Magnetic force microscope - AbsoluteAstronomy.com

Magnetic force microscope (MFM) is a variety of atomic force microscope

Atomic force microscope

Atomic force microscopy or scanning force microscopy is a very high-resolution type of scanning probe microscopy, with demonstrated resolution on the order of fractions of a nanometer, more than 1000 times better than the optical diffraction limit...

, where 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 AFM (NC-AFM) mode.

Overview

In MFM measurements, the magnetic force between the sample and the tip can be expressed as

where

is the magnetic moment

Magnetic moment

The magnetic moment of a magnet is a quantity that determines the force that the magnet can exert on electric currents and the torque that a magnetic field will exert on it...

of the tip (approximated as a point dipole),

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 :

1982 - Scanning Tunneling Microscopy (STM)

Tunneling current between the tip and sample is used as the signal.
Both the tip and sample must be electrically conductive.

1986 - Atomic force microscopy (AFM)

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.

1987 - Magnetic Force Microscopy (MFM)

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
Raster scan
A raster scan, or raster scanning, is the rectangular pattern of image capture and reconstruction in television. By analogy, the term is used for raster graphics, the pattern of image storage and transmission used in most computer bitmap image systems...

.

MFM components

The main components of an MFM system are:
Piezoelectric scanning

Piezoelectricity

Piezoelectricity is the charge which accumulates in certain solid materials in response to applied mechanical stress. The word piezoelectricity means electricity resulting from pressure...

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
Cantilever
A cantilever is a beam anchored at only one end. The beam carries the load to the support where it is resisted by moment and shear stress. Cantilever construction allows for overhanging structures without external bracing. Cantilevers can also be constructed with trusses or slabs.This is in...

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

AFM probe

Consumable and measuring device with a sharp tip on the free swinging end of a cantilever which is protruding from a holder plate used in Atomic force microscopes . The dimensions of the cantilever are in the scale of micrometers. The radius of the tip is in the scale of a few nanometers...

with a magnetic coating.

In the past, tips were made of etched magnetic metals such as nickel
Nickel
Nickel is a chemical element with the chemical symbol Ni and atomic number 28. It is a silvery-white lustrous metal with a slight golden tinge. Nickel belongs to the transition metals and is hard and ductile...

.
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
Silicon dioxide
The chemical compound silicon dioxide, also known as silica , is an oxide of silicon with the chemical formula '. It has been known for its hardness since antiquity...

(SiO₂), or silicon nitride
Silicon nitride
Silicon nitride is a chemical compound of silicon and nitrogen. If powdered silicon is heated between 1300° and 1400°C in an atmosphere of nitrogen, trisilicon tetranitride, Si3N4, is formed. The silicon sample weight increases progressively due to the chemical combination of silicon and nitrogen...

(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
Coercivity
In materials science, the coercivity, also called the coercive field or coercive force, of a ferromagnetic material is the intensity of the applied magnetic field required to reduce the magnetization of that material to zero after the magnetization of the sample has been driven to saturation...

, 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

The scanning method when using an MFM is called the "lift height" method. When the tip scans the surface of a sample at close distances (< 100 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.

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 = F_z/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 a proof 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 F_z 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:

where the amplitude and phase shifts are given by:

Here the quality factor of resonance, resonance angular frequency, and damping factor are:

Dynamic mode of operation refers to measurements of the shifts in the resonance frequency.
The cantilever is driven to its resonance frequency and frequency shifts are detected.
Assuming small vibration amplitudes (which is generally true in MFM measurements), to a first-order approximation, the resonance frequency can be related to the natural frequency and the force gradient. That is, the shift in the resonance frequency is a result of changes in the spring constant due to the (repelling and attraction) forces acting on the tip.

The change in the natural resonance frequency is given by

, where

For instance, the coordinate system is such that positive z is away from or perpendicular to the sample surface, so that an attractive force would be in the negative direction (F<0), and thus the gradient is positive. Consequently, for attractive forces, the resonance frequency of the cantilever decreases (as described by the equation). The image is encoded in such a way that attractive forces are generally depicted in black color, while repelling forces are coded white.

Calculating forces acting on magnetic tips

Analytically, the magnetostatic energy (U) of the tip-sample system can be calculated in one of two ways:

One can either compute the magnetization (M) of the tip in the presence of the magnetic stray field (H) of the sample or
Compute the magnetization of the sample in the presence of the magnetic stray field of the tip (whichever is easier)

Then, integrate the (dot) product of the magnetization and stray field over the interaction volume
as

and compute the gradient of the energy over distance to obtain the force F. Assuming that the cantilever deflects along the z-axis, and the tip is magnetized along a certain direction (e.g. the z-axis), then the equations can be simplified to

Since the tip is magnetized along a specific direction, it will be sensitive to the component of the magnetic stray field of the sample which is aligned to the same direction.

Imaging samples

The MFM can be used to image various magnetic structures including domain walls (Bloch and Neel), closure domains, recorded magnetic bits, etc. Furthermore, motion of domain wall can also be studied in an external magnetic field. MFM images of various materials can be seen in the following books and journal publications: thin films, nanoparticles, nanowires, permalloy disks and recording media.

Advantages

The popularity of MFM originates from several reasons, which include::

The sample does not need to be electrically conductive.
Measurement can be performed at ambient temperature, in ultra high vacuum (UHV), in liquid environment, and at different temperatures.
Measurement is nondestructive to the crystal lattice or structure.
Long-range magnetic interactions are not sensitive to surface contamination.
No special surface preparation or coating is required.
Deposition of thin non-magnetic layers on the sample does not alter the results.
Detectable magnetic field intensity, H, is in the range of 10 A/m
Detectable magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...

, B, is in the range of 0.1 gauss
Gauss (unit)
The gauss, abbreviated as G, is the cgs unit of measurement of a magnetic field B , named after the German mathematician and physicist Carl Friedrich Gauss. One gauss is defined as one maxwell per square centimeter; it equals 1 tesla...

(10 microteslas).
Typical measured forces are as low as 10⁻¹⁴ N, with the spatial resolutions as low as 20 nm.
MFM can be combined with other scanning methods like STM.

Limitations

There are some shortcomings or difficulties when working with an MFM, such as:

The recorded image depends on the type of the tip and magnetic coating, due to tip-sample interactions.
Magnetic field of the tip and sample can change each other's magnetization, M, which can result in nonlinear interactions. This hinders image interpretation.
Relatively short lateral scanning range (order of hundreds micrometers).
Scanning (lift) height affects the image.
Housing of the MFM system is important to shield electromagnetic noise (Faraday cage
Faraday cage
A Faraday cage or Faraday shield is an enclosure formed by conducting material or by a mesh of such material. Such an enclosure blocks out external static and non-static electric fields...

), acoustic noise (anti-vibration tables), air flow (air isolation), and static charge on the sample.

External links

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