Characterization of Micro-Magnets on Oscillators and Effects of Small Offsets From Ideal Alignment

We report the use and theoretical analysis of a fiber-optic interferometer system with variable applied DC and AC magnetic fields and magnetic field gradients for the characterization of micro-magnets on oscillators. The system has measured and calibrated displacements to determine the resonant frequencies(~0.8-800kHz), quality factors(~30-1000), amplitudes (0.001-10 nm) and spring constants (~0.1 N/m) of resonances. The driven response to AC magnetic field gradients (~1x10^-4 - 1x10^-3 T/m) has provided direct measurement of how changing alignment of the magnetic moment alters the forces on the oscillator. We find the torque and force contributions to the motion of the magnet are of similar magnitude, and misalignments of the magnetic moment on the order of micrometers make it difficult to extract the magnitude of the magnetic moment. Conversely, intentional introduction of small angular offsets (~10 degrees) causes a 3-fold increase in the force measured due to the strength of the torque term. We are also exploiting direct ac torque excitation to measure the much smaller magnetic moments of thin-film ferromagnets on cantilevers. Study of these micro-magnets supports our nuclear magnetic resonance force microscopy (NMRFM) studies.