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In
classical electromagnetism Classical electromagnetism or classical electrodynamics is a branch of theoretical physics that studies the interactions between electric charges and currents using an extension of the classical Newtonian model; It is, therefore, a classical fie ...
, magnetization is the vector field that expresses 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. Mathematica ...
of permanent or induced
magnetic dipole 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 electromagnets ...
s in a magnetic material. Movement within this field is described by direction and is either Axial or Diametric. The origin of the magnetic moments responsible for magnetization can be either microscopic
electric current An electric current is a stream of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is measured as the net rate of flow of electric charge through a surface or into a control volume. The moving ...
s resulting from the motion of
electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no ...
s in
atom Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas, ...
s, or the
spin Spin or spinning most often refers to: * Spinning (textiles), the creation of yarn or thread by twisting fibers together, traditionally by hand spinning * Spin, the rotation of an object around a central axis * Spin (propaganda), an intentionally b ...
of the electrons or the nuclei. Net magnetization results from the response of a material to an external
magnetic field A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...
.
Paramagnetic 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, ...
materials have a weak induced magnetization in a magnetic field, which disappears when the magnetic field is removed.
Ferromagnetic Ferromagnetism is a property of certain materials (such as iron) which results in a large observed magnetic permeability, and in many cases a large magnetic coercivity allowing the material to form a permanent magnet. Ferromagnetic materials ...
and
ferrimagnetic A ferrimagnetic material is a material that has populations of atoms with opposing magnetic moments, as in antiferromagnetism, but these moments are unequal in magnitude so a spontaneous magnetization remains. This can for example occur when t ...
materials have strong magnetization in a magnetic field, and can be ''magnetized'' to have magnetization in the absence of an external field, becoming a
permanent magnet A magnet is a material or object that produces a magnetic field. This magnetic field is invisible but is responsible for the most notable property of a magnet: a force that pulls on other ferromagnetic materials, such as iron, steel, nickel, ...
. Magnetization is not necessarily uniform within a material, but may vary between different points. Magnetization also describes how a material responds to an applied
magnetic field A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...
as well as the way the material changes the magnetic field, and can be used to calculate the
force In physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity (e.g. moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a ...
s that result from those interactions. It can be compared to
electric polarization In classical electromagnetism, polarization density (or electric polarization, or simply polarization) is the vector field that expresses the density of permanent or induced electric dipole moments in a dielectric material. When a dielectric is ...
, which is the measure of the corresponding response of a material to an
electric field An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field ...
in
electrostatics Electrostatics is a branch of physics that studies electric charges at rest ( static electricity). Since classical times, it has been known that some materials, such as amber, attract lightweight particles after rubbing. The Greek word for amb ...
. Physicists and engineers usually define magnetization as the quantity of
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 electromagnets ...
per unit volume. It is represented by a
pseudovector In physics and mathematics, a pseudovector (or axial vector) is a quantity that is defined as a function of some vectors or other geometric shapes, that resembles a vector, and behaves like a vector in many situations, but is changed into its ...
M.


Definition

The magnetization field or M-field can be defined according to the following equation: \mathbf M = \frac Where \mathrm\mathbf is the elementary
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 electromagnets ...
and ''\mathrmV'' is the
volume element In mathematics, a volume element provides a means for integrating a function with respect to volume in various coordinate systems such as spherical coordinates and cylindrical coordinates. Thus a volume element is an expression of the form :dV = ...
; in other words, the M-field is the distribution of magnetic moments in the region or
manifold In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n-dimensional manifold, or ''n-manifold'' for short, is a topological space with the property that each point has a ...
concerned. This is better illustrated through the following relation: \mathbf m=\iiint \mathbf M\,\mathrmV where m is an ordinary magnetic moment and the triple integral denotes integration over a volume. This makes the M-field completely analogous to the electric polarisation field, or P-field, used to determine the
electric dipole moment The electric dipole moment is a measure of the separation of positive and negative electrical charges within a system, that is, a measure of the system's overall polarity. The SI unit for electric dipole moment is the coulomb-meter (C⋅m). The ...
p generated by a similar region or manifold with such a polarization: \mathbf P = , \quad \mathbf p = \iiint \mathbf P\,\mathrmV Where \mathrm\mathbf is the elementary electric dipole moment. Those definitions of P and M as a "moments per unit volume" are widely adopted, though in some cases they can lead to ambiguities and paradoxes. The M-field is measured in ''
ampere The ampere (, ; symbol: A), often shortened to amp,SI supports only the use of symbols and deprecates the use of abbreviations for units. is the unit of electric current in the International System of Units (SI). One ampere is equal to ele ...
s per
meter The metre ( British spelling) or meter ( American spelling; see spelling differences) (from the French unit , from the Greek noun , "measure"), symbol m, is the primary unit of length in the International System of Units (SI), though its pr ...
'' (A/m) in SI units.


In Maxwell's equations

The behavior of
magnetic field A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...
s (B, H),
electric field An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field ...
s (E, D),
charge density In electromagnetism, charge density is the amount of electric charge per unit length, surface area, or volume. Volume charge density (symbolized by the Greek letter ρ) is the quantity of charge per unit volume, measured in the SI system in co ...
(''ρ''), and
current density In electromagnetism, current density is the amount of charge per unit time that flows through a unit area of a chosen cross section. The current density vector is defined as a vector whose magnitude is the electric current per cross-sectional ar ...
(J) is described by
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. ...
. The role of the magnetization is described below.


Relations between B, H, and M

The magnetization defines the auxiliary magnetic field H as :\mathbf=\mu_0(\mathbf) (
SI units The International System of Units, known by the international abbreviation SI in all languages and sometimes Pleonasm#Acronyms and initialisms, pleonastically as the SI system, is the modern form of the metric system and the world's most wid ...
) :\mathbf = \mathbf + 4 \pi \mathbf (
Gaussian units Gaussian units constitute a metric system of physical units. This system is the most common of the several electromagnetic unit systems based on cgs (centimetre–gram–second) units. It is also called the Gaussian unit system, Gaussian-cgs unit ...
) which is convenient for various calculations. The
vacuum permeability 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 constant, ...
μ0 is, by definition, V· s/( A· m) (in SI units). A relation between M and H exists in many materials. In diamagnets and
paramagnet 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, ...
s, the relation is usually linear: :\mathbf = \chi\mathbf, \, \mathbf = \mu\mathbf=\mu_0 (1+\chi)\mathbf, where ''χ'' is called the volume magnetic susceptibility, and μ is called the
magnetic permeability In electromagnetism, permeability is the measure of magnetization that a material obtains in response to an applied magnetic field. Permeability is typically represented by the (italicized) Greek letter ''μ''. The term was coined by Willia ...
of the material. The
magnetic potential energy In physics, potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors. Common types of potential energy include the gravitational potent ...
per unit volume (i.e. magnetic
energy density In physics, energy density is the amount of energy stored in a given system or region of space per unit volume. It is sometimes confused with energy per unit mass which is properly called specific energy or . Often only the ''useful'' or extract ...
) of the paramagnet (or diamagnet) in the magnetic field is: :-\mathbf \cdot \mathbf=-\chi\mathbf \cdot \mathbf=-\frac\frac, the negative gradient of which is the
magnetic force In physics (specifically in electromagnetism) the Lorentz force (or electromagnetic force) is the combination of electric and magnetic force on a point charge due to electromagnetic fields. A particle of charge moving with a velocity in an elect ...
on the paramagnet (or diamagnet) per unit volume (i.e. force density). In diamagnets (\chi <0) and paramagnets (\chi >0), usually , \chi, \ll 1, and therefore \mathbf \approx \chi\frac. In
ferromagnet Ferromagnetism is a property of certain materials (such as iron) which results in a large observed magnetic permeability, and in many cases a large magnetic coercivity allowing the material to form a permanent magnet. Ferromagnetic materials ...
s there is no one-to-one correspondence between M and H because of
magnetic hysteresis Magnetic hysteresis occurs when an external magnetic field is applied to a ferromagnet such as iron and the atomic dipoles align themselves with it. Even when the field is removed, part of the alignment will be retained: the material has become ...
.


Magnetic polarization

Alternatively to the magnetization, one can define the magnetic polarization, (often the symbol is used, not to be confused with current density). :\mathbf=\mu_0\mathbf + \mathbf (
SI units The International System of Units, known by the international abbreviation SI in all languages and sometimes Pleonasm#Acronyms and initialisms, pleonastically as the SI system, is the modern form of the metric system and the world's most wid ...
). This is by direct analogy to the
electric polarization In classical electromagnetism, polarization density (or electric polarization, or simply polarization) is the vector field that expresses the density of permanent or induced electric dipole moments in a dielectric material. When a dielectric is ...
, \mathbf=\varepsilon_0\mathbf + \mathbf. The magnetic polarization thus differs from the magnetization by a factor of : :\mathbf=\mu_0\mathbf (
SI units The International System of Units, known by the international abbreviation SI in all languages and sometimes Pleonasm#Acronyms and initialisms, pleonastically as the SI system, is the modern form of the metric system and the world's most wid ...
). Whereas magnetization is measured typically in amperes/meter, the magnetic polarization is measured in teslas.


Magnetization current

The magnetization ''M'' makes a contribution to the
current density In electromagnetism, current density is the amount of charge per unit time that flows through a unit area of a chosen cross section. The current density vector is defined as a vector whose magnitude is the electric current per cross-sectional ar ...
J, known as the ''magnetization current.'' : \mathbf_\mathrm = \nabla \times \mathbf and for the ''bound surface current'': : \mathbf_\mathrm = \mathbf \times \mathbf so that the total current density that enters Maxwell's equations is given by : \mathbf = \mathbf_\mathrm + \nabla \times \mathbf + \frac where Jf is the electric current density of free charges (also called the ''free current''), the second term is the contribution from the magnetization, and the last term is related to the
electric polarization In classical electromagnetism, polarization density (or electric polarization, or simply polarization) is the vector field that expresses the density of permanent or induced electric dipole moments in a dielectric material. When a dielectric is ...
P.


Magnetostatics

In the absence of free electric currents and time-dependent effects,
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. ...
describing the magnetic quantities reduce to :\begin \mathbf &= 0\\ \mathbf &= -\nabla\cdot\mathbf \end These equations can be solved in analogy with
electrostatic Electrostatics is a branch of physics that studies electric charges at rest (static electricity). Since classical times, it has been known that some materials, such as amber, attract lightweight particles after rubbing. The Greek word for am ...
problems where :\begin \mathbf &= 0 \\ \mathbf &= \frac \end In this sense −∇⋅M plays the role of a fictitious "magnetic charge density" analogous to the electric charge density ''ρ''; (see also
demagnetizing field The demagnetizing field, also called the stray field (outside the magnet), is the magnetic field (H-field) generated by the magnetization in a magnet. The total magnetic field in a region containing magnets is the sum of the demagnetizing fields ...
).


Dynamics

The time-dependent behavior of magnetization becomes important when considering nanoscale and nanosecond timescale magnetization. Rather than simply aligning with an applied field, the individual magnetic moments in a material begin to precess around the applied field and come into alignment through relaxation as energy is transferred into the lattice.


Reversal

Magnetization reversal, also known as switching, refers to the process that leads to a 180° (arc) re-orientation of the magnetization
vector Vector most often refers to: *Euclidean vector, a quantity with a magnitude and a direction *Vector (epidemiology), an agent that carries and transmits an infectious pathogen into another living organism Vector may also refer to: Mathematic ...
with respect to its initial direction, from one stable orientation to the opposite one. Technologically, this is one of the most important processes in
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 particl ...
that is linked to the magnetic
data storage Data storage is the recording (storing) of information ( data) in a storage medium. Handwriting, phonographic recording, magnetic tape, and optical discs are all examples of storage media. Biological molecules such as RNA and DNA are c ...
process such as used in modern
hard disk drive A hard disk drive (HDD), hard disk, hard drive, or fixed disk is an electro-mechanical data storage device that stores and retrieves digital data using magnetic storage with one or more rigid rapidly rotating platters coated with magn ...
s. As it is known today, there are only a few possible ways to reverse the magnetization of a metallic magnet: # an applied
magnetic field A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...
#
spin injection Spin or spinning most often refers to: * Spinning (textiles), the creation of yarn or thread by twisting fibers together, traditionally by hand spinning * Spin, the rotation of an object around a central axis * Spin (propaganda), an intentionally ...
via a beam of particles with
spin Spin or spinning most often refers to: * Spinning (textiles), the creation of yarn or thread by twisting fibers together, traditionally by hand spinning * Spin, the rotation of an object around a central axis * Spin (propaganda), an intentionally b ...
# magnetization reversal by circularly polarized light; i.e., incident electromagnetic radiation that is circularly polarized


Demagnetization

Demagnetization is the reduction or elimination of magnetization. One way to do this is to heat the object above its
Curie temperature In physics and materials science, the Curie temperature (''T''C), or Curie point, is the temperature above which certain materials lose their permanent magnetic properties, which can (in most cases) be replaced by induced magnetism. The Cur ...
, where thermal fluctuations have enough energy to overcome exchange interactions, the source of ferromagnetic order, and destroy that order. Another way is to pull it out of an electric coil with alternating current running through it, giving rise to fields that oppose the magnetization. One application of demagnetization is to eliminate unwanted magnetic fields. For example, magnetic fields can interfere with electronic devices such as cell phones or computers, and with machining by making cuttings cling to their parent.


See also

*
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, on ...
* Orbital magnetization


References

{{Authority control Electric and magnetic fields in matter