| Three dimensional imaging of nanometer-scale electron spin distributions by magnetic resonance force microscopy (MRFM) requires the completion of complementary tasks: acquisition of data by a piezoelectric scanner operating in a cryogenic UHV environment, and the reconstruction of the spin distribution from raw data ill-suited to conventional Fourier techniques. This dissertation reports the design and operation of a cryogenic scanner, the acquisition of raw MRFM data with a 3D voxel pitch of 80 nm at 80 K, and the reconstruction of the sample spin distribution via the Landweber algorithms.; Our MRFM research program dictates a scan system operable at liquid helium and liquid nitrogen temperatures with 3D sub-atomic (10 pm) resolution, a transverse (x,y) range of not less than 100 nm, and a vertical (z) range of 100 μm. The precision xyz requirements are met with a conventional four-quadrant piezoceramic tube operated as a quasi-static scanner. Long-range z motion is achieved by a stick-slip inertial slider actuated by piecewise parabolic waveforms applied to the piezoceramic tube. Scanner damping for the inertial slider is improved by using two opposite quadrants for actuation, and the other two for velocity feedback. Reproducible z steps as small as two nm are obtained with feedback control. The stick-slip motion of the slider is evaluated by a reset-integrator friction model introduced by Haessig.; As with conventional magnetic resonance imaging, the raw data are a convolution of the spin density with the resonant “sensitive slice” geometry determined by an applied magnetic field gradient. With our MRFM technique, the field is supplied solely by the magnetic tip, and our sensitive slice is approximately a thin hemispherical shell, 4.2 μm diameter at 2.0 GHz, with a shell-thickness of 9 nm. The scan volume is only a fraction of the size of the sensitive slice. Nevertheless, the Landweber iterative algorithms converged rapidly on the raw data in simulation and in practice, with reconstruction fidelity limited by the noise in the data. |
