18 The Temperature Behavior of Resonant and Non-resonant Microwave Absorption in Ni-Zn Ferrites

2. Ferrites
Ferrites, also known as magnetic ceramics, are a very well established group of magnetic 
materials (Valenzuela, 2005a). Ferrites possess three different crystal structures: spinels, 
garnets, which belong to cubic systems, and hexagonal, which can be considered as derived 
from magnetoplumbite. In this review, the focus will be on spinel ferrites, and in particular 
on the Ni-Zn “family” which will be taken as an example. A brief review of crystal structure, 
magnetic structure and magnetic properties of these ferrites is given. 
2.1 Spinel structure
The spinel structure is a cubic structure extremely stable, with a dominant ionic character. In 
addition to charge compensation, the cation/anion ratio is ¾. More than 140 oxides and 80 
sulphides have been systematically studied (Hill & al 1979). Most of the commercially 
important spinels are synthetic, but the most important and probably the oldest one with 
practical applications, magnetite, Fe
3
O
4
, is a natural oxide. Magnetite has also the 
remarkable feature of the simultaneous presence of ferrous (Fe
2+
) and ferric (Fe
3+
) iron on 
equivalent crystal sites, which provides unusual electrical and magnetic properties. In 
addition to the 2,3 spinels (2,3 refers to divalent and trivalent cations, respectively), formed 
by a combination of one divalent and two trivalent cations to balance the 8 negative charges 
provided by the oxygen in the formula D
+2
T
+32
O
-24
, there are other combinations with 
spinel structure, which provide 3 cations with a total valency of 8, such as 2,4 (Co
2
GeO
4
), 
1,3,4 (LiFeTiO
4
), 1,3 (Li
0.5
Fe
2.5
O
4
), 1,2,5 (LiNiVO
4
), and 1,6 (Na
2
WO
4
) spinels.
The crystal structure, belonging to the Fd3m space group, can be described as a close-packed 
(fcc) arrangement of oxygens, which includes tetrahedral and octahedral interstitial sites. One-
half of the interstitial octahedral sites and one-eighth of the tetrahedral sites are occupied by 
cations. They are known also as “A” sites (tetrahedral) and “B” sites (octahedral). 
The unit cell is formed by eight formula units AB
2
O
4
, with eight A sites, 16 B sites and 32 
oxygen. This unit cell can be divided into octants of edge a/2 (a = unit cell parameter) for a 
better view of the two sites, Fig. 2.1. In this representation, a tetrahedral cation is taken as 
the origin of the cell. The nearest neighbors of both sites are illustrated in Fig. 2.2.
When divalent cations occupy the A sites and trivalent cations enter the B sites, the spinel is 
known as having a “normal” cation distribution. This arrangement can be represented as 
(D
+2
) [T
3+2
]. A variant of this structure is the “inverse” spinel, where A sites contain a 
trivalent cation, while B sites contain the divalent and the remaining trivalent cation, (T
3+
) 
[D
2+
T
3+
]. In some cases, an intermediate distribution can be achieved by playing with 
thermal treatments, leading to (D
1−δ
T
δ
)[D
δ
T
2-δ
], where δ is the “degree of inversion”. The 
distribution of cations on the two spinel sites depend on a complex interplay of cation 
radius, electrostatic energy, crystal field energy, and polarization effects (covalency 
contribution, for instance).
A remarkable feature of stability of spinel structure is that it can form an extremely large 
variety of total solid solutions. Some conditions apply; first, electrical neutrality, i.e., the 
addition of the charge of all cations should balance oxygen total charge (-8 for a formula); 
second, the ratio of cations/oxygen should remain ¾, and finally, there should be relatively 
small differences between cation radii. In solid solutions, composition can be changed on a 
continuous basis, leading also to continuous variations in the physical properties. This 
allows a very precise tailoring of magnetic properties, which is a major advantage for any 
application. Divalent cation in the 2,3 spinel formula can be formed by any combination of 
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The Temperature Behavior of Resonant and Non-resonant Microwave Absorption in Ni-Zn Ferrites 
389 
Fig. 2.1. Unit cell of the spinel structure. Cations on A sites are represented by small black 
circles, cations on octahedral B sites by small open circles, and large circles are oxygens. The 
unit cell parameter is a.
Fig. 2.2. Nearest neighbors of a) A site, b) B site and c) oxygen site. 
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Electromagnetic Waves 
390 
divalent Ni
2+
, Co
2+
, Mn
2+
, Fe
2+
, Cu
2+
, Zn
2+
, Cd
2+
, Mg
2+
, Ca
2+
. Ferric ions can also be 
substituted, or combined with Al
3+
, V
3+
, Cr
3+
, Mn
3+
, Ga
3+
, In
3+
, etc. One of the most 
interesting and representative solid solution is Ni-Zn ferrites, with formula Ni
1-x
Zn
x
Fe
2
O
4
, 
with 0 
≤ x ≤ 1.0 (Ravindranathan & Patil, 1987).