magnetic susceptibility | Physics Library

Definition 0.1. In Electromagnetism, the volume magnetic susceptibility, represented by the symbol χ_v, is defined by

M⃗ = χvH⃗,

where in SI units M is the magnetization of the material (the magnetic dipole moment per unit volume, measured in amperes per meter), and H is the magnetic field strength, also measured in amperes per meter.

The magnetic induction B is related to H by

B⃗ = μ0 (H⃗ + M⃗ ) = μ0 (1 + χv )⃗H = μ⃗H,

where μ₀ is the magnetic constant and (1 + χ_v) is the relative permeability of the material in SI units.

Thus, the magnetic susceptibility χ_v and the magnetic permeability μ are related by

μ = μ (1 + χ ). 0 v

Remark 0.1. There are two other commonly used measures of susceptibility: the mass magnetic susceptibility, χ_g or χ_m, and the molar magnetic susceptibility, χ_mol:

χv χmass = ---, ρ

and

M χv χmol = M χm = -----, ρ

where ρ is the density and M is the molar mass.

0.0.1 Susceptibility sign convention

If χ_v is positive, then

1 + χv > 1

in SI units. Materials with positive susceptibility include paramagnetic, ferromagnetic, ferrimagnetic, and antiferromagnetic materials.

For diamagnetic materials, χ_v is negative, and therefore

1 + χv < 1

in SI units.

0.1 Magnetic Susceptibility Tensor

For most anisotropic crystals, magnetic susceptibility cannot in general be represented by a single scalar. Instead, it is represented by a second-rank tensor χ. The magnetization M may then depend on the orientation of the sample and need not be parallel to the applied magnetic field H.

The volume magnetic susceptibility tensor is defined by

Mi = χijHj,

with summation over the repeated index j. Here M_i is the ith component of the magnetization, H_j is the jth component of the applied magnetic field, and χ_ij are the components of the 3 × 3 susceptibility tensor.

References

[1] G. P. Arrighini, M. Maestro, and R. Moccia (1968). Magnetic Properties of Polyatomic Molecules: Magnetic Susceptibility of H₂O, NH₃, CH₄, and H₂O₂. J. Chem. Phys. 49, 882–889. doi:10.1063/1.1670155.

[2] S. Otake, M. Momiuchi, and N. Matsuno (1980). Temperature Dependence of the Magnetic Susceptibility of Bismuth. J. Phys. Soc. Jpn. 49(5), 1824–1828. doi:10.1143/JPSJ.49.1824.

[3] J. Heremans, C. H. Olk, and D. T. Morelli (1994). Magnetic Susceptibility of Carbon Structures. Phys. Rev. B 49(21), 15122–15125. doi:10.1103/PhysRevB.49.15122.

[4] R. E. Glick (1961). On the Diamagnetic Susceptibility of Gases. J. Phys. Chem. 65(9), 1552–1555. doi:10.1021/j100905a020.

[5] R. Dupree and C. J. Ford (1973). Magnetic susceptibility of the noble metals around their melting points. Phys. Rev. B 8(4), 1780–1782. doi:10.1103/PhysRevB.8.1780.

[6] J. R. Zimmerman and M. R. Foster (1957). Standardization of NMR high resolution spectra. J. Phys. Chem. 61, 282–289. doi:10.1021/j150549a006.

[7] R. Engel, D. Halpern, and S. Bienenfeld (1973). Determination of magnetic moments in solution by nuclear magnetic resonance spectrometry. Anal. Chem. 45, 367–369. doi:10.1021/ac60324a054.

[8] P. W. Kuchel, B. E. Chapman, W. A. Bubb, P. E. Hansen, C. J. Durrant, and M. P. Hertzberg (2003). Magnetic susceptibility: solutions, emulsions, and cells. Concepts Magn. Reson. A 18, 56–71. doi:10.1002/cmr.a.10066.

[9] K. Frei and H. J. Bernstein (1962). Method for determining magnetic susceptibilities by NMR. J. Chem. Phys. 37, 1891–1892. doi:10.1063/1.1733393.

[10] R. E. Hoffman (2003). Variations on the chemical shift of TMS. J. Magn. Reson. 163, 325–331. doi:10.1016/S1090-7807(03)00142-3.

"magnetic susceptibility" is owned by bci1.
(view preamble)