Magnetization
Encyclopedia
In classical electromagnetism
, magnetization or magnetic polarization is the vector field
that expresses the density
of permanent or induced magnetic dipole moments in a magnetic material. The origin of the magnetic moments responsible for magnetization can be either microscopic electric current
s resulting from the motion of electron
s in atom
s, or the spin
of the electrons or the nuclei. Net magnetization results from the response of a material to an external magnetic field
, together with any unbalanced magnetic dipole moments that may be inherent in the material itself; for example, in ferromagnets. Magnetization is not always homogeneous
within a body, but rather varies between different points. Magnetization also describes how a material responds to an applied magnetic field
as well as the way the material changes the magnetic field, and can be used to calculate the force
s that result from those interactions. It can be compared to electric polarization
, which is the measure of the corresponding response of a material to an electric field
in electrostatics
. Physicists and engineers define magnetization as the quantity of magnetic moment
per unit volume. It is represented by a vector M.
Here, M represents magnetization; m is the vector that defines the magnetic moment
; V represents volume; and N is the number of magnetic moments in the sample. The quantity N/V is usually written as n, the number density of magnetic moments. The Mfield is measured in amperes per meter (A/m) in SI units.
s (B, H), electric fields (E, D), charge density
(ρ), and current density
(J) is described by Maxwell's equations
. The role of the magnetization is described below.
(SI units)
(Gaussian units
)
which is convenient for various calculations. The vacuum permeability
μ_{0} is, by definition, V
·s
/(A
·m
).
A relation between M and H exists in many materials. In diamagnets and paramagnets, the relation is usually linear:
where χ_{m} is called the volume magnetic susceptibility
.
In ferromagnets there is no onetoone correspondence between M and H because of hysteresis
.
J, known as the magnetization current or bound current:
so that the total current density that enters Maxwell's equations is given by
where J_{f} 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 P.
describing the magnetic quantities reduce to
These equations can be easily solved in analogy with electrostatic problems where
In this sense plays the role of a "magnetic charge density" analogous to the electric charge density (see also demagnetizing field
).
Magnetization is volume density of magnetic moment
. That is: if a certain volume has magnetization then the volume element has a magnetic moment of
The timedependent 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.
Electromagnetism
Electromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...
, magnetization or magnetic polarization is the vector field
Vector field
In vector calculus, a vector field is an assignmentof a vector to each point in a subset of Euclidean space. A vector field in the plane for instance can be visualized as an arrow, with a given magnitude and direction, attached to each point in the plane...
that expresses the density
Density
The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...
of permanent or induced magnetic dipole moments in a magnetic material. The origin of the magnetic moments responsible for magnetization can be either microscopic electric current
Electric current
Electric current is a flow of electric charge through a medium.This charge is typically carried by moving electrons in a conductor such as wire...
s resulting from the motion of electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
s in atom
Atom
The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...
s, or the spin
Spin (physics)
In quantum mechanics and particle physics, spin is a fundamental characteristic property of elementary particles, composite particles , and atomic nuclei.It is worth noting that the intrinsic property of subatomic particles called spin and discussed in this article, is related in some small ways,...
of the electrons or the nuclei. Net magnetization results from the response of a material to an external magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
, together with any unbalanced magnetic dipole moments that may be inherent in the material itself; for example, in ferromagnets. Magnetization is not always homogeneous
Homogeneity (physics)
In general, homogeneity is defined as the quality or state of being homogeneous . For instance, a uniform electric field would be compatible with homogeneity...
within a body, but rather varies between different points. Magnetization also describes how a material responds to an applied magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
as well as the way the material changes the magnetic field, and can be used to calculate the force
Force
In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...
s that result from those interactions. It can be compared to electric polarization
Polarization density
In classical electromagnetism, polarization density is the vector field that expresses the density of permanent or induced electric dipole moments in a dielectric material. When a dielectric is placed in an external electric field, its molecules gain electric dipole moment and the dielectric is...
, which is the measure of the corresponding response of a material to an electric field
Electric field
In physics, an electric field surrounds electrically charged particles and timevarying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...
in electrostatics
Electrostatics
Electrostatics is the branch of physics that deals with the phenomena and properties of stationary or slowmoving electric charges....
. Physicists and engineers define magnetization as the quantity of magnetic moment
Magnetic moment
The magnetic moment of a magnet is a quantity that determines the force that the magnet can exert on electric currents and the torque that a magnetic field will exert on it...
per unit volume. It is represented by a vector M.
Definition
Magnetization can be defined according to the following equation:Here, M represents magnetization; m is the vector that defines the magnetic moment
Magnetic moment
The magnetic moment of a magnet is a quantity that determines the force that the magnet can exert on electric currents and the torque that a magnetic field will exert on it...
; V represents volume; and N is the number of magnetic moments in the sample. The quantity N/V is usually written as n, the number density of magnetic moments. The Mfield is measured in amperes per meter (A/m) in SI units.
Magnetization in Maxwell's equations
The behavior of magnetic fieldMagnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
s (B, H), electric fields (E, D), charge density
Charge density
The linear, surface, or volume charge density is the amount of electric charge in a line, surface, or volume, respectively. It is measured in coulombs per meter , square meter , or cubic meter , respectively, and represented by the lowercase Greek letter Rho . Since there are positive as well as...
(ρ), and current density
Current density
Current density is a measure of the density of flow of a conserved charge. Usually the charge is the electric charge, in which case the associated current density is the electric current per unit area of cross section, but the term current density can also be applied to other conserved...
(J) is described by Maxwell's equations
Maxwell's equations
Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. These fields in turn underlie modern electrical and communications technologies.Maxwell's equations...
. The role of the magnetization is described below.
Relations between B, H, and M
The magnetization defines the auxiliary magnetic field H as(SI units)
(Gaussian units
Gaussian units
Gaussian units comprise a metric system of physical units. This system is the most common of the several electromagnetic unit systems based on cgs units. It is also called the Gaussian unit system, Gaussiancgs units, or often just cgs units...
)
which is convenient for various calculations. The vacuum permeability
Vacuum permeability
The physical constant μ0, commonly called the vacuum permeability, permeability of free space, or magnetic constant is an ideal, physical constant, which is the value of magnetic permeability in a classical vacuum...
μ_{0} is, by definition, V
Volt
The volt is the SI derived unit for electric potential, electric potential difference, and electromotive force. The volt is named in honor of the Italian physicist Alessandro Volta , who invented the voltaic pile, possibly the first chemical battery. Definition :A single volt is defined as the...
·s
Second
The second is a unit of measurement of time, and is the International System of Units base unit of time. It may be measured using a clock....
/(A
Ampere
The ampere , often shortened to amp, is the SI unit of electric current and is one of the seven SI base units. It is named after AndréMarie Ampère , French mathematician and physicist, considered the father of electrodynamics...
·m
Metre
The metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one tenmillionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology...
).
A relation between M and H exists in many materials. In diamagnets and paramagnets, the relation is usually linear:
where χ_{m} is called the volume magnetic susceptibility
Magnetic susceptibility
In electromagnetism, the magnetic susceptibility \chi_m is a dimensionless proportionality constant that indicates the degree of magnetization of a material in response to an applied magnetic field...
.
In ferromagnets there is no onetoone correspondence between M and H because of hysteresis
Hysteresis
Hysteresis is the dependence of a system not just on its current environment but also on its past. This dependence arises because the system can be in more than one internal state. To predict its future evolution, either its internal state or its history must be known. If a given input alternately...
.
Magnetization current
The magnetization M makes a contribution to the current densityCurrent density
Current density is a measure of the density of flow of a conserved charge. Usually the charge is the electric charge, in which case the associated current density is the electric current per unit area of cross section, but the term current density can also be applied to other conserved...
J, known as the magnetization current or bound current:
so that the total current density that enters Maxwell's equations is given by
where J_{f} 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 P.
Magnetostatics
In the absence of free electric currents and timedependent effects, Maxwell's equationsMaxwell's equations
Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. These fields in turn underlie modern electrical and communications technologies.Maxwell's equations...
describing the magnetic quantities reduce to
These equations can be easily solved in analogy with electrostatic problems where
In this sense plays the role of a "magnetic charge density" analogous to the electric charge density (see also demagnetizing field
Demagnetizing field
The demagnetizing field, also called the stray field, is the magnetic field generated by the magnetization in a magnet. The total magnetic field in a region containing magnets is the sum of the demagnetizing fields of the magnets and the magnetic field due to any free currents or displacement...
).
Magnetization is volume density of magnetic moment
Magnetic moment
The magnetic moment of a magnet is a quantity that determines the force that the magnet can exert on electric currents and the torque that a magnetic field will exert on it...
. That is: if a certain volume has magnetization then the volume element has a magnetic moment of
Magnetization dynamics

 Main article: Magnetization dynamicsMagnetization dynamicsRotation Physics:A magnetic moment m in the presence of a magnetic field H experiences a torque \tau that attempts to bring the moment and field vectors into alignment...
 Main article: Magnetization dynamics
The timedependent 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.
Demagnetization
In addition to magnetization, there is also demagnetization. Demagnetization is the process by which the magnetic field of an object is reduced or eliminated. The process of demagnetizing can be accomplished in many ways. One technique used for demagnetization is to heat the object above its Curie Temperature. The reason for this is that when a magnetic material is heated to its Curie Temperature, the material's magnetivity is eliminated. One other way of achieving demagnetization is to use an electric coil. If the object is retracted out of a coil with aternating current running through it, the object's dipoles will become randomized and the object will be demagnetized.Applications of Demagnetization
One application of demagnetization is to eliminate unwanted magnetic fields. The reason for doing this is that magnetic fields can have unwanted effects on different devices. In particular magnetic fields can affect electronic devices such as cell phones or computers. If such a device is going to be coming into contact with other possibly magnetic objects, the magnetic fields might need to be reduced in order to protect the electronic device. Therefore demagnetization is sometimes used to keep magnetic fields from damaging electrical devices.See also
 Permeability (electromagnetism)Permeability (electromagnetism)In electromagnetism, permeability is the measure of the ability of a material to support the formation of a magnetic field within itself. In other words, it is the degree of magnetization that a material obtains in response to an applied magnetic field. Magnetic permeability is typically...
 Magnetic susceptibilityMagnetic susceptibilityIn electromagnetism, the magnetic susceptibility \chi_m is a dimensionless proportionality constant that indicates the degree of magnetization of a material in response to an applied magnetic field...
 Earth's magnetic fieldEarth's magnetic fieldEarth's magnetic field is the magnetic field that extends from the Earth's inner core to where it meets the solar wind, a stream of energetic particles emanating from the Sun...
 Geomagnetic reversalGeomagnetic reversalA geomagnetic reversal is a change in the Earth's magnetic field such that the positions of magnetic north and magnetic south are interchanged. The Earth's field has alternated between periods of normal polarity, in which the direction of the field was the same as the present direction, and reverse...
 Geomagnetic excursionGeomagnetic excursionA geomagnetic excursion, like a geomagnetic reversal, is a significant change in the Earth's magnetic field. Unlike reversals however, an excursion does not permanently change the large scale orientation of the field, but rather represents a dramatic, typically shortlived decrease in field...