Construction of a ³He magnetic force microscope with a vector magnet

We constructed a $^3$He magnetic force microscope operating at the base temperature of 300 mK under a vector magnetic field of 2-2-9 T in the $x-y-z$ direction. Fiber optic interferometry as a detection scheme is employed in which two home-built fiber walkers are used for the alignment between the cantilever and the optical fiber. The noise level of the laser interferometer is close to its thermodynamic limit. The capabilities of the sub-Kelvin and vector field are demonstrated by imaging the coexistence of magnetism and superconductivity in a ferromagnetic superconductor (ErNi$_2$B$_2$C) at $T$=500 mK and by probing a dipole shape of a single Abrikosov vortex with an in-plane tip magnetization.