Magnetic susceptibility


In electromagnetism, the magnetic susceptibility is a measure of how much a material will become magnetized in an applied magnetic field. It is the ratio of magnetization to the applied magnetizing field intensity. This allows a simple classification, into two categories, of most materials' responses to an applied magnetic field: an alignment with the magnetic field,, called paramagnetism, or an alignment against the field,, called diamagnetism.
Magnetic susceptibility indicates whether a material is attracted into or repelled out of a magnetic field. Paramagnetic materials align with the applied field and are attracted to regions of greater magnetic field. Diamagnetic materials are anti-aligned and are pushed away, toward regions of lower magnetic fields. On top of the applied field, the magnetization of the material adds its own magnetic field, causing the field lines to concentrate in paramagnetism, or be excluded in diamagnetism. Quantitative measures of the magnetic susceptibility also provide insights into the structure of materials, providing insight into bonding and energy levels. Furthermore, it is widely used in geology for paleomagnetic studies and structural geology.
The magnetizability of materials comes from the atomic-level magnetic properties of the particles of which they are made. Usually, this is dominated by the magnetic moments of electrons. Electrons are present in all materials, but without any external magnetic field, the magnetic moments of the electrons are usually either paired up or random so that the overall magnetism is zero. 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.

Definition

Volume susceptibility

Magnetic susceptibility is a dimensionless proportionality constant that indicates the degree of magnetization of a material in response to an applied magnetic field. A related term is magnetizability, the proportion between magnetic moment and magnetic flux density. A closely related parameter is the permeability, which expresses the total magnetization of material and volume.
The volume magnetic susceptibility, represented by the symbol , is defined in the International System of Units — in other systems there may be additional constants — by the following relationship:
Here
is therefore a dimensionless quantity.
Using SI units, the magnetic induction is related to by the relationship
where is the vacuum permeability, and is the relative permeability of the material. Thus the volume magnetic susceptibility and the magnetic permeability are related by the following formula:
Sometimes an auxiliary quantity called intensity of magnetization and measured in teslas, is defined as
This allows an alternative description of all magnetization phenomena in terms of the quantities and, as opposed to the commonly used and.

Mass susceptibility and molar susceptibility

There are two other measures of susceptibility, the mass magnetic susceptibility, measured in m3/kg and the molar magnetic susceptibility measured in m3/mol that are defined below, where is the density in kg/m3 and is molar mass in kg/mol:

In CGS units

Note that the definitions above are according to SI conventions. However, many tables of magnetic susceptibility give cgs values. These units rely on a different definition of the permeability of free space:
The dimensionless cgs value of volume susceptibility is multiplied by 4 to give the dimensionless SI volume susceptibility value:
For example, the cgs volume magnetic susceptibility of water at 20 °C is, which is using the SI convention.
In physics it is common to see cgs mass susceptibility given in cm3/g or emu/g·Oe−1, so to convert to SI volume susceptibility we use the conversion
where is the density given in g/cm3, or
The molar susceptibility is measured cm3/mol or emu/mol·Oe−1 in cgs and is converted by considering the molar mass.

Paramagnetism and diamagnetism

If is positive, a material can be paramagnetic. In this case, the magnetic field in the material is strengthened by the induced magnetization. Alternatively, if is negative, the material is diamagnetic. In this case, the magnetic field in the material is weakened by the induced magnetization. Generally, nonmagnetic materials are said to be para- or diamagnetic because they do not possess permanent magnetization without external magnetic field. Ferromagnetic, ferrimagnetic, or antiferromagnetic materials possess permanent magnetization even without external magnetic field and do not have a well defined zero-field susceptibility.

Experimental measurement

Volume magnetic susceptibility is measured by the force change felt upon a substance when a magnetic field gradient is applied. 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. Today, high-end measurement systems use a superconductive magnet. An alternative is to measure the force change on a strong compact magnet upon insertion of the sample. This system, widely used today, is called the Evans balance. For liquid samples, the susceptibility can be measured from the dependence of the NMR frequency of the sample on its shape or orientation.
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.

Tensor susceptibility

The magnetic susceptibility of most crystals is not a scalar quantity. Magnetic response is dependent upon the orientation of the sample and can occur in directions other than that of the applied field. In these cases, volume susceptibility is defined as a tensor
where and refer to the directions of the applied field and magnetization, respectively. The tensor is thus rank 2, dimension describing the component of magnetization in the th direction from the external field applied in the th direction.

Differential susceptibility

In ferromagnetic crystals, the relationship between and is not linear. To accommodate this, a more general definition of differential susceptibility is used
where is a tensor derived from partial derivatives of components of with respect to components of. 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. When the material is not saturated, the effect will be nonlinear and dependent upon the domain wall configuration of the material.
Several experimental techniques allow for the measurement of the electronic properties of a material. An important effect in metals under strong magnetic fields, is the oscillation of the differential susceptibility as function of. 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 the frequency domain

When the magnetic susceptibility is measured in response to an AC magnetic field, this is called AC susceptibility. AC susceptibility are complex number quantities, and various phenomena, such as resonance, can be seen in AC susceptibility that cannot in constant-field susceptibility. In particular, when an AC field is applied perpendicular to the detection direction, 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.

Examples

Application in the geosciences

is a useful parameter to describe and analyze rocks. Additionally, the anisotropy of magnetic susceptibility within a sample determines parameters as directions of paleocurrents, maturity of paleosol, flow direction of magma injection, tectonic strain, etc. It is a non-destructive tool, which quantifies the average alignment and orientation of magnetic particles within a sample.