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FOMP
The magnetocrystalline anisotropy energy of a ferromagnetic crystal can be expressed as a power series of direction cosines of the magnetic moment with respect to the crystal axes. The coefficient of those terms are the ''anisotropy constant''. In general the expansion is limited to few terms. Normally the magnetization curve is continuous respect to applied field up to saturation but, in certain intervals of the anisotropy constant values, irreversible field induced rotations of the magnetization are possible implying first order magnetization transition between equivalent magnetization minima, the so-called first order magnetization process (FOMP). Theory The ''total energy'' of a uniaxial magnetic crystal in an applied magnetic field can be written as a summation of the anisotropy term up to six order, neglecting the sixfold planar contribution, \displaystyle E_A=K_1\sin^2\theta+K_2\sin^4\theta+K_3\sin^6\theta and the field dependent Zeeman energy term \displaystyle E_H=-HM_s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fomp ExamplesN
The magnetocrystalline anisotropy energy of a ferromagnetic crystal can be expressed as a power series of direction cosines of the magnetic moment with respect to the crystal axes. The coefficient of those terms are the ''anisotropy constant''. In general the expansion is limited to few terms. Normally the magnetization curve is continuous respect to applied field up to saturation but, in certain intervals of the anisotropy constant values, irreversible field induced rotations of the magnetization are possible implying first order magnetization transition between equivalent magnetization minima, the so-called first order magnetization process (FOMP). Theory The ''total energy'' of a uniaxial magnetic crystal in an applied magnetic field can be written as a summation of the anisotropy term up to six order, neglecting the sixfold planar contribution, \displaystyle E_A=K_1\sin^2\theta+K_2\sin^4\theta+K_3\sin^6\theta and the field dependent Zeeman energy term \displaystyle E_H=-HM_s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fomp Magnetic PhaseN
The magnetocrystalline anisotropy energy of a ferromagnetic crystal can be expressed as a power series of direction cosines of the magnetic moment with respect to the crystal axes. The coefficient of those terms are the ''anisotropy constant''. In general the expansion is limited to few terms. Normally the magnetization curve is continuous respect to applied field up to saturation but, in certain intervals of the anisotropy constant values, irreversible field induced rotations of the magnetization are possible implying first order magnetization transition between equivalent magnetization minima, the so-called first order magnetization process (FOMP). Theory The ''total energy'' of a uniaxial magnetic crystal in an applied magnetic field can be written as a summation of the anisotropy term up to six order, neglecting the sixfold planar contribution, \displaystyle E_A=K_1\sin^2\theta+K_2\sin^4\theta+K_3\sin^6\theta and the field dependent Zeeman energy term \displaystyle E_H=-HM_s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fomp PhaseN
The magnetocrystalline anisotropy energy of a ferromagnetic crystal can be expressed as a power series of direction cosines of the magnetic moment with respect to the crystal axes. The coefficient of those terms are the ''anisotropy constant''. In general the expansion is limited to few terms. Normally the magnetization curve is continuous respect to applied field up to saturation but, in certain intervals of the anisotropy constant values, irreversible field induced rotations of the magnetization are possible implying first order magnetization transition between equivalent magnetization minima, the so-called first order magnetization process (FOMP). Theory The ''total energy'' of a uniaxial magnetic crystal in an applied magnetic field can be written as a summation of the anisotropy term up to six order, neglecting the sixfold planar contribution, \displaystyle E_A=K_1\sin^2\theta+K_2\sin^4\theta+K_3\sin^6\theta and the field dependent Zeeman energy term \displaystyle E_H=-HM_s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fomp PolycrystalN
The magnetocrystalline anisotropy energy of a ferromagnetic crystal can be expressed as a power series of direction cosines of the magnetic moment with respect to the crystal axes. The coefficient of those terms are the ''anisotropy constant''. In general the expansion is limited to few terms. Normally the magnetization curve is continuous respect to applied field up to saturation but, in certain intervals of the anisotropy constant values, irreversible field induced rotations of the magnetization are possible implying first order magnetization transition between equivalent magnetization minima, the so-called first order magnetization process (FOMP). Theory The ''total energy'' of a uniaxial magnetic crystal in an applied magnetic field can be written as a summation of the anisotropy term up to six order, neglecting the sixfold planar contribution, \displaystyle E_A=K_1\sin^2\theta+K_2\sin^4\theta+K_3\sin^6\theta and the field dependent Zeeman energy term \displaystyle E_H=-HM_s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magnetocrystalline Anisotropy
In physics, a ferromagnetic material is said to have magnetocrystalline anisotropy if it takes more energy to magnetize it in certain directions than in others. These directions are usually related to the principal axes of its crystal lattice. It is a special case of magnetic anisotropy. In other words, the excess energy required to magnetize a specimen in a particular direction over that required to magnetize it along the easy direction is called crystalline anisotropy energy. Causes The spin-orbit interaction is the primary source of magnetocrystalline anisotropy. It is basically the orbital motion of the electrons which couples with crystal electric field giving rise to the first order contribution to magnetocrystalline anisotropy. The second order arises due to the mutual interaction of the magnetic dipoles. This effect is weak compared to the exchange interaction and is difficult to compute from first principles, although some successful computations have been made. Pra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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), permanent magnets, elementary particles (such as electrons), various molecules, and many astronomical objects (such as many planets, some moons, stars, etc). More precisely, the term ''magnetic moment'' normally refers to a system's magnetic dipole moment, the component of the magnetic moment that can be represented by an equivalent magnetic dipole: a magnetic north and south pole separated by a very small distance. The magnetic dipole component is sufficient for small enough magnets or for large enough distances. Higher-order terms (such as the magnetic quadrupole moment) may be needed in addition to the dipole moment for extended objects. The magnetic dipole moment of an object is readily defined in terms of the torque that the objec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 the magnetic field. A permanent magnet's magnetic field pulls on ferromagnetic materials such as iron, and attracts or repels other magnets. In addition, a nonuniform magnetic field exerts minuscule forces on "nonmagnetic" materials by three other magnetic effects: paramagnetism, diamagnetism, and antiferromagnetism, although these forces are usually so small they can only be detected by laboratory equipment. Magnetic fields surround magnetized materials, and are created by electric currents such as those used in electromagnets, and by electric fields varying in time. Since both strength and direction of a magnetic field may vary with location, it is described mathematically by a function assigning a vector to each point of space, cal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zeeman Energy
Zeeman energy, or the external field energy, is the potential energy of a magnetised body in an external magnetic field. It is named after the Dutch physicist Pieter Zeeman, primarily known for the Zeeman effect. In SI units, it is given by :E_ =-\mu_ \int_V\,\textbf M\cdot \textbf H_{\rm Ext} \, \mathrm dV where HExt is the external field, M the local magnetisation, and the integral is done over the volume of the body. This is the statistical average (over a unit volume macroscopic sample) of a corresponding microscopic Hamiltonial (energy) for each individual 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 ... m, which is however experiencing a ''local'' induction B: :H =-\textbf m \cdot \textbf B References * F. Barozzi, F. Gasparini, Fondamenti di Elettrotec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Saturation Magnetization
Seen in some magnetic materials, saturation is the state reached when an increase in applied external magnetic field ''H'' cannot increase the magnetization of the material further, so the total magnetic flux density ''B'' more or less levels off. (Though, magnetization continues to increase very slowly with the field due to paramagnetism.) Saturation is a characteristic of ferromagnetic and ferrimagnetic materials, such as iron, nickel, cobalt and their alloys. Different ferromagnetic materials have different saturation levels. Description Saturation is most clearly seen in the ''magnetization curve'' (also called ''BH'' curve or hysteresis curve) of a substance, as a bending to the right of the curve (see graph at right). As the ''H'' field increases, the ''B'' field approaches a maximum value asymptotically, the saturation level for the substance. Technically, above saturation, the ''B'' field continues increasing, but at the paramagnetic rate, which is several orders of m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maxima And Minima
In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given range (the ''local'' or ''relative'' extrema), or on the entire domain (the ''global'' or ''absolute'' extrema). Pierre de Fermat was one of the first mathematicians to propose a general technique, adequality, for finding the maxima and minima of functions. As defined in set theory, the maximum and minimum of a set are the greatest and least elements in the set, respectively. Unbounded infinite sets, such as the set of real numbers, have no minimum or maximum. Definition A real-valued function ''f'' defined on a domain ''X'' has a global (or absolute) maximum point at ''x''∗, if for all ''x'' in ''X''. Similarly, the function has a global (or absolute) minimum point at ''x''∗, if for all ''x'' in ''X''. The value of the function at a m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minima
In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given range (the ''local'' or ''relative'' extrema), or on the entire domain (the ''global'' or ''absolute'' extrema). Pierre de Fermat was one of the first mathematicians to propose a general technique, adequality, for finding the maxima and minima of functions. As defined in set theory, the maximum and minimum of a set are the greatest and least elements in the set, respectively. Unbounded infinite sets, such as the set of real numbers, have no minimum or maximum. Definition A real-valued function ''f'' defined on a domain ''X'' has a global (or absolute) maximum point at ''x''∗, if for all ''x'' in ''X''. Similarly, the function has a global (or absolute) minimum point at ''x''∗, if for all ''x'' in ''X''. The value of the function at a m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anisotropy Energy
Anisotropic energy is energy that is directionally specific. The word anisotropy means "directionally dependent", hence the definition. The most common form of anisotropic energy is magnetocrystalline anisotropy, which is commonly studied in ferromagnets. In ferromagnets, there are islands or domains of atoms that are all coordinated in a certain direction; this spontaneous positioning is often called the "easy" direction, indicating that this is the lowest energy state for these atoms. In order to study magnetocrystalline anisotropy, energy (usually in the form of an electric current) is applied to the domain, which causes the crystals to deflect from the "easy" to "hard" positions. The energy required to do this is defined as the anisotropic energy. The easy and hard alignments and their relative energies are due to the interaction between spin magnetic moment of each atom and the crystal lattice of the compound being studied. See also *Magnetic anisotropy In condensed matter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
