Page 296 - Electrical Properties of Materials

278 Magnetic materials

11.7.1 The Stern–Gerlach experiment
The proof for the existence of discrete magnetic moments was first obtained by
Otto Stern received the Nobel Stern and Gerlach in an experiment shown schematically in Fig. 11.17. Atoms
Prize in 1943. of a chosen substance (it was silver in the first experiment) are evaporated in
the oven. They move then with the average thermal velocity, and those crossing
the diaphragms S 1 and S 2 may be expected to reach the target plane in a straight
line—provided they are non-magnetic. If, however, they do possess a magnetic
moment, they will experience a force expressed by

∂H
F =(μ m ) z μ 0 . (11.40)
∂z

Thus, the deflection of the atoms in the vertical plane depends on the mag-
nitude of this force. ∂H/∂z is determined by the design of the magnet [a strong
variation in the z-component of the magnetic field may be achieved by making
the upper pole piece wedge-shaped as shown in Fig. 11.17(b)] and is a con-
stant in the experiment. Hence, the actual amount of deflection is a measure of
(μ m ) z .
Were the magnetic moments entirely randomly oriented, the trace of the
atoms on the target plane would be a uniform smear along a vertical line. But
that is not what happens in practice. The atoms in the target plane appear in
distinct spots as shown in Fig. 11.17(c).
For silver J = 1 , and the beam is duly split into two, corresponding with
2
the angular momenta z = /2 and – /2. If the experiment is repeated with
other substances, the result is always the same. One gets a discrete number of
beams, corresponding with the discrete number of angular momenta the atom
may have.

11.7.2 Paramagnetism
We are now in a position to work out, with the aid of quantum theory, the
paramagnetic susceptibility of a substance containing atoms with quantum
numbers, J = 0. When we apply a magnetic field, all the atoms will have
some magnetic moments in the direction of the magnetic field. The relative
numbers of atoms, possessing the same angular momentum, are determined
again by Boltzmann statistics. The mathematical procedure for obtaining the

Target Target
plane plane
S S Magnet
1 2
Oven N
Atoms
deposited
S

(a) (b) (c)
Fig. 11.17
Schematic representation of the Stern–Gerlach experiment.