The simple classification, their magnetization M is

The response of a material when subjected to an external magnetic field is the root of magnetism. When a magnetic material is exposed to a magnetic field of strength H, the magnetic moments response to the field, they are aligned in the direction of applied magnetic field, and thereby the material is magnetized.42 The overall induced magnetization, denoted as flux density B in Tesla, is given by:
B ?= ?_0 (H ?+M ?)
with ?0 = 4? × 10-7 the permeability of vacuum, and M magnetization is given by:
M ?=m ?/V
where m is the net magnetic moment of a volume V of the magnetic material.
General speaking, all materials are to some extent magnetic and in a simple classification, their magnetization M is linearly proportional to the magnetic field H via volumetric magnetic susceptibility ?¬ , which are often defined by how the magnetic material vary with an applied magnetic field, and may be written as:
M ?= ?H ?
with ¬? a dimensionless parameter. In most crystals, the magnetic susceptibility is a tensor.
Substituting Eq. 1.3 into Eq. 1.1, Eq. 1. can be rewritten as:
B ?=?_0 (1+?) H ?=?_0 ?_r H ?
?_r=B ?/H ?
in which ?r is the relative permeability of a magnetic material.
The difference between “magnetic” materials and the rest is how they respond to an external magnetic field. The classification considers the orientation of atomic magnetic moments with respect to each other. In the following the main classes of magnetism are presented (Figure 2.10).43
Diamagnetism: A material is called a diamagnet if it has no magnetic dipoles in the absence of an external magnetic field and shows a very weak induced dipole in the opposite direction of the applied magnetic field as shown in Figure 2.10 a. Therefore, diamagnetic materials show small magnetic responses with the negative magnetic susceptibility (? 1 and 0

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