Fundamentals of Electromagnetics - RF/Microwave Interaction with Biological Tissues - page 15

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tan d = (1.27)

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As for the electric polarization, the imaginary part of the permeability is
nonzero only when the real part varies as a function of frequency. Further-
more, each part can be calculated from the variation of the other part over the
whole frequency range.
In certain materials, the application of a magnetic field may induce an
extremely strong magnetization, of the order of 10 8 A m -1 , which is 10 times
more than the highest fields which can be produced in laboratory. This char-
acterizes the phenomena that are called ferromagnetism , ferrimagnetim , anti-
ferromagnetism , and antiferrimagnetism . An even simple explanation of the
underlying physics is far beyond the scope of this topic. Classical physics
indeed fails in trying to model these phenomena. In fact, quantitative model-
ing of ferromagnetism was the reason Dirac developed quantum mechanics.
The phenomenon is based on an exchange probability for some electrons
between neighboring atoms in the crystalline structure, which corresponds to
a spin coupling. The interaction from neighbor to neighbor is positive if the
spins are parallel, which characterizes ferromagnetism; it is negative if the
spins are antiparallel, which characterizes antiferromagnetism. The conditions
for the exchange to take place are the following:

1. The distance between the electron and nucleus may be neither too large
nor too small: it must be of the order of 0.27-0.30 nm; the materials
in which this distance is smaller than 0.26-0.27 nm are practically
antiferromagnetic.
2. The atoms must have nonsaturated layers to be able to accept electrons.
3. The temperature has to be lower than a critical temperature, called the
Curie temperature , to avoid too much thermal disorder; above this tem-
perature, the materials become paramagnetic.

Conditions 1 and 2 imply the material has a nonsaturated layer at the right
distance from the nucleus: It is the third layer, and it is nonsaturated in the
case of iron, nickel, and cobalt, which are the ferromagnetic materials.
Ferrites are ferrimagnetic materials. They are ceramics, generally composed
of oxides of iron and other metals. Their chemical formula is very often
ZO·Fe 2 O 3 , where Z represents one or more divalent metals (cobalt, copper,
manganese, nickel, and zinc). In most common ferrites, Z is for the combina-
tions Mn + Zn or Ni + Zn. The size of the grains in ferrites is of the order of
1-20 mm. The oxygen anions play an important role in ferrimagnetics: Their
presence results in a magnetization much smaller than that of ferromagnetic
materials, because the magnetic cations are distributed in a nonmagnetic
oxygen network. Furthermore, because of the oxygen ions, the alignment of
the cation moments is antiparallel in some places of the network. When the
antiparallel subnetworks have magnetic moments equal per unit volume, the
material is antiferromagnetic.