heterostructures. A monotonic decrease of the anomalous Hall resistivity ($\mathrm{\Delta }{\rho }_{\mathrm{AHE}}$) with decreasing temperature is observed for TmIG/Pt, and a sign reversal of $\mathrm{\Delta }{\rho }_{\mathrm{AHE}}$ occurs at around 80 K. With the addition of a Cu interlayer, the $\mathrm{\Delta }{\rho }_{\mathrm{AHE}}$ similarly decreases as a function of temperature, but maintains the same sign across the full temperature range. This indicates that both the magnetic-proximity effect and spin Hall effect in the TmIG/Pt bilayer contribute to the AHE signal with opposing signs. The spin-Hall contribution to the AHE is dominant at room temperature but decreases with decreasing temperature. Meanwhile, the magnetic-proximity contribution to the AHE becomes dominant with decreasing temperatures, leading to a change of sign for $\mathrm{\Delta }{\rho }_{\mathrm{AHE}}$. We exclude a dominant influence of a ferrimagnetic compensation point in the temperature region by complementary magnetic hysteresis and neutron diffraction measurements. Our work, based on a simple method, sheds light on the origin of the AHE in magnetic insulator heterostructures, where the competition between the magnetic-proximity effect and spin Hall effect governs the sign and amplitude of the AHE.

We studied the effect of hydrostatic pressure on the magnetic properties of the highly anisotropic van der Waals ferromagnetic metal ${\mathrm{Fe}}_3\mathrm{Ge}{\mathrm{Te}}_2$ (FGT) with the field applied along the easy axis. The paramagnetic-to-ferromagnetic transition occurs at the Curie temperature $T_c=180\mathrm{K}$ at ambient pressure, and $T_c$ decreases monotonically by up to 15 K as the pressure increases up to 1.44 GPa, while the magnetization is suppressed by the pressure. By using high-pressure x-ray diffraction techniques, we found that the Fe-Fe bond lengths tend to decrease, and the Fe-Ge(Te)-Fe bond angles deviate away from ${90}^{\circ }$ under hydrostatic pressures, indicating the modification of the exchange interactions. First-principles calculations further confirm the pressure effects. These results suggest that the competition between direct-, super-, and double-exchange interactions plays a crucial role in the pronounced magnetic response under the hydrostatic pressure, i.e., the direct-exchange becomes stronger at a higher pressure and, hence, leading to increased antiferromagnetic components and thus deceased $T_c$. The highly tunable magnetic properties under hydrostatic pressure in this system provide robust routes for spin manipulation in low-dimensional material systems.