View source for Physics:Magnetic hysteresis

{{Short description|Application of an external magnetic field to a ferromagnet}}
[[Image:StonerWohlfarthMainLoop.svg|thumb|right|400px|[[Physics: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 ''saturation remanence''. ]]

'''Magnetic hysteresis''' occurs when an external [[Physics:Magnetic field|magnetic field]] is applied to a [[Physics:Ferromagnetism|ferromagnet]] such as [[Chemistry:Iron|iron]] and the atomic [[Physics:Dipole|dipole]]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 [[Physics: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 [[Engineering:Hard disk drive|hard disk drive]].

The relationship between field strength {{math|<var>H</var>}} and [[Physics:Magnetization|magnetization]] {{math|<var>M</var>}}  is not linear in such materials. If a magnet is demagnetized ({{math|1=''H'' = ''M'' = 0}}) and the relationship between {{mvar|H}} and {{mvar|M}}  is plotted for increasing levels of field strength, {{mvar|M}} follows the ''initial magnetization curve''. This curve increases rapidly at first and then approaches an [[Asymptote|asymptote]] called [[Physics:Saturation (magnetic)|magnetic saturation]]. If the magnetic field is now reduced monotonically, {{mvar|M}} follows a different curve.  At zero field strength, the [[Physics:Magnetization|magnetization]] is offset from the origin by an amount called the [[Remanence|remanence]]. If the {{math|''H''-''M''}} relationship is plotted for all strengths of applied magnetic field the result is a [[Hysteresis|hysteresis]] loop called the ''main loop''. The width of the middle section along the H axis is twice the coercivity of the material.<ref name=Chikazumi>{{cite book| last1=Chikazumi|first1=Sōshin| title=Physics of ferromagnetism| date=1997| publisher=Oxford University Press| location=Oxford|isbn=9780191569852| edition=2nd}}</ref>{{rp|at=Chapter 1}}

A closer look at a magnetization curve generally reveals a series of small, random jumps in magnetization called [[Physics:Barkhausen effect|Barkhausen jumps]]. This effect is due to crystallographic defects such as dislocations.<ref name=Chikazumi/>{{rp|at=Chapter 15}}

Magnetic hysteresis loops are not exclusive to materials with ferromagnetic ordering. Other magnetic orderings, such as [[Physics:Spin glass|spin glass]] ordering, also exhibit this phenomenon.<ref>{{cite journal |last1=Monod |first1=P. |last2=Prejean |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|Physics:Ferromagnetism}}
The phenomenon of hysteresis in [[Physics:Ferromagnetism|ferromagnetic]] materials is the result of two effects: rotation of [[Physics:Magnetization|magnetization]] and changes in size or number of [[Physics:Magnetic domain|magnetic domain]]s. In general, the magnetization varies (in direction but not magnitude) across a magnet, but in sufficiently small magnets, it doesn't. In these [[Physics: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''. Within 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 [[Physics:Magnetic moment|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'').

==Measurement==

Magnetic hysteresis can be characterized in various ways. In general, the magnetic material is placed in a varying applied {{math|''H''}} field, as induced by an electromagnet, and the resulting [[Physics:Magnetic flux density|magnetic flux density]] ({{math|''B''}} field) is measured, generally by the inductive [[Physics:Electromotive force|electromotive force]] introduced on a pickup coil nearby the sample. This produces the characteristic {{math|''B''-''H''}} curve; because the hysteresis indicates a memory effect of the magnetic material, the shape of the {{math|''B''-''H''}} curve depends on the history of changes in {{math|''H''}}.

Alternatively, the hysteresis can be plotted as [[Physics:Magnetization|magnetization]] {{math|''M''}} in place of {{math|''B''}}, giving an {{math|''M''-''H''}} curve. These two curves are directly related since <math>B = \mu_0(H + M)</math>.

The measurement may be ''closed-circuit'' or ''open-circuit'', according to how the magnetic material is placed in a [[Physics:Magnetic circuit|magnetic circuit]].

* In ''open-circuit'' measurement techniques (such as a [[Physics:Vibrating-sample magnetometer|vibrating-sample magnetometer]]), the sample is suspended in free space between two poles of an electromagnet. Because of this, a [[Physics:Demagnetizing field|demagnetizing field]] develops and the {{math|''H''}} field internal to the magnetic material is different than the applied {{math|''H''}}. The normal B-H curve can be obtained after the demagnetizing effect is corrected.
* In ''closed-circuit'' measurements (such as the hysteresisgraph), the flat faces of the sample are pressed directly against the poles of the electromagnet. Since the pole faces are highly permeable, this removes the demagnetizing field, and so the internal {{math|''H''}} field is equal to the applied {{math|''H''}} field.

With hard magnetic materials (such as sintered [[Physics:Neodymium magnet|neodymium magnet]]s), the detailed microscopic process of magnetization reversal depends on whether the magnet is in an open-circuit or closed-circuit configuration, since the magnetic medium around the magnet influences the interactions between domains in a way that cannot be fully captured by a simple demagnetization factor.<ref name="FliegansTosoni2020">{{cite journal|last1=Fliegans|first1=J.|last2=Tosoni|first2=O.|last3=Dempsey|first3=N. M.|last4=Delette|first4=G.|title=Modeling of demagnetization processes in permanent magnets measured in closed-circuit geometry|journal=Applied Physics Letters|volume=116|issue=6|year=2020|pages=062405|issn=0003-6951|doi=10.1063/1.5134561|bibcode=2020ApPhL.116f2405F|s2cid=214353446|url=https://hal.archives-ouvertes.fr/hal-03084028/file/2020_Fliegans_APL_116_062405_Modeling%20of%20demagnetization%20processes%20in%20permanent%20magnets%20measured%20in%20closed%20circuit%20geometry.pdf.pdf}}</ref>

==Models==
The most known empirical models in hysteresis are [[Physics:Preisach model of hysteresis|Preisach]] and Jiles-Atherton models. 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 thermodynamic foundation, is the vectorial incremental nonconservative consistent hysteresis (VINCH) model of Lavet et al. (2011). is inspired by the [[Engineering:Work hardening|kinematic hardening]] laws and by the [[Physics:Thermodynamics|thermodynamics]] of [[Physics:Irreversible process|irreversible process]]es.<ref>{{cite book |last1=François-Lavet |first1=V. |last2=Henrotte |first2=F. |last3=Stainier |first3=L. |last4=Noels |first4=L. |last5=Geuzaine |first5=C. |chapter=Vectorial incremental nonconservative consistent hysteresis model |chapter-url=http://vincent.francois-l.be/VINCH_model.pdf |hdl=2268/99208 |title=Proceedings of the 5th International Conference on Advanded COmputational Methods in Engineering (ACOMEN2011) |date=2011 |isbn=978-2-9601143-1-7 |pages=10– |url=}}</ref>  In particular, in addition to provide an accurate modeling, the stored magnetic energy and the dissipated energy are known at all times. The obtained incremental formulation is variationally consistent, i.e., all internal variables follow from the minimization of a thermodynamic potential. That allows easily obtaining a vectorial model while Preisach and Jiles-Atherton are fundamentally scalar models.

The [[Physics:Stoner–Wohlfarth model|Stoner–Wohlfarth model]] is a physical model explaining hysteresis in terms of anisotropic response ("easy" / "hard" axes of each crystalline grain).

[[Physics:Micromagnetics|Micromagnetics]] simulations attempt to capture and explain in detail the space and time aspects of interacting magnetic domains, often based on the Landau-Lifshitz-Gilbert equation.

Toy models such as the [[Physics:Ising model|Ising model]] can help explain qualitative and thermodynamic aspects of hysteresis (such as the Curie point phase transition to paramagnetic behaviour), though they are not used to describe real magnets.

==Applications==

There are a great variety in applications of the theory of hysteresis in magnetic materials. Many of these make use of their ability to retain a memory, for example [[Physics:Magnetic tape|magnetic tape]], hard disks, and [[Finance:Credit card|credit card]]s. In these applications, ''hard'' magnets (high coercivity) like [[Chemistry:Iron|iron]] are desirable so the memory is not easily erased.

''Soft'' magnets (low coercivity) are used as cores in [[Engineering:Transformer|transformer]]s and [[Physics:Electromagnet|electromagnet]]s. The response of the magnetic moment to a magnetic field boosts the response of the coil wrapped around it. Low coercivity reduces that energy loss associated with hysteresis.

Magnetic hysteresis material (soft nickel-iron rods) has been used in damping the angular motion of satellites in low Earth orbit since the dawn of the space age.<ref>{{cite tech report |title=Magnetic Hysteresis Damping of Satellite Attitude Motion|url=http://www.dtic.mil/dtic/tr/fulltext/u2/610465.pdf|archive-url=https://web.archive.org/web/20161002124203/http://www.dtic.mil/dtic/tr/fulltext/u2/610465.pdf|url-status=dead|archive-date=October 2, 2016|author=((General Electric Spacecraft Department)) |date=16 November 1964 |id=64SD4252 |accessdate=1 October 2016 |publisher=U.S. Naval Weapons Laboratory, Dahlgren, Virginia}}</ref>

== See also ==
* [[Degaussing]]

== References ==
{{Reflist}}


{{DEFAULTSORT:Magnetic hysteresis}}
[[Category:Magnetostatics]]
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{{Sourceattribution|Magnetic hysteresis}}