27.2 Theory of Diamagnetism and Paramagnetism

The origin of the magnetic behavior of any substance can be traced to the atomic structure and arrangements of a large number of atoms in bulk matter.

Every atom can be considered to be a short magnet having essentially dipole moment on account of similarity of orbiting electrons with a current carrying coil.

However, electrons have two types of angular momenta and each type of angular momentum is associated with magnetic dipole moment. These angular momenta of electrons are called orbital angular momentum and spin angular momentu. Rigorous treatment is out of the scope, but it should be mentioned that is purely a Quantum degree of freedom. The resultant dipole moments due to & s and the effect of the external fields on them, result into three types of magnetism.

The dipole moment s, due to spin angular momentum of each electron is not appreciably affected by moderate fields, whereas l due to (which is in opposite direction i.e. & i are anti-parallel to each other) is found to have changed, the change being always opposite in direction to the applied magnetic field. This qualitative description enables us to understand the magnetic behavior as follows.

Diamagnets

Individual atoms have total s = 0 due to all (even numbered) electrons. According to Pauli's exclusion principle; total _l # 0. But due to randomness in arrangement of a large number of atoms, the substance has net = 0. However, when placed in a uniform external field, the atoms will orient their changed _l anti-parallel to the field. Hence, net induced in the substance will also be anti-parallel to the field B and such a substance will be repelled away.

Paramagnetism

Individual atoms have total _l # 0 due to all (odd numbered) electrons. Each atom is itself a short magnet, having net dipole moment # 0. However, randomness (due to thermal agitation) of the orientations of of all atoms implies that total = 0 in the substance. But, when external field is applied, the alignment of net of each atom becomes parallel to . Despite the effect on _l being opposite to that on , there is no effect of on ( which is greater than _l ). This results in a resultant in s direction and this is aligned along by the torque exerted by .

The substance therefore acquires small net dipole moment that is induced, parallel to the field, and therefore weak attraction occurs.

The induced dipole moment reduces to zero, i.e. the randomness in orientations of s of each atoms reverts when the external field in removed. The substance therefore becomes de-magnetized. The paramagnets are therefore temporary magnets, having magnetism induced only as long as external fields are imposed.

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Index

Origin of Magnetism

27.1 Diamagnetism, Paramagnetism and Ferromagnetism
27.2 Theory of Diamagnetism and paramagnetism
27.3 Theory of Ferromagnetism and curie temperature of Ferromagnets

Chapter 28