Scanning nanoscale superconducting quantum interference devices (nanoSQUIDs) are of growing interest for highly sensitive quantitative imaging of magnetic, spintronic, and transport properties of low-dimensional systems. Utilizing specifically designed grooved quartz capillaries pulled into a sharp pipette, we have fabricated the smallest SQUID-on-tip (SOT) devices with effective diameters down to 39 nm. Integration of a resistive shunt in close proximity to the pipette apex combined with self-aligned deposition of In and Sn, have resulted in SOT with a flux noise of 42 n$Phi_0$Hz$^{-1/2}$, yielding a record low spin noise of 0.29 $mu_B$Hz$^{-1/2}$. In addition, the new SOTs function at sub-Kelvin temperatures and in high magnetic fields of over 2.5 T. Integrating the SOTs into a scanning probe microscope allowed us to image the stray field of a single Fe$_3$O$_4$ nanocube at 300 mK. Our results show that the easy magnetization axis direction undergoes a transition from the (111) direction at room temperature to an in-plane orientation, which could be attributed to the Verwey phase transition in Fe$_3$O$_4$.
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