Section 15_Magnetic_Properties_1

Section 15_Magnetic_Properties_1 - Physics 927 E.Y.Tsymbal...

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Physics 927 E.Y.Tsymbal 1 Section 15: Magnetic properties of materials Definition of fundamental quantities When a material medium is placed in a magnetic field, the medium is magnetized. This magnetization is described by the magnetization vector M , the dipole moment per unit volume. Since the magnetization is induced by the field, we may assume that M is proportional to H . That is, χ = M B . (1) The proportionality constant is known as the magnetic susceptibility of the medium. Note that the magnetic susceptibility bears no physical relationship to the electric susceptibility, although the same symbol is used for both. Note also that our discussion assumes that the medium is magnetically isotropic. But real crystals are anisotropic, and the susceptibility is represented by a second-rank tensor. In order to avoid mathematical complications, however, we shall ignore anisotropic effects in our treatment. Note, that in Eq. (1) we assumed that M is proportional to B , the external field, and in doing so we ignored such things as demagnetization field, which were included in the electric case. The neglect of these factors is justifiable in the case of paramagnetic and diamagnetic materials because M is very small compared to B (typically 5 / ~10 = B M ), unlike the electric case, in which ~ 1. But when we deal with ferromagnetic materials, where M is quite large, this omission is no longer tenable, and the above effects must be included. Because of small value of the magnetic susceptibility we will not make distinction between magnetic field and magnetic induction. Note also that in Eq.(1) can be dependent on the applied magnetic field. In this case, we can define the magnetic susceptibility as follows M B = . (2) The magnetization can be defined as E M B = , (3) where E is the total energy of the system. Definitions (2) and (3) are more general and can be used in calculations. Classification of materials All magnetic materials may be grouped into three magnetic classes, depending on the magnetic ordering and the sign, magnitude and temperature dependence of the magnetic susceptibility. We will discuss properties of five classes of materials: diamagnetic, paramagnetic, ferromagnetic, antiferromagnetic and ferrimagnetic. There is no magnetic order at any temperature in diamagnetic and paramagnetic materials, whereas there is a magnetic order at low temperatures in ferromagnetic, antiferromagnetic and ferrimagnetic materials.
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Physics 927 E.Y.Tsymbal 2 In diamagnetic materials the magnetic susceptibility is negative. Usually its magnitude is of the order of -10 -6 to -10 -5 . The negative value of the susceptibility means that in an applied magnetic field diamagnetic materials acquire the magnetization, which is pointed opposite to the applied field. In diamagnetic materials the susceptibility nearly has a constant value independent of temperature. Ionic crystals and inert gas atoms are diamagnetic. These substances have atoms or ions with
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This note was uploaded on 03/11/2012 for the course PHYSICS 927 taught by Professor Staff during the Fall '11 term at UNL.

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Section 15_Magnetic_Properties_1 - Physics 927 E.Y.Tsymbal...

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