Page 301 - Electrical Properties of Materials

Magnetic resonance 283

means loss of photons, or in other words, absorption of electromagnetic energy.
Hence, there is a dip in the transmission spectrum as shown in Fig. 11.21. Since
the absorption occurs rather sharply in the vicinity of the frequency E/h,it
is referred to as resonant absorption, and the whole phenomenon is known as 1
paramagnetic resonance. Transmission
In practice the energy diagram is not quite like the one shown in Fig. 11.20
(because of the presence of local electric fields) and a practical measuring ap-
paratus is much more complicated than our simple waveguide (in which the
absorption would hardly be noticeable) but the principle is the same.
ΔE f
h
11.8.2 Electron spin resonance
Fig. 11.21
This is really a special case of paramagnetic resonance, when only the spin of Transmission of electromagnetic
the electron matters. It is mainly used by organic chemists as a tool to analyse
waves as a function of frequency
chemical reactions. When chemical bonds break up, electrons may be left un-
through a paramagnetic material.
paired, that is the ‘fragments’ may possess a net spin (in which case they are There is resonant absorption where
called free radicals). The resonant absorption of electromagnetic waves indic- hf = E.
ates the presence of free radicals, and the magnitude of the response can serve
as a measure of their concentration.

11.8.3 Ferromagnetic, antiferromagnetic, and ferrimagnetic
resonance
When a crystal with ordered magnetic moments is illuminated by an electro-
magnetic wave, the mechanism of resonant absorption is quite complicated,
owing to the interaction of the magnetic moments. The resonant frequencies
cannot be predicted from first principles (though semiclassical theories exist)
but they have been measured under various conditions for all three types of
materials.

11.8.4 Nuclear magnetic resonance
If electrons, by virtue of their spins, can cause resonant absorption of electro-
magnetic waves, one would expect protons to behave in a similar manner. The
main difference between the two particles is in mass and in the sign of the
electric charge; so the analogous formula,
1 e
f = g μ 0 H, (11.49) m p is the mass of the proton.
2π 2m p
should apply.
The linear dependence on magnetic field is indeed found experimentally, but
the value of g is not 2 but 5.58, indicating that the proton is a more complex
particle than the electron.
Neutrons also possess a spin, so they can also be excited from spin ‘down’
into spin ‘up’ states. Although they are electrically neutral, the resonant
frequency can be expressed in the same way, and the measured g-factor is 3.86.
The resonance is sharp in liquids but broader, by a few orders of magnitude,
in solids. The reason for this is that the nuclear moments are affected by the
local fields, which may vary in a solid from place to place but average to zero
in a liquid.