Magnetic Force Microscopy ( MFM ) fundamentals
PAGE 79 attoMICROSCOPY
MFM is a technique derived from AFM , in which an etched silicon cantilever / tip combined with optical deflection detection is used to precisely measure local forces such as those caused by van der Waals or Coulomb interaction . MFM uses cantilevers with very low spring constant K and with magnetic coatings ( typically NiCr or cobalt ), sensitive to the magnetic interaction between tip and sample .
The figure below shows a schematic of attocube ’ s cantilever-based attoMFM , designed particularly for low temperature and high magnetic field applications . The attoMFM uses a single-mode , fiber-based interferometer to detect tip deflections with noise densities as low as 0.5 pm / Hz 1 / 2 . As with most MFMs , the attoMFM applies an AC modulation technique to achieve highest detection sensitivity . In AC mode , the cantilever is mechanically excited at its natural resonance frequency f0 using an oscillator swinging perpendicular to the sample surface . The magnetic interaction offsets the equilibrium position of the tip . This effect is hard to detect , and therefore ignored in most cases . In addition to the pure DC offset , the natural resonance frequency ( as well as amplitude and phase ) of the cantilever is also affected by the magnetic interaction . This frequency shift Δf = f res
- f 0 can be detected by classical lock-in techniques and is the most relevant physical quantity to measure due to its direct proportionality to the derivative of the local force F : ∂F z
/ ∂z ~ 2 K Δf / f 0
. The measurement therefore yields information about the actual local magnetic stray field : ∂F z
/ ∂z ~ m tip , z ∂ 2 H z
/ ∂z 2 ( where m tip , z is the magnetization of the tip perpendicular to the sample surface ) with very high spatial resolution . Using a phase-locked loop ( PLL ) technique , resonance frequency shifts as small as 1 μHz can be detected . To separate magnetic information from other influences , two techniques are commonly used : constant height mode and constant distance mode . In constant height mode , the MFM tip is scanned at a fixed height above the mean sample plane . In constant distance mode on the other hand , the distance between tip and sample is kept precisely constant to compensate any surface corrugation .
Constant height mode is typically applied on sufficiently flat samples , after the sample and scan planes have been aligned parallel to each other . The MFM tip is positioned at typically 10 – 100 nm above the sample surface , and is then scanned across the surface with scan speeds of up to several 10 μm / s . Any shifts in resonance frequency or phase are recorded simultaneously . Due to its ease of use and high scan speeds , this technique best fits a variety of samples such as hard discs and superconductors . In contrast , constant distance mode tracks the surface topography at a defined distance . This technique best suits samples with rough surfaces . However , this mode leads to considerably longer acquisition times than constant height mode .
Optical fiber
MFM cantilever Dither
Sample attoMICROSCOPY
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