Editing Hysteresis (section)

==In materials==

===Magnetic hysteresis===
{{main|Magnetic hysteresis}}
<!--NOTE TO EDITORS: This section is linked to from [[Kilogram]] and [[Magnetic field]]. Please do not rename without changing the referring link.-->
[[Image:StonerWohlfarthMainLoop.svg|thumb|right|400px|[[Stoner–Wohlfarth model|Theoretical model]] of [[magnetization]] {{math|<var>m</var>}} against [[magnetic field]]  {{math|<var>h</var>}}. Starting at the origin, the upward curve is the ''initial magnetization curve''. The downward curve after saturation, along with the lower return curve, form the ''main loop''. The intercepts {{math|<var>h</var><sub>c</sub>}} and {{math|<var>m</var><sub>rs</sub>}} are the ''[[coercivity]]'' and ''[[remanence#Saturation remanence|saturation remanence]]''. ]]

When an external [[magnetic field]] is applied to a [[ferromagnetism|ferromagnetic material]] such as [[iron]], the atomic [[Magnetic domain|domain]]s align themselves with it. Even when the field is removed, part of the alignment will be retained: the material has become ''magnetized''. Once magnetized, the magnet will stay magnetized indefinitely. To [[Magnet#Demagnetizing ferromagnets|demagnetize]] it requires heat or a magnetic field in the opposite direction. This is the effect that provides the element of memory in a [[hard disk drive]].

The relationship between field strength {{math|<var>H</var>}} and magnetization {{math|<var>M</var>}}  is not linear in such materials. If a magnet is demagnetized ({{math|<var>H&nbsp;{{=}}&nbsp;M&nbsp;{{=}}&nbsp;0</var>}}) and the relationship between {{math|<var>H</var>}} and  {{math|<var>M</var>}}  is plotted for increasing levels of field strength,  {{math|<var>M</var>}} follows the ''initial magnetization curve''. This curve increases rapidly at first and then approaches an [[asymptote]] called [[Saturation (magnetic)|magnetic saturation]]. If the magnetic field is now reduced monotonically, {{math|<var>M</var>}} follows a different curve.  At zero field strength, the magnetization is offset from the origin by an amount called the [[remanence]]. If the {{math|<var>H-M</var>}} relationship is plotted for all strengths of applied magnetic field the result is a hysteresis loop called the ''main loop''. The width of the middle section is twice the [[coercivity]] of the material.<ref name=Chikazumi1997ch1>{{harvnb|Chikazumi|1997|loc=Chapter 1}}</ref>

A closer look at a magnetization curve generally reveals a series of small, random jumps in magnetization called [[Barkhausen effect|Barkhausen jumps]]. This effect is due to [[crystallographic defect]]s such as [[dislocation]]s.<ref name=Chikazumi1997ch15>{{harvnb|Chikazumi|1997|loc=Chapter 15}}</ref>

Magnetic hysteresis loops are not exclusive to materials with ferromagnetic ordering. Other magnetic orderings, such as [[spin glass]] ordering, also exhibit this phenomenon.<ref>{{cite journal |last1=Monod |first1=P. |last2=PréJean |first2=J. J. |last3=Tissier |first3=B. |year=1979 |title=Magnetic hysteresis of CuMn in the spin glass state |journal=J. Appl. Phys. |volume=50 |issue=B11|pages=7324 |doi=10.1063/1.326943 |bibcode = 1979JAP....50.7324M }}</ref>

====Physical origin====
{{Main|Ferromagnetism}}
The phenomenon of hysteresis in [[ferromagnetism|ferromagnetic]] materials is the result of two effects: rotation of [[magnetization]] and changes in size or number of [[magnetic domain]]s. In general, the magnetization varies (in direction but not magnitude) across a magnet, but in sufficiently small magnets, it does not. In these [[Single domain (magnetic)|single-domain]] magnets, the magnetization responds to a magnetic field by rotating. Single-domain magnets are used wherever a strong, stable magnetization is needed (for example, [[magnetic recording]]).

Larger magnets are divided into regions called ''domains''. Across each domain, the magnetization does not vary; but between domains are relatively thin ''domain walls'' in which the direction of magnetization rotates from the direction of one domain to another. If the magnetic field changes, the walls move, changing the relative sizes of the domains. Because the domains are not magnetized in the same direction, the [[magnetic moment]] per unit volume is smaller than it would be in a single-domain magnet; but domain walls involve rotation of only a small part of the magnetization, so it is much easier to change the magnetic moment. The magnetization can also change by addition or subtraction of domains (called ''nucleation'' and ''denucleation'').

====Magnetic hysteresis models====
The most known empirical models in hysteresis are [[Preisach model of hysteresis|Preisach]] and [[Jiles-Atherton model]]s. These models allow an accurate modeling of the hysteresis loop and are widely used in the industry. However, these models lose the connection with thermodynamics and the energy consistency is not ensured. A more recent model, with a more consistent thermodynamical foundation, is  the vectorial incremental nonconservative consistent hysteresis (VINCH) model of Lavet et al. (2011)<ref>Vincent Francois-Lavet et al (2011-11-14). [http://vincent.francois-l.be/VINCH_model.pdf Vectorial Incremental Nonconservative Consistent Hysteresis model].</ref>

====Applications====
{{Main|Magnet#Common uses}}

There are a great variety of applications of the hysteresis in ferromagnets. Many of these make use of their ability to retain a memory, for example [[magnetic tape]], [[hard disks]], and [[credit card]]s. In these applications, ''hard'' magnets (high coercivity) like [[iron]] are desirable, such that as much energy is absorbed as possible during the write operation and the resultant magnetized information is not easily erased.

On the other hand, magnetically ''soft'' (low coercivity) iron is used for the cores in [[electromagnet]]s. The low coercivity minimizes the energy loss associated with hysteresis, as the magnetic field periodically reverses in the presence of an alternating current. The low energy loss during a hysteresis loop is the reason why soft iron is used for transformer cores and electric motors.

===Electrical hysteresis===

Electrical hysteresis typically occurs in [[ferroelectric]] material, where domains of polarization contribute to the total polarization. Polarization is the [[electrical dipole moment]] (either [[coulomb|C]]·[[metre|m]]<SUP>−2</SUP> or [[coulomb|C]]·[[metre|m]]). The mechanism, an organization of the polarization into domains, is similar to that of magnetic hysteresis.

===Liquid–solid-phase transitions===
Hysteresis manifests itself in state transitions when [[melting point|melting temperature]] and freezing temperature do not agree. For example, [[agar]] melts at {{cvt|85|°C}} and solidifies from {{cvt|32 to 40|°C}}. This is to say that once agar is melted at 85&nbsp;°C, it retains a liquid state until cooled to 40&nbsp;°C. Therefore, from the temperatures of 40 to 85&nbsp;°C, agar can be either solid or liquid, depending on which state it was before.