122 CHAPTER 12. PERMANENT MAGNETS12.7. HARD FERRITESThe ferrites used for permanent-magnet purposes are the hexaferrites, also called
hard ferrites or M-type ferrites. These are hexagonal compounds of the general formula
with Me = Ba, Sr, or Pb which owe their hard-magnetic properties to their
comparatively large magnetocrystalline anisotropy. The hard ferrites play a dominant role
on the permanent-magnet market, which is mainly due to the low price per unit of available
energy, the wide availability of the raw materials, and the high chemical stability.
The M ferrites crystallize in the magnetoplumbite structure, characterized by a close
packing of oxygen and Me ions with Fe atoms at the interstitial positions. There are five of
such interstitial positions, meaning that the magnetically ordered structure is composed of
five different magnetic sublattices.
Each of the ions in carries a magnetic moment of The moment
of the Fe ions residing on the same crystallographic position are ferromagnetically aligned
but the coupling between Fe moments at the different crystallographic positions may be
ferromagnetic as well as antiferromagnetic. All these couplings are determined by the so-
called superexchange interaction, mediated by the O atoms. There is a strong preference
for ferromagnetic coupling when the angle Fe-O-Fe approaches 180° and the distance
Fe–O–Fe becomes smaller. This is the reason why the magnetic moments of the five
Fe sublattices are not mutually parallel. Two of the Fe sublattices have their moments
oriented antiparallel to those of the other three. This ferrimagnetic arrangement of the
resultant spin structure leads to a net moment per unit cell of only (at 4.2 K).
More details regarding the superexchange interaction can be found in the review of Guillot
(1994).
The Curie temperatures of the compounds are fairly high and equal to
740, 750, and 725 K for Me = Ba, Sr, and Pb, respectively. Of particular interest in the
M ferrites is the temperature dependence of the saturation polarization Results for the
Ba compound are shown in Fig. 12.7.1. It may be inferred from this figure that between
and room temperature, the values increase with decreasing temperature much more
slowly than would be expected on the basis of the Brillouin function. As a consequence,
while the temperature coefficient of
these materials have a relatively low value of at room temperature (much lower than the
value corresponding to the saturation moment of per formula unit mentioned above)
is fairly high
The magnetocrystalline anisotropy in the M ferrites is generally considered as arising
from spin–orbit coupling. It is characterized by a comparatively high positive value of the
anisotropy constant while higher order constants are negligibly small. This
situation corresponds to an easy magnetization direction along the c-axis.
The temperature dependence of for is shown in Fig. 12.7.1, together with
the temperature dependence of the anisotropy field Because decreases
more strongly with temperature than in the lower temperature range, one finds that
first slightly increases with temperature before it eventually decreases. This is a rather
unusual behavior of the anisotropy field. It leads to an unusual behavior also for the coer
civity. In magnets made of hard ferrites, the coercivity increases when the temperature is
raised above room temperature whereas it decreases in all other permanent-magnet mate
rials known. This is an advantageous property for high-temperature applications of such
magnets.