Movatterモバイル変換

Magnetization

From Wikipedia, the free encyclopedia

Physical quantity, density of magnetic moment per volume

This article is about magnetization as it appears in Maxwell's equations of classical electrodynamics. For a microscopic description of how magnetic materials react to a magnetic field, seemagnetism. For mathematical description of fields surrounding magnets and currents, seemagnetic field.

Electromagnetism

Electricity Magnetism Optics History Computational Textbooks Phenomena
Electrostatics Charge density Conductor Coulomb law Electret Electric charge Electric dipole Electric field Electric flux Electric potential Electrostatic discharge Electrostatic induction Gauss's law Insulator Permittivity Polarization Potential energy Static electricity Triboelectricity
Magnetostatics Ampère's law Biot–Savart law Gauss's law for magnetism Magnetic dipole Magnetic field Magnetic flux Magnetic scalar potential Magnetic vector potential Magnetization Permeability Right-hand rule
Electrodynamics Bremsstrahlung Cyclotron radiation Displacement current Eddy current Electromagnetic field Electromagnetic induction Electromagnetic pulse Electromagnetic radiation Faraday's law Jefimenko equations Larmor formula Lenz's law Liénard–Wiechert potential London equations Lorentz force Maxwell's equations Maxwell tensor Poynting vector Synchrotron radiation
Electrical network Alternating current Capacitance Current density Direct current Electric current Electric power Electrolysis Electromotive force Impedance Inductance Joule heating Kirchhoff's laws Network analysis Ohm's law Parallel circuit Resistance Resonant cavities Series circuit Voltage Watt Waveguides
Magnetic circuit AC motor DC motor Electric machine Electric motor Gyrator–capacitor Induction motor Linear motor Magnetomotive force Permeance Reluctance (complex) Reluctance (real) Rotor Stator Transformer
Covariant formulation Electromagnetic tensor Electromagnetism and special relativity Four-current Four-potential Mathematical descriptions Maxwell equations in curved spacetime Relativistic electromagnetism Stress–energy tensor
Scientists Ampère Biot Coulomb Davy Einstein Faraday Fizeau Gauss Heaviside Helmholtz Henry Hertz Hopkinson Jefimenko Joule Kelvin Kirchhoff Larmor Lenz Liénard Lorentz Maxwell Neumann Ohm Ørsted Poisson Poynting Ritchie Savart Singer Steinmetz Tesla Thomson Volta Weber Wiechert
v t e

Common symbols	M
SI unit	Ampere-meter⁻¹
InSI base units	m⁻¹⋅A
Dimension	L⁻¹I

Inclassical electromagnetism,magnetization is thevector field that expresses thedensity of permanent or inducedmagnetic dipole moments in a magnetic material. Accordingly, physicists and engineers usually define magnetization as the quantity ofmagnetic moment per unit volume.^[1]It is represented by apseudovectorM. Magnetization can be compared toelectric polarization, which is the measure of the corresponding response of a material to anelectric field inelectrostatics.

Magnetization also describes how a material responds to an appliedmagnetic field as well as the way the material changes the magnetic field, and can be used to calculate theforces that result from those interactions.

The origin of the magnetic moments responsible for magnetization can be either microscopicelectric currents resulting from the motion ofelectrons inatoms, or thespin of the electrons or the nuclei. Net magnetization results from the response of a material to an externalmagnetic field.

Paramagnetic materials have a weak induced magnetization in a magnetic field, which disappears when the magnetic field is removed.Ferromagnetic andferrimagnetic materials have strong magnetization in a magnetic field, and can bemagnetized to have magnetization in the absence of an external field, becoming apermanent magnet. Magnetization is not necessarily uniform within a material, but may vary between different points.

Definition

[edit]

The magnetization field orM-field can be defined according to the following equation: $\mathbf {M} ={\frac {\mathrm {d} \mathbf {m} }{\mathrm {d} V}}$

Where $\mathrm {d} \mathbf {m}$ is the elementarymagnetic moment and $\mathrm {d} V$ is thevolume element; in other words, theM-field is the distribution of magnetic moments in the region ormanifold concerned. This is better illustrated through the following relation: $\mathbf {m} =\iiint \mathbf {M} \,\mathrm {d} V$ wherem is an ordinary magnetic moment and the triple integral denotes integration over a volume. This makes theM-field completely analogous to theelectric polarization field, orP-field, used to determine theelectric dipole momentp generated by a similar region or manifold with such a polarization: $\mathbf {P} ={\mathrm {d} \mathbf {p} \over \mathrm {d} V},\quad \mathbf {p} =\iiint \mathbf {P} \,\mathrm {d} V,$ where $\mathrm {d} \mathbf {p}$ is the elementary electric dipole moment.

Those definitions ofP andM as a "moments per unit volume" are widely adopted, though in some cases they can lead to ambiguities and paradoxes.^[1]

TheM-field is measured inamperes permeter (A/m) inSI units.^[2]

In Maxwell's equations

[edit]

The behavior ofmagnetic fields (B,H),electric fields (E,D),charge density (ρ), andcurrent density (J) is described byMaxwell's equations. The role of the magnetization is described below.

Relations between B, H, and M

[edit]

Main article:Magnetic field

The magnetization defines the auxiliary magnetic fieldH as

\mathbf {B} =\mu _{0}(\mathbf {H+M} )

(SI)

\mathbf {B} =\mathbf {H} +4\pi \mathbf {M}

(Gaussian system)

which is convenient for various calculations. Thevacuum permeabilityμ₀ is, approximately,4π×10⁻⁷ V·s/(A·m).

A relation betweenM andH exists in many materials. Indiamagnets andparamagnets, the relation is usually linear:

\mathbf {M} =\chi \mathbf {H} ,\,\mathbf {B} =\mu \mathbf {H} =\mu _{0}(1+\chi )\mathbf {H} ,

whereχ is called thevolume magnetic susceptibility, and μ is called themagnetic permeability of the material. Themagnetic potential energy per unit volume (i.e. magneticenergy density) of the paramagnet (or diamagnet) in the magnetic field is:

-\mathbf {M} \cdot \mathbf {B} =-\chi \mathbf {H} \cdot \mathbf {B} =-{\frac {\chi }{1+\chi }}{\frac {\mathbf {B} ^{2}}{\mu _{0}}},

the negative gradient of which is themagnetic force 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 $\mathbf {M} \approx \chi {\frac {\mathbf {B} }{\mu _{0}}}$ .

Inferromagnets there is no one-to-one correspondence betweenM andH because ofmagnetic hysteresis.

Magnetic polarization

[edit]

Alternatively to the magnetization, one can define themagnetic polarization,I (often the symbolJ is used, not to be confused with current density).^[3]

\mathbf {B} =\mu _{0}\mathbf {H} +\mathbf {I}

(SI).

This is by direct analogy to theelectric polarization, $\mathbf {D} =\varepsilon _{0}\mathbf {E} +\mathbf {P}$ .The magnetic polarization thus differs from the magnetization by a factor ofμ₀:

\mathbf {I} =\mu _{0}\mathbf {M}

(SI).

Whereas magnetization is given with the unit ampere/meter, the magnetic polarization is given with the unit tesla.

Magnetization current

[edit]

When the microscopic currents induced by the magnetization (black arrows) do not balance out, bound volume currents (blue arrows) and bound surface currents (red arrows) appear in the medium.

The magnetizationM makes a contribution to thecurrent densityJ, known as themagnetization current.^[4]

\mathbf {J} _{\mathrm {m} }=\nabla \times \mathbf {M}

and for thebound surface current:

\mathbf {K} _{\mathrm {m} }=\mathbf {M} \times \mathbf {\hat {n}}

so that the total current density that enters Maxwell's equations is given by

\mathbf {J} =\mathbf {J} _{\mathrm {f} }+\nabla \times \mathbf {M} +{\frac {\partial \mathbf {P} }{\partial t}}

whereJ_f is the electric current density of free charges (also called thefree current), the second term is the contribution from the magnetization, and the last term is related to theelectric polarizationP.

Magnetostatics

[edit]

Main article:Magnetostatics

In the absence of free electric currents and time-dependent effects,Maxwell's equations describing the magnetic quantities reduce to

{\begin{aligned}\mathbf {\nabla \times H} &=\mathbf {0} \\\mathbf {\nabla \cdot H} &=-\nabla \cdot \mathbf {M} \end{aligned}}

These equations can be solved in analogy withelectrostatic problems where

{\begin{aligned}\mathbf {\nabla \times E} &=\mathbf {0} \\\mathbf {\nabla \cdot E} &={\frac {\rho }{\epsilon _{0}}}\end{aligned}}

In this sense −∇⋅M plays the role of a fictitious "magnetic charge density" analogous to theelectric charge densityρ; (see alsodemagnetizing field).

Dynamics

[edit]

Main article:Magnetization 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

[edit]

Magnetization reversal, also known as switching, refers to the process that leads to a 180° (arc) re-orientation of the magnetizationvector with respect to its initial direction, from one stable orientation to the opposite one. Technologically, this is one of the most important processes inmagnetism that is linked to the magneticdata storage process such as used in modernhard disk drives.^[5] As it is known today, there are only a few possible ways to reverse the magnetization of a metallic magnet:

an appliedmagnetic field^[5]
spin injection via a beam of particles withspin^[5]
magnetization reversal by circularly polarized light;^[6] i.e., incident electromagnetic radiation that iscircularly polarized

Demagnetization

[edit]

Main article:Degaussing

Demagnetization is the reduction or elimination of magnetization.^[7] One way to do this is to heat the object above itsCurie temperature, where thermal fluctuations have enough energy to overcomeexchange 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.^[8]

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.^[8]

A third, more recently discovered method is ultrafast demagnetization, which uses intense, femtosecond laser pulses.^[9] Unlike heating above the Curie temperature, this process is extremely fast (occurring in less than a picosecond) and is considered a non-equilibrium process. The laser pulse deposits energy directly into the material's electrons. This energy is then rapidly transferred to the spin system through mechanisms like electron-magnon scattering, causing the magnetic order to collapse long before the material's lattice has had time to heat up significantly. This phenomenon is a key area of research for developing future high-speed magnetic data storage and spintronic devices.

References

[edit]

^^a ^bC.A. Gonano; R.E. Zich; M. Mussetta (2015)."Definition for Polarization P and Magnetization M Fully Consistent with Maxwell's Equations"(PDF).Progress in Electromagnetics Research B.64:83–101.doi:10.2528/PIERB15100606. Archived fromthe original(PDF) on 2020-10-17. Retrieved2016-02-12.
^"Units for Magnetic Properties"(PDF). Lake Shore Cryotronics, Inc. Archived fromthe original(PDF) on 2019-01-26. Retrieved2015-06-10.
^Francis Briggs Silsbee (1962).Systems of Electrical Units. U.S. Department of Commerce, National Bureau of Standards.
^A. Herczynski (2013)."Bound charges and currents"(PDF).American Journal of Physics.81 (3):202–205.Bibcode:2013AmJPh..81..202H.doi:10.1119/1.4773441. Archived fromthe original(PDF) on 2020-09-20. Retrieved2016-02-12.
^^a ^b ^cStohr, J.; Siegmann, H. C. (2006),Magnetism: From fundamentals to Nanoscale Dynamics, Springer-Verlag,Bibcode:2006mffn.book.....S
^Stanciu, C. D.; et al. (2007),Physical Review Letters, vol. 99, p. 217204,doi:10.1103/PhysRevLett.99.217204,hdl:2066/36522,PMID 18233247,S2CID 6787518
^"Magnetic Component Engineering". Magnetic Component Engineering. Archived fromthe original on December 17, 2010. RetrievedApril 18, 2011.
^^a ^b"Demagnetization".Introduction to Magnetic Particle Inspection. NDT Resource Center. Archived fromthe original on February 14, 2014. RetrievedApril 18, 2011.
^Beaurepaire, E.; Merle, J.-C.; Daunois, A.; Bigot, J.-Y. (1996-05-27)."Ultrafast Spin Dynamics in Ferromagnetic Nickel".Physical Review Letters.76 (22):4250–4253.doi:10.1103/PhysRevLett.76.4250.