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

Abstract

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.

Application of reconstitution multiple scale asymptotics for a two-to-one internal resonance in Magnetic Resonance Force Microscopy

“…(20) indicate to the dependency of the magnetic moment on the initial conditions. From here on this paper we use an adiabatic assumption.…”

“…To formulate the magnetic force components we follow Berman [20] and derive an expression for the total magnetic field B tot which is composed of the following three components: an external magnetic field ext B , a dipole magnetic field of the spin d B…”

“…The cantilever maximal displacement is then measured using an interferometer enabling registration of the magnetic dependent frequency shift. 3 Existing theoretical MRFM investigations are based on lumped-mass models that enable estimation of the shift in the response resonance frequency [19,20]. These models assume that the planar cantilever motion consists of a linearly damped and forced harmonic oscillator augmented by a nonlinear interaction with the measured spin magnetic moment.…”

Advances in mechanical detection of magnetic resonance

“…152,153 This change in the cantilever spring constant is observed as a spin-dependent shift in the resonance frequency of the cantilever.…”

“…The frequency shift in the OSCAR experiment is given by, 149,153 in our notation, ⌬f =2f 0 G z / k 0 x m with G = ‫ץ‬B z / ‫ץ‬x. Converting this to an equivalent period shift for purposes of comparison, the signal-to-noise ratio for the OS-…”