Editing Coercivity

{{Short description|Resistance of a ferromagnetic material to demagnetization by an external magnetic field}}
{{About|the property of magnetic fields|other uses|Coercion (disambiguation)}}

[[Image:B-H loop.png|thumb|upright=1.5|A family of hysteresis loops for [[grain-oriented electrical steel]], a soft magnetic material. ''B''<sub>R</sub> denotes ''[[retentivity]]'' and ''H''<sub>C</sub> is the ''coercivity''.  The wider the outside loop is, the higher the coercivity. Movement on the loops is counterclockwise.]]

'''Coercivity''', also called the '''magnetic coercivity''', '''coercive field''' or '''coercive force''', is a measure of the ability of a [[ferromagnetic]] material to withstand an external [[magnetic field]] without becoming [[Magnetization|demagnetized]]. Coercivity is usually measured in [[oersted]] or [[ampere]]/meter units and is denoted {{math|''H''<sub>C</sub>}}.

An analogous property in [[electrical engineering]] and [[materials science]], '''electric coercivity''', is the ability of a [[ferroelectric]] material to withstand an external [[electric field]] without becoming [[polarization density|depolarized]].

Ferromagnetic materials with high coercivity are called magnetically ''hard'', and are used to make [[permanent magnet]]s.  Materials with low coercivity are said to be magnetically ''soft''.  The latter are used in  [[transformer]] and [[inductor]] [[magnetic core|cores]], [[recording head]]s, [[microwave]] devices, and [[magnetic shielding]].

==Definitions==

[[File:Coercivities in B-H curve.svg|thumb|Graphical definition of different coercivities in flux-vs-field hysteresis curve (B-H curve), for a hypothetical hard magnetic material.]]
[[File:Coercivities in M-H curve.svg|thumb|Equivalent definitions for coercivities in terms of the magnetization-vs-field (M-H) curve, for the same magnet.]]

Coercivity in a [[ferromagnet|ferromagnetic material]] is the intensity of the applied [[magnetic field]] (''H'' field) required to demagnetize that material, after the magnetization of the sample has been driven to [[saturation (magnetic)|saturation]] by a strong field. This demagnetizing field is applied opposite to the original saturating field. There are however different definitions of coercivity, depending on what counts as 'demagnetized', thus the bare term "coercivity" may be ambiguous:

* The ''normal coercivity'', {{math|''H''<sub>Cn</sub>}}, is the ''H'' field required to reduce the [[magnetic flux]] (average ''B'' field inside the material) to zero.
* The ''intrinsic coercivity'', {{math|''H''<sub>Ci</sub>}}, is the ''H'' field required to reduce the [[magnetization]] (average ''M'' field inside the material) to zero.
* The ''remanence coercivity'', {{math|''H''<sub>Cr</sub>}}, is the ''H'' field required to reduce the [[remanence]] to zero, meaning that when the ''H'' field is finally returned to zero, then both ''B'' and ''M'' also fall to zero (the material reaches the origin in the hysteresis curve).<ref name="Bertotti1998">{{cite book|author=Giorgio Bertotti|title=Hysteresis in Magnetism: For Physicists, Materials Scientists, and Engineers|url=https://books.google.com/books?id=ybVQAwAAQBAJ|date=21 May 1998|publisher=Elsevier Science|isbn=978-0-08-053437-4}}</ref>

The distinction between the normal and intrinsic coercivity is negligible in soft magnetic materials, however it can be significant in hard magnetic materials.<ref name="Bertotti1998"/> The strongest [[rare-earth magnet]]s lose almost none of the magnetization at ''H''<sub>Cn</sub>.

==Experimental determination==
{| class="wikitable floatright"
|+ Coercivities of some magnetic materials
|-
! Material
! Coercivity<br />(kA/m)
|-
| [[Supermalloy]]<br />(16[[iron|Fe]]:79[[nickel|Ni]]:5[[molybdenum|Mo]])
| 0.0002<ref name=Tumanski>{{cite book|last1=Tumanski|first1=S.|title=Handbook of magnetic measurements|date=2011|publisher=CRC Press|location=Boca Raton, FL|isbn=9781439829523}}</ref>{{rp|131,133}}
|-
| [[Permalloy]] ([[iron|Fe]]:4[[nickel|Ni]])
| 0.0008–0.08<ref>{{Cite journal|title=Thickness and grain-size dependence of the coercivity in permalloy thin films|journal=Journal of Applied Physics|volume=81|issue=8|pages=4122|author=M. A. Akhter-D. J. Mapps-Y. Q. Ma Tan-Amanda Petford-Long-R. Doole|doi=10.1063/1.365100|year=1997|last2=Mapps|last3=Ma Tan|last4=Petford-Long|last5=Doole|bibcode=1997JAP....81.4122A}}</ref>
|-
| [[Iron filings]] (0.9995 [[mass fraction (chemistry)|wt]])
| 0.004–37.4<ref name="mysite.du.edu">{{Cite web |last=Calvert |first=J. B. |date=6 December 2003 |orig-date=13 December 2002 |title=Iron |url=http://mysite.du.edu/~jcalvert/phys/iron.htm |url-status=dead |archive-url=https://web.archive.org/web/20070915131344/http://mysite.du.edu/%7Ejcalvert/phys/iron.htm#Magn |archive-date=2007-09-15 |access-date=2023-11-04 |website=mysite.du.edu}}</ref><ref name="Magnetic Properties of Solids">{{cite web|url=http://hyperphysics.phy-astr.gsu.edu/Hbase/tables/magprop.html|title=Magnetic Properties of Solids|publisher=Hyperphysics.phy-astr.gsu.edu|access-date=22 November 2014}}</ref>
|-
| [[Electrical steel]] (11Fe:Si)
| 0.032–0.072<ref>{{cite web|url=http://cartech.ides.com/datasheet.aspx?E=193~192~191~190~189&CK=1967748|title=timeout|publisher=Cartech.ides.com|access-date=22 November 2014}}{{Dead link|date=July 2020 |bot=InternetArchiveBot |fix-attempted=yes }}</ref>
|-
| [[Wrought iron|Raw iron]] (1896)
| 0.16<ref>{{cite book|url=https://books.google.com/books?id=G0cOAAAAYAAJ&pg=PA133|title=Dynamo-electric machinery|access-date=22 November 2014|last1=Thompson|first1=Silvanus Phillips|year=1896}}</ref>
|-
| [[Nickel]] (0.99 wt)
| 0.056–23<ref name="Magnetic Properties of Solids"/><ref>{{Cite journal|title=Influence of rf magnetron sputtering conditions on the magnetic, crystalline, and electrical properties of thin nickel films|journal=Journal of Applied Physics|volume=75|issue=10|pages=5779|author=M. S. Miller-F. E. Stageberg-Y. M. Chow-K. Rook-L. A. Heuer|doi=10.1063/1.355560|year=1994|last2=Stageberg|last3=Chow|last4=Rook|last5=Heuer|bibcode=1994JAP....75.5779M}}</ref>
|-
| [[Ferrite (magnet)|Ferrite]] magnet<br />(Zn<sub>x</sub>FeNi<sub>1−x</sub>O<sub>3</sub>)
| 1.2–16<ref>{{Cite journal|journal=IEEE Transactions on Magnetics|volume=33|issue=5|pages=3748–3750|doi=10.1109/20.619559|year=1997|last1=Zhenghong Qian|last2=Geng Wang|last3=Sivertsen|first3=J.M.|last4=Judy|first4=J.H.|title=Ni ''Zn'' ferrite thin films prepared by Facing Target Sputtering|bibcode=1997ITM....33.3748Q}}</ref>
|-
| 2Fe:Co,<ref>{{cite book|url=https://books.google.com/books?id=y0FF19lud5YC&pg=PA142|title=Handbook of Charged Particle Optics, Second Edition|access-date=22 November 2014|isbn=9781420045550|last1=Orloff|first1=Jon|date=2017-12-19|publisher=CRC Press }}</ref> iron pole
| 19<ref name="Magnetic Properties of Solids"/>
|-
| [[Cobalt]] (0.99 wt)
| 0.8–72<ref name="Pubs">{{Cite journal|title=Magnetic Cobalt Nanowire Thin Films|journal=The Journal of Physical Chemistry B|volume=109|issue=5|pages=1919–22|doi=10.1021/jp045554t|pmid=16851175|year=2005|last1=Luo|first1=Hongmei|last2=Wang|first2=Donghai|last3=He|first3=Jibao|last4=Lu|first4=Yunfeng}}</ref>
|-
| [[Alnico]]
| 30–150<ref>{{Cite web |title=Cast ALNICO Permanent Magnets |url=https://www.arnoldmagnetics.com/wp-content/uploads/2017/10/Cast-Alnico-Permanent-Magnet-Brochure-101117-1.pdf |access-date=4 November 2023 |website=Arnold Magnetic Technologies}}</ref>
|-
| Disk drive recording medium <br />([[chromium|Cr]]:[[cobalt|Co]]:[[platinum|Pt]])
| 140<ref>{{Cite journal|journal=IEEE Transactions on Magnetics|volume=27|issue=6|pages=5052–5054|doi=10.1109/20.278737|year=1991|last1=Yang|first1=M.M.|last2=Lambert|first2=S.E.|last3=Howard|first3=J.K.|last4=Hwang|first4=C.|title=Laminated CoPt ''Cr''/Cr films for low noise longitudinal recording|bibcode=1991ITM....27.5052Y}}</ref>
|-
| [[Neodymium magnet]] (NdFeB)
| 800–950<ref>{{Cite journal|title=High-remanence rapidly solidified Nd-Fe-B: Die-upset magnets (invited)|journal=Journal of Applied Physics|volume=73|issue=10|pages=5751|author=C. D. Fuerst-E. G. Brewer|doi=10.1063/1.353563|year=1993|last2=Brewer|bibcode=1993JAP....73.5751F}}</ref><ref>{{cite web|url=http://wondermagnet.com/magfaq.html|title=WONDERMAGNET.COM - NdFeB Magnets, Magnet Wire, Books, Weird Science, Needful Things|publisher=Wondermagnet.com|access-date=22 November 2014|archive-date=11 February 2015|archive-url=https://web.archive.org/web/20150211041455/http://www.wondermagnet.com/magfaq.html|url-status=dead}}</ref>
|-
| 12[[iron|Fe]]:13[[platinum|Pt]] ({{chem2|Fe48Pt52}})
| ≥980<ref>{{harvnb|Chen|Nikles|2002}}</ref>
|-
| <!--Someone with access plug in the proportions-->?([[dysprosium|Dy]],[[niobium|Nb]],[[gallium|Ga]]([[cobalt|Co]]):2[[neodymium|Nd]]:14[[iron|Fe]]:[[boron|B]])
| 2040–2090<ref>{{cite journal |last1=Bai |first1=G. |last2=Gao |first2=R.W. |last3=Sun |first3=Y. |last4=Han |first4=G.B. |last5=Wang |first5=B. |title=Study of high-coercivity sintered NdFeB magnets |journal=Journal of Magnetism and Magnetic Materials |date=January 2007 |volume=308 |issue=1 |pages=20–23 |doi=10.1016/j.jmmm.2006.04.029 |bibcode=2007JMMM..308...20B }}</ref><ref>{{cite journal |last1=Jiang |first1=H. |last2=Evans |first2=J. |last3=O’Shea |first3=M.J. |last4=Du |first4=Jianhua |title=Hard magnetic properties of rapidly annealed NdFeB thin films on Nb and V buffer layers |journal=Journal of Magnetism and Magnetic Materials |date=2001 |volume=224 |issue=3 |pages=233–240 |doi=10.1016/S0304-8853(01)00017-8 |bibcode=2001JMMM..224..233J }}</ref>
|-
| Samarium-cobalt magnet <br />(2[[samarium|Sm]]:17[[iron|Fe]]:3[[nitrogen|N]]; 10{{nbsp}}[[kelvin|K]])
| <40–2800<ref>{{cite journal |last1=Nakamura |first1=H. |last2=Kurihara |first2=K. |last3=Tatsuki |first3=T. |last4=Sugimoto |first4=S. |last5=Okada |first5=M. |last6=Homma |first6=M. |title=Phase Changes and Magnetic Properties of Sm 2 Fe 17 N x Alloys Heat-Treated in Hydrogen |journal=IEEE Translation Journal on Magnetics in Japan |date=October 1992 |volume=7 |issue=10 |pages=798–804 |doi=10.1109/TJMJ.1992.4565502 }}</ref><ref>{{cite journal |last1=Rani |first1=R. |last2=Hegde |first2=H. |last3=Navarathna |first3=A. |last4=Cadieu |first4=F. J. |title=High coercivity Sm 2 Fe 17 N x and related phases in sputtered film samples |journal=Journal of Applied Physics |date=15 May 1993 |volume=73 |issue=10 |pages=6023–6025 |id={{INIST|4841321}} |doi=10.1063/1.353457 |bibcode=1993JAP....73.6023R }}</ref>
|-
| [[Samarium–cobalt magnet|Samarium-cobalt magnet]]
| 3200<ref>{{Cite journal |last1=de Campos |first1=M. F. |last2=Landgraf |first2=F. J. G. |last3=Saito |first3=N. H. |last4=Romero |first4=S. A. |last5=Neiva |first5=A. C. |last6=Missell |first6=F. P. |last7=de Morais |first7=E. |last8=Gama |first8=S. |last9=Obrucheva |first9=E. V. |last10=Jalnin |first10=B. V. |date=1998-07-01 |title=Chemical composition and coercivity of SmCo5 magnets |url=https://pubs.aip.org/jap/article/84/1/368/491720/Chemical-composition-and-coercivity-of-SmCo5 |journal=Journal of Applied Physics |language=en |volume=84 |issue=1 |pages=368–373 |doi=10.1063/1.368075 |bibcode=1998JAP....84..368D |issn=0021-8979|url-access=subscription }}</ref>
|}

Typically the coercivity of a magnetic material is determined by measurement of the [[magnetic hysteresis]] loop, also called the ''magnetization curve'', as illustrated in the figure above. The apparatus used to acquire the data is typically a [[vibrating-sample magnetometer|vibrating-sample]] or alternating-gradient [[magnetometer]]. The applied field where the data line crosses zero is the coercivity. If an [[antiferromagnet]] is present in the sample, the coercivities measured in increasing and decreasing fields may be unequal as a result of the [[exchange bias]] effect.{{citation needed|date=January 2021}}

The coercivity of a material depends on the time scale over which a magnetization curve is measured.  The magnetization of a material measured at an applied reversed field which is nominally smaller than the coercivity may, over a long time scale, slowly [[Relaxation (physics)|relax]] to zero.  Relaxation occurs when reversal of magnetization by domain wall motion is [[Arrhenius equation|thermally activated]] and is dominated by [[magnetic viscosity]].<ref>{{harvnb|Gaunt|1986}}</ref> The increasing value of coercivity at high frequencies is a serious obstacle to the increase of [[Bit rate|data rates]] in high-[[bandwidth (computing)|bandwidth]] magnetic recording, compounded by the fact that increased storage density typically requires a higher coercivity in the media.{{Citation needed|date=September 2010}}

==Theory==
At the coercive field, the [[vector (geometry)|vector component]] of the magnetization of a ferromagnet measured along the applied field direction is zero.  There are two primary modes of [[magnetization reversal]]: [[single domain (magnetic)|single-domain]] rotation and [[Domain wall (magnetism)|domain wall]] motion. When the magnetization of a material reverses by rotation, the magnetization component along the applied field is zero because the vector points in a direction orthogonal to the applied field. When the magnetization reverses by domain wall motion, the net magnetization is small in every vector direction because the moments of all the individual domains sum to zero.  Magnetization curves dominated by rotation and [[magnetocrystalline anisotropy]] are found in relatively perfect magnetic materials used in fundamental research.<ref>{{harvnb|Genish|Kats|Klein|Reiner|2004}}</ref> Domain wall motion is a more important reversal mechanism in real engineering materials since defects like [[grain boundary|grain boundaries]] and [[impurity|impurities]] serve as [[nucleation]] sites for reversed-magnetization domains.  The role of domain walls in determining coercivity is complicated since defects may ''pin'' domain walls in addition to nucleating them.  The dynamics of domain walls in ferromagnets is similar to that of grain boundaries and [[plasticity (physics)|plasticity]] in [[metallurgy]] since both domain walls and grain boundaries are planar defects.{{citation needed|date=January 2021}}

==Significance==
As with any [[hysteresis|hysteretic]] process, the area inside the magnetization curve during one cycle represents the [[work (thermodynamics)|work]] that is performed on the material by the external field in reversing the magnetization, and is dissipated as heat. Common dissipative processes in magnetic materials include [[magnetostriction]] and domain wall motion. The coercivity is a measure of the degree of magnetic hysteresis and therefore characterizes the lossiness of soft magnetic materials for their common applications.

The saturation remanence and coercivity are figures of merit for hard magnets, although [[maximum energy product]] is also commonly quoted. The 1980s saw the development of [[rare-earth magnet]]s with high energy products but undesirably low [[Curie temperature]]s. Since the 1990s new [[exchange spring magnet|exchange spring]] hard magnets with high coercivities have been developed.<ref>{{harvnb|Kneller|Hawig|1991}}</ref>

==See also==
*[[Magnetic susceptibility]]
*[[Remanence]]

==References==
{{Reflist|colwidth=30em}}
{{Refbegin}}
*{{cite journal
|doi=10.1021/nl015649w
|first1=Min
|last1=Chen
|first2=David E.
|last2=Nikles
|title=Synthesis, self-assembly, and magnetic properties of Fe<sub>''x''</sub>Co<sub>''y''</sub>Pt<sub>100-''x''-''y''</sub> nanoparticles
|journal=[[Nano Letters]]
|volume=2
|pages=211–214
|year=2002
|issue=3
|bibcode=2002NanoL...2..211C
}}
*{{cite journal
|last = Gaunt
|first = P.
|title = Magnetic viscosity and thermal activation energy
|journal = [[Journal of Applied Physics]]
|volume = 59
|pages = 4129–4132
|year = 1986
|doi = 10.1063/1.336671
|bibcode = 1986JAP....59.4129G
|issue = 12
}}
*{{cite journal
|last1 = Genish
|first1 = Isaschar
|last2 = Kats
|first2 = Yevgeny
|last3 = Klein
|first3 = Lior
|last4 = Reiner
|first4 = James W.
|last5 = Beasley
|first5 = M. R.
|title = Local measurements of magnetization reversal in thin films of SrRuO<sub>3</sub>
|journal = [[Physica Status Solidi C]]
|volume = 1
|issue = 12
|pages = 3440–3442
|year = 2004
|doi = 10.1002/pssc.200405476
|bibcode = 2004PSSCR...1.3440G
}}
*{{cite journal
|last1 = Kneller
|first1 = E. F.
|last2 = Hawig
|first2 = R.
|title =  The exchange-spring magnet: a new material principle for permanent magnets
|journal = [[IEEE Transactions on Magnetics]]
|volume = 27
|issue = 4
|pages = 3588–3600
|year = 1991
|doi = 10.1109/20.102931
|bibcode = 1991ITM....27.3588K
}}
*{{cite journal
|last = Livingston
|first = J. D.
|title = A review of coercivity mechanisms
|journal = [[Journal of Applied Physics]]
|volume = 52
|pages = 2541–2545
|year = 1981
|doi = 10.1063/1.328996
|bibcode = 1981JAP....52.2544L
|issue = 3
}}
{{Refend}}

==External links==
*[https://web.archive.org/web/20160303180902/http://www.bama.ua.edu/~tmewes/Java/Reversal/reversal.shtml Magnetization reversal applet (coherent rotation)]
*For a table of coercivities of various magnetic recording media, see "[https://web.archive.org/web/20100714063005/http://www.fujifilmusa.com/shared/bin/Degauss_Data_Tape.pdf Degaussing Data Storage Tape Magnetic Media]" ([[PDF]]), at fujifilmusa.com.

{{Authority control}}

[[Category:Physical quantities]]
[[Category:Magnetic hysteresis]]