In electromagnetism, the magnetic susceptibility (Latin: susceptibilis, "receptive"; denoted χ) is a measure of how much a material will become magnetized in an applied magnetic field. Mathematically, it is the ratio of magnetization M (magnetic moment per unit volume) to the applied magnetizing field intensity H. This allows a simple classification of most materials' response to an applied magnetic field into two categories: an alignment with the magnetic field, χ>0, called paramagnetism, or an alignment against the field, χ<0, called diamagnetism.
This alignment has several effects. First, the magnetic susceptibility indicates whether a material is attracted into or repelled out of a magnetic field. Paramagnetic materials align with the field, so are attracted to the magnetic field. Diamagnetic materials are anti-aligned, so are pushed away from magnetic fields. Second, on top of the applied field, the magnetic moment 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.
Fundamentally, the magnetic moment of materials comes from the magnetism of the particles they are made of. 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 in some way either paired up or randomized so 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 don't can be very complex, and can not be explained with classical physics. However, it is a useful simplification to simply measure the magnetic susceptibility of a material, and apply the macroscopic form of Maxwell's equations. This allows classical physics to make useful predictions without getting into the underlying quantum mechanical details.
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 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:
χv is therefore a dimensionless quantity.
where μ0 is the vacuum permeability (see table of physical constants), and (1 + χv) is the relative permeability of the material. Thus the volume magnetic susceptibility χv and the magnetic permeability μ are related by the following formula:
This allows an alternative description of all magnetization phenomena in terms of the quantities I and B, as opposed to the commonly used M and H.
There are two other measures of susceptibility, the mass magnetic susceptibility (χmass or χg, sometimes χm), measured in m3/kg (SI) and the molar magnetic susceptibility (χmol) measured in m3/mol that are defined below, where ρ is the density in kg/m3 and M is molar mass in kg/mol:
Note that the definitions above are according to SI conventions. However, many tables of magnetic susceptibility give cgs values (more specifically emu-cgs, short for electromagnetic units, or Gaussian-cgs; both are the same in this context). These units rely on a different definition of the permeability of free space:
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.
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 ρcgs is the density given in g/cm3, or
The molar susceptibility is measured cm3/mol or emu/mol·Oe−1 in cgs and is calculated using the molar mass in g/mol.
If χ is positive, a material can be paramagnetic. In this case, the magnetic field in the material is strengthened by the induced magnetization. Alternatively, if χ 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.
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.
The magnetic susceptibility of most crystals is not a scalar quantity. 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., x and y in Cartesian coordinates) of the applied field and magnetization, respectively. The tensor is thus rank 2 (second order), dimension (3,3) describing the component of magnetization in the ith direction from the external field applied in the jth direction.
In ferromagnetic crystals, the relationship between M and H is not linear. To accommodate this, a more general definition of differential susceptibility is used
ij 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. 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 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.
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 quantities, and various phenomena, such as resonance, can be seen in AC susceptibility that cannot 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 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.
|Material||Temp.||Pressure||Molar susc., χmol||Mass susc., χmass||Volume susc., χv||Molar mass, M||Density,|
|(103 kg/m3 |
|Paraffin oil, 220–260 cSt||22||1||−1.01×10−8||−8.0×10−7||−8.8×10−6||−7.0×10−7||0.878|
|Fused silica glass||22||1||−5.12×10−9||−4.07×10−7||−1.128×10−5||−8.98×10−7||2.20|
|Graphite χ∥ (to c-axis)||r.t.||1||−7.5×10−11||−6.0×10−6||−6.3×10−9||−5.0×10−7||−1.4×10−5||−1.1×10−6||12.01||2.267|
The CRC Handbook of Chemistry and Physics has one of the only published magnetic susceptibility tables. Some of the data (e.g., for aluminium, bismuth, and diamond) is listed as cgs, which has caused confusion to some readers. "cgs" is an abbreviation of centimeters–grams–seconds; it represents the form of the units, but cgs does not specify units. Correct units of magnetic susceptibility in cgs is cm3/mol or cm3/g. Molar susceptibility and mass susceptibility are both listed in the CRC. Some table have listed magnetic susceptibility of diamagnets as positives. It is important to check the header of the table for the correct units and sign of magnetic susceptibility readings.
An amorphous metal transformer (AMT) is a type of energy efficient transformer found on electric grids. The magnetic core of this transformer is made with a ferromagnetic amorphous metal.
The typical material (Metglas) is an alloy of iron with boron, silicon, and phosphorus in the form of thin (e.g. 25 µm) foils rapidly cooled from melt. These materials have high magnetic susceptibility, very low coercivity and high electrical resistance.
The high resistance and thin foils lead to low losses by eddy currents when subjected to alternating magnetic fields. On the downside amorphous alloys have a lower saturation induction and often a higher magnetostriction compared to conventional crystalline iron-silicon electrical steel.Barnett effect
The Barnett effect is the magnetization of an uncharged body when spun on its axis. It was discovered by American physicist Samuel Barnett in 1915.
An uncharged object rotating with angular velocity ω tends to spontaneously magnetize, with a magnetization given by:
with γ = gyromagnetic ratio for the material, χ = magnetic susceptibility.
The magnetization occurs parallel to the axis of spin. Barnett was motivated by a prediction by Owen Richardson in 1908, later named the Einstein–de Haas effect, that magnetizing a ferromagnet can induce a mechanical rotation. He instead looked for the opposite effect, that is, that spinning a ferromagnet could change its magnetization. He established the effect with a long series of experiments between 1908 and 1915.Curie constant
The Curie constant is a material-dependent property that relates a material's magnetic susceptibility to its temperature.
The Curie constant, when expressed in SI units, is given by
where is the number of magnetic atoms (or molecules) per unit volume, is the Landé g-factor, is the Bohr magneton, is the angular momentum quantum number and is Boltzmann's constant. For a two-level system with magnetic moment , the formula reduces to
while the corresponding expressions in Gaussian units are
The constant is used in Curie's Law, which states that for a fixed value of a magnetic field, the magnetization of a material is (approximately) inversely proportional to temperature.
This equation was first derived by Pierre Curie.
Because of the relationship between magnetic susceptibility , magnetization and applied magnetic field is almost linear at low fields, then
this shows that for a paramagnetic system of non-interacting magnetic moments, magnetization is inversely related to temperature .Curie temperature
In physics and materials science, the Curie temperature (TC), or Curie point, is the temperature above which certain materials lose their permanent magnetic properties, to be replaced by induced magnetism. The Curie temperature is named after Pierre Curie, who showed that magnetism was lost at a critical temperature.The force of magnetism is determined by the magnetic moment, a dipole moment within an atom which originates from the angular momentum and spin of electrons. Materials have different structures of intrinsic magnetic moments that depend on temperature; the Curie temperature is the critical point at which a material's intrinsic magnetic moments change direction.
Permanent magnetism is caused by the alignment of magnetic moments and induced magnetism is created when disordered magnetic moments are forced to align in an applied magnetic field. For example, the ordered magnetic moments (ferromagnetic, Figure 1) change and become disordered (paramagnetic, Figure 2) at the Curie temperature. Higher temperatures make magnets weaker, as spontaneous magnetism only occurs below the Curie temperature. Magnetic susceptibility above the Curie temperature can be calculated from the Curie–Weiss law, which is derived from Curie's law.
In analogy to ferromagnetic and paramagnetic materials, the Curie temperature can also be used to describe the phase transition between ferroelectricity and paraelectricity. In this context, the order parameter is the electric polarization that goes from a finite value to zero when the temperature is increased above the Curie temperature.Curie–Weiss law
The Curie–Weiss law describes the magnetic susceptibility χ of a ferromagnet in the paramagnetic region above the Curie point:
where C is a material-specific Curie constant, T is absolute temperature, measured in kelvins, and Tc is the Curie temperature, measured in kelvins. The law predicts a singularity in the susceptibility at T = Tc. Below this temperature the ferromagnet has a spontaneous magnetization.De Haas–van Alphen effect
The de Haas–van Alphen effect, often abbreviated to dHvA, is a quantum mechanical effect in which the magnetic susceptibility of a pure metal crystal oscillates as the intensity of the magnetic field B is increased. Other quantities also oscillate, such as the electrical resistivity (Shubnikov–de Haas effect), specific heat, and sound attenuation and speed. It is named after Wander Johannes de Haas and his student Pieter M. van Alphen. The dHvA effect comes from the orbital motion of itinerant electrons in the material. An equivalent phenomenon at low magnetic fields is known as Landau diamagnetism.Diamagnetism
Diamagnetic materials are repelled by a magnetic field; an applied magnetic field creates an induced magnetic field in them in the opposite direction, causing a repulsive force. In contrast, paramagnetic and ferromagnetic materials are attracted by a magnetic field. Diamagnetism is a quantum mechanical effect that occurs in all materials; when it is the only contribution to the magnetism, the material is called diamagnetic. In paramagnetic and ferromagnetic substances the weak diamagnetic force is overcome by the attractive force of magnetic dipoles in the material. The magnetic permeability of diamagnetic materials is less than μ0, the permeability of vacuum. In most materials diamagnetism is a weak effect which can only be detected by sensitive laboratory instruments, but a superconductor acts as a strong diamagnet because it repels a magnetic field entirely from its interior.
Diamagnetism was first discovered when Sebald Justinus Brugmans observed in 1778 that bismuth and antimony were repelled by magnetic fields. In 1845, Michael Faraday demonstrated that it was a property of matter and concluded that every material responded (in either a diamagnetic or paramagnetic way) to an applied magnetic field. On a suggestion by William Whewell, Faraday first referred to the phenomenon as diamagnetic (the prefix dia- meaning through or across), then later changed it to diamagnetism.Dysprosium
Dysprosium is a chemical element with symbol Dy and atomic number 66. It is a rare earth element with a metallic silver luster. Dysprosium is never found in nature as a free element, though it is found in various minerals, such as xenotime. Naturally occurring dysprosium is composed of seven isotopes, the most abundant of which is 164Dy.
Dysprosium was first identified in 1886 by Paul Émile Lecoq de Boisbaudran, but it was not isolated in pure form until the development of ion exchange techniques in the 1950s. Dysprosium has relatively few applications where it cannot be replaced by other chemical elements. It is used for its high thermal neutron absorption cross-section in making control rods in nuclear reactors, for its high magnetic susceptibility in data storage applications, and as a component of Terfenol-D (a magnetostrictive material). Soluble dysprosium salts are mildly toxic, while the insoluble salts are considered non-toxic.Evans balance
An Evans balance, also known as a Johnson-Matthey balance (after the most prolific producer of the Evans balance) is a device for measuring magnetic susceptibility. Magnetic susceptibility is related to the force experienced by a substance in a magnetic field. Various practical devices are available for the measurement of susceptibility, which differ in the shape of the magnetic field and the way the force is measured.In the Gouy balance there is a homogeneous field in the central region between two (flat) poles of a permanent magnet, or an electromagnet. The sample, in the form of a powder in a cylindrical tube, is suspended in such a way the one end lies in the centre of the field and the other is effectively outside the magnetic field. The force is measured by an analytical balance
The Evans balance employs a similar sample configuration, but measures the force on the magnet.Faraday balance
A Faraday balance is a device for measuring magnetic susceptibility. Magnetic susceptibility is related to the force experienced by a substance in a magnetic field. Various practical devices are available for the measurement of susceptibility, which differ in the shape of the magnetic field and the way the force is measured.In the Faraday balance the field is homogeneous. The pole pieces of the magnet are so shaped that there is a region in which the product of the field strength and field gradient in the z direction is constant. The sample is placed in this region. The force in this case is independent of the packing of the sample and depends only on the total mass of the material present. The method is sensitive and highly reproducible and can be applied to single crystals. The force is measured as a weight change, using a torsion balance.
An alternative method for measuring magnetic susceptibility is the Gouy balance. In this technique there is an inhomogeneous field in the central region between two (flat) poles of a permanent magnet, or an electromagnet. The sample, in the form of a powder in a cylindrical tube, is suspended in such a way the one end lies in the centre of the field and the other is effectively outside the magnetic field. Errors due to inefficient packing in the sample tube are difficult to eliminate.Geoarchaeology
Geoarchaeology is a multi-disciplinary approach which uses the techniques and subject matter of geography, geology and other Earth sciences to examine topics which inform archaeological knowledge and thought. Geoarchaeologists study the natural physical processes that affect archaeological sites such as geomorphology, the formation of sites through geological processes and the effects on buried sites and artifacts post-deposition. Geoarchaeologists' work frequently involves studying soil and sediments as well as other geographical concepts to contribute an archaeological study. Geoarchaeologists may also use computer cartography, geographic information systems (GIS) and digital elevation models (DEM) in combination with disciplines from human and social sciences and earth sciences. Geoarchaeology is important to society because it informs archaeologists about the geomorphology of the soil, sediments and the rocks on the buried sites and artifacts they're researching on. By doing this we are able locate ancient cities and artifacts and estimate by the quality of soil how "prehistoric" they really are.Gouy balance
The Gouy balance, invented by Louis Georges Gouy, is a device for measuring the magnetic susceptibility of a sample.Kubo gap
In atomic physics, the kubo gap is the average spacing that exists between consecutive energy levels. The units of measure are meV or millielectron volts. It varies with an inverse relationship to the nuclearity.
As the material in question is viewed from the bulk and atomic levels, we can see that the kubo gap goes from a smaller to larger value respectively. As the kubo gap increases there is also a decrease in the density of states located at the Fermi level. The kubo gap can also have an effect on the properties associated with the material. It is possible to control the kubo gap which will then cause the system to become metallic or nonmetallic. The electrical conductivity and magnetic susceptibility are also both influenced by the kubo gap and vary according to the relative size of the kubo gap.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 unpaired electrons. Molecular compounds that contain one or more unpaired electrons are paramagnetic. The magnitude of the paramagnetism is expressed as an effective magnetic moment, μeff. For first-row transition metals the magnitude of μeff is, to a first approximation, a simple function of the number of unpaired electrons, the spin-only formula. In general, spin-orbit coupling causes μeff to deviate from the spin-only formula. For the heavier transition metals, lanthanides and actinides, spin-orbit coupling cannot be ignored. Exchange interaction can occur in clusters and infinite lattices, resulting in ferromagnetism, antiferromagnetism or ferrimagnetism depending on the relative orientations of the individual spins.Paramagnetism
Paramagnetism is a form of magnetism whereby certain 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, diamagnetic materials are repelled by magnetic fields and form induced magnetic fields in the direction opposite to that of the applied magnetic field. Paramagnetic materials include most chemical elements and some compounds; they have a relative magnetic permeability slightly greater than 1 (i.e., a small positive magnetic susceptibility) and hence are attracted to magnetic fields. The magnetic moment induced by the applied field is linear in the field strength and rather weak. It typically requires a sensitive analytical balance to detect the effect and modern measurements on paramagnetic materials are often conducted with a SQUID magnetometer.
Paramagnetism is due to the presence of unpaired electrons in the material, so all atoms with incompletely filled atomic orbitals are paramagnetic. Due to their spin, unpaired electrons have a magnetic dipole moment and act like tiny magnets. An external magnetic field causes the electrons' spins to align parallel to the field, causing a net attraction. Paramagnetic materials include aluminium, oxygen, titanium, and iron oxide (FeO).
Unlike ferromagnets, paramagnets do not retain any magnetization in the absence of an externally applied magnetic field because thermal motion randomizes the spin orientations. (Some paramagnetic materials retain spin disorder even at absolute zero, meaning they are paramagnetic in the ground state, i.e. in the absence of thermal motion.) Thus the total magnetization drops to zero when the applied field is removed. Even in the presence of the field there is only a small induced magnetization because only a small fraction of the spins will be oriented by the field. This fraction is proportional to the field strength and this explains the linear dependency. The attraction experienced by ferromagnetic materials is non-linear and much stronger, so that it is easily observed, for instance, in the attraction between a refrigerator magnet and the iron of the refrigerator itself.Permeability (electromagnetism)
In electromagnetism, permeability is the measure of the ability of a material to support the formation of a magnetic field within itself otherwise known as distributed inductance in Transmission Line Theory. Hence, it is the degree of magnetization that a material obtains in response to an applied magnetic field. Magnetic permeability is typically represented by the (italicized) Greek letter µ. The term was coined in September 1885 by Oliver Heaviside. The reciprocal of magnetic permeability is magnetic reluctivity.
In SI units, permeability is measured in henries per meter (H/m), or equivalently in newtons (kg⋅m/s2) per ampere squared (N·A−2). The permeability constant µ0, also known as the magnetic constant or the permeability of free space, is a measure of the amount of resistance encountered when forming a magnetic field in a classical vacuum. Until May 20, 2019, the magnetic constant has the exact (defined) value µ0 = 4π × 10−7 H/m ≈ 12.57 × 10−7 H/m.
On May 20, 2019 a revision to the SI system will go into effect, making the vacuum permeability no longer a constant but rather a value that needs to be determined experimentally; 4π × 1.000 000 000 82 (20) 10−7 H·m−1 is a recently measured value in the new system. It will be proportional to the dimensionless fine-structure constant with no other dependencies.A closely related property of materials is magnetic susceptibility, which is a dimensionless proportionality factor that indicates the degree of magnetization of a material in response to an applied magnetic field.Superdiamagnetism
Superdiamagnetism (or perfect diamagnetism) is a phenomenon occurring in certain materials at low temperatures, characterised by the complete absence of magnetic permeability (i.e. a magnetic susceptibility = −1) and the exclusion of the interior magnetic field.
Superdiamagnetism established that the superconductivity of a material was a stage of phase transition. Superconducting magnetic levitation is due to superdiamagnetism, which repels a permanent magnet which approaches the superconductor, and flux pinning, which prevents the magnet floating away.
Superdiamagnetism is a feature of superconductivity. It was identified in 1933, by Walther Meissner and Robert Ochsenfeld, but it is considered distinct from the Meissner effect which occurs when the superconductivity first forms, and involves the exclusion of magnetic fields that already penetrate the object.Thermomagnetic convection
Ferrofluids can be used to transfer heat, since heat and mass transport in such magnetic fluids can be controlled using an external magnetic field.
B. A. Finlayson first explained in 1970 (in his paper "Convective instability of ferromagnetic fluids", Journal of Fluid Mechanics, 40:753-767) how an external magnetic field imposed on a ferrofluid with varying magnetic susceptibility, e.g., due to a temperature gradient, results in a nonuniform magnetic body force, which leads to thermomagnetic convection. This form of heat transfer can be useful for cases where conventional convection fails to provide adequate heat transfer, e.g., in miniature microscale devices or under reduced gravity conditions.
Ozoe group has studied thermomagnetic convection both experimentally and numerically. They showed how to enhance, suppress and invert the convection modes. They have also carried out scaling analysis for paramagnetic fluids in microgravity conditions.A comprehensive review of thermomagnetic convection (in A. Mukhopadhyay, R. Ganguly, S. Sen, and I. K. Puri, "Scaling analysis to characterize thermomagnetic convection", International Journal of Heat and Mass Transfer 48:3485-3492, (2005)) also shows that this form of convection can be correlated with a dimensionless magnetic Rayleigh number. Subsequently, this group explained that fluid motion occurs due to the presence of a Kelvin body force that has two terms. The first term can be treated as a magnetostatic pressure, while the second is important only if there is a spatial gradient of the fluid susceptibility, e.g., in a non-isothermal system. Colder fluid that has a larger magnetic susceptibility is attracted towards regions with larger field strength during thermomagnetic convection, which displaces warmer fluid of lower susceptibility. They showed that thermomagnetic convection can be correlated with a dimensionless magnetic Rayleigh number. Heat transfer due to this form of convection can be much more effective than buoyancy-induced convection for systems with small dimensions.The ferrofluid magnetization depends on the local value of the applied magnetic field H as well as on the fluid magnetic susceptibility. In a ferrofluid flow encompassing varying temperatures, the susceptibility is a function of the temperature. This produces a force that can be expressed in the Navier–Stokes or momentum equation governing fluid flow as the "Kelvin body force (KBF)".
The KBF creates a static pressure field that is symmetric about a magnet, e.g., a line dipole, that produces a curl-free force field, i.e., curl(ℑ) = 0 for constant temperature flow. Such a symmetric field does not alter the velocity. However, if the temperature distribution about the imposed magnetic field is asymmetric so is the KBF in which case curl(ℑ) ≠ 0. Such an asymmetric body force leads to ferrofluid motion across isotherms.Vespel
Vespel is the trademark of a range of durable high-performance polyimide-based plastics manufactured by DuPont. The one shown in the structure on the right was the first to be commercialized.