View source for Magnetic susceptibility

{{Short description|Degree to which a material becomes magnetized in an applied magnetic field}}

In [[electromagnetism]], the '''magnetic susceptibility''' ({{ety|la|susceptibilis|receptive}}; denoted {{mvar|χ}}, [[Chi (letter)|chi]]) is a measure of how much a material will become [[Magnetization|magnetized]] in an applied [[magnetic field]]. It is the ratio of magnetization {{math|'''M'''}} ([[magnetic moment]] per unit volume) to the applied magnetizing field intensity {{math|'''H'''}}. This allows a simple classification, into two categories, of most materials' responses to an applied magnetic field: an alignment with the magnetic field, {{math|''χ'' > 0}}, called [[paramagnetism]], or an alignment against the field, {{math|''χ'' < 0}}, called [[diamagnetism]].

Magnetic susceptibility indicates whether a material is attracted into or repelled out of a magnetic field. Paramagnetic materials align with the applied field and are attracted to regions of greater magnetic field. Diamagnetic materials are anti-aligned and are pushed away, toward regions of lower magnetic fields. On top of the applied field, the magnetization of the material adds its own magnetic field, causing the [[field line]]s to concentrate in paramagnetism, or be excluded in diamagnetism.<ref>Roger Grinter, ''The Quantum in Chemistry: An Experimentalist's View'', John Wiley & Sons, 2005, {{ISBN|0470017627}} page 364</ref> Quantitative measures of the magnetic susceptibility also provide insights into the structure of materials, providing insight into [[Chemical bond|bonding]] and [[energy level]]s. Furthermore, it is widely used in [[geology]] for [[paleomagnetic]] studies and [[structural geology]].<ref name=":0">{{Cite book|url=https://earthref.org/MagIC/books/Tauxe/Essentials/#Q1-1-2|title=Essentials of Paleomagnetism: Fifth Web Edition|last=Tauxe|first=Lisa|publisher=UC Press|year=2019}}</ref>

The magnetizability of materials comes from the atomic-level magnetic properties of the particles of which they are made. Usually, this is dominated by the magnetic moments of [[electron]]s. Electrons are present in all materials, but without any external magnetic field, the magnetic moments of the electrons are usually either paired up or random so that the overall magnetism is zero (the exception to this usual case is [[ferromagnetism]]). The fundamental reasons why the magnetic moments of the electrons line up or do not are very complex and cannot be explained by [[classical physics]]. However, a useful simplification is to measure the magnetic susceptibility of a material and apply the [[Maxwell's equations#Macroscopic formulation|macroscopic form of Maxwell's equations]]. This allows classical physics to make useful predictions while avoiding the underlying [[quantum mechanical]] details.

==Definition==
{{See also|Permeability (electromagnetism)#Relative permeability and magnetic susceptibility}}

=== Volume susceptibility ===
Magnetic susceptibility is a dimensionless proportionality constant that indicates the degree of magnetization of a material in response to an applied magnetic field. A related term is '''magnetizability''', the proportion between [[magnetic moment]] and [[magnetic field|magnetic flux density]].<ref>{{cite encyclopedia |year=1997 |title=magnetizability, {{math|''ξ''}} |encyclopedia=IUPAC Compendium of Chemical Terminology—The Gold Book |publisher=[[International Union of Pure and Applied Chemistry]] |edition=2nd |url=http://goldbook.iupac.org/search.py?search_text=magnetizability |access-date=2011-10-13 |archive-url=https://web.archive.org/web/20160304070609/http://goldbook.iupac.org/search.py?search_text=magnetizability |archive-date=2016-03-04 |url-status=dead }}</ref> A closely related parameter is the [[Permeability (electromagnetism)|permeability]], which expresses the total magnetization of material and volume.

The ''volume magnetic susceptibility'', represented by the symbol {{math|''χ''<sub>v</sub>}} (often simply {{math|''χ''}}, sometimes {{math|''χ''<sub>m</sub>}}&nbsp;– magnetic, to distinguish from the [[electric susceptibility]]), is defined in the [[International System of Units]]&nbsp;– in other systems there may be additional constants – by the following relationship:<ref>{{cite book|last1=O'Handley|first1=Robert C.|title=Modern Magnetic Materials|date=2000|publisher=Wiley|location=Hoboken, NJ| isbn=9780471155669}}</ref><ref>{{Cite book|last1=Freeman|first1=Richard|chapter=Essentials of Electricity and Magnetism| date=2019| url=https://oxford.universitypressscholarship.com/view/10.1093/oso/9780198726500.001.0001/oso-9780198726500-chapter-1| title=Electromagnetic Radiation|publisher=Oxford University Press|doi=10.1093/oso/9780198726500.003.0001| isbn=978-0-19-872650-0| access-date=2022-02-18|last2=King|first2=James|last3=Lafyatis|first3=Gregory}}</ref>

<math display="block">\mathbf{M} = \chi_\text{v} \mathbf{H}.</math>


Here,
* {{math|'''M'''}} is the [[magnetization]] of the material (the [[magnetic dipole moment]] per unit volume), with unit [[ampere]]s per meter, and
* {{math|'''H'''}} is the magnetic field strength, also with the unit amperes per meter.

{{math|''χ''<sub>v</sub>}} is therefore a [[dimensionless quantity]].

Using [[SI electromagnetism units|SI units]], the [[magnetic field|magnetic induction]] {{math|'''B'''}} is related to {{math|'''H'''}} by the relationship

<math display="block">\mathbf{B} \ = \ \mu_0\left(\mathbf{H} + \mathbf{M}\right) \ = \ \mu_0\left(1 + \chi_\text{v}\right) \mathbf{H} \ = \ \mu \mathbf{H}</math>

where {{math|''μ''<sub>0</sub>}} is the [[vacuum permeability]] (see table of [[physical constant]]s), and {{math|(1 + ''χ''<sub>v</sub>)}} is the [[Permeability (electromagnetism)#Relative permeability and magnetic susceptibility|relative permeability]] of the material. Thus the ''volume magnetic susceptibility'' {{math|''χ''<sub>v</sub>}} and the [[magnetic permeability]] {{math|''μ''}} are related by the following formula:
<math display="block">\mu = \mu_0\left(1 + \chi_\text{v}\right).</math>

Sometimes<ref>{{cite web|author=Richard A. Clarke |url=http://info.ee.surrey.ac.uk/Workshop/advice/coils/mu/#itns |title=Magnetic properties of materials |publisher=Info.ee.surrey.ac.uk |access-date=2011-11-08}}</ref> an auxiliary quantity called ''intensity of magnetization'' {{math|'''I'''}} (also referred to as ''magnetic polarisation'' {{math|'''J'''}}) and with unit [[tesla (unit)|teslas]], is defined as
<math display="block">\mathbf{I} = \mu_0 \mathbf{M} .</math>

This allows an alternative description of all magnetization phenomena in terms of the quantities {{math|'''I'''}} and {{math|'''B'''}}, as opposed to the commonly used {{math|'''M'''}} and {{math|'''H'''}}.

=== Molar susceptibility and mass susceptibility ===
There are two other measures of susceptibility, the ''molar magnetic susceptibility'' ({{math|''χ''<sub>m</sub>}}) with unit m<sup>3</sup>/mol, and the ''mass magnetic susceptibility'' ({{math|''χ''<sub>ρ</sub>}}) with unit m<sup>3</sup>/kg that are defined below, where {{math|''ρ''}} is the [[density]] with unit kg/m<sup>3</sup> and {{math|''M''}} is [[molar mass]] with unit kg/mol:
<math display="block">\begin{align}
  \chi_\rho &= \frac{\chi_\text{v}}{\rho}; \\
   \chi_\text{m} &= M\chi_\rho = \frac{M}{\rho} \chi_\text{v}.
\end{align}</math>

=== In CGS units ===
The definitions above are according to the [[International System of Quantities]] (ISQ) upon which the [[International System of Units|SI]] is based. However, many tables of magnetic susceptibility give the values of the corresponding quantities of the [[Centimetre–gram–second system of units|CGS]] system (more specifically [[Centimetre–gram–second system of units#Electromagnetic units (EMU)|CGS-EMU]], short for electromagnetic units, or [[Gaussian units|Gaussian-CGS]]; both are the same in this context). The quantities characterizing the permeability of free space for each system have different defining equations:<ref name="bennett">{{cite journal|author1=Bennett, L. H.|author2=Page, C. H.|author3=Swartzendruber, L. J.|name-list-style=amp| year=1978| title=Comments on units in magnetism|journal=Journal of Research of the National Bureau of Standards|publisher=[[NIST]], USA|volume=83|issue=1|pages=9–12|pmid=34565970|doi=10.6028/jres.083.002|pmc=6752159|doi-access=free}}</ref>
<math display="block">\mathbf{B}^\text{CGS} = \mathbf{H}^\text{CGS} + 4\pi\mathbf{M}^\text{CGS} = \left(1 + 4\pi\chi_\text{v}^\text{CGS}\right) \mathbf{H}^\text{CGS} .</math>

The respective CGS susceptibilities are multiplied by 4{{pi}} to give the corresponding ISQ quantities (often referred to as SI quantities) with the same units:<ref name="bennett" />
<math display="block">\chi_\text{m}^\text{SI} = 4\pi\chi_\text{m}^\text{CGS}</math>
<math display="block">\chi_\text{ρ}^\text{SI} = 4\pi\chi_\text{ρ}^\text{CGS}</math>
<math display="block">\chi_\text{v}^\text{SI} = 4\pi\chi_\text{v}^\text{CGS}</math>

For example, the CGS volume magnetic susceptibility of water at 20&nbsp;°C is {{val|7.19e-7}}, which is {{val|9.04e-6}} using the [[International System of Units|SI]] convention, both quantities being dimensionless. Whereas for most electromagnetic quantities, which system of quantities it belongs to can be disambiguated by incompatibility of their units, this is not true for the susceptibility quantities.

In physics it is common to see CGS mass susceptibility with unit cm<sup>3</sup>/g or emu/g⋅Oe<sup>−1</sup>, and the CGS molar susceptibility with unit cm<sup>3</sup>/mol or emu/mol⋅Oe<sup>−1</sup>.

==Paramagnetism and diamagnetism==
If {{math|''χ''}} is positive, a material can be [[paramagnetic]]. In this case, the magnetic field in the material is strengthened by the induced magnetization. Alternatively, if {{math|''χ''}} is negative, the material is [[diamagnetic]]. In this case, the magnetic field in the material is weakened by the induced magnetization. Generally, nonmagnetic materials are said to be para- or diamagnetic because they do not possess permanent magnetization without external magnetic field. [[Ferromagnetic]], [[ferrimagnetism|ferrimagnetic]], or [[antiferromagnetic]] materials possess permanent magnetization even without external magnetic field and do not have a well defined zero-field susceptibility.

==Experimental measurement==
Volume magnetic susceptibility is measured by the force change felt upon a substance when a magnetic field gradient is applied.<ref>{{cite book
| author=L. N. Mulay
| title=Techniques of Chemistry
|editor1=A. Weissberger |editor2=B. W. Rossiter | publisher=Wiley-Interscience: New York
| volume=4
| page = 431
| year=1972
}}</ref> Early measurements are made using the [[Gouy balance]] where a sample is hung between the poles of an electromagnet. The change in weight when the electromagnet is turned on is proportional to the susceptibility. Today, high-end measurement systems use a [[superconductive]] magnet. An alternative is to measure the force change on a strong compact magnet upon insertion of the sample. This system, widely used today, is called the [[Evans balance]].<ref>{{cite web|url=http://www.sherwood-scientific.com/msb/msbindex.html |title=Magnetic Susceptibility Balances |publisher=Sherwood-scientific.com |access-date=2011-11-08}}</ref> For liquid samples, the susceptibility can be measured from the dependence of the [[nuclear magnetic resonance|NMR]] frequency of the sample on its shape or orientation.<ref>{{ 
cite journal
| author=J. R. Zimmerman, and M. R. Foster
| title=Standardization of NMR high resolution spectra
| journal=J. Phys. Chem.
| volume=61
| year=1957
| pages=282–289
| doi=10.1021/j150549a006
| issue=3
}}</ref><ref>{{
cite journal
| author1=Robert Engel | author2=Donald Halpern | author3=Susan Bienenfeld | name-list-style=amp
| title=Determination of magnetic moments in solution by nuclear magnetic resonance spectrometry
| journal=Anal. Chem.
| volume=45
| year=1973
| pages=367–369
| doi=10.1021/ac60324a054
| issue=2
| pmid=4762356 }}</ref><ref>{{
cite journal
| last1=Kuchel | first1=P.W.
| last2=Chapman | first2=B.E.
| last3=Bubb | first3=W.A.
| last4=Hansen | first4=P.E.
| last5=Durrant | first5=C.J.
| last6=Hertzberg | first6=M.P.
| title=Magnetic susceptibility: Solutions, emulsions, and cells
| journal=Concepts in Magnetic Resonance
| date=2003
| volume=18A | issue=1 | pages=56–71
| doi=10.1002/cmr.a.10066
| arxiv=q-bio/0601030
| s2cid=13013704
| url=https://onlinelibrary.wiley.com/doi/abs/10.1002/cmr.a.10066
}}</ref><ref>{{
cite journal
| author1=K. Frei | author2=H. J. Bernstein | name-list-style=amp
| title=Method for determining magnetic susceptibilities by NMR
| journal=J. Chem. Phys.
| volume=37
| year=1962
| pages=1891–1892
| doi=10.1063/1.1733393 | bibcode = 1962JChPh..37.1891F
| issue=8
}}</ref><ref>{{
cite journal
| author=R. E. Hoffman
| title=Variations on the chemical shift of TMS
| journal=J. Magn. Reson.
| volume=163
| year=2003
| pages=325–331
| doi=10.1016/S1090-7807(03)00142-3
| pmid=12914848
| issue=2 | bibcode = 2003JMagR.163..325H
}}</ref>

Another method using NMR techniques measures the magnetic field distortion around a sample immersed in water inside an MR scanner. This method is highly accurate for diamagnetic materials with susceptibilities similar to water.<ref name="Wapler_JMR">{{cite journal|last1=Wapler|first1=M. C.|last2=Leupold|first2=J.|last3=Dragonu|first3=I.|last4=von Elverfeldt|first4=D.| last5=Zaitsev|first5=M.|last6=Wallrabe|first6=U.|title=Magnetic properties of materials for MR engineering, micro-MR and beyond| journal=JMR|date=2014|volume=242|pages=233–242|doi=10.1016/j.jmr.2014.02.005| pmid=24705364|arxiv=1403.4760| bibcode=2014JMagR.242..233W| s2cid=11545416}}</ref>

==Tensor susceptibility==
The magnetic susceptibility of most [[crystal]]s is not a scalar quantity. Magnetic response {{math|'''M'''}} is dependent upon the orientation of the sample and can occur in directions other than that of the applied field {{math|'''H'''}}. In these cases, volume susceptibility is defined as a [[tensor]]:
<math display="block"> M_i = H_j \chi_{ij} </math>
where {{mvar|i}} and {{mvar|j}} refer to the directions (e.g., of the {{mvar|x}} and {{mvar|y}} [[Cartesian coordinates]]) of the applied field and magnetization, respectively. The tensor is thus degree 2 (second order), dimension (3,3) describing the component of magnetization in the {{mvar|i}}th direction from the external field applied in the {{mvar|j}}th direction.

==Differential susceptibility==
In [[ferromagnetic]] crystals, the relationship between {{math|'''M'''}} and {{math|'''H'''}} is not linear. To accommodate this, a more general definition of ''differential susceptibility'' is used:
<math display="block">\chi^{d}_{ij} = \frac{\partial M_i}{\partial H_j}</math>
where {{math|''χ''{{su|p=''d''|b=''ij''}}}} is a tensor derived from [[partial derivative]]s of components of {{math|'''M'''}} with respect to components of {{math|'''H'''}}. When the [[coercivity]] of the material parallel to an applied field is the smaller of the two, the differential susceptibility is a function of the applied field and self interactions, such as the [[magnetic anisotropy]]. When the material is not [[Saturation (magnetic)|saturated]], the effect will be nonlinear and dependent upon the [[Domain wall (magnetism)|domain wall]] configuration of the material.

Several experimental techniques allow for the measurement of the electronic properties of a material. An important effect in metals under strong magnetic fields, is the oscillation of the differential susceptibility as function of {{math|{{sfrac|1|''H''}}}}. This behaviour is known as the [[De Haas–Van Alphen effect]] and relates the period of the susceptibility with the [[Fermi surface]] of the material.

An analogue [[linear relation|non-linear relation]] between magnetization and magnetic field happens for [[antiferromagnetism#antiferromagnetic materials|antiferromagnetic materials]].<ref>{{cite journal|first1=Hrouda|last1= František |title=Low-field variation of magnetic susceptibility and its effect on the anisotropy of magnetic susceptibility of rocks |journal=Geophysical Journal International|volume =150|issue= 3|date= September 1, 2002|pages= 715–723 |issn=1365-246X |publisher = Oxford University Press|doi= 10.1046/j.1365-246X.2002.01731.x|bibcode= 2002GeoJI.150..715H|oclc=198890763|doi-access=free}}</ref>

==In the frequency domain==
When the magnetic susceptibility is measured in response to an [[Alternating current|AC]] magnetic field (i.e. a magnetic field that varies [[Sine wave|sinusoidally]]), this is called ''AC susceptibility''. AC susceptibility (and the closely related "AC permeability") are [[complex number]] quantities, and various phenomena, such as resonance, can be seen in AC susceptibility that cannot occur in constant-field ([[Direct current|DC]]) susceptibility. In particular, when an AC field is applied perpendicular to the detection direction (called the "transverse susceptibility" regardless of the frequency), the effect has a peak at the [[ferromagnetic resonance]] frequency of the material with a given static applied field. Currently, this effect is called the ''microwave permeability'' or ''network ferromagnetic resonance'' in the literature. These results are sensitive to the [[Domain wall (magnetism)|domain wall]] configuration of the material and [[eddy currents]].

In terms of ferromagnetic resonance, the effect of an AC-field applied along the direction of the magnetization is called ''parallel pumping''.

==Table of examples==
{{anchor|1=Examples}}
{| class="wikitable" align="center" style="margin:auto; text-align:center"
|+ Magnetic susceptibility of some materials
! rowspan="2" | Material
!               [[Temperature|{{abbr|Temp.|Temperature}}]]
!               [[Pressure]]
! colspan="2" | Molar susceptibility
! colspan="2" | Mass susceptibility
! colspan="2" | Volume susceptibility
!               [[Molar&nbsp;mass]]
!               [[Density]]
|-
! style="text-align:center;"| ([[Celsius|°C]])
! style="text-align:center;"| ([[Standard atmosphere (unit)|atm]])
! style="text-align:center;"| {{math|''χ''{{su|p=SI|b=m|lh=0.8em}}}}<br/>([[cubic metre|m<sup>3</sup>]]/[[Mole (unit)|mol]])
! style="text-align:center;"| {{math|''χ''{{su|p=CGS|b=m|lh=0.8em}}}}<br/>([[cubic centimetre|cm<sup>3</sup>]]/[[Mole (unit)|mol]])
! style="text-align:center;"| {{math|''χ''{{su|p=SI|b=ρ|lh=0.8em}}}}<br/>([[cubic metre|m<sup>3</sup>]]/[[kg]])
! style="text-align:center;"| {{math|''χ''{{su|p=CGS|b=ρ|lh=0.8em}}}}<br/>([[cubic centimetre|cm<sup>3</sup>]]/[[gram|g]])
! style="text-align:center;"| {{math|''χ''{{su|p=SI|b=v|lh=0.8em}}}}<br/>([[dimensionless|1]])
! style="text-align:center;"| {{math|''χ''{{su|p=CGS|b=v|lh=0.8em}}}}<br/>([[dimensionless|1]])
! style="text-align:center;"| {{math|''M''}}<br/>([[gram|g]]/[[Mole (unit)|mol]])
! style="text-align:center;"| {{math|''ρ''}}<br/>([[gram|g]]/[[cubic centimeter|cm<sup>3</sup>]])
|-
| align="left" | [[Helium]]<ref name="gases1">{{cite journal
 | author = R. E. Glick
 | title = On the Diamagnetic Susceptibility of Gases
 | year = 1961
 | journal = J. Phys. Chem.
 | volume = 65
 | issue = 9
 | pages = 1552–1555
 | doi = 10.1021/j100905a020
}}</ref>
| 20 || 1 || {{val|-2.38e-11}} || {{val|-1.89e-6}} || {{val|-5.93e-9}} || {{val|-4.72e-7}} || {{val|-9.85e-10}} || {{val|-7.84e-11}} || 4.0026 || {{val|1.66e-4}}
|-
| align="left" | [[Xenon]]<ref name="gases1" />
| 20 || 1 || {{val|-5.71e-10}} || {{val|-4.54e-5}} || {{val|-4.35e-9}} || {{val|-3.46e-7}} || {{val|-2.37e-8}} || {{val|-1.89e-9}} || 131.29 || {{val|5.46e-3}}
|-
| align="left" | [[Oxygen]]<ref name="gases1" />
| 20 || 0.209 || {{val|+4.3e-8}} || {{val|+3.42e-3}} || {{val|+1.34e-6}} || {{val|+1.07e-4}} || {{val|+3.73e-7}} || {{val|+2.97e-8}} || 31.99 || {{val|2.78e-4}}
|-
| align="left" | [[Nitrogen]]<ref name="gases1" />
| 20 || 0.781 || {{val|-1.56e-10}} || {{val|-1.24e-5}} || {{val|-5.56e-9}} || {{val|-4.43e-7}} || {{val|-5.06e-9}} || {{val|-4.03e-10}} || 28.01 || {{val|9.10e-4}}
|-
| align="left" | Air (NTP)<ref name="mri1">{{cite journal
  | author = John F. Schenck
  | title = The role of magnetic susceptibility in magnetic resonance imaging: MRI magnetic compatibility of the first and second kinds
  | year = 1996
  | journal = Medical Physics
  | volume = 23
  | issue = 6
 | pages = 815–850
  | doi = 10.1118/1.597854
  | pmid=8798169|bibcode = 1996MedPh..23..815S
 }}</ref>
| 20 || 1 || || || || || {{val|+3.6e-7}} || {{val|+2.9e-8}} || 28.97 || {{val|1.29e-3}}
|-
| align="left" | [[Water (data page)|Water]]<ref>{{cite journal
  | author1=G. P. Arrighini
  | author2=M. Maestro
  | author3=R. Moccia
  | name-list-style=amp
  | title=Magnetic Properties of Polyatomic Molecules: Magnetic Susceptibility of H<sub>2</sub>O, NH<sub>3</sub>, CH<sub>4</sub>, H<sub>2</sub>O<sub>2</sub>
  | journal=J. Chem. Phys.
  | volume=49
  | year=1968
  | pages=882–889
  | doi=10.1063/1.1670155|bibcode = 1968JChPh..49..882A
  | issue=2
 }}</ref>
| 20 || 1 || {{val|-1.631e-10}} || {{val|-1.298e-5}} || {{val|-9.051e-9}} || {{val|-7.203e-7}} || {{val|-9.035e-6}} || {{val|-7.190e-7}} || 18.015 || 0.9982
|-
| align="left" | [[Mineral oil|Paraffin oil]], 220–260{{nbsp}}[[centistokes|cSt]]<ref name="Wapler_JMR" />
| 22
| 1
|
|
| {{val|-1.01e-8}}
| {{val|-8.0e-7}}
| {{val|-8.8e-6}}
| {{val|-7.0e-7}}
|
| 0.878
|-
| align="left" | [[Poly(methyl methacrylate)|PMMA]]<ref name="Wapler_JMR" />
| 22
| 1
|
|
| {{val|-7.61e-9}}
| {{val|-6.06e-7}}
| {{val|-9.06e-6}}
| {{val|-7.21e-7}}
|
| 1.190
|-
| align="left" | [[Polyvinyl chloride|PVC]]<ref name="Wapler_JMR" />
| 22
| 1
|
|
| {{val|-7.80e-9}}
| {{val|-6.21e-7}}
| {{val|-1.071e-5}}
| {{val|-8.52e-7}}
|
| 1.372
|-
| align="left" | [[Fused quartz|Fused silica]] glass<ref name="Wapler_JMR" />
| 22
| 1
|
|
| {{val|-5.12e-9}}
| {{val|-4.07e-7}}
| {{val|-1.128e-5}}
| {{val|-8.98e-7}}
|
| 2.20
|-
| align="left" | [[Diamond]]<ref>
{{cite journal
 | author = J. Heremans, C. H. Olk and D. T. Morelli
 | title = Magnetic Susceptibility of Carbon Structures
 | year = 1994
 | journal = Phys. Rev. B
 | volume = 49
 | issue = 21
 | pages = 15122–15125
 | doi = 10.1103/PhysRevB.49.15122
 | pmid = 10010619
 | bibcode = 1994PhRvB..4915122H
}}</ref>
| [[Room temperature|r.t.]] ||1 || {{val|-7.4e-11}} || {{val|-5.9e-6}} || {{val|-6.2e-9}} || {{val|-4.9e-7}} || {{val|-2.2e-5}} || {{val|-1.7e-6}} || 12.01|| 3.513
|-
| align="left" | [[Graphite]]<ref name=graphite1>
 {{cite journal
  | author1=N. Ganguli | author2=K.S. Krishnan | name-list-style=amp
  | title = The Magnetic and Other Properties of the Free Electrons in Graphite
  | year = 1941
  | journal = Proceedings of the Royal Society
  | volume = 177
  | issue = 969
  | pages = 168–182
  | doi = 10.1098/rspa.1941.0002
  | bibcode = 1941RSPSA.177..168G
  | doi-access = free
  }}</ref> {{math|''χ''<sub>⊥</sub>}}
| r.t. || 1 || {{val|-7.5e-11}} || {{val|-6.0e-6}} || {{val|-6.3e-9}} || {{val|-5.0e-7}} || {{val|-1.4e-5}} || {{val|-1.1e-6}} || 12.01 || 2.267
|-
| align="left" | [[Graphite]]<ref name=graphite1/> {{math|''χ''<sub>∥</sub>}}
| r.t. || 1 || {{val|-3.2e-9}} || {{val|-2.6e-4}} || {{val|-2.7e-7}} || {{val|-2.2e-5}} || {{val|-6.1e-4}} || {{val|-4.9e-5}} || 12.01 || 2.267
|-
| align="left" | [[Graphite]]<ref name=graphite1/> {{math|''χ''<sub>∥</sub>}}
| −173 || 1 || {{val|-4.4e-9}} || {{val|-3.5e-4}} || {{val|-3.6e-7}} || {{val|-2.9e-5}} || {{val|-8.3e-4}} || {{val|-6.6e-5}} || 12.01 || 2.267
|-
| align="left" | [[Aluminium]]<ref name="magneticValues">{{Cite web|url=http://hyperphysics.phy-astr.gsu.edu/Hbase/tables/magprop.html|title=Magnetic Properties of Solids|last=Nave|first=Carl L|work=HyperPhysics|access-date=2008-11-09}}</ref>
| || 1 || {{val|+2.2e-10}} || {{val|+1.7e-5}} || {{val|+7.9e-9}} || {{val|+6.3e-7}} || {{val|+2.2e-5}} || {{val|+1.75e-6}} || 26.98 || 2.70
|-
| align="left" | [[Silver]]<ref>
 {{cite journal
  |author1=R. Dupree  |author2=C. J. Ford
  |name-list-style=amp | title = Magnetic susceptibility of the noble metals around their melting points
  | year = 1973
  | journal = Phys. Rev. B
  | volume = 8
  | issue = 4
  | pages = 1780–1782
  | doi = 10.1103/PhysRevB.8.1780|bibcode = 1973PhRvB...8.1780D
 }}</ref>
| 961 || 1 || {{val|+2.3e-10}} || {{val|+1.8e-5}} || || || {{val|-2.31e-5}} || {{val|-1.84e-6}} || 107.87 || 
|-
| align="left" | [[Bismuth]]<ref>
 {{cite journal
  |author1=S. Otake, M. Momiuchi  |author2=N. Matsuno
  |name-list-style=amp | title = Temperature Dependence of the Magnetic Susceptibility of Bismuth
  | year = 1980
  | journal = J. Phys. Soc. Jpn.
  | volume = 49
  | issue = 5
  | pages = 1824–1828
  | doi = 10.1143/JPSJ.49.1824|bibcode = 1980JPSJ...49.1824O
 }} The tensor needs to be averaged over all orientations: {{math|''χ'' {{=}} {{sfrac|1|3}}''χ''<sub>∥</sub> + {{sfrac|2|3}}''χ''<sub>⊥</sub>}}.</ref>
| 20 || 1 || {{val|-3.55e-9}} || {{val|-2.82e-4}} || {{val|-1.70e-8}} || {{val|-1.35e-6}} || {{val|-1.66e-4}} || {{val|-1.32e-5}} || 208.98 || 9.78
|-
| align="left" | [[Copper]]<ref name=mri1/>
| 20 || 1 ||  ||  || {{val|-1.0785e-9}} || || {{val|-9.63e-6}} || {{val|-7.66e-7}} || 63.546 || 8.92
|-
| align="left" | [[Nickel]]<ref name=mri1/>
| 20 || 1 ||  ||  ||  || || 600 || 48 || 58.69 || 8.9
|-
| align="left" | [[Iron]]<ref name=mri1/>
| 20 || 1 ||  ||  ||  || || {{val|200000}} || {{val|15900}} || 55.847 || 7.874
|}

==Sources of published data==
The [[CRC Handbook of Chemistry and Physics]] has one of the few published magnetic susceptibility tables. The data are listed as CGS quantities. The molar susceptibility of several elements and compounds are listed in the CRC.

== Application in the geosciences ==
In [[Earth science]], magnetism is a useful parameter to describe and analyze rocks. Additionally, the [[anisotropy]] of magnetic susceptibility (AMS) within a sample determines parameters as directions of [[paleocurrent]]s, maturity of [[paleosol]], flow direction of [[magma]] injection, [[Tectonics|tectonic]] strain, etc.<ref name=":0" /> It is a non-destructive tool which quantifies the average alignment and orientation of magnetic particles within a sample.<ref>{{Cite journal|last=Borradaile|first=Graham John|date=December 1988 |title=Magnetic susceptibility, petrofabrics and strain|journal=Tectonophysics|volume=156|issue=1–2|pages=1–20 |doi=10.1016/0040-1951(88)90279-X |bibcode=1988Tectp.156....1B}}</ref>

==See also==
{{div col|colwidth=20em}}
* [[Curie's law]]
* [[Electric susceptibility]]
* [[Iron]]
* [[Magnetic flux density]]
* [[Magnetochemistry]]
* [[Magnetometer]]
* [[Maxwell's equations]]
* [[Paleomagnetism]]
* [[Permeability (electromagnetism)]]
* [[Quantitative susceptibility mapping]]
* [[Susceptibility weighted imaging]]
{{Div col end}}

== References ==
{{Reflist}}

==External links==
*[https://web.archive.org/web/20160304030119/http://www.cond-mat.de/events/correl14/manuscripts/pavarini.pdf Linear Response Functions ] in Eva Pavarini, Erik Koch, Dieter Vollhardt, and Alexander Lichtenstein (eds.): DMFT at 25: Infinite Dimensions,  Verlag des Forschungszentrum Jülich, 2014 {{ISBN|978-3-89336-953-9}}

{{Authority control}}

{{DEFAULTSORT:Magnetic Susceptibility}}
[[Category:Physical quantities]]
[[Category:Magnetism]]
[[Category:Electric and magnetic fields in matter]]
[[Category:Scientific techniques]]