A theoretical and experimental assessment of adiabatic losses in force-gradient-detected magnetic resonance of nitroxide spin labels

We recently introduced a new theoretical description of Landau-Zener-Stückelberg-Majorana (LZSM) transitions that accounts for both adiabatic and spin-dephasing losses during sweeps through resonance. Here, we use this new description to assess signal loss due to cantilever tip motion in magnetic resonance force microscopy experiments on electron spins. We derive equations for spin-induced cantilever frequency shifts that account for the time-dependent magnetization present during cantilever-synchronized periods of irradiation and relaxation. We show that a frequency shift can be created by either a force- or force-gradient coupling mechanism, depending on the periodicity and timing of the microwave irradiation; the frequency shift decreases when the spin-lattice relaxation time becomes shorter than the cantilever oscillation period. Equations were validated by comparing with the magnetization computed by numerically integrating the time-dependent Bloch equations. Numerical simulations incorporating the new equations were compared to frequency-shift electron-spin signals collected as a function of magnetic field, tip-sample separation, microwave power, and microwave timing. The simulations quantitatively describe the observed signals with independently calibrated parameters and no per-curve adjustment. Finally, motivated by our new frequency-shift equations, we present a new experimental spin-excitation protocol that eliminates spurious signals arising from direct microwave excitation of the cantilever in a magnetic resonance force microscope experiment.