A magnetic domain is a region within a magnetic material in which the magnetization is in a uniform direction. This means that the individual magnetic moments of the atoms are aligned with one another and they point in the same direction. When cooled below a temperature called the Curie temperature, the magnetization of a piece of ferromagnetic material spontaneously divides into many small regions called magnetic domains. The magnetization within each domain points in a uniform direction, but the magnetization of different domains may point in different directions. Magnetic domain structure is responsible for the magnetic behavior of ferromagnetic materials like iron, nickel, cobalt and their alloys, and ferrimagnetic materials like ferrite. This includes the formation of permanent magnets and the attraction of ferromagnetic materials to a magnetic field. The regions separating magnetic domains are called domain walls, where the magnetization rotates coherently from the direction in one domain to that in the next domain. The study of magnetic domains is called micromagnetics.
Magnetic domains form in materials which have magnetic ordering; that is, their dipoles spontaneously align due to the exchange interaction. These are the ferromagnetic, ferrimagnetic and antiferromagnetic materials. Paramagnetic and diamagnetic materials, in which the dipoles align in response to an external field but do not spontaneously align, do not have magnetic domains.
Magnetic domain theory was developed by French physicist Pierre-Ernest Weiss who, in 1906, suggested existence of magnetic domains in ferromagnets. He suggested that large number of atomic magnetic moments (typically 1012-1018) were aligned parallel. The direction of alignment varies from domain to domain in a more or less random manner, although certain crystallographic axis may be preferred by the magnetic moments, called easy axes. Weiss still had to explain the reason for the spontaneous alignment of atomic moments within a ferromagnetic material, and he came up with the so-called Weiss mean field.
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In condensed matter physics, magnetic anisotropy describes how an object's magnetic properties can be different depending on direction. In the simplest case, there is no preferential direction for an object's magnetic moment. It will respond to an applied magnetic field in the same way, regardless of which direction the field is applied. This is known as magnetic isotropy. In contrast, magnetically anisotropic materials will be easier or harder to magnetize depending on which way the object is rotated.
Hysteresis is the dependence of the state of a system on its history. For example, a magnet may have more than one possible magnetic moment in a given magnetic field, depending on how the field changed in the past. Plots of a single component of the moment often form a loop or hysteresis curve, where there are different values of one variable depending on the direction of change of another variable. This history dependence is the basis of memory in a hard disk drive and the remanence that retains a record of the Earth's magnetic field magnitude in the past.
Magnetostatics is the study of magnetic fields in systems where the currents are steady (not changing with time). It is the magnetic analogue of electrostatics, where the charges are stationary. The magnetization need not be static; the equations of magnetostatics can be used to predict fast magnetic switching events that occur on time scales of nanoseconds or less. Magnetostatics is even a good approximation when the currents are not static – as long as the currents do not alternate rapidly.
Interactive course addressing bulk and thin-film magnetic materials that provide application-specific functionalities in different modern technologies such as e.g. wind energy harvesting, electric art
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This work focuses on the coupling of trimmed shell patches using Isogeometric Analysis, based on higher continuity splines that seamlessly meet the C 1 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackag ...
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