Magnetic force microscopy of alternating magnetic field gradient by frequency modulation of tip oscillation

Abstract

A new magnetic force microscopy (MFM) technique for measuring alternating magnetic field (ac magnetic field) was proposed by using frequency modulation (FM) phenomenon of tip oscillation. We detected a narrowband FM phenomenon in the tip oscillation of a high-coercivity MFM tip by applying an ac magnetic field to the tip by using a metal-in-gap (MIG) type ring head. In the experiment, the MFM tip was driven at a constant frequency fc near the resonant frequency of the cantilever by a piezoelectric element, and the ac magnetic field with a frequency fm up to 10 kHz was applied to the MFM tip. Two sideband spectra with a frequency of fc±fm were observed by applying ac magnetic field. The intensity of sideband spectra increased linearly with increasing applied current value of the MIG head. It was observed that FM occurred from the analysis of frequency spectra of the MFM signals. This FM phenomenon is caused by the force applied on the cantilever by the field gradient of the head. The FM phenomenon is understood by solving the differential equation for the harmonic oscillator of which the effective spring constant is changed periodically by ac magnetic field. The FM phenomenon can be used for imaging ac magnetic fields.

AC Magnetic Field Imaging of Perpendicular Magnetic Write Head without Image Distortion on Alternating Magnetic Force Microscopy using a Cone-Shape FePt-coated Tip

“…And the frequency of fc±2fm is dominating when coercivity of the magnetic component of the tip is smaller than the AC magnetic field. This is because, the spectrum intensity at fc±fm is proportional to the gradient of magnetic field component which is perpendicular to the sample surface 9) , and this indicates that direction of tip magnetization does not change when the fc±fm is dominant. In Fig.7 (a), the modulated frequency with highest peak of the spectra was fc±fm.…”

“…The lift height was 10 nm. The amplitude and phase information of the alternating force between the sample and the tip was extracted by using a lock-in amplifier where the input signal was the frequency demodulated signal of cantilever oscillation from a phase-locked loop (PLL) circuit and reference signal was the frequency signal of fm from signal generator 8), 9) .…”

“…In our previous work, we have developed a new MFM to image AC magnetic field with a wide frequency range that is referred to as alternating magnetic force microscopy (A-MFM) 9) . The A-MFM uses a frequency modulation (FM) of the cantilever oscillation by applying an AC magnetic field over it.…”

High frequency magnetic field imaging by frequency modulated magnetic force microscopy

“…5 This method uses the frequency modulation ͑FM͒ of a cantilever oscillation by applying ac magnetic field to a mechanically oscillated tip. We found that ac magnetic field caused the FM of a cantilever oscillation when ac magnetic field does not oscillated the cantilever by itself in the case that the frequency of ac magnetic field is far from the resonant frequency of the cantilever.…”

Stroboscopic imaging of an alternating magnetic field from a perpendicular magnetic recording head by frequency-modulated magnetic force microscopy

“…We mentioned this type of microscopy as frequency modulated-magnetic force microscopy (FM-MFM). 5 In this study, we proposed a stroboscopic analysis method for AC magnetic fields by varying the phase of the measured in-phase and quadrature signals via a signal processing technique. The stroboscopic imaging of a timevariable AC magnetic field for a perpendicular magnetic recording head, caused by the rotation of the magnetisation around the main pole using a head-current driving magnetic field, was demonstrated.…”