Ferrites have a paramount advantage over other types of magnetic materials, high electrical resistivity and resultant low eddy current losses over wide range. These materials are important in microwave components such as circulators and phase shifters. In some cases, the ferrite must act as a microwave field attenuator or absorb an incoming microwave signal. The most important application of ferrites is as square loop memory cores in computers. Semiconducting magnetic oxides are widely used as thermistors. At present, there is much interest in devices based on magneto-optical phenomena, especially the Faraday effect in garnet . High permeability ferrites find important applications in increasing the recording efficiency of magnetic heads stopples . The densities of ferrites are significantly lower than those of their thin metal counterparts; thus a component of the same size would be lighter in ferrite.
The thermal conductivity of ferrites is rather low. This feature becomes quite important in its application in power transformers where the considerable heat generated is not easily lost. Thus, the center of a core will accumulate the heat, and possibly exceeding the Curie point, the thermal conductivity of ferrites is in the range of (10 - 15) × 10−3 cal /sec·cm·˚C.
The rare-earth orthoferrites of the formula RFeO3, where R is a trivalent rare-earth ion, were first identified in 1950 by Forestier and Guit-Guillain  who also characterized their magnetic properties. They form an important series for magnetic studies and have been extensively studied, in the sixties and seventies both in polycrystalline and single crystalline form. The orthoferrite crystals in the first approximation are treated as perovskites but the true symmetry is orthorhombic, with the c-axis forming one of the pseudo axes. The angle between the c-axis and the a-b plane is 90.6 . A previous study on orthoferrites is done and this article considered as a review on the magnetic and spectroscopic properties of the rare earth ortho-ferrite (Ho ortho-ferrite and different types). The paper deals with some experimental studies as spin structure, magnetic symmetry in orthoferrite. It also studied the spin reorientation transition, the magnetic ordering at low temperature 2˚K - 6˚K, spectroscopy exchange interaction, domain wall and hysteresis loop .
2. Materials and Methods
Solid solution of the system La1−xHoxFeO3 (x = 0.0, 0.1, 0.2, 0.3 and 0.4) was prepared using a double sintering ceramic technique  . The pure stoichiometric oxide Fe2O3 and rare earth element oxides (Ho2O3) were weighted with molecular weight ratio, then the used oxides (powder) were mixed together. The mixture was ground in order to obtain a very fine powder. Then mixtures were pre-sintered at 950˚C for eight hours and slowly cooled to room temperature.
The fine powder was pressed at room temperature and pressure of 10 Kp/cm2 into the form of discs of diameter (1.3 cm) and triodes, samples were then finally sintered to 1200˚C for nine hours under the normal conditions of atmospheric pressure and slowly cooled to room temperature. A Flow chart of sample preparation stages is shown in Figure 1.
X-ray diffraction pattern was performed by using Shimadzu X-ray powder diffractometer. Infrared spectra for the prepared samples were carried out at room temperature by using a PERKIN-ELMER-1430 spectrometer where the infrared spectra are recorded in the range 200 to 1500 cm−1. The ESR spectra were recorded for the samples using JES-FE2xG Joel ESR spectrometer. The DC
Figure 1. Flow chart of sample preparation stages.
resistivity was measured using an electrometer (type Keithely 610C) as shown in Figure 2.
3. Result and Discussion
3.1. X-Ray Diffraction Analysis
The X-ray diffraction analysis of La1−xHoxFeO3 where (x = 0.0, 0.1, 0.2, 0.3 and 0.4) indicates that all the samples have an orthorhombic structure as shown in Figure 3. The diffraction peaks were shifted as the Ho content increases. Lattice parameter a, b and c, and the unit cell volume are listed in Table 1. The results indicate that the structure of the compound is similar to that of RFeO3 as reported by Geller and Wood .
The structure of RFeO3 (where R means La and Ho ions at A site) is not ideal perovskite and the Fe3+ ions and O2− ions depart from the ideal positions due to the difference between the radius of R ions and the Fe ions. In La1−xHoxFeO3 ferrite the distortion will be larger because there are two kinds of large ions, La and Ho ions at R site. In accordance to the literature data the material transfer to the orthoferrite system .
Figure 2. The DC resistivity cell. 1-Digital thermometer; 2-Cover; 3-Shield; 4-Sample; 5-Two electrodes; 6-Heater.
Figure 3. XRD of La1−xHoxFeO3 with x = 0.0, 0.1, 0.2, 0.3 and 0.4.
Table 1. The lattice parameters (a, b and c), volume of the lattice, tolerance factor t and the ratio c/a as a function of composition of the system La1−xHoxFeO3 ferrite.
A larger ion occupies A positions with coordination number 12 and Fe3+ ions occupy B with coordination number 6. Accordingly, the La3+ ions and Ho occupy the A position. The requirement of stability of this orthoferrites is that the Goldschmidt tolerance factor should be nearly unity . The tolerance factor (t) is given by the following equation:
where rA, rB and ro are the ionic radii of the A- and B-site ions and the O2− ion, respectively.
From Table 1, the values of lattice parameters a and b approximately equal . The volume of the unit cell increases with increasing Ho content because the radius of Ho = 0.86 Å is larger than La = 0.82 Å. The values of the lattice parameters a, b and c are near that of La FeO3 which has the values a = 5.53 Å, b = 5.57 Å, c = 7.8 Å and V = 241 Å3. The tolerance factor (t) as given in Table 1 decreases and ranges from 0.91 to 0.70 indicating that the lattice is distorted slightly by the addition of Ho3+ ions. The substitution of Ho3+ ions for La3+ ions causes c/a to decrease as shown in Table 1. The replacement of La3+ by Ho3+ at A sites may reduce the covalent bond formation by La3+ ions thereby decreasing the lattice parameter c and increase a.
The stability of the perovskite structure decreases by increase Ho ion as the tolerance factor decrease as given in Table 1. The density of the samples increases up to x = 0.2 and slowly decreases with increasing Ho content. The theoretical density Dx is greater than the bulk density due to the presence of pores in the material. The orthorhombic phase resists the movement of grain boundaries and prevents the grain growth leading to increase in the number of inner pores giving rise to the density as shown in Figure 4.
The crystallite size of BST was calculated using Scherer’s equation :
where k = 0.89 is constant, θ is the peak location, β is the full width at half maximum of the peak, and λ is the wavelength of the X-ray for Cu-Kα radiation (λ = 1.540598 Å). The behavior of crystallite size is shown in Figure 5. It was observed that the crystallite size tends to decrease with increasing Ho content. This is because Ho ions inhibit grain growth during sintering process leading to decrease of crystallite size.
The lattice parameters of La1−xHoxFeO3 were similar to that given by standard orthorhombic ferrite in literature as shown in Figure 6.
Figure 7 shows the relation between rA and rB for La1−xHoxFeO3 as a function of Ho content. The radius of the tetrahedral site rA decreases and rB increases.
Figure 4. The relation between the experimental density (D), theoretical density (Dx) and Ho content.
Figure 5. The relation between the crystallite size (d) and Ho (content).
Figure 6. The relation between the lattice parameters (a, b, and c) and Ho content.
Figure 7. The relation between the tetrahedral radius (rA), octahedral radius (rB) and Ho content.
The substitution of Ho3+ ions with radius 0.86 Å at A site increases rA. The migration of Fe3+ from B site as a of A site expansion causes a decrease of rB values.
3.2. FTIR Spectra
The IR spectra in a wide range of wavenumber (200 - 1500 cm−1) was carried out for La1−xHoxFeO3 for (x = 0.0, 0.1, 0.2, 0.3, and 0.4) as shown in Figure 8. The IR spectra show the presence of two characteristic absorption bands in the far
Figure 8. FTIR spectra of La1−xHoxFeO3 ferrite.
infrared region. The lower frequency band assigned to oxygen octahedral O-Fe-O bending vibration  whereas the higher frequency absorption band assigned to oxygen tetrahedron Fe-O stretching vibration. The other weak bands appeared near lower frequency absorption band, which was resulted from the vibration of La3+-O2− bond, which decrease by increasing Ho content .
The spectra of the entire ferrite sample have been used to locate the band positions and are given in Table 2. The lower frequency absorption band ν2 shifted to higher frequency as Hocontent increases and ν1 shift to lower frequency. The broadening of the spectral band is due to statistical distribution of cation over A and B positions.
The vibration frequency depends on the cation mass, cation-oxygen distance. The change in the lattice constant and bond length are responsible for this shift of the frequency. The shift in ν1 from 575 to 556 cm−1 is due to the change of A ions positions which probably causes the oxygen ions to shift towards the Ho ions.
Splitting occurred at the ν2 absorption band which is assigned to the formation of Fe2+ and confirms our discussion for explanation the conduction mechanism of our studied samples. It has been shown previously that the presence of Fe2+ ions at A sites can produce splitting in the IR absorption band. This is attributed to Jahn-Teller distortion produced by Fe2+ ions which produces local
Table 2. The variation of wave number of IR absorption peak with x content.
deformation in the crystal potential field and hence leads to the splitting of the absorption band.
The small band appears at 296 cm−1 for the samples x = 0.3 and 0.4 and as a shoulder for x = 0.2 and which assigned as υ4 may be attributed to the Ho3+-O2− bond vibration. This absorption band does not appear for the sample x = 0.0 and 0.1. From the IR spectra it can be noticed that the intensity of both two characteristic bands υ1 and υ2 decreases as Hocontent increases. It is known that the intensity ratio is a function of the change in dipole moment with intermolecular distance dµ/dr . This value represents the contribution of Fe-O bond to the dipole moment, so the IR spectra give an idea about the change of molecular structure of ferrite due to the change in Fe-O bond by introducing Ho ions.
The calculated values of force constant are shown in Figure 9 as a function of Ho content and given from the following equation:
where C is the velocity of light in (cm/sec), ν is the wavenumber and μ is the reduced mass of Fe3+ and O2− ions and F1 and F2 are the force constants for A and B sites respectively.
There is a correlation between the structure and the geometry of the exchange bond, especially the angle and length of this chemical bond. The decrease in the bond angle Fe-O-Fe results in a weaker overlap between Fe 3d and O 2p shells and hence small negative charge on the oxygen atom which reduce the oxygen energy level. On the other hand, the electronic distribution of Fe-O is greatly affected when Ho ions with 4f4 5d6 6s2 orbitals are introduced in its neighborhood and affect (dμ/dr) of the Fe-O bond leading to the change of vibration frequency as shown in the IR absorption spectra.
3.3. DC Resistivity
It is known that the rare earth ferrites are a good electrical insulator and have resistivity at room temperature greater than 106 Ω·cm . Figure 10 shows the plot of Lnρ as a function of inverse temperature for the samples La1−xHoxFeO3, x = (0.0, 0.1, 0.2, 0.3 and 0.4). The resistivity decreases with increasing temperature.
Also, one can distinguish two regions of different activation energies. The change in the slope of these lines takes place around the Curie temperature TC which is indexed in Table 3. The values of Tc in our studied ferrite ranged from
Figure 9. The force constant as a function of Ho content.
Figure 10. The relation between DC resistivity of La1−xHoxFeO3 and 1000/T.
Table 3. Effect of composition on phase transition temperature and activation energy of the system La1−xHoxFeO3 ferrite.
(413 - 345 K) which is near the value given previously . All the curves can be described by the equation:
where Ef and Ep are the activation energies below and above the Tc. The samples containing Ho have lower resistivity than LaFeO3. The resistivity decreases by increasing Ho content due to the formation of Fe2+ after Ho doping as illustrated in IR section, that will participate in the conduction process and decreases the resistivity .
Table 3 gives the activation energies in the two regions as a function of Ho content. The region below Tc is characterized by low activation energy of all samples which strongly suggest the conduction mechanism in the given ferrite formed by hopping electron between Fe2+ and Fe3+ at A site. In this temperature interval the activation energies values vary from 0.87 to 0.09 eV. The jump in the activation energy ΔE equals to Ep – Ef was obtained for all samples. The ΔE jump is smaller for Ho content. The large slopes of the straight lines at higher temperatures can be regarded as due to thermally activated mobility of charge carriers and not to generation of new charge carriers. This would provide a simple explanation for the low resistivity at high temperature. The resistivity decreases gradually from room temperature to the TC temperature with an abrupt change at TC due to the transition from ferrimagnetic to paramagnetic state.
3.4. ESR Spectra
The first derivative ESR spectra of the given ferrite La1−xHoxFeO3 are shown in Figure 11, these spectra were converted to absorption spectra which were used to estimate the line width ΔH and the resonance field Hr.
Absorbed microwave power by the ferrite in arbitrary unit as a function of magnetic field is shown in Figure 12.
The line shape of the ESR spectra has a maximum value at a resonance field Hr. The line shape of the ESR spectra for the first sample was found to have nearly Lorentzian shape. For x = 0.2, 0.3 and 0.4 The ESR spectra deviate from Lorentzian shape and hyperfine interaction takes place between the first spinel phase (La ferrite) and the second orthorhombic phase (La Ho ferrite) and two peaks appear. The X-ray diffraction patterns of La1−xHoxFeO3 indicate that all samples possess an orthorhombic structure.
As given in literature, the porosity increased by Ho addition  . The decreased of Hr for the orthorhombic phase from 3590 to 2250 Gauss may be due to the increase of porosity. The line width changes from 1000 to 1363 Gauss by Ho addition. For instance, the dielectric loss of ferrites at microwave frequency largely depends on their ESR line width. For increasing the line width of broadening ΔH, the electric energy loss in the sample also increases. We can conclude from the above discussion that different composition with Ho addition has higher ΔH values and exhibit high loss than the sample without Ho content.
Figure 11. ESR spectra for the system La1−xHoxFeO3 ferrite.
This is very important in the application for manufacturing the materials which is used as cores of transformers in microwave region.
The spectroscopic splitting factor g for the samples was calculated and is given in Table 4. They have completely different values from the value of free electron (2.0023). Byeon and Hong studied the effect of Fe2+ concentration in Mn-Zn ferrite on the line width of the ESR spectra . They attributed the increase of the line width to the increase of Fe2+ concentration. In the present study the concentration of Fe2+ increase with Ho content as obtained from the IR analysis of the given ferrite, which is accompanied by the increase in the ESR line width. This is in agreement with the study of Galt-Clogston   which state that the presence of Fe2+ ions at octahedral site can cause broadening of the line width.
The spin lattice relaxation process τ is characterized by time constant which is a function of static magnetic field and depends on the rate at which microwave energy can be absorbed and dissipated. The relaxation time is correlated with the
Figure 12. The variation of ESR absorption curves with compositions of the system La1−xHoxFeO3 ferrite.
Table 4. The line width of broadening ΔH, spectroscopic splitting factor (g) and the spin lattice relaxation process τ as a function of composition for La1−xHoxFeO3 ferrite.
line width. The spin-spin relaxation time, which arises from the influence of one magnetic ion on another, limits the broadening of the line width. In this case spin-spin relaxation time increased with increasing Ho addition leading to the increase in the line width. The spin relaxation time is given by the following equation:
where g is the spectroscopic splitting factor and Δβpp is the separation between the two peaks in ESR spectra.
3.5. Dielectric Constant (є) of La1−xHox FeO3 Ferrite
The dielectric relaxation process in ferrite can be identified with electron hopping among Fe2+ and Fe3+ sites with the arrangement of its different nearest neighbor either in the form of impurity band conduction or variable range hopping. The dielectric relaxation process occurs when the jumping frequency of localized electric charge carriers becomes nearly equal that of applied ac electric field. The dielectric constant of the system La1−xHoxFeO3 increases by increasing temperature as shown in Figure 13.
It is noticed that the dielectric constant (є) decreases by increasing Ho content at 1 KHz. The electronic exchange interaction Fe2+ ↔ Fe3+ gives local displacement of electrons in the direction of an applied electric field which induces polarization in ferrite. The formation of orthorhombic phase as a result of Ho addition decreases the conduction process between Fe2+ and Fe3+ leading to the decrease of electric polarization and hence the dielectric constant. The behavior of our results is similar to that in previous work .
Figure 14 shows the variation of tanδ (dielectric loss) as a function of temperature at different Ho content at 1 KHz. The slight increase was found till 170˚C above which the increase is much faster with increasing temperature. This can be illustrated to increase g the A.C. conductivity with rising temperature because the hopping rate of electrons between Fe3+ ions and Fe2+ are thermally activated. The behavior of our results is similar to that in previous work .
The X-ray diffraction analysis of the samples of the system La1−xHoxFeO3 ensures
Figure 13. The dielectric constant (є) of La1−xHoxFeO3 as a function of temperature T(K) at constant frequency 1 KHz.
Figure 14. Dielectric loss as a function of temperature T(K) at different Ho content.
the orthorhombic-phase structure without any residuals of the original constituent oxides. The lattice parameters (a, b and c), the volume of the lattice (V), increase by increasing Ho content. The measured density is less than that predicted from X-ray measurements and the porosity increases by increasing Ho content. The DC electrical conductivity of the system La1−xHoxFeO3 increases linearly with increasing temperature which ensures the semiconducting nature of the samples and decreases with increasing Ho content. IR spectra of the system La1−xHoxFeO3 ferrite showed two main characteristic absorption bands in the far infrared region. For x = 0.2, 0.3 and 0.4, the ESR spectra deviate from Lorentzian shape and hyperfine interaction takes place between the first spinel phase and the second orthorhombic phase and two peaks appear. The X-ray diffraction patterns of La1−xHoxFeO3 indicate that all samples possess an orthorhombic structure. The dielectric constant of the composition La1−xHoxFeO3 (x = 0.0, 0.1, 0.2, 0.3 and 0.4) increases by increasing temperature and decreases by increasing Ho content.
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