In
electromagnetism
In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions o ...
, the magnetic susceptibility (
Latin
Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through ...
: , "receptive"; denoted ) is a measure of how much a material will become magnetized in an applied magnetic field. It is the ratio of
magnetization
In classical electromagnetism, magnetization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material. Movement within this field is described by direction and is either Axial or D ...
(magnetic moment per unit volume) 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
Paramagnetism is a form of magnetism whereby some materials are weakly attracted by an externally applied magnetic field, and form internal, induced magnetic fields in the direction of the applied magnetic field. In contrast with this behavior ...
, 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 exception to this usual case is
ferromagnetism). 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
In classical electromagnetism, magnetization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material. Movement within this field is described by direction and is either Axial or D ...
of a material in response to an applied
magnetic field. A related term is magnetizability, the proportion between
magnetic moment
In electromagnetism, the magnetic moment is the magnetic strength and orientation of a magnet or other object that produces a magnetic field. Examples of objects that have magnetic moments include loops of electric current (such as electroma ...
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 (often simply , sometimes – magnetic, to distinguish from the
electric susceptibility), is defined in the
International System of Units
The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. ...
– in other systems there may be additional constants – by the following relationship:
Here
* is the
magnetization
In classical electromagnetism, magnetization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material. Movement within this field is described by direction and is either Axial or D ...
of the material (the
magnetic dipole moment per unit volume), with unit
amperes per meter, and
* is the
magnetic field strength, also with the unit amperes per meter.
is therefore a
dimensionless quantity
A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or 1 ...
.
Using
SI units, the
magnetic induction is related to by the relationship
where is the
vacuum permeability (see table of
physical constant
A physical constant, sometimes fundamental physical constant or universal constant, is a physical quantity that is generally believed to be both universal in nature and have constant value in time. It is contrasted with a mathematical constant ...
s), 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'' (also referred to as ''magnetic polarisation'' ) and with unit
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 .
Molar susceptibility and mass susceptibility
There are two other measures of susceptibility, the ''molar magnetic susceptibility'' () with unit m
3/mol, and the ''mass magnetic susceptibility'' () with unit m
3/kg that are defined below, where is the
density
Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematicall ...
with unit kg/m
3 and is
molar mass with unit kg/mol:
In CGS units
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:
The respective CGS susceptibilities are multiplied by 4 to give the corresponding ISQ quantities (often referred to as SI quantities) with the same units:
For example, the CGS volume magnetic susceptibility of water at 20 °C is , which is using the
SI convention, both quantities being dimensionless. Whereas for most electromagnetic quantities, which system of quantities it belongs to can be disambiguated by incompatibility of their units, this is not true for the susceptibility quantities.
In physics it is common to see CGS mass susceptibility with unit cm
3/g or emu/g⋅Oe
−1, and the CGS molar susceptibility with unit cm
3/mol or emu/mol⋅Oe
−1.
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
Evans may refer to:
People
*Evans (surname)
* List of people with surname Evans
Places United States
*Evans Island, an island of Alaska
*Evans, Colorado
*Evans, Georgia
*Evans County, Georgia
*Evans, New York
*Evans Mills, New York
*Evans City ...
. 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
crystal
A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macro ...
s 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
In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tensor ...
where and refer to the directions (e.g., of the and
Cartesian coordinates
A Cartesian coordinate system (, ) in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in ...
) of the applied field and magnetization, respectively. The
tensor
In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tensor ...
is thus degree 2 (second order), dimension (3,3) 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
In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tensor ...
derived from
partial derivative
In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary). Pa ...
s 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
In condensed matter physics, magnetic anisotropy describes how an object's magnetic properties can be different depending on direction. In the simplest case, there is no preferential direction for an object's magnetic moment. It will respond t ...
. When the material is not
saturated, the effect will be nonlinear and dependent upon the
domain wall
A domain wall is a type of topological soliton that occurs whenever a discrete symmetry is spontaneously broken. Domain walls are also sometimes called kinks in analogy with closely related kink solution of the sine-Gordon model or models with pol ...
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.
An analogue
non-linear relation between magnetization and magnetic field happens for
antiferromagnetic materials.
In the frequency domain
When the magnetic susceptibility is measured in response to an
AC magnetic field (i.e. a magnetic field that varies sinusoidally), this is called ''AC susceptibility''. AC susceptibility (and the closely related "AC permeability") are
complex number
In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the fo ...
quantities, and various phenomena, such as resonance, can be seen in AC susceptibility that cannot occur in constant-field (
DC) susceptibility. 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
A domain wall is a type of topological soliton that occurs whenever a discrete symmetry is spontaneously broken. Domain walls are also sometimes called kinks in analogy with closely related kink solution of the sine-Gordon model or models with pol ...
configuration of the material and
eddy currents
Eddy currents (also called Foucault's currents) are loops of electrical current induced within conductors by a changing magnetic field in the conductor according to Faraday's law of induction or by the relative motion of a conductor in a magn ...
.
In terms of
ferromagnetic resonance, the effect of an AC-field applied along the direction of the magnetization is called ''parallel pumping''.
Table of examples
Sources of published data
The
CRC Handbook of Chemistry and Physics
The ''CRC Handbook of Chemistry and Physics'' is a comprehensive one-volume reference resource for science research. First published in 1914, it is currently () in its 103rd edition, published in 2022. It is sometimes nicknamed the "Rubber Bible ...
has one of the few published magnetic susceptibility tables. The data are listed as CGS quantities. The molar susceptibility of several elements and compounds are listed in the CRC.
Application in the geosciences
Magnetism
Magnetism is the class of physical attributes that are mediated by a magnetic field, which refers to the capacity to induce attractive and repulsive phenomena in other entities. Electric currents and the magnetic moments of elementary particles ...
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.
It is a non-destructive tool, which quantifies the average alignment and orientation of magnetic particles within a sample.
See also
*
Curie constant In magnetism, the Curie constant is a material-dependent property that relates a material's magnetic susceptibility to its temperature through Curie's law.
The Curie constant, when expressed in SI units, has the unit kelvin (K), by
C = \fracn g^2 ...
*
Electric susceptibility
*
Iron
Iron () is a chemical element with symbol Fe (from la, ferrum) and atomic number 26. It is a metal that belongs to the first transition series and group 8 of the periodic table. It is, by mass, the most common element on Earth, right in ...
*
Magnetic constant
The vacuum magnetic permeability (variously ''vacuum permeability'', ''permeability of free space'', ''permeability of vacuum''), also known as the magnetic constant, is the magnetic permeability in a classical vacuum. It is a physical constan ...
*
Magnetic flux density
*
Magnetism
Magnetism is the class of physical attributes that are mediated by a magnetic field, which refers to the capacity to induce attractive and repulsive phenomena in other entities. Electric currents and the magnetic moments of elementary particles ...
*
Magnetochemistry
Magnetochemistry is concerned with the magnetic properties of chemical compounds. Magnetic properties arise from the spin and orbital angular momentum of the electrons contained in a compound. Compounds are diamagnetic when they contain no unpair ...
*
Magnetometer
A magnetometer is a device that measures magnetic field or magnetic dipole moment. Different types of magnetometers measure the direction, strength, or relative change of a magnetic field at a particular location. A compass is one such device, ...
*
Maxwell's equations
Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits ...
*
Paleomagnetism
Paleomagnetism (or palaeomagnetismsee ), is the study of magnetic fields recorded in rocks, sediment, or archeological materials. Geophysicists who specialize in paleomagnetism are called ''paleomagnetists.''
Certain magnetic minerals in roc ...
*
Permeability (electromagnetism)
*
Quantitative susceptibility mapping
Quantitative Susceptibility Mapping (QSM) provides a novel contrast mechanism in Magnetic Resonance Imaging (MRI) different from traditional Susceptibility Weighted Imaging. The voxel intensity in QSM is linearly proportional to the underlying ti ...
*
Susceptibility weighted imaging
References
External links
Linear Response Functions in Eva Pavarini, Erik Koch, Dieter Vollhardt, and Alexander Lichtenstein (eds.): DMFT at 25: Infinite Dimensions, Verlag des Forschungszentrum Jülich, 2014
{{DEFAULTSORT:Magnetic Susceptibility
Physical quantities
Magnetism
Electric and magnetic fields in matter
Scientific techniques