The magnetic response of Ni-Zn ferrites at microwave frequencies has been recently investigated by means of resonance techniques, by several authors. In this chapter, we present a review of recent results obtained on the resonant microwave absorption (electron paramagnetic resonance, EPR, and ferromagnetic resonance, FMR) in the X-band (9.5 GHz), of polycrystalline Ni-Zn ferrites (ZnxNi1-xFe2O4) for several temperature ranges. We begin at high temperatures in the paramagnetic state (
We investigate also the behavior of nonresonant properties by means of the low-field microwave absorption (LFMA). This absorption, which occurs at applied fields of the same order of magnitude than the anisotropy field,
We use as well a novel nonresonant microwave absorption technique known as magnetically modulated microwave absorption spectroscopy, MAMMAS. This technique is particularly well adapted to detect phase transitions of many types, as it is based on the change of microwave absorption regime during a change of crystalline, magnetic or electronic structure. MAMMAS is briefly described and applied to Ni-Zn 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, Fe3O4, is a natural oxide. Magnetite has also the remarkable feature of the simultaneous presence of ferrous (Fe2+) and ferric (Fe3+) 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+2T+3 2O-2 4, there are other combinations with spinel structure, which provide 3 cations with a total valency of 8, such as 2,4 (Co2GeO4), 1,3,4 (LiFeTiO4), 1,3 (Li0.5Fe2.5O4), 1,2,5 (LiNiVO4), and 1,6 (Na2WO4) 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 AB2O4, with eight A sites, 16 B sites and 32 oxygen. This unit cell can be divided into octants of edge
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) [T3+ 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, (T3+) [D2+ T3+]. In some cases, an intermediate distribution can be achieved by playing with thermal treatments, leading to (D1−δTδ)[DδT2-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.
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
divalent Ni2+, Co2+, Mn2+, Fe2+, Cu2+, Zn2+, Cd2+, Mg2+, Ca2+. Ferric ions can also be substituted, or combined with Al3+, V3+, Cr3+, Mn3+, Ga3+, In3+, etc. One of the most interesting and representative solid solution is Ni-Zn ferrites, with formula Ni1-xZnxFe2O4, with 0 ≤
2.2. Nickel-zinc ferrites
In spite of having a large cation radius, Zn2+ 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 ZnFe2O4 is a normal spinel. In contrast, divalent nickel shows a strong tendency to occupy B sites. This means that nickel ferrite, NiFe2O4 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:
The cell parameter, Fig. 2.3a, shows a linear dependence with composition
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 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.
For zinc ferrite (
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 (
A plot of saturation magnetization (at low temperatures) as a function of the composition starts at σs ~ 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
After many years, NiZn ferrites remain as an excellent system to study magnetic properties of solids.
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,
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, H0 =
with the spin
where N =
A series expansion of (3.4) for not so low temperatures (kB
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),
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 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<
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 d
4. Microwave absorption in ferrites
In this Section, we discuss the microwave absorption of polycrystalline Ni-Zn ferrites as a function of measuring temperature. The resonant mode is first considered. The description and analysis of these properties is quite useful, as NiZn ferrites offer a wide variety of magnetic structures and phenomena. The study of non resonant absorption also sheds light on magnetic structure phenomena of ferrites.
4.1. High temperatures (T >TC)
By “high temperature” we mean a temperature higher than the transition from the ordered (ferrimagnetic) phase to the disordered (paramagnetic) phase. This transition is the Curie temperature,
The reported Curie temperature for this composition is ~ 435 K (Globus et al 1977); the spectrum at 460 K corresponds therefore to the paramagnetic state. In these conditions, the thermal energy is high enough to overwhelm the internal field that results in the long range order of spins, and they are free to interact with the DC field,
(where ω is the resonance frequency, γ is the gyromagnetic factor),
4.2. Intermediate temperatures (T < TC)
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
The internal field is the combination of all the factors associated with the long range order in the ferrite: the exchange field,
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,
The internal field can therefore be expressed as:
Figure 4.2 shows the behavior of the resonance field,
The total linewidth, Δ
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, Δ
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 Δ
4.3. Low temperatures (T << TC)
Ni-Zn ferrites present other interesting phenomena at
Several features are significant in these plots. Beginning with the high temperatures (upper part of Fig. 4.4), it is evident that the amplitude of the signal at both sides of
Also, it can be observed that the field corresponding to the peak to peak magnetic field values, maxima (for negative fields) and the minima (for positive fields) increases as
By a comparison between the two sets of curves separated by
The transition from the collinear arrangement to the Yafet-Kittel triangular structure can be detected (as temperature decreases) by means of MAMMAS experiments, as shown in Fig.
4.7. As explained in Section 3, the sample is subjected to a small magnetic field, and its microwave absorption is monitored as temperature is slowly changed. The MAMMAS response exhibits, from room temperature, a continuous decrease to a minimum value at about 240 K. Then, the absorption increases again as the temperature keeps decreasing. These features point to a change in the microwave absorption regime due to a change in the material structure. In this case, all evidence is associated with the transition from the
collinear ferromagnetic structure with iron in A sites of the spinel coupled by a superexchange interaction with iron cations (and nickel cations) on B sites, for
As a conclusion, we can state that ferrites are complex materials: they offer a crystal complexity, with complex magnetic structures and complex magnetic properties. However, complexity can always be a rich source of knowledge. In addition to the well known ferromagnetic resonance methods, some significant steps can be done by investigating the microwave response of ferrites, particularly by using two novel research techniques, based on nonresonant absorption: low field and magnetically modulated microwave abosorption, which provide an original insight into these materials.