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

3. Microwave absorption 
Microwave absorption has become a very powerful investigation and characterization tool 
in the study of magnetic materials, both in the paramagnetic, disordered state (electron 
paramagnetic resonance, EPR) and the ferri or ferromagnetic, ordered phase (electron 
ferromagnetic resonance, FMR) (see, for instance, Kittel 2005, Pilbrow 1990). The radiation 
emerging from interaction with a solid possesses changes (with respect to the incident 
radiation) that in principle, allow deducing the structural and magnetic properties of the 
material. To simplify, we can consider the interaction of a spin with a constant magnetic 
field. If the magnetic moment is originated only by the spin,
µ = gµ
B
S
= γS
(3.1) 
where g is the gyromagnetic factor (in general depending on L and S, the quantum 
mechanical numbers of orbital and spin momenta), γ is the total gyromagnetic ratio. In an 
external field, H
0
= H
0
µ
z
, and energy is expressed as:
 
E
= - µ•H = - µ
z
H
= - γm
s
ħH (3.2) 
with the spin m
s
= ± ½ , corresponding to the two orientation of the magnetic moment, i.e., 
parallel (m
s
= - ½), or antiparallel (m
s
= + ½) to the magnetic field; the population of both 
levels is given by the Boltzmann statistics,
 f 
= N
+
/N
-
= exp {-ΔE/k
B
T
}
(3.3) 
where N = N
+
+ N
-
is the total population of atoms with spin parallel (N
-
) and antiparallel 
(N
+
) to the magnetic field, k
B
is the Boltzmann constant, and -ΔE the energy difference 
between the two levels. The net magnetic moment per atom is then: 
µ
z
= (gµ
B
/2)[( N
+
+ N
-
)/N] = (gµ
B
/2)[(1-f)/(1+f)] (3.4) 
A series expansion of (3.4) for not so low temperatures (k
B
T
>> ΔE) leads to the Curie law,
µ
z
 = (gµ
B
/3)(ΔE/k
B
T
) = CH/T (3.5) 
with C = gµ
B2
/3k
B
. It is possible to induce transitions between the two spin states by 
application of electromagnetic radiation of the relevant frequency, which satisfies the Bohr 
condition, 
E
H
H
γ
ω
ω
γ
Δ =
=
=
ħ
ħ
(3.6) 
This shows the resonance conditions. Equation (3.6) is also known as the Larmor resonance 
condition. 
In the case of magnetic materials with a spontaneous magnetization (ferri and ferromagnetic 
materials), H includes the internal field, in most cases leading to a lower external field 
needed to attain the resonance conditions. Both EPR and FMR have been used to investigate 
a wide variety of materials such as ferrites (Montiel et al 2004, Wu et al 2006) and 
amorphous alloys (Valenzuela et al 2005b, Montiel et al 2006).
In addition to these methods, nonresonant microwave absorption, or low field microwave 
absorption (LFMA) has been observed in many materials, such as amorphous metallic thin 
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Electromagnetic Waves 
394 
films (Rivoire & Suran 1995), amorphous ribbons (Medina et al 1999), glass coated 
amorphous microwires (Chiriac et al 2000), ferrites (Montiel et al 2004), multilayer thin films 
(de Cos et al 2007). LFMA is strongly associated with magnetic order since in all cases it is 
present only below the transition temperature between the paramagnetic-ferrimagnetic (or 
para-ferromagnetic) phases. LFMA has also shown to be sensitive to mechanical stresses 
(Montiel et al 2006). In this chapter, we show that LFMA can also be used to detect changes 
in the magnetic structure. From the experimental point of view, LFMA needs an accurate 
measurement of the magnetic field for low fields, and the possibility to reverse the field, i.e., 
typically in the -1000< H < +1000 Oe. This can be challenging in the case of large 
electromagnets, which tend to keep a non negligible remanent field.
Another nonresonant method recently proposed for the investigation of magnetic transition 
is the method known as magnetically modulated microwave absorption spectroscopy 
(MAMMAS) (Alvarez & Zamorano 2004, Alvarez et al 2007), which is based on a simple 
idea: the nonresonant microwave absorption regime in a given material changes when a 
phase transition occurs. Since the microwave absorption depends on the wide definition of 
structure (crystalline, electronic, magnetic, etc.), virtually any phase change can be detected, 
with the significant advantage that microwave absorption is extremely sensitive. 
Experimentally, the sample is subjected to a low magnetic field (clearly lower than the 
resonance field in the temperature range), and the microwave absorption is measured as the 
sample temperature is slowly varied. Phase transitions appear typically as a minimum in a 
dP/dH vs T plot.