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Ac susceptibility and magnetic interaction in Mg–Ni–Fe–O system
December 2002
Materials Letters 57 (2002) 925 – 928 www.elsevier.com/locate/matlet
Ac susceptibility and magnetic interaction in Mg–Ni–Fe–O system Mazhar U. Rana*, Tahir Abbas Department of Physics and Materials Science, Bahauddin Zakariya University, Multan 60800, Pakistan Received 23 November 2001; received in revised form 18 April 2002; accepted 29 April 2002
Abstract A series of Mg1 xNixFe2O4 spinel ferrites with x = 0, 0.25, 0.50, 0.75 and 1.0 have been prepared using standard ceramic method. Lande-g factor ( g), effective magnetic moments ( Peff), Curie temperature (Tc), paramagnetic Curie temperature (h(K)) and exchange integral ( J/k) were calculated from ac susceptibility measurements using mutual inductance technique. With the addition of Ni ions g-values, Peff and h(K) show increasing trend up to x = 0.75 while Tc continues to decrease. For x>0.75 decreasing trend in magnetic moments (nB) and h(K) is exhibited, which could be correlated to the redistribution of cations on A and B sites. The dominant interaction in all the samples is A – B interaction, which is due to the negative values of h(K), showing the magnetic ordering is antiferromagnetic. The Y – K angle increases gradually with increasing Ni contents and extrapolates to 60j for NiFe2O4. From the computation of Y – K angles for Mg1 xNixFe2O4, it can be concluded that mixed nickel ferrites exhibit a non-colinearity of the Y – K type while MgFe2O4 show a Neel type of ordering. D 2002 Elsevier Science B.V. All rights reserved. Keywords: Magnesium ferrites; Susceptibility; Magnetic moments; Interaction; Y – K angles
1. Introduction Magnesium ferrites belong to a class of compounds having the general formula M2 + Fe23 + O4 and crystallizing with the spinel structure, a mixed spinel, have been the subject of study for a long time [1,2]. A number of investigators have studied the influence of divalent Zn [3], trivalent In [4] and tetravalent Ti [5– 7] substitution in its various properties. The effect of
*
Corresponding author. Tel.: +92-61-220-089; fax: +92-61220-091. E-mail address: [email protected] (M.U. Rana).
Ge substitution in Mg – ferrites have been also studied [2]. The basic magnetic properties of ferrites are very sensitive function of the distribution of the metallic ions among the available A and B sites [8]. In the present study, the influence of addition of Ni in MgFe2O4 ferrite system has been investigated. The low field ac susceptibility (v) method reported earlier [9] was used for these investigations. 1/v vs. T plots have been drawn and the exchange integral for each sample have been calculated using paramagnetic temperature h obtained from these curves. Such calculations have been carried out by Neel [10] and Srivastava et al. [11]. In these calculations, spontaneous magnetization and susceptibility data in para-
0167-577X/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 5 7 7 X ( 0 2 ) 0 0 8 9 7 - 2
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M.U. Rana, T. Abbas / Materials Letters 57 (2002) 925–928
magnetic region with the application of molecular field theory [12] was used. We present here the direct calculation of the strongest ferrimagnetic exchange constants in the paramagnetic region.
2. Experimental The polycrystalline solid solution of Mg1 xNix Fe2O4 ferrites of different compositions (with x ranging from 0.0 to 1.0 in steps of 0.25) were prepared by standard ceramic technique using analytical reagent grade MgCO3, NiO and Fe2O3 in the form of grained powder having 99.99% purity supplied by GmMH (Emerk, Germany). The required weight percentage of the oxide materials were crushed to fine powder (particle size < 50 Am) in an agate mortar and the grinding continued for about an hour till a homogeneous mixture was obtained. The final ground powder was cold-pressed at a pressure of 30 kN/mm2 using Paul-Otto Weber hydraulic press. The samples were heat-treated at 1000 jC for 45 h. For the completion of the reaction, final sintering was carried out in air at 1200 jC for 5 h in a box furnace. A Shimadzu XD-5 diffractometer equipped with Cu-Ka radiation source was employed to identify the phase constitution and structure of air-cooled pallets. Temperature-dependent magnetic susceptibility for Mg1 xNixFe2O4 was measured over a temperature range where the samples obey the Curie –Weiss law using mutual inductance technique. The asymptote to the 1/v vs. T curves gives the values of the Curie constant C and paramagnetic
Fig. 1. Lattice constant vs. Ni-concentration in the Mg1 xNixFe2O4 ferrite system.
Fig. 2. Representative curves for 1/v vs. temperature in the Mg1 xNixFe2O4 ferrite system.
Curie temperature h(K). From the values of C and h(K) the g-values, effective magnetic moments and the dominant exchange interaction for the respected sample are calculated.
3. Results and discussion For all the samples, X-ray diffraction patterns show single phase spinel structure. Lattice constant values for different compositions are shown in Fig. 1. The inverse of the susceptibility vs. temperature curves for three representative concentrations of Mg1 xNix Fe2O4 ferrite are shown in Fig. 2. In the molecular field approximation, the constant C of the Curie – Weiss law is proportional to the square of the effective
Fig. 3. Effective magnetic moments vs. Ni-concentration in the Mg1 xNixFe2O4 ferrite system.
M.U. Rana, T. Abbas / Materials Letters 57 (2002) 925–928
927
Fig. 4. Paramagnetic Curie temperature vs. Ni-concentration in the Mg1 xNixFe2O4 ferrite system.
Fig. 6. Exchange integral vs. Ni-concentration in the Mg1 xNix Fe2O4 ferrite system.
atomic magnetic moment (Fig. 3) and the paramagnetic Curie temperature h (Fig. 4) is given by the following relation [13];
value equal to 1.0. The effective magnetic moment calculated from the g-value varies from 1.58 to 2.21 AB. The increase in the magnetic moment follows the increase in the g-values with the substitution of Ni ions (more magnetic nature than Mg) in the Mg1 x NixFe2O4 ferrite system as presented in Table 2. The following conclusion can be drawn from the susceptibility analysis:
h ¼ JSðS þ 1Þ=3k where J is the exchange integral, S is the spin and k is the Boltzmann constant. The hyperbolic form of the 1/ v vs. T for all concentration is observed as predicted by Neel’s theory (Figs. 5 and 6). The g-values presented in Table 1, varies from 1.80 to 2.21 in going from MgFe2O4 to NiFe2O4. The g-value for MgFe2O4 is 1.80, while the value of g = 2.03 – 2.06 is reported in the literature [14 – 17]. With the substitution of Ni, the g-value increases and is 2.21 for the NiFe2O4 ferrite, which is in good agreement with the value reported by Gorter [14]. The increase in the gvalue with the addition of Ni2 + ion is attributed to the fact that Ni2 + ions are more magnetic and have spin
(i)
Ni is more magnetic than Mg, which results in an increase of effective magnetic moments; (ii) Because of the addition of Ni, the paramagnetic Curie temperature increases; (iii) Canting and frustration leads to non-colinear type of arrangement on the B sublattice. Experimentally, the exchange interaction between the spin of the divalent metal ions present in the ferrite system and the strength of magnetic interaction and ordering is calculated by the paramagnetic Curie temperature, h(K), determined from the 1/v vs. T curves of each concentration in Mg1 xNixFe2O4 Table 1 The values of Lande g-factor, effective magnetic moment ( Peff), paramagnetic Curie temperature (h(K)) and exchange integral ( J/k) for Mg1 xNixFe2O4 ferrites
Fig. 5. Curie temperature vs. Ni-concentration in the Mg1 xNix Fe2O4 ferrite system.
Sample
g
Peff
h(K)
J/k (K)
MgFe2O4 Mg0.75NixFe2O4 Mg0.50NixFe2O4 Mg0.25NixFe2O4 NiFe2O4
1.80 1.85 1.89 2.16 2.21
1.58 1.60 1.63 2.16 2.21
31 35 56 63 45
16.4 17.5 19.2 21.6 15.42
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M.U. Rana, T. Abbas / Materials Letters 57 (2002) 925–928
Table 2 Magnetic moments (nB), Curie temperature (Tc) and the Y – K angles (aY – K) in MgNi – ferrites Sample
nB
Tc (K)
aY – K (j)
MgFe2O4 Mg0.75NixFe2O4 Mg0.50NixFe2O4 Mg0.25NixFe2O4 NiFe2O4
1.31 1.41 2.09 4.49 3.45
590 560 500 475 440
29.85 31.70 34.31 45.05 60.50
ferrite family. The values of the exchange integral are presented in Table 2. The values of h(K) increase with increasing Ni contents up to x = 0.75, which results in the strengthening of A – B interaction correspondingly between two sublattices. This can be explained on the basis of the ionic distribution among A- and B-sites. The results in Table 2 indicate that both Mg and Ni ions occupy the B-site and with the substitution of Ni in MgFe2O4, more and more Ni2 + ions start occupying the B-site, while there is no change in Fe3 + ions on either site, which results in the increase of magnetization of B-sublattice (mB) and reduction of magnetization of A-site (mA) is attributed to the fact that Ni is more magnetic, having spin 1, and magnetic moment 2.3 AB, as compared to Mg ions. This reduces the BB interaction and the AB interaction starts increasing up to 75% contents of Ni because of the antiparallel arrangement of magnetic moments of sites A and B. This can be understood by applying the Weiss molecular field theory when a too-high value of especially a, the molecular field constant associated with site A, is the interaction within the sublattice with the smallest magnetization [18]. With continuous substitution of Ni, i.e., above 75% maximum antiparallelism between the number of FeA and FeB ions cannot be maintained against the increasing antiparallel interaction with the B ion lattice. The magnetization then falls, which can be seen by the decreasing value of magnetic moment nB. The value of magnetic moment decreases from 4.49 to 3.45 AB with the increase in the aY – K from 29.85j to 60.50j as shown in Table 2. The increase in the effective magnetic moments from susceptibility measurement is consistent with A – B interaction as reported earlier [19]. The increase in JAB is due to the antiparallel nature of sites A and B with the substitution of Ni and the decrease in magnetic moments is due to the weakening of A – B interaction beyond
x = 0.75, which can be explained on the basis of canting and triangular spin arrangement of Y – K type on B-sublattice.
4. Conclusion The dominant interaction in all the ferrite samples is A – B interaction, which is due to the negative values of characteristic temperature h(K), showing that the magnetic ordering is antiferromagnetic. The Y – K angles increase gradually with increasing nickel contents and extrapolate to 60j for NiFe2O4. From the computation of Y –K angles for Mg1 xNixFe2O4, it can be concluded that the mixed magnesium ferrites exhibit a non-colinearity of the Y – K type while for MgFe2O4 shows a Neel type of ordering.
References [1] L.M. Corless, J.M. Hasting, Phys. Rev. 90 (6) (1953) 1013 – 1018. [2] D.R. Sagar, C. Parkash, B. Kishan, SSC 68 (2) (1988) 193 – 195. [3] O.S. Josyulu, J.S. Sobhanadri, Phys. Status Solidi, A 65 (1981) 479. [4] P.P. Kirichok, A.I. Antoshchuk, Inorg. Mater. 13 (1978) 1073. [5] G. Blasse, Philips Res. Rep. (Suppl. No. 3) (1964) 91. [6] E.D. Grave, C. Dauwe, A. Govaert, J. De Sittler, Appl. Phys. 12 (1977) 131. [7] E. De Grave, J. De Sittler, R. Vandenberghe, Appl. Phys. 7 (1975) 77. [8] J. Samuel Smart, Phys. Rev. 94 (4) (1954) 847. [9] M. Rana, M.Ch. Ashraf, T. Abbas, Mod. Phys. Lett. B 5 (1991) 1669. [10] L. Neel, Ann. Phys. 3 (1948) 137; Ann. Phys. 8 (1987) 3668. [11] G.M. Srivastava, G. Srivavasan, N.G. Nanadikar, Phys. Rev. B 19 (1979) 411. [12] P.W. Anderson, Phys. Rev. 115 (1959) 2. [13] M.U. Rana, M.U. Islam, T. Abbas, SSC 99 (1) (1996) 43 – 45. [14] E.W. Gorter, Philips Res. Rep. 9 (1954) 259 – 443. [15] G. Blasse, Philips Res. Rep. (Suppl. 3) (1954) Eindhoven. [16] E.J.W. Verwey, H.L. Heilmann, J. Chem. Phys. 15 (4) (1947) 174 – 180. [17] K.J. Stainly, Oxide Magnetic Materials, Clarendon Press, Oxford, 1972. [18] J. Smit, H.P.J. Wijn, Ferrites, Wiley, New York 1959, pp. 155 – 156. [19] M.U. Rana, M.U. Islam, I. Ahmad, T. Abbas, JMMM 187 (1998) 242 – 246.
Materials Letters 57 (2002) 925 – 928 www.elsevier.com/locate/matlet
Ac susceptibility and magnetic interaction in Mg–Ni–Fe–O system Mazhar U. Rana*, Tahir Abbas Department of Physics and Materials Science, Bahauddin Zakariya University, Multan 60800, Pakistan Received 23 November 2001; received in revised form 18 April 2002; accepted 29 April 2002
Abstract A series of Mg1 xNixFe2O4 spinel ferrites with x = 0, 0.25, 0.50, 0.75 and 1.0 have been prepared using standard ceramic method. Lande-g factor ( g), effective magnetic moments ( Peff), Curie temperature (Tc), paramagnetic Curie temperature (h(K)) and exchange integral ( J/k) were calculated from ac susceptibility measurements using mutual inductance technique. With the addition of Ni ions g-values, Peff and h(K) show increasing trend up to x = 0.75 while Tc continues to decrease. For x>0.75 decreasing trend in magnetic moments (nB) and h(K) is exhibited, which could be correlated to the redistribution of cations on A and B sites. The dominant interaction in all the samples is A – B interaction, which is due to the negative values of h(K), showing the magnetic ordering is antiferromagnetic. The Y – K angle increases gradually with increasing Ni contents and extrapolates to 60j for NiFe2O4. From the computation of Y – K angles for Mg1 xNixFe2O4, it can be concluded that mixed nickel ferrites exhibit a non-colinearity of the Y – K type while MgFe2O4 show a Neel type of ordering. D 2002 Elsevier Science B.V. All rights reserved. Keywords: Magnesium ferrites; Susceptibility; Magnetic moments; Interaction; Y – K angles
1. Introduction Magnesium ferrites belong to a class of compounds having the general formula M2 + Fe23 + O4 and crystallizing with the spinel structure, a mixed spinel, have been the subject of study for a long time [1,2]. A number of investigators have studied the influence of divalent Zn [3], trivalent In [4] and tetravalent Ti [5– 7] substitution in its various properties. The effect of
*
Corresponding author. Tel.: +92-61-220-089; fax: +92-61220-091. E-mail address: [email protected] (M.U. Rana).
Ge substitution in Mg – ferrites have been also studied [2]. The basic magnetic properties of ferrites are very sensitive function of the distribution of the metallic ions among the available A and B sites [8]. In the present study, the influence of addition of Ni in MgFe2O4 ferrite system has been investigated. The low field ac susceptibility (v) method reported earlier [9] was used for these investigations. 1/v vs. T plots have been drawn and the exchange integral for each sample have been calculated using paramagnetic temperature h obtained from these curves. Such calculations have been carried out by Neel [10] and Srivastava et al. [11]. In these calculations, spontaneous magnetization and susceptibility data in para-
0167-577X/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 5 7 7 X ( 0 2 ) 0 0 8 9 7 - 2
926
M.U. Rana, T. Abbas / Materials Letters 57 (2002) 925–928
magnetic region with the application of molecular field theory [12] was used. We present here the direct calculation of the strongest ferrimagnetic exchange constants in the paramagnetic region.
2. Experimental The polycrystalline solid solution of Mg1 xNix Fe2O4 ferrites of different compositions (with x ranging from 0.0 to 1.0 in steps of 0.25) were prepared by standard ceramic technique using analytical reagent grade MgCO3, NiO and Fe2O3 in the form of grained powder having 99.99% purity supplied by GmMH (Emerk, Germany). The required weight percentage of the oxide materials were crushed to fine powder (particle size < 50 Am) in an agate mortar and the grinding continued for about an hour till a homogeneous mixture was obtained. The final ground powder was cold-pressed at a pressure of 30 kN/mm2 using Paul-Otto Weber hydraulic press. The samples were heat-treated at 1000 jC for 45 h. For the completion of the reaction, final sintering was carried out in air at 1200 jC for 5 h in a box furnace. A Shimadzu XD-5 diffractometer equipped with Cu-Ka radiation source was employed to identify the phase constitution and structure of air-cooled pallets. Temperature-dependent magnetic susceptibility for Mg1 xNixFe2O4 was measured over a temperature range where the samples obey the Curie –Weiss law using mutual inductance technique. The asymptote to the 1/v vs. T curves gives the values of the Curie constant C and paramagnetic
Fig. 1. Lattice constant vs. Ni-concentration in the Mg1 xNixFe2O4 ferrite system.
Fig. 2. Representative curves for 1/v vs. temperature in the Mg1 xNixFe2O4 ferrite system.
Curie temperature h(K). From the values of C and h(K) the g-values, effective magnetic moments and the dominant exchange interaction for the respected sample are calculated.
3. Results and discussion For all the samples, X-ray diffraction patterns show single phase spinel structure. Lattice constant values for different compositions are shown in Fig. 1. The inverse of the susceptibility vs. temperature curves for three representative concentrations of Mg1 xNix Fe2O4 ferrite are shown in Fig. 2. In the molecular field approximation, the constant C of the Curie – Weiss law is proportional to the square of the effective
Fig. 3. Effective magnetic moments vs. Ni-concentration in the Mg1 xNixFe2O4 ferrite system.
M.U. Rana, T. Abbas / Materials Letters 57 (2002) 925–928
927
Fig. 4. Paramagnetic Curie temperature vs. Ni-concentration in the Mg1 xNixFe2O4 ferrite system.
Fig. 6. Exchange integral vs. Ni-concentration in the Mg1 xNix Fe2O4 ferrite system.
atomic magnetic moment (Fig. 3) and the paramagnetic Curie temperature h (Fig. 4) is given by the following relation [13];
value equal to 1.0. The effective magnetic moment calculated from the g-value varies from 1.58 to 2.21 AB. The increase in the magnetic moment follows the increase in the g-values with the substitution of Ni ions (more magnetic nature than Mg) in the Mg1 x NixFe2O4 ferrite system as presented in Table 2. The following conclusion can be drawn from the susceptibility analysis:
h ¼ JSðS þ 1Þ=3k where J is the exchange integral, S is the spin and k is the Boltzmann constant. The hyperbolic form of the 1/ v vs. T for all concentration is observed as predicted by Neel’s theory (Figs. 5 and 6). The g-values presented in Table 1, varies from 1.80 to 2.21 in going from MgFe2O4 to NiFe2O4. The g-value for MgFe2O4 is 1.80, while the value of g = 2.03 – 2.06 is reported in the literature [14 – 17]. With the substitution of Ni, the g-value increases and is 2.21 for the NiFe2O4 ferrite, which is in good agreement with the value reported by Gorter [14]. The increase in the gvalue with the addition of Ni2 + ion is attributed to the fact that Ni2 + ions are more magnetic and have spin
(i)
Ni is more magnetic than Mg, which results in an increase of effective magnetic moments; (ii) Because of the addition of Ni, the paramagnetic Curie temperature increases; (iii) Canting and frustration leads to non-colinear type of arrangement on the B sublattice. Experimentally, the exchange interaction between the spin of the divalent metal ions present in the ferrite system and the strength of magnetic interaction and ordering is calculated by the paramagnetic Curie temperature, h(K), determined from the 1/v vs. T curves of each concentration in Mg1 xNixFe2O4 Table 1 The values of Lande g-factor, effective magnetic moment ( Peff), paramagnetic Curie temperature (h(K)) and exchange integral ( J/k) for Mg1 xNixFe2O4 ferrites
Fig. 5. Curie temperature vs. Ni-concentration in the Mg1 xNix Fe2O4 ferrite system.
Sample
g
Peff
h(K)
J/k (K)
MgFe2O4 Mg0.75NixFe2O4 Mg0.50NixFe2O4 Mg0.25NixFe2O4 NiFe2O4
1.80 1.85 1.89 2.16 2.21
1.58 1.60 1.63 2.16 2.21
31 35 56 63 45
16.4 17.5 19.2 21.6 15.42
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M.U. Rana, T. Abbas / Materials Letters 57 (2002) 925–928
Table 2 Magnetic moments (nB), Curie temperature (Tc) and the Y – K angles (aY – K) in MgNi – ferrites Sample
nB
Tc (K)
aY – K (j)
MgFe2O4 Mg0.75NixFe2O4 Mg0.50NixFe2O4 Mg0.25NixFe2O4 NiFe2O4
1.31 1.41 2.09 4.49 3.45
590 560 500 475 440
29.85 31.70 34.31 45.05 60.50
ferrite family. The values of the exchange integral are presented in Table 2. The values of h(K) increase with increasing Ni contents up to x = 0.75, which results in the strengthening of A – B interaction correspondingly between two sublattices. This can be explained on the basis of the ionic distribution among A- and B-sites. The results in Table 2 indicate that both Mg and Ni ions occupy the B-site and with the substitution of Ni in MgFe2O4, more and more Ni2 + ions start occupying the B-site, while there is no change in Fe3 + ions on either site, which results in the increase of magnetization of B-sublattice (mB) and reduction of magnetization of A-site (mA) is attributed to the fact that Ni is more magnetic, having spin 1, and magnetic moment 2.3 AB, as compared to Mg ions. This reduces the BB interaction and the AB interaction starts increasing up to 75% contents of Ni because of the antiparallel arrangement of magnetic moments of sites A and B. This can be understood by applying the Weiss molecular field theory when a too-high value of especially a, the molecular field constant associated with site A, is the interaction within the sublattice with the smallest magnetization [18]. With continuous substitution of Ni, i.e., above 75% maximum antiparallelism between the number of FeA and FeB ions cannot be maintained against the increasing antiparallel interaction with the B ion lattice. The magnetization then falls, which can be seen by the decreasing value of magnetic moment nB. The value of magnetic moment decreases from 4.49 to 3.45 AB with the increase in the aY – K from 29.85j to 60.50j as shown in Table 2. The increase in the effective magnetic moments from susceptibility measurement is consistent with A – B interaction as reported earlier [19]. The increase in JAB is due to the antiparallel nature of sites A and B with the substitution of Ni and the decrease in magnetic moments is due to the weakening of A – B interaction beyond
x = 0.75, which can be explained on the basis of canting and triangular spin arrangement of Y – K type on B-sublattice.
4. Conclusion The dominant interaction in all the ferrite samples is A – B interaction, which is due to the negative values of characteristic temperature h(K), showing that the magnetic ordering is antiferromagnetic. The Y – K angles increase gradually with increasing nickel contents and extrapolate to 60j for NiFe2O4. From the computation of Y –K angles for Mg1 xNixFe2O4, it can be concluded that the mixed magnesium ferrites exhibit a non-colinearity of the Y – K type while for MgFe2O4 shows a Neel type of ordering.
References [1] L.M. Corless, J.M. Hasting, Phys. Rev. 90 (6) (1953) 1013 – 1018. [2] D.R. Sagar, C. Parkash, B. Kishan, SSC 68 (2) (1988) 193 – 195. [3] O.S. Josyulu, J.S. Sobhanadri, Phys. Status Solidi, A 65 (1981) 479. [4] P.P. Kirichok, A.I. Antoshchuk, Inorg. Mater. 13 (1978) 1073. [5] G. Blasse, Philips Res. Rep. (Suppl. No. 3) (1964) 91. [6] E.D. Grave, C. Dauwe, A. Govaert, J. De Sittler, Appl. Phys. 12 (1977) 131. [7] E. De Grave, J. De Sittler, R. Vandenberghe, Appl. Phys. 7 (1975) 77. [8] J. Samuel Smart, Phys. Rev. 94 (4) (1954) 847. [9] M. Rana, M.Ch. Ashraf, T. Abbas, Mod. Phys. Lett. B 5 (1991) 1669. [10] L. Neel, Ann. Phys. 3 (1948) 137; Ann. Phys. 8 (1987) 3668. [11] G.M. Srivastava, G. Srivavasan, N.G. Nanadikar, Phys. Rev. B 19 (1979) 411. [12] P.W. Anderson, Phys. Rev. 115 (1959) 2. [13] M.U. Rana, M.U. Islam, T. Abbas, SSC 99 (1) (1996) 43 – 45. [14] E.W. Gorter, Philips Res. Rep. 9 (1954) 259 – 443. [15] G. Blasse, Philips Res. Rep. (Suppl. 3) (1954) Eindhoven. [16] E.J.W. Verwey, H.L. Heilmann, J. Chem. Phys. 15 (4) (1947) 174 – 180. [17] K.J. Stainly, Oxide Magnetic Materials, Clarendon Press, Oxford, 1972. [18] J. Smit, H.P.J. Wijn, Ferrites, Wiley, New York 1959, pp. 155 – 156. [19] M.U. Rana, M.U. Islam, I. Ahmad, T. Abbas, JMMM 187 (1998) 242 – 246.