Myndyk c , R. Witte a , J. Menzel e , R. Schuster bf , H. Hahn a , P. Heitjans bg and K.
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Box , Nekemte, Ethiopia. The fundamental requirements for the shift of critical frequency to microwave frequencies are smaller grains with single domain, high resistivity, high saturation magnetization, moderate permeability, moderate magnetic anisotropy, and low spin relaxation time.
With these guidelines an attempt to produce high performance ferrite for high frequency applications the present work aimed to synthesize cobalt substituted Ni-Zn ferrites using sol-gel method. Investigation of effects of cobalt on crystallite size, saturation magnetization, initial permeability, magnetic anisotropy, and spin relaxation time reveals the suitability of these materials for high frequency applications.
Further in this paper cat ion distribution was proposed from the basis of variations in these properties. The results of this paper are thus useful to tailor the properties apt for high frequency applications.
Ferrites are the most widely used cores in high frequency power electronics, broadband transformers, pulse transformers, antennas, and sensors because of their excellent magnetic and electrical properties.
However, at higher frequencies, magnetic cores with improved resistivity, high saturation magnetization, and high permeability are inevitable to minimize eddy current losses and magnetic losses [ 1 — 4 ]. The limiting frequency is controlled by spin rotation of domains and as such the use of ferrite core in the GHz range is considered to be a complicated task.
The recent developments in nanotechnology signify that the electrical resistivity can be increased manyfold with the generation of a vast number of grains and grain boundaries if the material is produced in nanoform [ 6 , 7 ].
The improvement in saturation magnetization can be achieved by modifying the crystallite size of the material comparable to characteristic length, a responsible parameter for exchange coupling to take place among the nanograins [ 8 , 9 ]. The efficient performance of the core at higher frequencies is expected to be synchronized with the rotation of domains under a small AC field and the process of rotation is known to be critically affected by magnetic anisotropy [ 10 ]. The magneto crystalline anisotropy determines the direction and stability of the magnetization within the material.
Critical size below which a spherical particle exists as a single-magnetic domain depends on magnetic anisotropy. Also, the coercivity and the permeability are controlled by the magnetic anisotropy constant. Thus in order to shift the critical frequency of operation to GHz range, it is necessary to achieve the best combination between saturation magnetization, resistivity, particle size, and initial permeability which requires a wide range of variations in magnetic anisotropy.
Cobalt ions with their slight higher magnetic moment as compared to that of nickel have a tendency to occupy both tetrahedral and octahedral interstitial sites of nickel zinc ferrite keeping the majority of cobalt ions at -site [ 11 ]. The presence of cobalt at -site, in general, produces a large positive magnetic anisotropy due to trigonal distortion of the lattice [ 12 , 13 ].
The incorporation of cobalt in nickel zinc ferrite of negative uniaxial anisotropy ensures the combination of low or vanishing magneto crystalline anisotropy and adjustable induced anisotropy. The wide range of variation small negative value to high positive value in magnetic anisotropy due to cobalt substitution in nickel zinc ferrites permits understanding clearly the changes taking place in saturation magnetization, coercivity, and initial permeability with reference to shift of critical frequency.
The method of preparation of samples was described elsewhere [ 14 ]. The X-rays were produced using a sealed tube and the wavelength of X-ray was 0. The X-rays were detected using a fast counting detector based on silicon strip technology Bruker LynxEye detector. The TEM Hitachi H at required magnifications is used to obtain structural information from the samples that are very much thin to transmit electrons.
The Curie temperature was determined using the Soohoo method [ 15 ]. X-ray diffraction patterns of and samples are shown in Figures 1 a and 1 b. The intense sharp peaks indicate well crystalline single phase spinel structure.
No peaks corresponding to any additional crystalline component are detected in the patterns. Accurate estimation of lattice constant has been done from the extrapolation of calculated lattice constant against the Nelson-Riley function [ 16 ]: for which the function is zero.
Figures 2 a and 2 b show the variation of lattice constant and crystallite size with cobalt concentration. An increase in lattice constant from 8. The steep increase in crystallite size has been noticed for initial concentrations and a small increase at higher concentrations.
The average particle size has been estimated from volume averages of number of TEM pictures for a particular sample. Figure 2 b shows the variation in particle size with cobalt concentration. The increase in particle size can be attributed to the agglomeration of particles besides an increase in lattice parameter. The observed increase in magnetic moment with increase in cobalt concentration also supports the agglomeration of particles.
The particle size has been observed to be higher than the crystallite size for any cobalt substituted ferrite composition and the difference may be attributed to agglomeration of particles due to increase in saturation magnetization as evident from TEM pictures of all the samples. Similar observations suggesting difference in crystallite size obtained from XRD and particle size from TEM are reported [ 19 — 21 ].
It is well known that normal and inverse cubic spinels have two fundamental absorption bands: the first band is due to tetrahedral and the second is due to octahedral complexes. The existence of two wide bands and reveals that these samples are single phase spinel ferrites. In the spectra it has been observed that both and shift slightly towards lower frequencies but not in a systematic trend with Co addition.
The IR bands and their intensities for all samples under investigation are plotted with cobalt content x and are shown in Figure 5 a. The force constant and decreases Figure 5 b with increasing cobalt content.
The observed variations in wave numbers , and force constant at both sites indicate the tendency of cobalt ions to occupy both - and -sites. The magnetic properties associated with the hysteresis loops such as particle size, saturation magnetization , remnant magnetization , coercivity , and the loop squareness ratio values of ferrite samples are listed in Table 1. An increase in saturation magnetization and coercivity is noticed with increasing cobalt concentration.
The observed variations can be understood on the basis of super exchange interactions among the tetrahedral and octahedral [ ] site ions in the spinel lattice [ 24 ]. Saturation magnetization depends on the type and the number of ions located at the tetrahedral and octahedral [ ] sites in the spinel structure because this distribution affects the magnetizations, and of the and sublattices, respectively. The net magnetization is given as. When the cobalt ions are introduced in the spinel lattice replacing nickel ions, some of the cobalt ions entering into -sites tend to push some of the iron ions into -sites.
These iron ions migrating from -sites to -sites and the cobalt ions 3 entering directly into -sites in place of nickel ions 2 collectively increase the magnetic moment of the B sublattice. As cobalt ions produce large anisotropy in Ni-Zn ferrite [ 26 , 27 ], magneto crystalline anisotropy has been estimated from the following formula: where is saturation magnetization and is coercive field. The magnetic anisotropy increases with increasing cobalt concentration as shown in Figure 8.
The magnetic anisotropy is directly proportional to the coercive force and a large variation in coercive force has been noticed with increasing cobalt concentration. The large increase in magnetic anisotropy for higher cobalt concentrations suggests that higher amount of cobalt tends to occupy -site. A gradual decrease in Curie temperature has been noticed with increasing cobalt concentration as shown in Figure 8.
The observed changes in Curie temperature have been explained on the basis of super-exchange interactions among - and -sites in the spinel lattice. The exchange interaction between ions lying on - and -sites depends on the magnetic moments of the ions occupying the sublattices and the distance between the ions.
The distance between the - and -sites increases with the occupancy of cobalt ions at both the sites consequently weakening the - super-exchange interactions [ 28 , 29 ]. Therefore the thermal energy required to offset the alignment of the magnetic moment decreases, leading to decrease in Curie temperature. Another factor which determines the Curie temperature is the stabilizing energy of the ions occupying a particular site.
Cobalt ions have lesser values of stabilization energies at - and -sites compared to those of nickel ions. The decrease in stabilization energy results in the decrease of Curie temperature. On the basis of this site preference and from the variations in wave numbers , , force constant, saturation magnetization, and magnetic anisotropy an approximate cation distribution for the series has been proposed Table 2.
The mean radii of the tetrahedral and octahedral sites and are calculated using the following expressions and plotted as a function , depicted in Figure 6 : To ensure the exactness of the proposed distribution, lattice constant for the Ni-Co-Zn ferrite has been estimated theoretically using and from the following relation: where is the radius of oxygen ion. A close agreement between the theoretical lattice constant and experimental lattice constant from X-ray diffraction measurements Figure 2 a shows the correctness of the proposed distribution.
The entry of cobalt into both the sites has been further verified calculating bond lengths , and site edges , , and of the spinel lattice considering theoretical lattice constant and oxygen parameter. The oxygen parameter can be determined using the relation For face centred cubic structure the value of oxygen parameter is 0. Substitution of larger radius ion will cause distortion in the cubic lattice and therefore the oxygen parameter may differ from its usual value 0.
The increase in reveals the increasing effect of that trigonal distortion at -sites [ 17 ]. The tetrahedral and octahedral bond lengths , were obtained using the relations [ 18 ] The tetrahedral edge , octahedral edge , and unshared edge have been calculated using the relations The hopping lengths and between the magnetic ions at the -site and -sites were estimated using the relations see [ 22 , 23 ]. The obtained values of and other above mentioned parameters are represented in Figures 9 and These plots indicate that tetrahedral bond length , tetrahedral edge , and unshared octahedral edge meagerly increase with increase in.
From this fact it can be concluded that relatively larger quantity of cobalt enters into -sites compared to that of -sites. Similar observation is also reflected in variation in hopping lengths Figure 12 with increasing cobalt content. The number of Bohr magnetons per formula unit is calculated by considering saturation magnetization and molecular weight of each composition using the following relation [ 30 ]:.
The trends in the variation in number of Bohr magnetons per formula unit obtained from the proposed cation distribution and that from the saturation magnetization measurements are found to be in agreement Figure The difference in value of the number of Bohr magnetons is due to the fact that the number of Bohr magnetons obtained from the saturation magnetization measurements is at room temperature and that obtained from cation distribution calculations corresponds to low temperature.
In the present paper the effect of cobalt substitution on structural and magnetic properties in ferrite has been investigated. XRD patterns revealed the formation of single phase cubic spinel structure. The site occupancy of cations helps in understanding the variation in magnetic anisotropy and hence permits understanding clearly the changes taking place in saturation magnetization, coercivity, and initial permeability with reference to shift of critical frequency.
The authors declare that there is no conflict of interests regarding the publication of this paper. The authors sincerely thank Mr. Chaitanya Varma et al. This is an open access article distributed under the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We will be providing unlimited waivers of publication charges for accepted articles related to COVID Sign up here as a reviewer to help fast-track new submissions.
Special Issues. Mahesh Kumar, 3 and K. Academic Editor: Ali Hussain Reshak. Received 20 Oct Accepted 15 Jan Published 04 Mar Abstract The fundamental requirements for the shift of critical frequency to microwave frequencies are smaller grains with single domain, high resistivity, high saturation magnetization, moderate permeability, moderate magnetic anisotropy, and low spin relaxation time.
Introduction Ferrites are the most widely used cores in high frequency power electronics, broadband transformers, pulse transformers, antennas, and sensors because of their excellent magnetic and electrical properties. Experimental The method of preparation of samples was described elsewhere [ 14 ]. Results and Discussions 3. X-Ray Diffraction Analysis X-ray diffraction patterns of and samples are shown in Figures 1 a and 1 b. Figure 1.
The idea of elementary magnets is due to Walther Ritz and Pierre Weiss. Already before the Rutherford model of atomic structure, several theorists commented that the magneton should involve Planck's constant h. In the summer of , the values for the natural units of atomic angular momentum and magnetic moment were obtained by the Danish physicist Niels Bohr as a consequence of his atom model. A magnetic moment of a charged particle can be generated by two ways.
The Use of Ferrites at Microwave Frequencies
The Use of Ferrites at Microwave Frequencies describes the applications of ferrites at microwave frequencies and the apparatus involved. Topics covered range from the properties of ferrites to gyromagnetic and non-reciprocal effects, ferrite isolators, circulators, and modulators. The use of ferrites in variable frequency filter cavities is also discussed. Mathematical explanations are reduced to the strict minimum and only the results of calculations are indicated. This book consists of seven chapters and opens with a review of the theory of magnetism, touching on subjects such as the BOHR magneton, diamagnetism and paramagnetism, ferromagnetism and antiferromagnetism, ferrimagnetism, and demagnetizing. The next chapter deals with the elementary theory of gyromagnetic effects and covers the kinetic moment theorem, precession of the spin moment, gyromagnetic resonance, complex permeability, and gyromagnetic effects in the atom.
Magnetic Phenomena and Their Interpretation—Classical Approach
Box , Nekemte, Ethiopia. The fundamental requirements for the shift of critical frequency to microwave frequencies are smaller grains with single domain, high resistivity, high saturation magnetization, moderate permeability, moderate magnetic anisotropy, and low spin relaxation time. With these guidelines an attempt to produce high performance ferrite for high frequency applications the present work aimed to synthesize cobalt substituted Ni-Zn ferrites using sol-gel method. Investigation of effects of cobalt on crystallite size, saturation magnetization, initial permeability, magnetic anisotropy, and spin relaxation time reveals the suitability of these materials for high frequency applications.