# PlanetPhysics/Magnetic Susceptibility

In Electromagnetism, the *volume magnetic susceptibility* , represented by the symbol is defined by the following equation

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

On the other hand, the magnetic induction is related to by the equation

where is the magnetic constant, and is the relative permeability of the material.

Note that the magnetic susceptibility and the magnetic permeability of a material are related as follows:

There are two other measures of susceptibility, the *mass magnetic susceptibility* , or , and the
*molar magnetic susceptibility* ,

where is the density and M is the molar mass.

#### Susceptibility Sign conventionEdit

If is positive, then (or, in cgs units, and the material can be paramagnetic, ferromagnetic, ferrimagnetic, or anti-ferromagnetic; then, the magnetic field inside the material is strengthened by the presence of the material, that is, the magnetization value is greater than the external H-value.

On the other hand there are certain materials--called *diamagnetic* -- for which negative, and thus **Failed to parse (syntax error): {\displaystyle (1+Ï‡v) < 1}**
(in SI units).

### Magnetic Susceptibility Tensor, Edit

The magnetic susceptibility of most crystals (that are anisotropic) cannot be represented only by a scalar, but it is instead representable by a tensor ** . Then, the crystal magnetization is dependent upon the orientation of the sample and can have non-zero values along directions other than that of the applied magnetic field . Note that even non-crystalline materials may have a residual anisotropy, and thus require a similar treatment.
**

In all such magnetically anisotropic materials, the volume magnetic susceptibility tensor is then defined as follows:

where and refer to the directions (such as, for example, x, y, z in Cartesian coordinates) of, respectively, the applied magnetic field and the magnetization of the material. This rank 2 tensor (of dimension (3,3)) relates the component of the magnetization in the -th direction, to the component of the external magnetic field applied along the -th direction.

## All SourcesEdit

^{[1]}^{[2]}^{[3]}^{[2]}^{[4]}^{[5]}^{[6]}^{[7]}^{[8]}^{[9]}

## ReferencesEdit

- ↑
G. P. Arrighini, M. Maestro, and R. Moccia (1968). Magnetic Properties of Polyatomic Molecules: Magnetic Susceptibility of .
*J. Chem. Phys.*49: 882-889. doi:10.1063/1.1670155. - ↑
^{2.0}^{2.1}S. Otake, M. Momiuchi and N. Matsuno (1980). Temperature Dependence of the Magnetic Susceptibility of Bismuth. J. Phys. Soc. Jap. 49 (5): 1824-1828. doi:10.1143/JPSJ.49.1824. Cite error: Invalid`<ref>`

tag; name "OMM80" defined multiple times with different content - ↑
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. - ↑
R. Dupree and C. J. Ford (1973). Magnetic susceptibility of the noble metals around their melting points.
*Phys. Rev. B*8 (4): 1780â€“1782. doi:10.1103/PhysRevB.8.1780. ====Magnetic Moments and Nuclear Magnetic Resonance Spectrometry==== - ↑
J. R. Zimmerman, and M. R. Foster (1957). Standardization of NMR high resolution spectra.
*J. Phys. Chem.*61: 282-289. . - ↑ Robert Engel, Donald Halpern, and Susan Bienenfeld (1973). Determination of magnetic moments in solution by nuclear magnetic resonance spectrometry. Anal. Chem. 45: 367-369. doi:10.1021/ac60324a054.
- ↑
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. . - ↑ K. Frei and H. J. Bernstein (1962). Method for determining magnetic susceptibilities by NMR. J. Chem. Phys. 37: 1891-1892. .
- ↑
R. E. Hoffman (2003). Variations on the chemical shift of TMS.
*J. Magn. Reson.*163: 325-331. .