This dissertation describes the development and usage of the experimental technique -- Magnetic Resonance Force Microscopy (MRFM) -- to study electron spin resonance at low temperature in sensitivity as high as two electron spins. MRFM detects magnetic resonance by sensing the small force acting on the cantilever by the paramagnetic electron spins in the sample through magnetic coupling. I have applied this technique to measure the fluctuating magnetic moments of few electron spin ensembles known as the statistical polarization or the spin noise.
In this dissertation, I describe the basic principles and setup of the MRFM experiments. I have used the MRFM experiment to verify that applying negative feedback to the cantilever can reduce the cantilever response time without sacrificing the signal-to-noise ratio in the force detection. Using the new spin manipulation scheme and the microwave resonator I designed for low temperature MRFM experiments, MRFM force spectra are measured and understood by modeling the spins undergoing magnetic resonance in an inhomogeneous magnetic field.
I have used the high sensitivity MRFM experiment to observe the real-time fluctuation of the electron spin magnetic moments. From the statistics of this fluctuation, the number of resonating spins and the correlation time of the statistical polarization are measured. I have shown that the spin correlation time is due to the one and two phonon relaxation processes in the silicon dioxide sample by measuring the spin correlation time in various sample temperature. As the fluctuating time scale of the statistical polarization is not dominated by the MRFM instrumentation processes, the measured spin correlation time can be used to enhance image contrast by the relaxation-weighted imaging.