DEVICE MOBILITY MEASUREMENTSThe device is first characterized in the dark state by applying a constant drainsource voltage V ds = 100 mV and sweeping the back-gate voltage V bg . The effective field-effect mobility of the device with 90 nm Au contacts and KOH/O 2 plasma surface pretreatment is estimated from the back gate sweep using the equation � = !" !" !" !" × ! !! ! ! !" where L=1 µm is the channel length, W = 2 µm channel width C i = 1.3×10 -4 Fm -2 the back gate capacitance (C i = ε 0 ε r /d; ε r = 3.9, d = 270 nm). For the device shown in Figure 1a in the manuscript, we obtain the fieldeffect mobility µ = 4 cm 2 /Vs, typical of monolayer MoS 2 devices.

Under conditions where the angular momentum of a ferromagnetic particle is dominated by intrinsic spin, applied torque is predicted to cause gyroscopic precession of the particle. If the particle is sufficiently isolated from the environment, a measurement of spin precession can potentially yield sensitivity to torque beyond the standard quantum limit. Levitation of a micron-scale ferromagnetic particle above a superconductor is a possible method of near frictionless suspension enabling observation of ferromagnetic particle precession and ultrasensitive torque measurements. We experimentally investigate the dynamics of a micron-scale ferromagnetic particle levitated above a superconducting niobium surface. We find that the levitating particles are trapped in potential minima associated with residual magnetic flux pinned by the superconductor and, using an optical technique, characterize the quasiperiodic motion of the particles in these traps.

Room temperature optically detected magnetic resonance of a single quantum object with nanoscale position control is an outstanding challenge in many areas, particularly in the life sciences. We introduce a novel approach to control the nitrogen-vacancy (NV) centers hosted in a single fluorescent nanodiamond (FND) for which an anti-Brownian electrokinetic trap (ABEL) performs the position control and an integrated radiofrequency (RF) circuit provides enhanced magnetic flux density for ensemble spin-state control simultaneously. We demonstrate static magnetic field sensing in platforms compatible with ABEL trap. With the advances in the synthesis and functionalization of stable arbitrarily small FNDs, we foresee the use of our device for the trapping and manipulation of single molecular-sized FNDs in aqueous solution.