Rayleigh law

Last updated

The Rayleigh law describes the behavior of ferromagnetic materials at low fields.

Ferromagnetic materials consist of magnetic domains. When a small external field is applied, domains parallel to the external field start to grow. In this region, domain walls are moving. They are hindered by material defects. Lord Rayleigh investigated this first [1] and quantified the magnetization as a linear and quadratic term in the field:

Here is the initial susceptibility, describing the reversible part of magnetisation reversal. The Rayleigh constant describes the irreversible Barkhausen jumps.

The Rayleigh law was derived theoretically by Louis Néel., [2] [3]

The same law describes polarization [4] and direct [5] and converse [6] piezoelectric response of some ferroelectric and ferroelectric-ferroelastic materials. The common feature for ferromagnetic, ferroelectric and ferroelastic materials (i.e., ferroic materials) are domains whose boundaries (domain walls) can be moved by magnetic, electric or mechanical fields.

Related Research Articles

<span class="mw-page-title-main">Ferromagnetism</span> Mechanism by which materials form into and are attracted to magnets

Ferromagnetism is a property of certain materials that results in a significant, observable magnetic permeability, and in many cases, a significant magnetic coercivity, allowing the material to form a permanent magnet. Ferromagnetic materials are noticeably attracted to a magnet, which is a consequence of their substantial magnetic permeability.

<span class="mw-page-title-main">Magnetism</span> Class of physical phenomena

Magnetism is the class of physical attributes that occur through a magnetic field, which allows objects to attract or repel each other. Because both electric currents and magnetic moments of elementary particles give rise to a magnetic field, magnetism is one of two aspects of electromagnetism.

<span class="mw-page-title-main">Superparamagnetism</span> Form of magnetism

Superparamagnetism is a form of magnetism which appears in small ferromagnetic or ferrimagnetic nanoparticles. In sufficiently small nanoparticles, magnetization can randomly flip direction under the influence of temperature. The typical time between two flips is called the Néel relaxation time. In the absence of an external magnetic field, when the time used to measure the magnetization of the nanoparticles is much longer than the Néel relaxation time, their magnetization appears to be in average zero; they are said to be in the superparamagnetic state. In this state, an external magnetic field is able to magnetize the nanoparticles, similarly to a paramagnet. However, their magnetic susceptibility is much larger than that of paramagnets.

Ferroelectricity is a characteristic of certain materials that have a spontaneous electric polarization that can be reversed by the application of an external electric field. All ferroelectrics are also piezoelectric and pyroelectric, with the additional property that their natural electrical polarization is reversible. The term is used in analogy to ferromagnetism, in which a material exhibits a permanent magnetic moment. Ferromagnetism was already known when ferroelectricity was discovered in 1920 in Rochelle salt by Joseph Valasek. Thus, the prefix ferro, meaning iron, was used to describe the property despite the fact that most ferroelectric materials do not contain iron. Materials that are both ferroelectric and ferromagnetic are known as multiferroics.

Magnetoresistance is the tendency of a material to change the value of its electrical resistance in an externally-applied magnetic field. There are a variety of effects that can be called magnetoresistance. Some occur in bulk non-magnetic metals and semiconductors, such as geometrical magnetoresistance, Shubnikov–de Haas oscillations, or the common positive magnetoresistance in metals. Other effects occur in magnetic metals, such as negative magnetoresistance in ferromagnets or anisotropic magnetoresistance (AMR). Finally, in multicomponent or multilayer systems, giant magnetoresistance (GMR), tunnel magnetoresistance (TMR), colossal magnetoresistance (CMR), and extraordinary magnetoresistance (EMR) can be observed.

<span class="mw-page-title-main">Curie temperature</span> Temperature above which magnetic properties change

In physics and materials science, the Curie temperature (TC), 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 Curie temperature is named after Pierre Curie, who showed that magnetism was lost at a critical temperature.

In electromagnetism, the magnetic susceptibility is a measure of how much a material will become magnetized in an applied magnetic field. It is the ratio of magnetization M to the applied magnetic field intensity H. This allows a simple classification, into two categories, of most materials' responses to an applied magnetic field: an alignment with the magnetic field, χ > 0, called paramagnetism, or an alignment against the field, χ < 0, called diamagnetism.

<span class="mw-page-title-main">Ferrimagnetism</span> Type of magnetic phenomenon

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 the populations consist of different atoms or ions (such as Fe2+ and Fe3+).

Remanence or remanent magnetization or residual magnetism is the magnetization left behind in a ferromagnetic material after an external magnetic field is removed. Colloquially, when a magnet is "magnetized", it has remanence. The remanence of magnetic materials provides the magnetic memory in magnetic storage devices, and is used as a source of information on the past Earth's magnetic field in paleomagnetism. The word remanence is from remanent + -ence, meaning "that which remains".

<span class="mw-page-title-main">Polarization density</span> Vector field describing the density of electric dipole moments in a dielectric material

In classical electromagnetism, polarization density is the vector field that expresses the volumetric 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 said to be polarized.

In electricity (electromagnetism), the electric susceptibility is a dimensionless proportionality constant that indicates the degree of polarization of a dielectric material in response to an applied electric field. The greater the electric susceptibility, the greater the ability of a material to polarize in response to the field, and thereby reduce the total electric field inside the material. It is in this way that the electric susceptibility influences the electric permittivity of the material and thus influences many other phenomena in that medium, from the capacitance of capacitors to the speed of light.

<span class="mw-page-title-main">Magnetization</span> Physical quantity, density of magnetic moment per volume

In classical electromagnetism, magnetization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material. Accordingly, physicists and engineers usually define magnetization as the quantity of magnetic moment per unit volume. It is represented by a pseudovector M. Magnetization can be compared to electric polarization, which is the measure of the corresponding response of a material to an electric field in electrostatics.

Multiferroics are defined as materials that exhibit more than one of the primary ferroic properties in the same phase:

In physics, the Landau–Lifshitz–Gilbert equation, named for Lev Landau, Evgeny Lifshitz, and T. L. Gilbert, is a name used for a differential equation describing the dynamics of magnetization M in a solid. It is a modified version by Gilbert of the original equation of Landau and Lifshitz. The LLG equation is similar to the Bloch equation, but they differ in the form of the damping term. The LLG equation describes a more general scenario of magnetization dynamics beyond the simple Larmor precession. In particular, the effective field driving the precessional motion of M is not restricted to real magnetic fields; it incorporates a wide range of mechanisms including magnetic anisotropy, exchange interaction, and so on.

Flexoelectricity is a property of a dielectric material where there is coupling between electrical polarization and a strain gradient. Flexoelectricity is closely related to piezoelectricity, but while piezoelectricity refers to polarization due to uniform strain, flexoelectricity refers specifically to polarization due to strain that changes from point to point in the material. This nonuniform strain breaks centrosymmetry, meaning that unlike in piezoelectricity, flexoelectric effects occur in both centrosymmetric and asymmetric crystal structures. Flexoelectricity is not the same as Ferroelasticity.

In its most general form, the magnetoelectric effect (ME) denotes any coupling between the magnetic and the electric properties of a material. The first example of such an effect was described by Wilhelm Röntgen in 1888, who found that a dielectric material moving through an electric field would become magnetized. A material where such a coupling is intrinsically present is called a magnetoelectric.

<span class="mw-page-title-main">Magnetic levitation</span> Suspension of objects by magnetic force.

Magnetic levitation (maglev) or magnetic suspension is a method by which an object is suspended with no support other than magnetic fields. Magnetic force is used to counteract the effects of the gravitational force and any other forces.

<span class="mw-page-title-main">Antisymmetric exchange</span> Contribution to magnetic exchange interaction

In Physics, antisymmetric exchange, also known as the Dzyaloshinskii–Moriya interaction (DMI), is a contribution to the total magnetic exchange interaction between two neighboring magnetic spins, and . Quantitatively, it is a term in the Hamiltonian which can be written as

A domain wall is a term used in physics which can have similar meanings in magnetism, optics, or string theory. These phenomena can all be generically described as topological solitons which occur whenever a discrete symmetry is spontaneously broken.

<span class="mw-page-title-main">Dragan Damjanovic</span> Swiss-Bosnian-Herzegovinian materials scientist

Dragan Damjanovic is a Swiss-Bosnian-Herzegovinian materials scientist. From 2008 to 2022, he was a professor of material sciences at EPFL and head of the Group for Ferroelectrics and Functional Oxides.

References

  1. Rayleigh, Lord (1887). "On the behaviour of iron and steel under the operation of feeble magnetic forces". Philosophical Magazine . 23 (142): 225–248. doi:10.1080/14786448708628000. ISSN   1941-5982.
  2. Néel, Louis (1942). "Théories des lois d'aimantation de Lord Rayleigh". Cahiers Phys. 12: 1–20.
  3. Néel, Louis (1955). "Some theoretical aspects of rock-magnetism" (PDF). Adv. Phys. 4 (14): 191–243. Bibcode:1955AdPhy...4..191N. doi:10.1080/00018735500101204.
  4. Turik, A.V. (1963). "Theory of polarization and hysteresis of ferroelectrics". Soviet Physics - Solid State. 5 (4): 885–887.
  5. Damjanovic, D. (1997). "Stress and frequency dependence of the direct piezoelectric effect in ferroelectric ceramics". J. Appl. Phys. 82 (4): 1788–1797. Bibcode:1997JAP....82.1788D. doi:10.1063/1.365981.
  6. Taylor, D.V.; Damjanovic, D.; Setter, N. (1999). "Nonlinear contributions to dielectric and piezoelectric properties in lead zirconate titanate thin films". Ferroelectrics. 224 (4): 299–306. Bibcode:1999Fer...224..299T. doi:10.1080/00150199908210580.