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

2.2 Nickel-zinc ferrites
In spite of having a large cation radius, Zn
2+
has a strong preference for A sites, which are 
smaller than B sites. Ferric ions manifest no preference for A or B sites. Therefore, zinc ferrite 
ZnFe
2
O
4
is a normal spinel. In contrast, divalent nickel shows a strong tendency to occupy B 
sites. This means that nickel ferrite, NiFe
2
O
4 
tends to be an inverse spinel. Ni-Zn solid 
solutions (when prepared by solid state reaction with a slow cooling from the sintering 
temperature) exhibit therefore a cation distribution which is normal with respect to Zn, and 
inverse for Ni. This means that Zn will occupy A sites (with ferric ions completing the 
“filling” of A sites), while nickel and the remaining ferric cations share B sites: 
(Zn
x
Fe
1-x
) [Ni
1-x
Fe
1+x
] 
The cell parameter, Fig. 2.3a, shows a linear dependence with composition x. Since Zn
2+
is a 
relatively large cation occupying the small A sites, the cell parameter increases with Zn 
content. The Curie temperature exhibits a strong decrease with zinc concentration, Fig. 2.3b. 
For x = 1, zinc ferrite (ZnFe
2
O
4
) manifests an antiferromagnetic behavior with a Néel 
temperature of 9 K. While the increase in cell parameter is quite linear, the decrease in T
C
is 
more rapid. This fact can be understood by recalling that as Zn content increases, in addition 
to the expansion of the unit cell (and therefore, cations become far apart), there is an effect of 
dilution, since Zn cations are diamagnetic. However, there is also a change in magnetic 
structure, since for the very high content of Zn, the ferrite changes from ferrimagnetic (with 
a high T
C
= 858 K for x = 0), to an antiferromagnetic arrangement with a very low Néel 
temperature. This result will be briefly discussed below.
(a)
(b) 
Fig. 2.3. Variation in the cell parameter, (a), and the Curie transition, (b), both as a function 
of Zn content x (Adapted from Valenzuela, 2005a).
The ferrimagnetic order in ferrites is the result of superexchange interactions. The 3d 
unpaired spins of transition metals exhibit an antiparallel arrangement which occurs 
through anions, as schematically shown in Fig. 2.4. This interaction takes place by means of 
0.0
0.2
0.4
0.6
0.8
1.0
0
200
400
600
800
T
C
(K
)
x
0.0
0.2
0.4
0.6
0.8
1.0
8.32
8.36
8.40
8.44
a
(A
)
x 
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The Temperature Behavior of Resonant and Non-resonant Microwave Absorption in Ni-Zn Ferrites 
391 
p orbitals of oxygen. Since p orbitals are linear, this interaction sensitively depends not only 
on the distance between cations and anion, but also on the angle between them. It is 
expected to be a maximum for a 180° angle. The first discussion on superexchange 
interactions was proposed by Anderson (1959). 
The main superexchange interactions in spinels are the A-O-B and the B-O-B interactions. 
The former takes place between a cation in an A site, which becomes antiparallel to cations 
on the nearest B site. The latter consists on the antiparallel arrangement between two cations 
on neighboring B sites. The A-O-B interaction is expected to be significantly stronger than 
the B-O-B one, since the angle between these sites is close to 180° (see Fig. 2.2 (c)); the B-O-B 
geometry involves a 90° angle, quite different from the linear geometry of p orbitals.
Fig. 2.4. Schematical representation of the superechange interactions in oxides. The spins in 
the unfilled 3d orbitals of transitions metals, on the sides, can interact with cation nearest 
neighbors through the 2p oxygen orbitals, in the center. This interaction can be extremely 
strong, leading to high Curie temperatures. 
For x = 0, the cation distribution is as follows: (Fe)[NiFe]. By assuming that A-O-B 
interaction is dominant, the iron in the A site will be aligned in an antiparallel direction with 
respect to spins of cations on B sites. If we simplify the magnetic structure of Fig. 2.2 (c) and 
represent one A site and two B sites around an oxygen anion (in the basic formula, the ratio 
of A to B sites is ½), and if all of them are assumed to be on the same plane, we can draw a 
cartoon like the one on Fig. 2.3. Nickel ferrite, with one Fe
3+
on the A site, the other one on a 
B site and the Ni on the other B site should have a magnetic structure like the one in Fig. 2.5 
(a). The interaction Fe(A)-O-Fe(B) is among the strongest in spinels, as Fe
3+
has a 3d orbital 
half-filled and the angle between sites is close to 180°. Accordingly, the Curie temperature is 
maximum for this family (858 K), and it has the same value for most inverse spinels (such as 
CoFe
2
O
4
, for instance). 
For zinc ferrite (x = 1), the site occupancy is: (Zn) [Fe
2
]. The A site contains only Zn ions 
(with no magnetic moment) and therefore the only interaction in the system is B-O-B. Irons 
on both B sites become antiparallel and the ferrite is antiferromagnetic, with a Néel 
temperature of 9 K. This low value of superexchange interaction is explained mostly by the 
angle between interacting cations (90°), and also by the expansion of the unit cell, as a 
consequence of the larger size of Zn cations [Fig. 2.3.(a)]. For compositions in the 0.5 < x < 
0.8 range, with a distribution: (Zn
x
Fe
1-x
)[Ni
1-x
Fe
1+x
], where both interactions become 
comparable, the magnetic structure can be represented by a triangular arrangement known 
as the Yafet-Kittel structure, first proposed by these authors (Yafet and Kittel 1952). 
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Electromagnetic Waves 
392 
(a) 
(b) 
(c) 
Fig. 2.5. Simplified representation of an A and two B sites around an oxygen. Arrows 
represent the spins as they can be expected for (a) nickel ferrite (x = 0), (b) zinc ferrite (x = 1), 
and (c) a composition rich in Zn (0.5 < x < 0.8). 
A plot of saturation magnetization (at low temperatures) as a function of the composition 
starts at σ
s
~ 2.33 Bohr magneton/formula unit, since the ferric cations are in opposition 
(Fig. 2.5 (a)) leaving only the nickel magnetic moment as a result, as shown in Fig. 2.6. If the 
A-O-B interaction were dominant on all the composition range, the total magnetic moment 
would exhibit an increase with x up to a value of 10 Bohr magnetons for x = 1 (broken line in 
Fig. 2.6), a condition with all A sites occupied by Zn (with no magnetic moment) and both B 
sites with Fe, and spins in a parallel orientation. But the weakening of this interaction results 
in the competition of B-O-B interaction, leading to the antiparallel arrangement on sites B, 
with the variations in saturation magnetization illustrated in Fig. 2.6.
0.0
0.2
0.4
0.6
0.8
1.0
0
2
4
6
8
10
σ
s
/f
o
rm
ul
a un
it
(
µ
B
)
x
Fig. 2.6. Behavior of saturation magnetization of Ni
1-x
Zn
x
Fe
2
O
4
ferrites at very low 
temperature, as a function of Zn content. 
After many years, NiZn ferrites remain as an excellent system to study magnetic properties 
of solids.
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The Temperature Behavior of Resonant and Non-resonant Microwave Absorption in Ni-Zn Ferrites 
393