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.