magnetic susceptibility

The ratio of magnetization M to magnetic field strength H; symbol ?, expressed as a pure number. It expresses the dependence of a magnetic field in a material on an external field which results only from current in the magnetizing coils. It is related to permeability, and constant except for ferromagnetic materials.

In electrical engineering, the magnetic susceptibility is the degree of magnetization of a material in response to an applied magnetic field. The dimensionless volume magnetic susceptibility, represented by the symbol (also represented in the literature by κ or Κ), is defined by the relationship

where

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

The magnetic induction B is related to H by the relationship

where μ0 is the permeability of free space (see table of physical constants), and is the relative permeability of the material. However, many tables of magnetic susceptibility give cgs values that rely on a different definition of the permeability of free space. For example, the cgs volume magnetic susceptibility of water at 20°C is -7.19x10 using the SI convention.

There are two other measures of susceptibility, the mass magnetic susceptibility in cm (χ or χg) and the molar magnetic susceptibility (χm) in cm that are defined as follows where ρ is the density in g•cm. In this case, the magnetic field is strengthened by the presence of the material. As a result, the magnetic field is weakened in the presence of the material.

Volume magnetic susceptibility is measured by the force change felt upon the application of a magnetic field (L. To accommodate this, a more general definition using a tensor derived from derivatives of components of M with respect to components of H

called the differential susceptibility describes ferromagnetic materials, where i and j refer to the directions (e.g., x, y and z in Cartesian coordinates) of the applied field and magnetization, respectively. The tensor is thus rank 2, dimension (3,3) describing the response of the magnetization in the j-th direction from an incremental change in the i-th direction of the applied field.

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. 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.

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

The magnetic susceptibility and the magnetic permeability (μ) are related by the following formula:

where is the relative permeability of the material.