Magnetization 2404348 223054759 2008-07-02T10:56:13Z MER-C 1749459 Reverted edits by [[Special:Contributions/202.83.171.19|202.83.171.19]] ([[User talk:202.83.171.19|talk]]) to last version by Sbyrnes321 '''Magnetization''' is defined as the quantity of [[magnetic moment]] per unit volume. 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 (physics)|spin]] of the electrons. 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 [[ferromagnet]]s. Magnetization is not always [[homogeneity (physics)|homogeneous]] within a body, but rather a function of position. ==Magnetization in Maxwell's equations== The behavior of [[magnetic field]]s (<math>\mathbf{B}</math>, <math>\mathbf{H}</math>), [[electric fields]] (<math>\mathbf{E}</math>, <math>\mathbf{D}</math>), [[charge density]] (<math>\rho\,</math>), and [[current density]] (<math>\mathbf{J}</math>) is described by [[Maxwell's equations]]. The role of the magnetization is described below. ====Relations between '''B''', '''H''' and '''M'''==== The magnetization defines the auxiliary magnetic field <math>\mathbf{H}</math> as :<math>\mathbf{B} = \mu_0\mathbf{(H + M)}</math> which is convenient for various calculations. A relation between <math>\mathbf{M}</math> and <math>\mathbf{H}</math> exists in many materials. In [[diamagnet]]s and [[paramagnet]]s, the relation is usually linear: :<math>\mathbf{M} = \chi_m\mathbf{H}</math> where <math>\chi_m\,</math> is called the [[magnetic susceptibility|volume magnetic susceptibility]]. In [[ferromagnet]]s there is no one-to-one correspondence between <math>\mathbf{M}</math> and <math>\mathbf{H}</math> because of [[hysteresis]]. ====Magnetization current==== The magnetization <math>\mathbf{M}</math> makes a contribution to the [[current density]] <math>\mathbf{J}</math>, known as the '''magnetization current''' or '''bound current''': :<math> \mathbf{J_m} = \nabla\times\mathbf{M} </math> so that the total current density that enters Maxwell's equations is given by :<math> \mathbf{J} = \mathbf{J_f} + \nabla\times\mathbf{M} + \frac{\partial\mathbf{P}}{\partial t}</math> where <math>\mathbf{J_f}</math> 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]] <math>\mathbf{P}</math>. ====Magnetostatics==== In the absence of free electric currents and time-dependent effects, [[Maxwell's equations]] describing the magnetic quantities reduce to :<math> \mathbf{\nabla\cdot H} = - \nabla\cdot\mathbf{M} \qquad \mathbf{\nabla\times H} = 0 </math> These equations can be easily solved in analogy with [[electrostatic]] problems where :<math> \mathbf{\nabla\cdot E} = \frac{\rho}\epsilon_0 \qquad \qquad \qquad \mathbf{\nabla\times E} = 0 </math> In this sense <math>-\epsilon_0\nabla\cdot\mathbf{M}</math> plays the role of a "magnetic charge density" analogous to the electric charge density <math>\rho\,</math>. Magnetization is volume density of [[magnetic moment]]. That is: if a certain volume has magnetization <math>\mathbf{M}</math> then volume element <math>dV</math> has magnetic moment of <math>d \mathbf{m} = \mathbf{M} dV</math>. ==Types of magnetism== ===Diamagnetism=== This is the most common magnetic behavior. The [[diamagnetic]] magnetization is proportional and opposing to the applied magnetic field. All materials present a diamagnetic response, although it may be shadowed by stronger magnetic behaviors. Diamagnetism can be explained by the normal response of the orbiting [[electron]]s considering the [[Lenz's law]]. This is a weak form of magnetism that is non permanent and persists only while external field is applied. The magnitude of induced magnetic moment is very small and in a direction opposite to that of applied field. Therefore, relative permeability is less than 1 and [[magnetic susceptibility]] is negative. When placed between the poles of a strong electromagnet, diamagnetic materials are pushed out towards the region where the field is weaker. ===Paramagnetism=== [[Paramagnetic]] materials present a magnetization that is proportional to the applied field and reinforces it. This arises from the existence of [[magnetic dipole]]s in the material. Paramagnetism varies [[inverse]]ly with [[temperature]] and is characterized by the material's saturation magnetization. When placed between the poles of a strong electromagnet, paramagnetic materials are pulled towards the region where the field is stronger. ===Superparamagnetism=== [[Superparamagnetic]] materials are paramagnetic materials whose magnetization saturates at very large fields. They are obtained using magnetic nanoparticle aggregates with large net magnetic moments. Each particle is a single magnetic domain. Consequently, the alignment of spins under applied field is no longer impeded by domain walls. Above the [[blocking temperature]], thermal vibrations randomly fluctuate the net spins, cancelling one another and the net moment of the collective particles is zero at zero field (no coercive field). If a magnetic field is applied, the particles will align producing a net moment. This behavior is characteristic of paramagnetic materials, but the difference is that each nanoparticle has a large net moment, so the saturation of magnetization occurs at very large fields of several teslas. ===Ferromagnetism=== [[Ferromagnetic]] materials present a magnetization much larger than other materials. Ferromagnetism arises from the strong coupling between the neighboring magnetic dipoles in the material. Ferromagnetic materials can present spontaneous magnetization, and this gives rise to the [[hysteresis]] loops. Ferromagnetic materials can be characterized by their [[Permeability (electromagnetism)|permeability]], [[Curie temperature]] (temperature of the phase change to paramagnetic behavior), [[Coercivity | coercive field]] (field strength needed to demagnetize the material), and remnant magnetization (magnetization at zero external field). ==See also== * [[Permeability (electromagnetism)]] * [[Magnetic susceptibility]] * [[Earth's magnetic field]] * [[Geomagnetic reversal]] * [[Geomagnetic excursion]] ==Sources== <references/> <div style="-moz-column-count:2; column-count:2;"> {{Wiktionarypar|magnetization}} </div> [[Category:Electric and magnetic fields in matter]] [[cs:Magnetizace]] [[de:Magnetisierung]] [[el:Μαγνήτιση]] [[es:Magnetización]] [[pl:Namagnesowanie]] [[ru:Намагниченность]] [[zh:磁化向量]] [[uk:вектор намагніченості]]