Magnetic force microscopy (MFM) is a variety of atomic force microscopy, in which a sharp magnetized tip scans a magnetic sample; the tip-sample magnetic interactions are detected and used to reconstruct the magnetic structure of the sample surface. Many kinds of magnetic interactions are measured by MFM, including magnetic dipole–dipole interaction. MFM scanning often uses non-contact atomic force microscopy (NC-AFM) and is considered to be non-destructive with respect to the test sample. In MFM, the test sample(s) do not need to be electrically conductive to be imaged.
Overview In MFM measurements, the magnetic force between the test sample and the tip can be expressed as
F → = μ o ( m → ⋅ ∇ ) H → {\displaystyle {\vec {F}}=\mu _{o}({\vec {m}}\cdot \nabla ){\vec {H}}\,\!}
where m → {\displaystyle {\vec {m}}\,\!} is the magnetic moment of the tip (approximated as a point dipole), H → {\displaystyle {\vec {H}}\,\!} is the magnetic stray field from the sample surface, and μ0 is the magnetic permeability of free space. Because the stray magnetic field from the sample can affect the magnetic state of the tip, and vice versa, interpretation of the MFM measurement is not straightforward. For instance, the geometry of the tip magnetization must be known for quantitative analysis. Typical resolution of 30 nm can be achieved, although resolutions as low as 10 to 20 nm are attainable.
Important dates A boost in the interest to MFM resulted from the following inventions: Scanning tunneling microscope (STM) 1982, Tunneling current between the tip and sample is used as the signal. Both the tip and sample must be electrically conductive. Atomic force microscopy (AFM) 1986, forces (atomic/electrostatic) between the tip and sample are sensed from the deflections of a flexible lever (cantilever). The cantilever tip flies above the sample with a typical distance of tens of nanometers. Magnetic Force Microscopy (MFM), 1987 Derives from AFM. The magnetic forces between the tip and sample are sensed. Image of the magnetic stray field is obtained by scanning the magnetized tip over the sample surface in a raster scan.
MFM components The main components of an MFM system are:
Piezoelectric scanning Moves the sample in an x, y and z directions. Voltage is applied to separate electrodes for different directions. Typically, a 1 volt potential results in 1 to 10 nm displacement. Image is put together by slowly scanning sample surface in a raster fashion. Scan areas range from a few to 200 micrometers. Imaging times range from a few minutes to 30 minutes. Restoring force constants on the cantilever range from 0.01 to 100 N/m depending on the material of the cantilever. Magnetized tip at one end of a flexible lever (cantilever); generally an AFM probe with a magnetic coating. In the past, tips were made of etched magnetic metals such as nickel. Nowadays, tips are batch fabricated (tip-cantilever) using a combination of micromachining and photolithography. As a result, smaller tips are possible, and better mechanical control of the tip-cantilever is obtained. Cantilever: can be made of single-crystalline silicon, silicon dioxide (SiO2), or silicon nitride (Si3N4). The Si3N4 cantilever-tip modules are usually more durable and have smaller restoring force constants (k). Tips are coated with a thin (< 50 nm) magnetic film (such as Ni or Co), usually of high coercivity, so that the tip magnetic state (or magnetization M) does not change during the imaging. The tip-cantilever module is driven close to the resonance frequency by a piezoelectric crystal with typical frequencies ranging from 10 kHz to 1 MHz.
Scanning procedure Often, MFM is operated with the so-called "lift height" method. When the tip scans the surface of a sample at close distances (< 10 nm), not only magnetic forces are sensed, but also atomic and electrostatic forces. The lift height method helps to enhance the magnetic contrast through the following:
First, the topographic profile of each scan line is measured. That is, the tip is brought into a close proximity of the sample to take AFM measurements. The magnetized tip is then lifted further away from the sample. On the second pass, the magnetic signal is extracted.
Modes of operation
Static (DC) mode The stray field from the sample exerts a force on the magnetic tip. The force is detected by measuring the displacement of the cantilever by reflecting a laser beam from it. The cantilever end is either deflected away or towards the sample surface by a distance Δz = Fz/k (perpendicular to the surface). Static mode corresponds to measurements of the cantilever deflection. Forces in the range of tens of piconewtons are normally measured.
Dynamic (AC) mode For small deflections, the tip-cantilever can be modeled as a damped harmonic oscillator with an effective mass (m) in [kg], an ideal spring constant (k) in [N/m], and a damper (D) in [N·s/m]. If an external oscillating force Fz is applied to the cantilever, then the tip will be displaced by an amount z. Moreover, the displacement will also harmonically oscillate, but with a phase shift between applied force and displacement given by:
F z = F o cos ( ω t ) , z = z o cos ( ω t + θ ) {\displaystyle F_{z}=F_{o}\cos(\omega t),\;z=z_{o}\cos(\omega t+\theta )\,\!}
where the amplitude and phase shifts are given by:
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