Magnetic Susceptibility – Magnetization

In electromagnetism, magnetic susceptibility is the measure of the magnetization of a substance. Magnetic susceptibility is a dimensionless proportionality factor that indicates the degree of magnetization of a material in response to an applied magnetic field. The magnitude of M is proportional to the applied field as follows:

The magnetic susceptibility and the relative permeability are related as follows:

This allows a simple classification of most material’s response to an applied magnetic field into two categories: an alignment with the magnetic field, χ>0, called paramagnetism, or an alignment against the field, χ<0, called diamagnetism.

• Diamagnetic Material. Diamagnetic materials are those that some people generally think of as non-magnetic. A magnetic field repels diamagnetic materials; an applied magnetic field creates an induced magnetic field in the opposite direction, causing a repulsive force. Diamagnetism results from changes in electron orbital motion induced by an external field. Diamagnetic materials include water, wood, most organic compounds such as petroleum and some plastics, and many metals, including copper, particularly the heavy ones with many core electrons, such as mercury, gold, and bismuth. The effect is extremely small (with susceptibilities on the order of -10-5) and in opposition to the applied field. Diamagnetic materials, like water, or water-based materials, have a relative magnetic permeability that is less than or equal to 1 and, therefore, a magnetic susceptibility less than or equal to 0 since susceptibility is defined as χv = μv − 1. Diamagnetic and paramagnetic materials are considered non-magnetic because the magnetizations are relatively small and persist only while an applied field is present. If χ (magnetic susceptibility) is negative, the material is diamagnetic. In this case, the magnetic field in the material is weakened by the induced magnetization. Magnetic fields repel diamagnetic materials. For example, the magnetic susceptibility of diamagnets such as water is χv = −9.05×10−6. The most strongly diamagnetic material is bismuth, χv = −1.66×10−4. Generally, non-magnetic materials are said to be para- or diamagnetic because they do not possess permanent magnetization without an external magnetic field.
• Paramagnetic Materials. Paramagnetic materials have permanent atomic dipoles, which are acted on individually and aligned in the direction of an external field. Diamagnetic and paramagnetic materials are considered non-magnetic because the magnetizations are relatively small and persist only while an applied field is present. If χ (magnetic susceptibility) is positive, a material can be paramagnetic. In this case, the magnetic field in the material is strengthened by induced magnetization. Paramagnetic materials include most chemical elements and some compounds. They have a relative magnetic permeability slightly greater than 1 (i.e., a small positive magnetic susceptibility) and hence are attracted to magnetic fields. Generally, non-magnetic materials are said to be para- or diamagnetic because they do not possess permanent magnetization without an external magnetic field.

A closely related property of materials is the relative permeability, which is the ratio of the permeability in a material to the permeability in a vacuum. In general, permeability is the measure of the resistance of a substance against the formation of a magnetic field.

Neither μr nor χ is constants, as they can vary with the position in the medium. They depend not only on the material but also on the magnitude of the field, H, the frequency of the applied magnetic field, humidity, temperature, and other parameters. Nearly all materials respond to a magnetic field by becoming magnetized, but most are paramagnetic with a response so faint that it is of no practical use. A few, however, contain atoms that have large dipole moments and can spontaneously magnetize (i.e., to align their dipoles in parallel). These are called ferromagnetic and ferrimagnetic materials (the second one is called ferrites for short) and are of real practical use. Ferromagnetic, ferrimagnetic, or antiferromagnetic materials possess permanent magnetization without an external magnetic field and do not have a well-defined zero-field susceptibility.

References:
Materials Science:
1. U.S. Department of Energy, Material Science. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.
2. U.S. Department of Energy, Material Science. DOE Fundamentals Handbook, Volume 2 and 2. January 1993.
3. William D. Callister, David G. Rethwisch. Materials Science and Engineering: An Introduction 9th Edition, Wiley; 9 edition (December 4, 2013), ISBN-13: 978-1118324578.
4. Eberhart, Mark (2003). Why Things Break: Understanding the World by the Way It Comes Apart. Harmony. ISBN 978-1-4000-4760-4.
5. Gaskell, David R. (1995). Introduction to the Thermodynamics of Materials (4th ed.). Taylor and Francis Publishing. ISBN 978-1-56032-992-3.
6. González-Viñas, W. & Mancini, H.L. (2004). An Introduction to Materials Science. Princeton University Press. ISBN 978-0-691-07097-1.
7. Ashby, Michael; Hugh Shercliff; David Cebon (2007). Materials: engineering, science, processing, and design (1st ed.). Butterworth-Heinemann. ISBN 978-0-7506-8391-3.
8. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.

See above:

Magnetic Properties