Editing Magnetic field (section)

===Magnetism===
{{Main|Magnetism}}
Most materials respond to an applied {{math|'''B'''}}-field by producing their own magnetization {{math|'''M'''}} and therefore their own {{math|'''B'''}}-fields. Typically, the response is weak and exists only when the magnetic field is applied. The term ''magnetism'' describes how materials respond on the microscopic level to an applied magnetic field and is used to categorize the magnetic [[phase (matter)|phase]] of a material. Materials are divided into groups based upon their magnetic behavior:
* [[Diamagnetism|Diamagnetic materials]]<ref name=Tilley>{{cite book |title=Understanding Solids |author=RJD Tilley |page=[https://archive.org/details/understandingsol0000till/page/368 368] |isbn=978-0-470-85275-0 |publisher=Wiley |year=2004 |url=https://archive.org/details/understandingsol0000till |url-access=registration }}</ref> produce a magnetization that opposes the magnetic field.
* [[Paramagnetism|Paramagnetic materials]]<ref name=Tilley/> produce a magnetization in the same direction as the applied magnetic field.
* [[Ferromagnetism|Ferromagnetic materials]] and the closely related [[Ferrimagnetism|ferrimagnetic materials]] and [[Antiferromagnetism|antiferromagnetic materials]]<ref name=Chikazumi>{{cite book |title=Physics of ferromagnetism|author1=Sōshin Chikazumi |author2=Chad D. Graham |url=https://books.google.com/books?id=AZVfuxXF2GsC |page=118 |edition=2|year=1997 |publisher=Oxford University Press |isbn=978-0-19-851776-4}}</ref><ref name=Aharoni>{{cite book |title=Introduction to the theory of ferromagnetism |page=27 |author=Amikam Aharoni |url=https://books.google.com/books?id=9RvNuIDh0qMC&pg=PA27 |edition=2 |year=2000 |publisher=Oxford University Press |isbn=978-0-19-850808-3}}</ref> can have a magnetization independent of an applied B-field with a complex relationship between the two fields.
* [[Superconductor]]s (and [[ferromagnetic superconductor]]s)<ref name=Bennemann>{{cite book |title=Superconductivity |editor1=K. H. Bennemann |editor2=John B. Ketterson |chapter-url=https://books.google.com/books?id=PguAgEQTiQwC&pg=PA640 |page=640 |isbn=978-3-540-73252-5 |year=2008 |publisher=Springer |chapter=Unconventional superconductivity in novel materials |author=M Brian Maple |display-authors=etal }}</ref><ref name=Lewis>{{cite book |title=Superconductivity research at the leading edge |author=Naoum Karchev |editor1=Paul S. Lewis |editor2=D. Di (CON) Castro |chapter-url=https://books.google.com/books?id=3AFo_yxBkD0C&pg=PA169 |page=169 |isbn=978-1-59033-861-2 |publisher=Nova Publishers |year=2003 |chapter=Itinerant ferromagnetism and superconductivity}}</ref> are materials that are characterized by perfect conductivity below a critical temperature and magnetic field. They also are highly magnetic and can be perfect diamagnets below a lower critical magnetic field. Superconductors often have a broad range of temperatures and magnetic fields (the so-named [[Type II superconductor#Mixed state|mixed state]]) under which they exhibit a complex hysteretic dependence of {{math|'''M'''}} on {{math|'''B'''}}.

In the case of paramagnetism and diamagnetism, the magnetization {{math|'''M'''}} is often proportional to the applied magnetic field such that:
<math display="block">\mathbf{B} = \mu \mathbf{H},</math>
where {{math|''μ''}} is a material dependent parameter called the [[permeability (electromagnetism)|permeability]]. In some cases the permeability may be a second rank [[tensor]] so that {{math|'''H'''}} may not point in the same direction as {{math|'''B'''}}. These relations between {{math|'''B'''}} and {{math|'''H'''}} are examples of [[constitutive equation]]s. However, superconductors and ferromagnets have a more complex {{math|'''B'''}}-to-{{math|'''H'''}} relation; see [[hysteresis#Magnetic hysteresis|magnetic hysteresis]].