Theory of frequency shifts in the oscillating cantilever-driven adiabatic reversals technique as a function of the spin location

The theory of the oscillating cantilever-driven adiabatic reversals (OSCAR) in magnetic resonance force microscopy (MRFM) is extended to describe the relation between an external magnetic field and a dipole magnetic field for an arbitrary location of the single spin. An analytical estimate for the OSCAR MRFM frequency shift is derived and shown to be in excellent agreement with numerical simulations. The dependence of the frequency shift on the position of the spin relative to the cantilever has characteristic maxima and minima which can be used to determine the spin location experimentally.