magnetic susceptibility
Definition 0.1
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:
Remark 0.1
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.
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
(in SI units).
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.
1
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
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.
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.
2
R. E. Glick (1961). On the Diamagnetic Susceptibility of Gases.
J. Phys. Chem. 65 (9): 1552-1555. doi:10.1021/j100905a020.
4
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.
5
J. R. Zimmerman, and M. R. Foster (1957). Standardization of NMR high resolution spectra. J. Phys. Chem. 61: 282-289.
.
6
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.
7
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.
.
8
K. Frei and H. J. Bernstein (1962). Method for determining magnetic susceptibilities by NMR. J. Chem. Phys. 37: 1891-1892.
.
9
R. E. Hoffman (2003). Variations on the chemical shift of TMS.
J. Magn. Reson. 163: 325-331.
.
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