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Magnetic susceptibility

January 19, 2024

In electromagnetism, the magnetic susceptibility (from Latin susceptibilis 'receptive'; denoted χ, chi) is a measure of how much a material will become magnetized in an applied magnetic field. It is the ratio of magnetization M (magnetic moment per unit volume) to the applied magnetizing field intensity H. This allows a simple classification, into two categories, of most materials' responses to an applied magnetic field: an alignment with the magnetic field, χ > 0, called paramagnetism, or an alignment against the field, 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 lines to concentrate in paramagnetism, or be excluded in diamagnetism.[1] Quantitative measures of the magnetic susceptibility also provide insights into the structure of materials, providing insight into bonding and energy levels. Furthermore, it is widely used in geology for paleomagnetic studies and structural geology.[2]

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 electrons. 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 macroscopic form of Maxwell's equations. This allows classical physics to make useful predictions while avoiding the underlying quantum mechanical details.

Definition edit

See also: Permeability (electromagnetism) § Relative permeability and magnetic susceptibility

Volume susceptibility edit

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 flux density.[3] A closely related parameter is the permeability, which expresses the total magnetization of material and volume.

The volume magnetic susceptibility, represented by the symbol χv (often simply χ, sometimes χm – magnetic, to distinguish from the electric susceptibility), is defined in the International System of Units – in other systems there may be additional constants – by the following relationship:[4][5]

 


Here,

  • M is the magnetization of the material (the magnetic dipole moment per unit volume), with unit amperes per meter, and
  • H is the magnetic field strength, also with the unit amperes per meter.

χv is therefore a dimensionless quantity.

Using SI units, the magnetic induction B is related to H by the relationship

 

where μ0 is the vacuum permeability (see table of physical constants), and (1 + χv) is the relative permeability of the material. Thus the volume magnetic susceptibility χv and the magnetic permeability μ are related by the following formula:

 

Sometimes[6] an auxiliary quantity called intensity of magnetization I (also referred to as magnetic polarisation J) and with unit teslas, is defined as

 

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

Molar susceptibility and mass susceptibility edit

There are two other measures of susceptibility, the molar magnetic susceptibility (χm) with unit m3/mol, and the mass magnetic susceptibility (χρ) with unit m3/kg that are defined below, where ρ is the density with unit kg/m3 and M is molar mass with unit kg/mol:

 

In CGS units edit

The definitions above are according to the International System of Quantities (ISQ) upon which the SI is based. However, many tables of magnetic susceptibility give the values of the corresponding quantities of the CGS system (more specifically CGS-EMU, short for electromagnetic units, or Gaussian-CGS; both are the same in this context). The quantities characterizing the permeability of free space for each system have different defining equations:[7]

 

The respective CGS susceptibilities are multiplied by 4π to give the corresponding ISQ quantities (often referred to as SI quantities) with the same units:[7]

 
 
 

For example, the CGS volume magnetic susceptibility of water at 20 °C is 7.19×10−7, which is 9.04×10−6 using the 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 cm3/g or emu/g⋅Oe−1, and the CGS molar susceptibility with unit cm3/mol or emu/mol⋅Oe−1.

Paramagnetism and diamagnetism edit

If 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 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, ferrimagnetic, or antiferromagnetic materials possess permanent magnetization even without external magnetic field and do not have a well defined zero-field susceptibility.

Experimental measurement edit

Volume magnetic susceptibility is measured by the force change felt upon a substance when a magnetic field gradient is applied.[8] 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.[9] For liquid samples, the susceptibility can be measured from the dependence of the NMR frequency of the sample on its shape or orientation.[10][11][12][13][14]

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.[15]

Tensor susceptibility edit

The magnetic susceptibility of most crystals is not a scalar quantity. Magnetic response M is dependent upon the orientation of the sample and can occur in directions other than that of the applied field H. In these cases, volume susceptibility is defined as a tensor:

 
where i and j refer to the directions (e.g., of the x and 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 ith direction from the external field applied in the jth direction.

Differential susceptibility edit

In ferromagnetic crystals, the relationship between M and H is not linear. To accommodate this, a more general definition of differential susceptibility is used:

 
where χd
ij is a tensor derived from partial derivatives of components of M with respect to components of 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 saturated, the effect will be nonlinear and dependent upon the 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 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 non-linear relation between magnetization and magnetic field happens for antiferromagnetic materials.[16]

In the frequency domain edit

When the magnetic susceptibility is measured in response to an AC magnetic field (i.e. a magnetic field that varies 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 (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 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 edit

Magnetic susceptibility of some materials
Material Temp. Pressure Molar susceptibility Mass susceptibility Volume susceptibility Molar mass Density
(°C) (atm) χSI
m
(m3/mol) 		χCGS
m
(cm3/mol) 		χSI
ρ
(m3/kg) 		χCGS
ρ
(cm3/g) 		χSI
v
(1) 		χCGS
v
(1) 		M
(g/mol) 		ρ
(g/cm3)
Helium[17] 20 1 −2.38×10−11 −1.89×10−6 −5.93×10−9 −4.72×10−7 −9.85×10−10 −7.84×10−11 4.0026 1.66×10−4
Xenon[17] 20 1 −5.71×10−10 −4.54×10−5 −4.35×10−9 −3.46×10−7 −2.37×10−8 −1.89×10−9 131.29 5.46×10−3
Oxygen[17] 20 0.209 +4.3×10−8 +3.42×10−3 +1.34×10−6 +1.07×10−4 +3.73×10−7 +2.97×10−8 31.99 2.78×10−4
Nitrogen[17] 20 0.781 −1.56×10−10 −1.24×10−5 −5.56×10−9 −4.43×10−7 −5.06×10−9 −4.03×10−10 28.01 9.10×10−4
Air (NTP)[18] 20 1 +3.6×10−7 +2.9×10−8 28.97 1.29×10−3
Water[19] 20 1 −1.631×10−10 −1.298×10−5 −9.051×10−9 −7.203×10−7 −9.035×10−6 −7.190×10−7 18.015 0.9982
Paraffin oil, 220–260 cSt[15] 22 1 −1.01×10−8 −8.0×10−7 −8.8×10−6 −7.0×10−7 0.878
PMMA[15] 22 1 −7.61×10−9 −6.06×10−7 −9.06×10−6 −7.21×10−7 1.190
PVC[15] 22 1 −7.80×10−9 −6.21×10−7 −1.071×10−5 −8.52×10−7 1.372
Fused silica glass[15] 22 1 −5.12×10−9 −4.07×10−7 −1.128×10−5 −8.98×10−7 2.20
Diamond[20] r.t. 1 −7.4×10−11 −5.9×10−6 −6.2×10−9 −4.9×10−7 −2.2×10−5 −1.7×10−6 12.01 3.513
Graphite[21] χ⊥ r.t. 1 −7.5×10−11 −6.0×10−6 −6.3×10−9 −5.0×10−7 −1.4×10−5 −1.1×10−6 12.01 2.267
Graphite[21] χ∥ r.t. 1 −3.2×10−9 −2.6×10−4 −2.7×10−7 −2.2×10−5 −6.1×10−4 −4.9×10−5 12.01 2.267
Graphite[21] χ∥ −173 1 −4.4×10−9 −3.5×10−4 −3.6×10−7 −2.9×10−5 −8.3×10−4 −6.6×10−5 12.01 2.267
Aluminium[22] 1 +2.2×10−10 +1.7×10−5 +7.9×10−9 +6.3×10−7 +2.2×10−5 +1.75×10−6 26.98 2.70
Silver[23] 961 1 +2.3×10−10 +1.8×10−5 −2.31×10−5 −1.84×10−6 107.87
Bismuth[24] 20 1 −3.55×10−9 −2.82×10−4 −1.70×10−8 −1.35×10−6 −1.66×10−4 −1.32×10−5 208.98 9.78
Copper[18] 20 1 −1.0785×10−9 −9.63×10−6 −7.66×10−7 63.546 8.92
Nickel[18] 20 1 600 48 58.69 8.9
Iron[18] 20 1 200000 15900 55.847 7.874

Sources of published data edit

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 edit

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 paleocurrents, maturity of paleosol, flow direction of magma injection, tectonic strain, etc.[2] It is a non-destructive tool which quantifies the average alignment and orientation of magnetic particles within a sample.[25]

See also edit

References edit

  1. ^ Roger Grinter, The Quantum in Chemistry: An Experimentalist's View, John Wiley & Sons, 2005, ISBN 0470017627 page 364
  2. ^ a b Tauxe, Lisa (2019). Essentials of Paleomagnetism: Fifth Web Edition. UC Press.
  3. ^ . IUPAC Compendium of Chemical Terminology—The Gold Book (2nd ed.). International Union of Pure and Applied Chemistry. 1997. Archived from the original on 2016-03-04. Retrieved 2011-10-13.
  4. ^ O'Handley, Robert C. (2000). Modern Magnetic Materials. Hoboken, NJ: Wiley. ISBN 9780471155669.
  5. ^ Freeman, Richard; King, James; Lafyatis, Gregory (2019). "Essentials of Electricity and Magnetism". Electromagnetic Radiation. Oxford University Press. doi:10.1093/oso/9780198726500.003.0001. ISBN 978-0-19-872650-0. Retrieved 2022-02-18.
  6. ^ Richard A. Clarke. "Magnetic properties of materials". Info.ee.surrey.ac.uk. Retrieved 2011-11-08.
  7. ^ a b Bennett, L. H.; Page, C. H. & Swartzendruber, L. J. (1978). "Comments on units in magnetism". Journal of Research of the National Bureau of Standards. NIST, USA. 83 (1): 9–12. doi:10.6028/jres.083.002. PMC 6752159. PMID 34565970.
  8. ^ L. N. Mulay (1972). A. Weissberger; B. W. Rossiter (eds.). Techniques of Chemistry. Vol. 4. Wiley-Interscience: New York. p. 431.
  9. ^ "Magnetic Susceptibility Balances". Sherwood-scientific.com. Retrieved 2011-11-08.
  10. ^ J. R. Zimmerman, and M. R. Foster (1957). "Standardization of NMR high resolution spectra". J. Phys. Chem. 61 (3): 282–289. doi:10.1021/j150549a006.
  11. ^ Robert Engel; Donald Halpern & Susan Bienenfeld (1973). "Determination of magnetic moments in solution by nuclear magnetic resonance spectrometry". Anal. Chem. 45 (2): 367–369. doi:10.1021/ac60324a054. PMID 4762356.
  12. ^ Kuchel, P.W.; Chapman, B.E.; Bubb, W.A.; Hansen, P.E.; Durrant, C.J.; Hertzberg, M.P. (2003). "Magnetic susceptibility: Solutions, emulsions, and cells". Concepts in Magnetic Resonance. 18A (1): 56–71. arXiv:q-bio/0601030. doi:10.1002/cmr.a.10066. S2CID 13013704.
  13. ^ K. Frei & H. J. Bernstein (1962). "Method for determining magnetic susceptibilities by NMR". J. Chem. Phys. 37 (8): 1891–1892. Bibcode:1962JChPh..37.1891F. doi:10.1063/1.1733393.
  14. ^ R. E. Hoffman (2003). "Variations on the chemical shift of TMS". J. Magn. Reson. 163 (2): 325–331. Bibcode:2003JMagR.163..325H. doi:10.1016/S1090-7807(03)00142-3. PMID 12914848.
  15. ^ a b c d e Wapler, M. C.; Leupold, J.; Dragonu, I.; von Elverfeldt, D.; Zaitsev, M.; Wallrabe, U. (2014). "Magnetic properties of materials for MR engineering, micro-MR and beyond". JMR. 242: 233–242. arXiv:1403.4760. Bibcode:2014JMagR.242..233W. doi:10.1016/j.jmr.2014.02.005. PMID 24705364. S2CID 11545416.
  16. ^ František, Hrouda (September 1, 2002). "Low-field variation of magnetic susceptibility and its effect on the anisotropy of magnetic susceptibility of rocks". Geophysical Journal International. Oxford University Press. 150 (3): 715–723. Bibcode:2002GeoJI.150..715H. doi:10.1046/j.1365-246X.2002.01731.x. ISSN 1365-246X. OCLC 198890763.
  17. ^ a b c d R. E. Glick (1961). "On the Diamagnetic Susceptibility of Gases". J. Phys. Chem. 65 (9): 1552–1555. doi:10.1021/j100905a020.
  18. ^ a b c d John F. Schenck (1996). "The role of magnetic susceptibility in magnetic resonance imaging: MRI magnetic compatibility of the first and second kinds". Medical Physics. 23 (6): 815–850. Bibcode:1996MedPh..23..815S. doi:10.1118/1.597854. PMID 8798169.
  19. ^ G. P. Arrighini; M. Maestro & R. Moccia (1968). "Magnetic Properties of Polyatomic Molecules: Magnetic Susceptibility of H2O, NH3, CH4, H2O2". J. Chem. Phys. 49 (2): 882–889. Bibcode:1968JChPh..49..882A. doi:10.1063/1.1670155.
  20. ^ J. Heremans, C. H. Olk and D. T. Morelli (1994). "Magnetic Susceptibility of Carbon Structures". Phys. Rev. B. 49 (21): 15122–15125. Bibcode:1994PhRvB..4915122H. doi:10.1103/PhysRevB.49.15122. PMID 10010619.
  21. ^ a b c N. Ganguli & K.S. Krishnan (1941). "The Magnetic and Other Properties of the Free Electrons in Graphite". Proceedings of the Royal Society. 177 (969): 168–182. Bibcode:1941RSPSA.177..168G. doi:10.1098/rspa.1941.0002.
  22. ^ Nave, Carl L. "Magnetic Properties of Solids". HyperPhysics. Retrieved 2008-11-09.
  23. ^ R. Dupree & C. J. Ford (1973). "Magnetic susceptibility of the noble metals around their melting points". Phys. Rev. B. 8 (4): 1780–1782. Bibcode:1973PhRvB...8.1780D. doi:10.1103/PhysRevB.8.1780.
  24. ^ S. Otake, M. Momiuchi & N. Matsuno (1980). "Temperature Dependence of the Magnetic Susceptibility of Bismuth". J. Phys. Soc. Jpn. 49 (5): 1824–1828. Bibcode:1980JPSJ...49.1824O. doi:10.1143/JPSJ.49.1824. The tensor needs to be averaged over all orientations: χ = 1/3χ∥ + 2/3χ⊥.
  25. ^ Borradaile, Graham John (December 1988). "Magnetic susceptibility, petrofabrics and strain". Tectonophysics. 156 (1–2): 1–20. Bibcode:1988Tectp.156....1B. doi:10.1016/0040-1951(88)90279-X.

External links edit

  • 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

January 19, 2024
magnetic, susceptibility, electromagnetism, magnetic, susceptibility, from, latin, susceptibilis, receptive, denoted, measure, much, material, will, become, magnetized, applied, magnetic, field, ratio, magnetization, magnetic, moment, unit, volume, applied, ma. In electromagnetism the magnetic susceptibility from Latin susceptibilis receptive denoted x chi is a measure of how much a material will become magnetized in an applied magnetic field It is the ratio of magnetization M magnetic moment per unit volume to the applied magnetizing field intensity H This allows a simple classification into two categories of most materials responses to an applied magnetic field an alignment with the magnetic field x gt 0 called paramagnetism or an alignment against the field x lt 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 lines to concentrate in paramagnetism or be excluded in diamagnetism 1 Quantitative measures of the magnetic susceptibility also provide insights into the structure of materials providing insight into bonding and energy levels Furthermore it is widely used in geology for paleomagnetic studies and structural geology 2 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 electrons 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 macroscopic form of Maxwell s equations This allows classical physics to make useful predictions while avoiding the underlying quantum mechanical details Contents 1 Definition 1 1 Volume susceptibility 1 2 Molar susceptibility and mass susceptibility 1 3 In CGS units 2 Paramagnetism and diamagnetism 3 Experimental measurement 4 Tensor susceptibility 5 Differential susceptibility 6 In the frequency domain 7 Table of examples 8 Sources of published data 9 Application in the geosciences 10 See also 11 References 12 External linksDefinition editSee also Permeability electromagnetism Relative permeability and magnetic susceptibility Volume susceptibility edit 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 flux density 3 A closely related parameter is the permeability which expresses the total magnetization of material and volume The volume magnetic susceptibility represented by the symbol xv often simply x sometimes xm magnetic to distinguish from the electric susceptibility is defined in the International System of Units in other systems there may be additional constants by the following relationship 4 5 M x v H displaystyle mathbf M chi text v mathbf H nbsp Here M is the magnetization of the material the magnetic dipole moment per unit volume with unit amperes per meter and H is the magnetic field strength also with the unit amperes per meter xv is therefore a dimensionless quantity Using SI units the magnetic induction B is related to H by the relationshipB m 0 H M m 0 1 x v H m H displaystyle mathbf B mu 0 left mathbf H mathbf M right mu 0 left 1 chi text v right mathbf H mu mathbf H nbsp where m0 is the vacuum permeability see table of physical constants and 1 xv is the relative permeability of the material Thus the volume magnetic susceptibility xv and the magnetic permeability m are related by the following formula m m 0 1 x v displaystyle mu mu 0 left 1 chi text v right nbsp Sometimes 6 an auxiliary quantity called intensity of magnetization I also referred to as magnetic polarisation J and with unit teslas is defined asI m 0 M displaystyle mathbf I mu 0 mathbf M nbsp This allows an alternative description of all magnetization phenomena in terms of the quantities I and B as opposed to the commonly used M and H Molar susceptibility and mass susceptibility edit There are two other measures of susceptibility the molar magnetic susceptibility xm with unit m3 mol and the mass magnetic susceptibility xr with unit m3 kg that are defined below where r is the density with unit kg m3 and M is molar mass with unit kg mol x r x v r x m M x r M r x v displaystyle begin aligned chi rho amp frac chi text v rho chi text m amp M chi rho frac M rho chi text v end aligned nbsp In CGS units edit The definitions above are according to the International System of Quantities ISQ upon which the SI is based However many tables of magnetic susceptibility give the values of the corresponding quantities of the CGS system more specifically CGS EMU short for electromagnetic units or Gaussian CGS both are the same in this context The quantities characterizing the permeability of free space for each system have different defining equations 7 B CGS H CGS 4 p M CGS 1 4 p x v CGS H CGS displaystyle 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 nbsp The respective CGS susceptibilities are multiplied by 4p to give the corresponding ISQ quantities often referred to as SI quantities with the same units 7 x m SI 4 p x m CGS displaystyle chi text m text SI 4 pi chi text m text CGS nbsp x r SI 4 p x r CGS displaystyle chi text r text SI 4 pi chi text r text CGS nbsp x v SI 4 p x v CGS displaystyle chi text v text SI 4 pi chi text v text CGS nbsp For example the CGS volume magnetic susceptibility of water at 20 C is 7 19 10 7 which is 9 04 10 6 using the 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 cm3 g or emu g Oe 1 and the CGS molar susceptibility with unit cm3 mol or emu mol Oe 1 Paramagnetism and diamagnetism editIf x is positive a material can be paramagnetic In this case the magnetic field in the material is strengthened by the induced magnetization Alternatively if x 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 ferrimagnetic or antiferromagnetic materials possess permanent magnetization even without external magnetic field and do not have a well defined zero field susceptibility Experimental measurement editVolume magnetic susceptibility is measured by the force change felt upon a substance when a magnetic field gradient is applied 8 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 9 For liquid samples the susceptibility can be measured from the dependence of the NMR frequency of the sample on its shape or orientation 10 11 12 13 14 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 15 Tensor susceptibility editThe magnetic susceptibility of most crystals is not a scalar quantity Magnetic response M is dependent upon the orientation of the sample and can occur in directions other than that of the applied field H In these cases volume susceptibility is defined as a tensor M i H j x i j displaystyle M i H j chi ij nbsp where i and j refer to the directions e g of the x and 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 i th direction from the external field applied in the j th direction Differential susceptibility editIn ferromagnetic crystals the relationship between M and H is not linear To accommodate this a more general definition of differential susceptibility is used x i j d M i H j displaystyle chi ij d frac partial M i partial H j nbsp where xdij is a tensor derived from partial derivatives of components of M with respect to components of 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 saturated the effect will be nonlinear and dependent upon the 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 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 non linear relation between magnetization and magnetic field happens for antiferromagnetic materials 16 In the frequency domain editWhen the magnetic susceptibility is measured in response to an AC magnetic field i e a magnetic field that varies 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 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 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 editMagnetic susceptibility of some materials Material Temp Pressure Molar susceptibility Mass susceptibility Volume susceptibility Molar mass Density C atm xSIm m3 mol xCGSm cm3 mol xSIr m3 kg xCGSr cm3 g xSIv 1 xCGSv 1 M g mol r g cm3 Helium 17 20 1 2 38 10 11 1 89 10 6 5 93 10 9 4 72 10 7 9 85 10 10 7 84 10 11 4 0026 1 66 10 4Xenon 17 20 1 5 71 10 10 4 54 10 5 4 35 10 9 3 46 10 7 2 37 10 8 1 89 10 9 131 29 5 46 10 3Oxygen 17 20 0 209 4 3 10 8 3 42 10 3 1 34 10 6 1 07 10 4 3 73 10 7 2 97 10 8 31 99 2 78 10 4Nitrogen 17 20 0 781 1 56 10 10 1 24 10 5 5 56 10 9 4 43 10 7 5 06 10 9 4 03 10 10 28 01 9 10 10 4Air NTP 18 20 1 3 6 10 7 2 9 10 8 28 97 1 29 10 3Water 19 20 1 1 631 10 10 1 298 10 5 9 051 10 9 7 203 10 7 9 035 10 6 7 190 10 7 18 015 0 9982Paraffin oil 220 260 cSt 15 22 1 1 01 10 8 8 0 10 7 8 8 10 6 7 0 10 7 0 878PMMA 15 22 1 7 61 10 9 6 06 10 7 9 06 10 6 7 21 10 7 1 190PVC 15 22 1 7 80 10 9 6 21 10 7 1 071 10 5 8 52 10 7 1 372Fused silica glass 15 22 1 5 12 10 9 4 07 10 7 1 128 10 5 8 98 10 7 2 20Diamond 20 r t 1 7 4 10 11 5 9 10 6 6 2 10 9 4 9 10 7 2 2 10 5 1 7 10 6 12 01 3 513Graphite 21 x r t 1 7 5 10 11 6 0 10 6 6 3 10 9 5 0 10 7 1 4 10 5 1 1 10 6 12 01 2 267Graphite 21 x r t 1 3 2 10 9 2 6 10 4 2 7 10 7 2 2 10 5 6 1 10 4 4 9 10 5 12 01 2 267Graphite 21 x 173 1 4 4 10 9 3 5 10 4 3 6 10 7 2 9 10 5 8 3 10 4 6 6 10 5 12 01 2 267Aluminium 22 1 2 2 10 10 1 7 10 5 7 9 10 9 6 3 10 7 2 2 10 5 1 75 10 6 26 98 2 70Silver 23 961 1 2 3 10 10 1 8 10 5 2 31 10 5 1 84 10 6 107 87Bismuth 24 20 1 3 55 10 9 2 82 10 4 1 70 10 8 1 35 10 6 1 66 10 4 1 32 10 5 208 98 9 78Copper 18 20 1 1 0785 10 9 9 63 10 6 7 66 10 7 63 546 8 92Nickel 18 20 1 600 48 58 69 8 9Iron 18 20 1 200000 15900 55 847 7 874Sources of published data editThe 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 editIn 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 paleocurrents maturity of paleosol flow direction of magma injection tectonic strain etc 2 It is a non destructive tool which quantifies the average alignment and orientation of magnetic particles within a sample 25 See also editCurie constant Electric susceptibility Iron Magnetic flux density Magnetochemistry Magnetometer Maxwell s equations Paleomagnetism Permeability electromagnetism Quantitative susceptibility mapping Susceptibility weighted imagingReferences edit Roger Grinter The Quantum in Chemistry An Experimentalist s View John Wiley amp Sons 2005 ISBN 0470017627 page 364 a b Tauxe Lisa 2019 Essentials of Paleomagnetism Fifth Web Edition UC Press magnetizability 3 IUPAC Compendium of Chemical Terminology The Gold Book 2nd ed International Union of Pure and Applied Chemistry 1997 Archived from the original on 2016 03 04 Retrieved 2011 10 13 O Handley Robert C 2000 Modern Magnetic Materials Hoboken NJ Wiley ISBN 9780471155669 Freeman Richard King James Lafyatis Gregory 2019 Essentials of Electricity and Magnetism Electromagnetic Radiation Oxford University Press doi 10 1093 oso 9780198726500 003 0001 ISBN 978 0 19 872650 0 Retrieved 2022 02 18 Richard A Clarke Magnetic properties of materials Info ee surrey ac uk Retrieved 2011 11 08 a b Bennett L H Page C H amp Swartzendruber L J 1978 Comments on units in magnetism Journal of Research of the National Bureau of Standards NIST USA 83 1 9 12 doi 10 6028 jres 083 002 PMC 6752159 PMID 34565970 L N Mulay 1972 A Weissberger B W Rossiter eds Techniques of Chemistry Vol 4 Wiley Interscience New York p 431 Magnetic Susceptibility Balances Sherwood scientific com Retrieved 2011 11 08 J R Zimmerman and M R Foster 1957 Standardization of NMR high resolution spectra J Phys Chem 61 3 282 289 doi 10 1021 j150549a006 Robert Engel Donald Halpern amp Susan Bienenfeld 1973 Determination of magnetic moments in solution by nuclear magnetic resonance spectrometry Anal Chem 45 2 367 369 doi 10 1021 ac60324a054 PMID 4762356 Kuchel P W Chapman B E Bubb W A Hansen P E Durrant C J Hertzberg M P 2003 Magnetic susceptibility Solutions emulsions and cells Concepts in Magnetic Resonance 18A 1 56 71 arXiv q bio 0601030 doi 10 1002 cmr a 10066 S2CID 13013704 K Frei amp H J Bernstein 1962 Method for determining magnetic susceptibilities by NMR J Chem Phys 37 8 1891 1892 Bibcode 1962JChPh 37 1891F doi 10 1063 1 1733393 R E Hoffman 2003 Variations on the chemical shift of TMS J Magn Reson 163 2 325 331 Bibcode 2003JMagR 163 325H doi 10 1016 S1090 7807 03 00142 3 PMID 12914848 a b c d e Wapler M C Leupold J Dragonu I von Elverfeldt D Zaitsev M Wallrabe U 2014 Magnetic properties of materials for MR engineering micro MR and beyond JMR 242 233 242 arXiv 1403 4760 Bibcode 2014JMagR 242 233W doi 10 1016 j jmr 2014 02 005 PMID 24705364 S2CID 11545416 Frantisek Hrouda September 1 2002 Low field variation of magnetic susceptibility and its effect on the anisotropy of magnetic susceptibility of rocks Geophysical Journal International Oxford University Press 150 3 715 723 Bibcode 2002GeoJI 150 715H doi 10 1046 j 1365 246X 2002 01731 x ISSN 1365 246X OCLC 198890763 a b c d R E Glick 1961 On the Diamagnetic Susceptibility of Gases J Phys Chem 65 9 1552 1555 doi 10 1021 j100905a020 a b c d John F Schenck 1996 The role of magnetic susceptibility in magnetic resonance imaging MRI magnetic compatibility of the first and second kinds Medical Physics 23 6 815 850 Bibcode 1996MedPh 23 815S doi 10 1118 1 597854 PMID 8798169 G P Arrighini M Maestro amp R Moccia 1968 Magnetic Properties of Polyatomic Molecules Magnetic Susceptibility of H2O NH3 CH4 H2O2 J Chem Phys 49 2 882 889 Bibcode 1968JChPh 49 882A doi 10 1063 1 1670155 J Heremans C H Olk and D T Morelli 1994 Magnetic Susceptibility of Carbon Structures Phys Rev B 49 21 15122 15125 Bibcode 1994PhRvB 4915122H doi 10 1103 PhysRevB 49 15122 PMID 10010619 a b c N Ganguli amp K S Krishnan 1941 The Magnetic and Other Properties of the Free Electrons in Graphite Proceedings of the Royal Society 177 969 168 182 Bibcode 1941RSPSA 177 168G doi 10 1098 rspa 1941 0002 Nave Carl L Magnetic Properties of Solids HyperPhysics Retrieved 2008 11 09 R Dupree amp C J Ford 1973 Magnetic susceptibility of the noble metals around their melting points Phys Rev B 8 4 1780 1782 Bibcode 1973PhRvB 8 1780D doi 10 1103 PhysRevB 8 1780 S Otake M Momiuchi amp N Matsuno 1980 Temperature Dependence of the Magnetic Susceptibility of Bismuth J Phys Soc Jpn 49 5 1824 1828 Bibcode 1980JPSJ 49 1824O doi 10 1143 JPSJ 49 1824 The tensor needs to be averaged over all orientations x 1 3 x 2 3 x Borradaile Graham John December 1988 Magnetic susceptibility petrofabrics and strain Tectonophysics 156 1 2 1 20 Bibcode 1988Tectp 156 1B doi 10 1016 0040 1951 88 90279 X External links editLinear Response Functions in Eva Pavarini Erik Koch Dieter Vollhardt and Alexander Lichtenstein eds DMFT at 25 Infinite Dimensions Verlag des Forschungszentrum Julich 2014 ISBN 978 3 89336 953 9 Retrieved from https en wikipedia org w index php title Magnetic susceptibility amp oldid 1188433567, wikipedia, wiki, book, books, library,

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