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J. Phys. Chem. C 2011, 115, 554–560
Structural, Magnetic, Electrical, and Magnetoelectric Properties of Sm- and Ho-Substituted Nickel Ferrites K. Kamala Bharathi,*,† G. Markandeyulu,‡ and C. V. Ramana†,§ Energy Systems Laboratory (ESL), Department of Mechanical Engineering, and Department of Materials Science and Engineering, UniVersity of Texas at El Paso, El Paso, Texas 79968, United States, and AdVanced Magnetic Materials Laboratory (AMMLa), Department of Physics, Indian Institute of Technology Madras, Chennai-600 036, India ReceiVed: July 1, 2010; ReVised Manuscript ReceiVed: September 19, 2010
Sm- and Ho-substituted and pure nickel ferrite materials, namely, NiFe1.925Sm0.075O4, NiFe1.925Ho0.075O4, and NiFe2O4, have been synthesized by the solid-state chemical reaction, and their structural, magnetic, dc electrical conductivity, ferromagnetic, ferroelectric, and dielectric properties have been evaluated. Sm- and Ho-substituted nickel ferrites crystallize in the cubic inverse spinel phase with a very small amount of SmFeO3 and HoFeO3 as the additional phase, respectively. X-ray diffraction studies indicate rhombohedral distortion in NiFe1.925Sm0.075O4 and NiFe1.925Ho0.075O4 compounds. The existence of ferroelectricity in NiFe1.925Sm0.075O4 and NiFe1.925Ho0.075O4 has been confirmed from the ferroelectric loops, and the respective transition temperatures are 543 and 677 K. The respective magnetocapacitance values are -1.8% and -1.2%. Magnetoelectric coefficients observed at 500 Oe in the NiFe1.925Sm0.075O4 and NiFe1.925Ho0.075O4 compounds are 1.82 and 1.84 mV cm-1 Oe-1, respectively. A considerable increase in the saturation magnetostriction value has been observed upon the substitution of Sm. Substitution of Sm and Ho for Fe at the B site increases the dielectric constant compared to that of pure nickel ferrite. Frequency variation of the dielectric constant shows a dispersion that can be modeled with a modified Debye function, which considers the possibility of more than one ion contributing to the relaxation. Electrical conductivity curves confirm the improved resistivity of the NiFe1.925Sm0.075O4 and NiFe1.925Ho0.075O4 compounds compared to that of pure nickel ferrite. Analysis of the temperature-dependent conductivity indicates that the small polaron and variable-range-hopping mechanisms are operative in the 220-300 and 160-220 K temperature regions, respectively. I. Introduction Ferrite materials have been received significant attention in recent years due to their wide range of applications in the fields of electronics, optoelectronics, magentics, magnetoelectronics, and electrochemical science and technology.1-24 Nickel ferrites, particularly, have been studied extensively due to their remarkable properties such as high saturation magnetization, large permeability at high frequency, and remarkably high electrical resistivity.6-8 Due to their low eddy current losses, there exist no other materials with such wide-ranging value to electronic applications in terms of power generation, conditioning, and conversion.10 These properties also make them unique for application in microwave devices which require strong coupling to electromagnetic signals.11 Unlike most materials, they possess both high permeability and moderate permittivity at frequencies from dc to the millimeter.11 Iron, cobalt, and nickel ferrites (transition-metal (TM) ferrites) that crystallize in an inverse spinel structure are some of the most versatile centrosymmetric magnetic materials.1,3 In the inverse spinel structure, the tetrahedral (A) sites are occupied by the Fe3+ ions and the octahedral sites (B) are occupied by the divalent metal ions (M2+) and Fe3+, in equal proportions. The angle A-O-B is closer to 180° than the angles B-O-B * To whom correspondence should be addressed. E-mail: kbkaruppanan@ utep.edu. † Department of Mechanical Engineering, University of Texas at El Paso. ‡ Indian Institute of Technology Madras. § Department of Materials Science and Engineering, University of Texas at El Paso.
and A-O-A, and therefore, the AB pair (Fe-Fe) has a strong superexchange (antiferromagnetic) interaction.1-3 The electrical resistivity of a ferrite at room temperature2 can, depending upon the chemical composition, firing temperature, atmosphere, and ions that substitute for Fe3+/Fe2+ ions, lie between about 10-2 and 1011 Ω cm. Low resistivity due to hopping of bonding electrons is caused by the simultaneous presence of Fe3+ and TM2+ ions on equivalent lattice sites.2 Currently, there is considerable interest in multiferroic magnetoelectrics, which are rare composite materials which exhibit ferromagnetism and ferroelectricity or ferroelasticity simultaneously.24-31 Some of the transition-metal ferrite based composite materials exhibit a high magnetostriction.26-31 The present work was performed on Sm- and Ho-doped nickel ferrite to understand the effect of Sm and Ho substitution on structural distortion, magnetostrictive characteristics, electrical and dielectric properties, and magnetoelectric properties of nickel ferrite. The results obtained are presented and discussed in this paper. II. Experimental Details The polycrystalline compounds were prepared starting from 99.99% pure NiO, Fe2O3, Sm2O3, and Ho2O3 by the conventional solid-state chemical reaction method. Powders of the starting materials were ground in a mortar and pestle for 1 h, and the mixtures were heat treated in air at 1200 °C for 12 h. For the electrical and magnetic measurements the powders were made into pellets which were then sintered at 1250 °C in air for 12 h.
10.1021/jp1060864 2011 American Chemical Society Published on Web 12/17/2010
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The X-ray diffraction (XRD) patterns of the samples were obtained at room temperature using a PANalytical (X’pert PRO) X-ray diffractometer employing Cu KR radiation (1.54 Å). The weight fraction of the individual phases was calculated from the Rietveld refinement (GSAS program); the weight fraction is defined as
Wp )
Sphmp Np
(1)
∑ Sphmp
p)1
where Wp is the weight fraction of phase p, Sph is the phase fraction scale factor of phase p, and mp is the unit cell mass of phase p. The bond angles and lengths were obtained from the Rietveld refinement of the XRD data. The bond angles for the atom sequence A-B-C were calculated using the formula
b VBA · b VBC Rc ) bBA ||V bBC | |V
(2)
Figure 1. XRD patterns of NiFe2O4 (a), NiFe1.925Sm0.075O4 (b), and NiFe1.925Ho0.075O4 (c). The calculated pattern obtained after the Rietveld refinement and the differences are also shown.
TABLE 1: Refined Values of the Bond Angles (deg) and Bond Lengths (Å) of NiFe2O4, NiFe1.925Ho0.075O4, and NiFe1.925Sm0.075O4 compound
Microstructural analysis was carried out employing a backscattered electron (BSE) image obtained with a Hitachi S-4800 scanning electron microscope. Magnetization and Curie temperature measurements were carried out employing a vibrating sample magnetometer. Magnetostriction measurements were carried out by the standard strain gauge method. Dielectric and impedance measurements were carried out using an HP 4192A impedance analyzer. Ferroelectric hysteresis loops were recorded at room temperature, for which the circuit suggested by Roestschi et al.32 was constructed and employed. Magnetoelectric (ME) measurements were carried out employing a homemade setup. The magnetocapacitance was obtained by measuring the change in the capacitance of a parallel plate capacitor with a NiFe1.925R0.075O4 pellet filling the space between the plates. The magnetic field was applied along the axis of the pellet. The dc electrical resistivity measurements were carried out under a vacuum of 10-2 Torr by the two-probe method in the temperature range 140-300 K employing a closed cycle refrigerator. The resistance was measured by employing a Keithley electrometer. The temperature was measured using a silicon diode sensor and employing a Lakeshore temperature controller (model 330).
NiFe2O4 NiFe1.925Sm0.075O4 NiFe1.925Ho0.075O4
Fe3+-O-Fe3+ Ni2+-O-Ni2+ O-Fe3+ (R3+) bond length (R3+) bond angle bond angle 159.2 157.6 157.9
90.6 90.1 90.2
2.050 2.183 2.191
0.059, respectively. The lattice constant increases from 8.335 to 8.346 Å. A small distortion in the lattice is observed upon the substitution of Fe by Sm and Ho in the B site from the changes in the Fe-O-Fe, R-O-Fe, and R-O-Ni bond angles and O-Fe and O-Ni bond lengths in the B site compared to the values in NiO · Fe2O3 (see Table 1). The O-Fe and O-Ni bond lengths are found to increase with the inclusion of Sm and Ho in the B site. XRD patterns at slow scan rates (step size of 0.002° with a dwell time of 15 min) were recorded for the (440) peak and are shown in Figure 2. After elimination of the effect of KR2 radiation, a clear splitting is observed as shown in Figure 2. Thus, the distortion is rhombohedral in these compounds. The splitting of the (440) peak into (-4,4,0) and (4,-4,0) peaks in rhombohedrally distorted face-centered cubic (fcc) structured materials has already been reported.34-36 Therefore, in the
III. Results and Discussion The XRD patterns of the Sm- and Ho-substituted and pure nickel ferrites are presented in Figure 1. The calculated patterns after the Rietveld refinement carried out using the GSAS program33 are also shown in Figure 1. The wrp (weighted refined parameter) and the χ2 (goodness of the fit) values of the fitting are as indicated. NiFe2O4 is found to form in the inverse spinel phase without any impurity phase, and the calculated value of the lattice constant is 8.335 Å, which agrees with the reported value.1,2 XRD data reveal that NiFe1.925R0.075O4 (R ) Sm, Ho) materials also form in the inverse spinel phase. Very small amounts of SmFeO3 and HoFeO3 phases are identified in the Sm- and Ho-substituted nickel ferrites, respectively. In NiFe1.925Sm0.075O4 the weight fractions of the inverse spinel phase and SmFeO3 are 0.936 and 0.066, respectively. The lattice constant calculated from Rietveld refinement increases from 8.335 to 8.348 Å. In the case of NiFe1.925Ho0.075O4 the weight fractions of the inverse spinel phase and HoFeO3 are 0.927 and
Figure 2. Slow scan XRD patterns of the (440) peaks of NiFe2O4 (a), NiFe1.925Ho0.075O4 (b), and NiFe1.925Sm0.075O4 (c). Splitting of the (440) peak in NiFe1.925R0.075O4 (R ) Sm and Ho) compared to NiFe2O4 is evident.
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Figure 4. Magnetization curves of NiFe1.925Sm0.075O4 (a) and NiFe1.925Ho0.075O4 (b) (the inset of (a) shows the magnetization curve of NiFe2O4 at 300 K).
Figure 3. BSE images of NiFe1.925Sm0.075O4 (a) and NiFe1.925Ho0.075O4 (b). The secondary phase is indicated with red arrows.
present case, the small distortion in the lattice observed upon the substitution of Fe by Sm and Ho in the B site can be understood from the changes in the Fe-O-Fe, R-O-Fe, and R-O-Ni bond angles (from 90.065° to 91.784°) and O-Fe and O-Ni bond lengths (from 2.05181 to 2.088 Å) in the B site compared to the values in NiFe2O4. The BSE images of NiFe1.925R0.075O4 (R ) Sm, Ho) compounds are shown in Figure 3. The BSE images of NiFe1.925R0.075O4 (R ) Sm, Ho) compounds show two distinct contrasts corresponding to their respective primary parent phases NiFe1.925R0.075O4 (R ) Sm, Ho) and the secondary RFeO3 phases. Typical secondary phase formation is indicated with some particles shown with arrows (Figure 3). Substitution of a small amount of Sm and Ho for Fe at the B site of their respective parent NiFe1.925R0.075O4 (R ) Sm, Ho) phases has been confirmed from the energy-dispersive X-ray measurements (not shown).
Magnetization curves of NiFe1.925Sm0.075O4 and NiFe1.925Ho0.075O4 are shown in Figure 4. The magnetization curve of pure NiFe2O4 is shown as an inset in Figure 4a for comparison. The saturation magnetization (Ms) value of NiFe1.925Sm0.075O4 (Figure 4a) is 42.5 emu/g at 300 K and 49 emu/g at 100 K. Ms values of NiFe1.925Ho0.075O4 at 300 and 80 K are 45 and 52 emu/ g, respectively (Figure 4b). For pure nickel ferrite, the Ms value at 300 K is 49.8 emu/g.1,2 Substitution of the Fe3+ magnetic ion by Sm3+ and Ho3+ ions in the B site reduces the net magnetic moment, leading to reduced Ms values. Since there is no itinerant exchange interaction as the moments are localized, the saturation magnetization values were calculated using Hund’s rules with the assumption that R3+ magnetic moments are parallel to the Fe moments in the B site. In the case of the Sm-doped compound the calculated Ms value is 1.96 µB, which is closer to that at 100 K (1.90 µB). In the case of the Ho-doped compound the calculated Ms value is 2.06 µB. Our results are in agreement with the literature if the reduced net magnetic moment and/or reduced Ms for nickel or nickel-zinc ferrites upon rare-earth ion substitution are taken into account. Rezlescu et al.7,8,20 have reported that the magnetic moment (at 300 K) of nickel-zinc ferrite (66 emu/g) decreased with partial substitution of Fe3+ by Ce3+ (64.4 emu/g), Sm3+ (65.6 emu/g), Gd3+ (65.9 emu/g), Tb3+ (64.6 emu/g), Dy3+ (64.8 emu/g), Er3+ (66.1 emu/g), and Yb3+ (65.3 emu/g) ions. Sielo et al.37 have reported a decrease in the saturation magnetization of nickel ferrite from 2 µB per formula unit to 1.91 µB per formula unit upon partial substitution of Fe3+ by Gd3+. In the present case, SmFeO3 and HoFeO3 are canted antiferromagnets with Neel temperatures of 500 and 700 K, respectively, with a feeble saturation magnetic moment of about 0.05 µB per formula unit.1 Therefore, contributions from SmFeO3 and HoFeO3 to the magnetic moments of the ferrites are considered insignificant. The magnetization vs temperature curves obtained for Smand Ho-substituted nickel ferrites are shown in Figure 5. The purpose of these measurements was to determine the Curie temperature (TC). It is evident that the TC values of NiFe1.925Sm0.075O4 (Figure 5a) and NiFe1.925Ho0.075O4 (Figure 5b) are 839 and 812 K, respectively. For pure nickel ferrite, TC ) 853 K.1,2 It is important to note that the TC value decreases in Sm- and Ho-substituted nickel ferrites compared to pure nickel ferrite. This reduction is caused by the weaker Fe-R (R ) Sm, Ho) superexchange interactions compared to the Fe-Fe interactions when Fe3+ is substituted by R3+ (Sm3+ and Ho3+)7,8,20 ions at the B site. Such a behavior and reduction in TC upon R ion substitution seems to be general behavior in nickel ferrites. The
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Figure 7. Magnetocapacitance curves of NiFe1.925Sm0.075O4 and NiFe1.925Ho0.075O4. Figure 5. Curie temperature curves of NiFe1.925Sm0.075O4 (a) and NiFe1.925Ho0.075O4 (b).
considering the effect of the R ion on the structure. A primary requirement for the existence of ferroelectricity is a structural distortion from the high-symmetry phase that removes the center of symmetry and allows electric polarization.27,29 Because of the larger ionic size of Sm3+ and Ho3+ in comparison to Fe3+, the centrosymmetric fcc structure is distorted by a small amount, leading to the development of a net electrical polarization. It must be emphasized that there are no reports on the phenomena of ferroelectricity and magnetocapacitance in RFeO3 (R ) La, Dy, Tb, Gd) materials. Therefore, such a behavior cannot be attributed to the RFeO3 (R ) Sm, Ho) secondary phases. Hence, the observed ferroelectricity in NiFe1.925R0.075O4 (R ) Sm, Ho) in the present case is completely intrinsic upon Sm and Ho substitution. The magnetocapacitance is measured by the relative change in the capacitance, which is
∆C ∆ε ∆d ) C ε d
Figure 6. Electrical polarization loops of (a) NiFe1.925Sm0.075O4, (b) NiFe1.925Ho0.075O4, and (c) NiFe2O4.
additional evidence for this TC reduction behavior can be derived from the literature.7,8,20 It has been demonstrated that Ersubstituted nickel-zinc ferrites,38 Y, Gd, and Tb rare-earth ion substituted nickel-zinc ferrites,39 and Al-substituted nickel ferrites40 exhibit behavior similar to that observed in this work. The ferroelectric hysteresis loop measurements at room temperature confirm the ferroelectricity in NiFe1.925R0.075O4 (R ) Sm, Ho). The ferroelectric loop characteristic curves of NiFe2O4 and NiFe1.925R0.075O4 (R ) Sm, Ho) are shown in Figure 6. A marked difference in the ferroelectric loop curves of nickel ferrites upon Sm and Ho substitution is evident (Figure 6a,b) when compared to that of pure NiFe2O4 (Figure 6c). NiFe1.925R0.075O4 (R ) Sm, Ho) compounds show well-saturated square ferroelectric loops, indicating their ferroelectric nature at room temperature. The remnant polarization values of Smand Ho-doped compounds are 0.28 and 0.32 µC/cm2, respectively. The saturated square loop behavior of NiFe1.925R0.075O4 (R ) Sm, Ho) compared to NiFe2O4 can be understood
(3)
where ε is the dielectric constant of the material and d is the thickness of the sample; thus, ∆d/d is the magnetostriction of the material. The magnetocapacitance data of NiFe1.925R0.075O4 (R ) Sm, Ho) are shown in Figure 7. The value of ∆C/C for a field of 3200 Oe was observed to be -1.8% for NiFe1.925Sm0.075O4 and -1.2% for NiFe1.925Ho0.075O4 (Figure 7). This could arise from either ∆ε/ε or both ∆ε/ε and ∆d/d. No magnetocapacitance was observed in the case of pure nickel ferrite. The satuaration magnetostriction (λS) values, determined from magnetostriction measurements, of NiFe2O4, NiFe1.925Sm0.075O4, and NiFe1.925Ho0.075O4 are -25 × 10-6, -34 × 10-6, and -24 × 10-6, respectively (Figure 8). The increase in λS in the case of the NiFe1.925Sm0.075O4 sample could be attributed to the large negative magnetostriction value of Sm.38 The λS ()∆d/d) values of the polycrystalline NiFe1.925Sm0.075O4 and NiFe1.925Ho0.075O4 compounds are seen to be 2 orders of magnitude less than the respective ∆ε/ε values. Therefore, the origin of magnetocapacitance (∆C/C) seems to be completely from ∆ε/ε. Magnetoresistance measurements were carried out on all the compounds at room temperature, and the resistance values did not change with the magnetic field. Therefore, the observed change in dielectric constant with magnetic field (∆ε/ε) is not due to the change in the resistance of the compounds. The science behind the magnetostriction behavior of NiFe1.925Sm0.075O4 and NiFe1.925Ho0.075O4 can be understood as follows. Crystal fields in cobalt/nickel ferrite are not capable
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Figure 8. Magnetostriction curves of NiFe2O4, NiFe1.925Sm0.075O4, and NiFe1.925Ho0.075O4.
Figure 9. ME coefficient curves of NiFe1.925Sm0.075O4 and NiFe1.925Ho0.075O4.
of removing the orbital degeneracy of the 3d orbital of Ni2+/ Co2+, and therefore, the orbital magnetic moment is of the same order of magnitude as the spin magnetic moment, leading to a large anisotropy and magnetostriction.1,2 The saturation magnetostriction (λS) of colbalt ferrite is -110 × 10-6 (negative), that of Fe3O4 is 40 × 10-6 (positive), that of magnesium ferrite is -8 × 10-6 (negative), and that of lithium ferrite is -5 × 10-6 (negative).1 It has been reported that partial substitution of Fe by Cr in copper ferrite leads to tetragonal distortion with c/a > 1, owing to the Jahn-Teller effect.17 On the other hand, rhombohedral distortion in Co-substituted nickel-zinc ferrite has been reported.18 Partial substitution of Fe3+ by a rare-earth ion in the spinel structure has been reported to lead to structural distortion19-21 that induces strains and significantly modifies the electrical and magnetic properties. Partial substitution of Fe3+ by Tb3+ and Dy3+ in the cobalt ferrite has been reported to cause an increase in the coercive field to about 2 kOe (∼30% increase),22 due to the contribution from the large single ion anisotropy from the rare-earth sublattice. It has been reported that nickel ferrite became ferroelectric upon the substitution of a small amount of Fe at the B site by Dy and Gd.23,24 In addition, a magnetocapacitance of about 4% in NiFe1.925Dy0.075O4, implying magnetoelectric coupling, has been reported. The variation of RE with the magnetic field is shown in Figure 9. An ac field of 2 Oe rms was applied perpendicular to the plane of the pellet during the measurement. The induced voltage was measured employing a lock-in amplifier. The ME coefficient was calculated using the formula
RE )
V(H) dH
(4)
Figure 10. Temperature variations of the dc conductivity of NiFe2O4 NiFe1.925Ho0.075O4 and NiFe1.925Sm0.075O4.
where V(H), d, and H are the ME voltage, thickness of the sample, and ac magnetic field, respectively. Maximum ME coefficients of 1.82 and 1.84 mV cm-1 Oe-1 were observed at 500 Oe for the NiFe1.925Sm0.075O4 and NiFe1.925Ho0.075O4 compounds, respectively. NiFe2O4 has not shown any induced ME effect. In the NiFe1.925Sm0.075O4 and NiFe1.925Ho0.075O4 compounds, with increasing dc magnetic field up to ∼500 Oe, the magnetization (and hence the magnetostriction) increases, causing the magnetoelectric coupling (RE) to increase. Beyond 500 Oe, the magnetization values of the respective compounds saturate, causing RE to decrease. The magnetoelectric coupling in these nickel ferrites is due to the R ion. Nonuniform displacement of the ions (because of magnetostriction) carrying a magnetic moment changes the dipolar fields and, thereby, the magnetic anisotropy.29 Sm3+ and Ho3+ ions have oblate and prolate 4f charge distributions, respectively.41 With the application of a magnetic field, rotation of the 4f charge cloud changes the overlap of the wave functions, causing the interionic distance to change. Thus, the observed magnetoelectric effect in Sm3+- and Ho3+-doped compounds can be attributed to the changes in the interionic distance and subsequent changes in the electric polarization. In addition to that, the reasons for observation of a magnetoelectric effect in rhombohedrally distorted Sm- and Ho-doped compounds could be the following. (1) The electric field moves the ions with respect to its ligands. This can change the anisotropy, magnitude, or local symmetry of the ligand field.29 (2) Opposite movement of differently charged ions (Fe3+ and 2+ Ni at the B site) and changes of the electron wave functions of the ions in the electric field modify the orbital overlap and, thus, the exchange integrals and energies. (3) Nonuniform movement (e.g., because of magnetostrictive distortion) of the ions carrying a magnetic moment changes the dipolar fields and, thereby, the magnetic anisotropy. The temperature variations of the dc electrical conductivity of the NiFe2O4, NiFe1.925Sm0.075O4, and NiFe1.925Ho0.075O4 materials are shown in Figure 10. Conductivity values of the NiFe2O4, NiFe1.925Sm0.075O4 and NiFe1.925Ho0.075O4 compounds at 300 K are 9.8 × 10-9, 3.4 × 10-10, and 3.1 × 10-10 Ω-1 cm-1, respectively. The room temperature resistivity of nickel ferrite increases with the substitution of Sm3+ and Ho3+ ions. The resistivity increase upon R ion substitution is common in nickel ferrites. Various mechanisms have been proposed for modification of the electrical characteristics. Rezlescu et al. and Sun et al.7-9,42 have reported that the electrical resistivity of nickel-zinc ferrite increases with partial substitution of Fe3+ by Ce3+, Sm3+, Gd3+, Tb3+, Dy3+, Er3+, and Yb3+, due to the
Properties of Sm- and Ho-Substituted Nickel Ferrites
J. Phys. Chem. C, Vol. 115, No. 2, 2011 559 TABLE 2: Dielectric Constant Values of NiFe2O4, NiFe1.925Ho0.075O4, and NiFe1.925Sm0.075O4 at Different Frequencies
Figure 11. Frequency variations of the dielectric constant of NiFe2O4 (a), NiFe1.925Ho0.075O4 (b), and NiFe1.925Sm0.075O4 (c). The experimental data are shown with symbols, while the solid lines represent the curves calculated using Debye’s modified function. Excellent agreement between the experimental data and calculated curves is noted.
formation of small amounts of RFeO3 phases which segregate at grain boundaries. Said43 reported that inclusion of Gd3+ for Fe3+ at the B site in nickel ferrite leads to an increase in resistivity due to the reduction of the number of Fe3+ ions at the B site. Due to the larger size of R3+ ions as compared to Fe3+, the lattice is distorted, leading to additional scattering and causing an increase of resistivity. The electrical conductivity decreases exponentially with decreasing temperature from 300 to 160 K, indicating the characteristic feature of semiconductors. Temperature-dependent conductivity in ferrites is due to both hopping of electrons and charge transport via excited states which can be expressed as2
( )
σ ) A1 exp
( )
( )
-E1 -E2 -E3 + A2 exp + A3 exp kBT kBT kBT
(5)
where E1 is the activation energy for intrinsic conduction and E2, E3, ... are the activation energies needed for hopping conduction. A1, A2, and A3 are constants, and kB is the Boltzmann constant. ln σ vs 1000/T plots (Figure 10) indicate two different slopes characteristic of the electrical conduction through an activated process having two different procedures.44-47 Activation energy values at different temperature ranges (300-220 and 220-160 K) were calculated from the ln σ vs 1000/T plot. Activation energy values determined from the slopes are higher in the 300-220 K region (0.29, 0.38, and 0.37 eV for NiFe2O4, NiFe1.925Sm0.075O4, and NiFe1.925Ho0.075O4, respectively) when compared to those obtained in the 220-160 K region (0.06, 0.07, and 0.08 eV for NiFe2O4, NiFe1.925Sm0.075O4, and NiFe1.925Ho0.075O4, respectively). The decreasing activation energy with decreasing temperature in these materials can be attributed to the small-polaron formation as noticed in other ferrites. The frequency variations of the dielectric constant (ε′) of Smand Ho-substituted nickel ferrites are presented and compared with that of pure nickel ferrite in Figure 11. It can be seen that ε′ decreases with increasing frequency (Figure 11). The decrease of ε′ with increasing frequency as observed for the NiFe1.925Sm0.075O4, NiFe1.925Ho0.075O4, and NiFe2O4 materials is a typical dielectric behavior of spinel ferrites.1-3 The values of ε′ (at 100 Hz) in Sm3+- and Ho3+-doped compounds are 4.9 × 104 and 1.51 × 105, respectively, and are higher than that of pure nickel ferrite (4.1 × 104). Dielectric constants for Zn-doped, Cr-doped,
compound
ε′ at 100 Hz
ε′ at 1 kHz
ε′ at 1 MHz
NiFe2O4 NiFe1.925Sm0.075O4 NiFe1.925Ho0.075O4
4.1 × 10 4.9 × 104 1.6 × 105
1.29 × 10 4.3 × 104 5.7 × 104
1.8 × 103 3.9 × 104 4.2 × 104
4
4
and Cu- and Al-codoped nickel ferrites are reported to be 1.6 × 103 (at 1 kHz), 1.25 × 103 (at 1 kHz) and 1.5 × 103 (at 6 kHz), respectively.47-49 A comparison of the ε′ values at different frequencies for Sm- and Ho-substituted and pure nickel ferrite is presented in Table 2. The ε′ value was found to be 1 order larger in NiFe1.925Ho0.075O4 compared to that in NiFe2O4. The increase in the dielectric constant with the inclusion of Sm3+ and Ho3+ could be due to the fact that, with the inclusion of R3+, the nickel ferrite lattice is distorted and the Fe (R)-O bond lengths at the B site increase, giving rise to an increase in the atomic polarizability and subsequently the dielectric constant. In addition to that, formation of small amounts of the respective RFeO3 phases at the grain boundaries leads to the accumulation of charges at the grain boundaries, resulting in interfacial polarization, which contributes to the additional increase in ε′. A decrease in ε′ with increasing frequency is due to the fact that the dipole lags behind the applied field at higher frequencies. The dispersion of ε′ can be explained on the basis of the contributions from various sources of polarizations.2 The larger value of ε′ at lower frequencies, perhaps, could be due to all the contributions (i.e, atomic, electronic, ionic, interfacial, and grain boundary). The decrease (and disappearance finally) in ionic and orientation polarizability with increasing frequency may be responsible for the decrease in ε′ at higher frequencies.2 Since more than one ion (O2-, R3+, and Fe3+ ions) contributes to the relaxation process, the data were fit to the modified Debye’s function that considers the possibility of more than one ion, contributing to the relaxation.50,51 The observed dispersion of the dielectric constant can be modeled using the equation
ε′ - ε∞ )
(ε0 - ε∞) 1 + (ωτ)2(1-R)
(6)
where ε′ is the real part of the dielectric constant, ε∞ is the dielectric constant at 13 MHz, τ is the mean relaxation time, and R is the spreading factor of the actual relaxation times about the mean value. The fitting to the model is as shown in Figure 11 using solid lines. The fitting yields τ ) 0.218, 0.421, and 0.429 µs for NiFe2O4, NiFe1.925Sm0.075O4, and NiFe1.925Ho0.075O4, respectively. Similarly, R values obtained are 0.47, 0.54, and 0.59 for NiFe2O4, NiFe1.925Sm0.075O4, and NiFe1.925Ho0.075O4, respectively. The existence of inertia to the charge movement would cause relaxation of the polarization. It must be emphasized that the τ and R values are much higher for Sm- and Ho-substituted nickel ferrites compared to pure nickel ferrite. An important conclusion about the mechanism involved in improving the dielectric property of the nickel ferrites upon substitution of Sm and Ho rare-earth ions can be derived by taking the larger values of the mean relaxation time and the spreading factor and the structural data into consideration simultaneously. The increased bond length in Sm3+- and Ho3+-doped nickel ferrites is evident from structural studies (Table 1). Therefore, compared to pure nickel ferrite, the inclusion of larger Sm3+ and Ho3+ ions leads to an increase in interionic distance, which in turn increases the hopping distance. This causes the mean relaxation
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Figure 12. Temperature variations of the dielectric constants of NiFe2O4 (a), NiFe1.925Sm0.075O4 (b), and NiFe1.925Ho0.075O4 (c).
time and spreading factor to increase in Sm3+- and Ho3+-doped nickel ferrites. The variation of ε′ as a function of temperature in the range of 300-750 K at different frequencies is shown in Figure 12. The data obtained for Sm- and Ho-substituted nickel ferrite are presented and compared with that of pure nickel ferrite. It is evident that ε′ is constant up to a particular temperature and then increases with increasing temperature. The ferroelectric transition temperature of NiFe1.925Sm0.075O4 is 543 K, and that of NiFe1.925Ho0.075O4 is 677 K. The transition temperature is seen to be independent of frequency, and thus, the observed ferroelectricity may not be attributed to the relaxor-type mechanism. IV. Conclusions Enhancement of the dielectric constant, magnetocapacitance, and electrical resistivity of nickel ferrite by partially substituting Fe with Sm and Ho is clearly demonstrated. Because of the larger ionic sizes of Sm3+ and Ho3+ in comparison to Fe3+, the centrosymmetric fcc structure is distorted by a small amount, resulting in the net electrical polarization of the material. Rhombohedral distortion is clearly observed in NiFe1.925Sm0.075O4 and NiFe1.925Sm0.075O4 from splitting of the (440) peak in XRD. The ferroelectric loop measurements confirm the existence of ferroelectricity in the NiFe1.925Sm0.075O4 and NiFe1.925Ho0.075O4 compounds. The ferroelectric transition temperature values of the NiFe1.925Sm0.075O4 and NiFe1.925Ho0.075O4 compounds are found to be 543 and 677 K, respectively. Maximum magnetoelectric coefficients of 1.82 and 1.84 mV cm-1 Oe-1 were observed at 500 Oe for the NiFe1.925Sm0.075O4 and NiFe1.925Ho0.075O4 compounds, respectively. The existence of ferroelectricity and magnetoelectric coupling shows the multifunctional nature of these materials. An increase in ε′ by 1 order of magnitude for Ho3+ suggests that NiO.Fe1.925Ho0.075O3 exhibits better electrical properties than NiFe2O4 and NiFe1.925Sm0.075O4. The dc electrical conductivity confirms the increased resistivity upon Sm3+ and Ho3+ substitution. From structural and electrical points of view, we found that NiFe1.925Ho0.075O4 > NiFe1.925Sm0.075O4 > NiFe2O4. References and Notes (1) Chikazumi, S. Physics of Ferromagnetism; Oxford University Press: New York, 1997. (2) Smith, J.; Wijn, H. P. J. Ferrites; Philips Technical Library: Eindhoven, The Netherlands, 1965. (3) Zhou, Z. H.; Wang, J.; Xue, J. M.; Chan, H. S. O. J. Mater. Chem. 2001, 11, 3110.
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