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

4.2 Intermediate temperatures (T < T
C
)
As temperature decreases below the Curie transition, several changes are apparent in the 
resonance spectra. First, the resonance field (usually taken as the intercept of the line with 
the field axis) decreases. Second, the lineshape becomes broader as T decreases, especially in 
the H > H
res
field region. These changes are due to the rise of the internal field, H
i
, leading to 
the long range order of magnetic moments. For T < T
C
, H
i
possesses a larger energy than the 
thermal energy of the ferrite. Accordingly, the total field in the Larmor relation should 
include now the contribution from the internal field, 
 
H
= H
res
+ H
i 
(4.2) 
The internal field is the combination of all the factors associated with the long range order in 
the ferrite: the exchange field, H
ex
, the anisotropy field, H
K
, the demagnetization field, H
d
, 
the porosity field, H
p
(which is the field due to the appearance of magnetic dipoles on 
pores), etc. An additional source of inhomogeneity in ferrites is associated with differences, 
as well as with disorder, in site occupancy by the cations. As discussed in Section 2, 
transition metal cations have different stabilization energies on sites with diverse symmetry, 
as the tetrahedral and octahedral sites of spinels. While some of them exhibit a clear 
“preference” for one of the sites (i.e., Zn
2+
for tetrahedral or A sites, Co
2+
, Ni
2+
, and Fe
2+
for 
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Electromagnetic Waves 
396 
octahedral or B sites), other cations can be found equally on both sites (Fe
3+
). To make things 
more complicated, it is possible to change the cation distribution by means of thermal 
treatments. The resonance phenomenon can be therefore slightly different when this 
occupancy of sites is not strictly homogeneous, since some terms of the internal field are not 
exactly the same for all the microwave absorbers.
The other source of inhomogeneity in the internal field is the disorder in the site occupancy. 
Even if the occupancy of sites is well determined (i.e., in Ni-Zn ferrite, all Zn cations on A 
sites, all Ni cations on B sites), there can be an inhomogeneous distribution of each of them 
on the sites. A simple example could be nickel ferrite, NiFe
2
O
4
, with all Ni
2+
on B sites (and 
of course, Fe
3+
on both sites). An extreme arrangement would be a long range order of Ni
2+
and Fe
3+
on octahedral sites; the cation nearest neighbor of any Ni
2+
is then one Ni
2+
and two 
Fe
3+
, and viceversa (see Fig. 2.2). On the other extreme, the “disordered” spinel would be the 
one with Ni
2+
and Fe
3+
randomly distributed on B sites. Obviously, the cation nearest 
neighbor of a given Ni
2+
could be, on equal probability another Ni
2+
or a Fe
3+
. Internal fields 
would not be strictly the same for each situation. These two sources of line broadening in 
FMR in ferrites depending on cation distribution could be written as H
dist
. To our 
knowledge, this contribution has not been discussed in literature.
The internal field can therefore be expressed as: 
 
H
i
= H
ex
+ H
K
+ H
d
+ H
p
+H
dis
(4.3) 
Figure 4.2 shows the behavior of the resonance field, H
res
, as a function of temperature. H
res
increases as temperature increases because the internal field decreases until it is 
overwhelmed by thermal vibrations at T
C
. For higher temperatures, the magnetic field 
needed to satisfy the Larmor relation has to be supplied entirely by the external field. 
200
300
400
500
1.5
2.0
2.5
3.0
H
res
(kOe)
T
(K)
Fig. 4.2. Variation of the resonance field, H
res
, with temperature for Ni
0.35
Zn
0.65
Fe
2
O
4
ferrites 
(adapted from Alvarez et al, 2010).
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The Temperature Behavior of Resonant and Non-resonant Microwave Absorption in Ni-Zn Ferrites 
397 
The total linewidth, ΔH (taken as the field between the maximum and the minimum in the 
resonance signal), has also an additive character in polycrystalline materials, and can be 
written: 
ΔH = ΔH
p
 + ΔH
K
 
+ ΔH
eddy
 
+ ΔH
d
+ ΔH
dist
(4.4) 
Where ΔH
p
 
is the linewidth broadening associated with porosity, ΔH
K
 
is due to magnetic 
anisotropy, ΔH
eddy
 
is related with eddy currents, ΔH
d
is the linewidth broadening produced 
by demagnetizing fields, and ΔH
dist
is the linewidth broadening originated by variations in 
cation distribution on the A and B sites of ferrite. It appears that anisotropy, and in particular 
magnetocrystalline anisotropy has a strong contribution to total linewidth. By measuring 
nickel ferrite with Co
2+ 
substitutions, Sirvetz & Saunders (1956) observed a minimum in 
linewitdth for the composition corresponding to the compensation of anisotropies (x = 0.025 in 
Co
x
Ni
1-x
Fe
2
O
4
), since nickel ferrite has a small negative contribution (single-ion contribution to 
anisotropy), while cobalt cations provide a strong positive contribution to the total 
magnetocrystalline anisotropy. More recently, Byun et al (2000) showed that in the case of Co-
substituted NiZnCu ferrites, ΔH increases for a Co composition higher than the 
magnetocrystalline anisotropy compensation point. Another source of linewidth broadening is 
certainly related with the polycrystalline nature of most samples. By modeling one ensemble 
of single domain nanoparticles, Sukhov et al (2008) have shown that the random distribution of 
anisotropy axis is directly associated with the broadening of the FMR signal. 
Figure 4.3 shows the behavior of linewidth with temperature for the same sample than Figs. 
4.2 and 4.1. A clear change in slope can be observed at about 430 K, and a smooth variation 
is also apparent at about 250 K. The former is associated with the Curie transition, which for 
this Ni/Zn ratio is ~ 430 K (Valenzuela, 2005a), and the latter with a change in magnetic 
structure which will be discussed later. By comparison with Fig. 4.2 it appears that 
linewidth, ΔH, is more sensitive to structural changes than the resonance field, H
res
.
100
200
300
400
500
0.0
0.2
0.4
0.6
0.8
1.0
Δ
H
(k
Oe)
T
(K)
Fig. 4.3. Variations in linewidth with temperature, for Ni
0.35
Zn
0.65
Fe
2
O
4
ferrites (adapted 
from Alvarez et al, 2010).
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Electromagnetic Waves 
398 
The increase in resonance field as temperature rises is due to the fact that internal field 
decreases (exchange interaction, anisotropy field, and the fields associated with magnetization, 
i.e., demagnetization fields on surfaces including the ones created by porosity). In contrast, 
linewidth decreases with temperature, essentially because one of the major contributions to 
ΔH is originated by magnetocrystalline anisotropy, and this contribution is proportional to this 
parameter (Byun et al 2000). At T > T
C
, as discussed in Section 4.1, the resonance line becomes 
narrow and symmetrical, as the spectrum for T = 460 K in Fig. 4.1.