Diamagnetic materials are anti-aligned and are pushed away, toward regions of lower magnetic fields.
[2] The magnetizability of materials comes from the atomic-level magnetic properties of the particles of which they are made.
The fundamental reasons why the magnetic moments of the electrons line up or do not are very complex and cannot be explained by classical physics.
However, a useful simplification is to measure the magnetic susceptibility of a material and apply the macroscopic form of Maxwell's equations.
This allows classical physics to make useful predictions while avoiding the underlying quantum mechanical details.
[3] A closely related parameter is the permeability, which expresses the total magnetization of material and volume.
The volume magnetic susceptibility, represented by the symbol χv (often simply χ, sometimes χm – magnetic, to distinguish from the electric susceptibility), is defined in the International System of Units – in other systems there may be additional constants – by the following relationship:[4][5]
Using SI units, the magnetic induction B is related to H by the relationship
The definitions above are according to the International System of Quantities (ISQ) upon which the SI is based.
However, many tables of magnetic susceptibility give the values of the corresponding quantities of the CGS system (more specifically CGS-EMU, short for electromagnetic units, or Gaussian-CGS; both are the same in this context).
The quantities characterizing the permeability of free space for each system have different defining equations:[7]
For example, the CGS volume magnetic susceptibility of water at 20 °C is 7.19×10−7, which is 9.04×10−6 using the SI convention, both quantities being dimensionless.
[8] Early measurements are made using the Gouy balance where a sample is hung between the poles of an electromagnet.
The change in weight when the electromagnet is turned on is proportional to the susceptibility.
An alternative is to measure the force change on a strong compact magnet upon insertion of the sample.
[10][11][12][13][14] Another method using NMR techniques measures the magnetic field distortion around a sample immersed in water inside an MR scanner.
This method is highly accurate for diamagnetic materials with susceptibilities similar to water.
Magnetic response M is dependent upon the orientation of the sample and can occur in directions other than that of the applied field H. In these cases, volume susceptibility is defined as a tensor:
where i and j refer to the directions (e.g., of the x and y Cartesian coordinates) of the applied field and magnetization, respectively.
where χdij is a tensor derived from partial derivatives of components of M with respect to components of H. When the coercivity of the material parallel to an applied field is the smaller of the two, the differential susceptibility is a function of the applied field and self interactions, such as the magnetic anisotropy.
An important effect in metals under strong magnetic fields, is the oscillation of the differential susceptibility as function of 1/H.
This behaviour is known as the De Haas–Van Alphen effect and relates the period of the susceptibility with the Fermi surface of the material.
In particular, when an AC field is applied perpendicular to the detection direction (called the "transverse susceptibility" regardless of the frequency), the effect has a peak at the ferromagnetic resonance frequency of the material with a given static applied field.
Currently, this effect is called the microwave permeability or network ferromagnetic resonance in the literature.
These results are sensitive to the domain wall configuration of the material and eddy currents.
In terms of ferromagnetic resonance, the effect of an AC-field applied along the direction of the magnetization is called parallel pumping.
The CRC Handbook of Chemistry and Physics has one of the few published magnetic susceptibility tables.
In Earth science, magnetism is a useful parameter to describe and analyze rocks.
Additionally, the anisotropy of magnetic susceptibility (AMS) within a sample determines parameters as directions of paleocurrents, maturity of paleosol, flow direction of magma injection, tectonic strain, etc.
[2] It is a non-destructive tool which quantifies the average alignment and orientation of magnetic particles within a sample.