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Semiconductivity in Ba2Ni2−xZnxFe12O22 Y-type hexaferrites
Journal of Magnetism and Magnetic Materials 195 (1999) 667}678
Semiconductivity in Ba Ni Zn Fe O Y-type hexaferrites \V V M.A. El Hiti, A.M. Abo El Ata* Faculty of Science, Physics Department, Tanta University, Tanta, Egypt Received 7 July 1998; received in revised form 18 December 1998
Abstract The electric, thermoelectric and magnetic properties were studied as a function of temperature and composition for a series of Ba Ni Zn Fe O Y-type hexaferrite samples (with x"0, 0.4, 0.8, 1.2, 1.6 and 2) prepared using the usual \V V ceramic technique. The experimental results indicated that the DC electrical conductivity p , thermoelectric power a, "! di! mobility k , carrier concentration n and initial magnetic permeability k increase whereas the Fermi energy E decreases as the temperature increases. a has a negative sign for all samples indicating that the majority of electric $ charge carriers are electrons. The study of initial magnetic permeability showed two peaks on k }¹ curves. The "rst peak nearly appears at Curie temperature ¹ for all samples except for the sample with x"2 while the second peak ¹ appears below room temperature for all samples. ¹ decreases due to the replacement of non-magnetic Zn> ions to magnetic Ni> ions. k , activation energies for hopping E , for carrier generation E and for electric conduction (E , E and E in & regions I, II and III) decreases to reach minimum at x"1.2 and start to increase for x'1.2. Each of p , a, n, k and "! energy at donor level E increase as the substitution of non-magnetic Zn> ions to magnetic Ni> ions increase reaching " maximum at x"1.2 and start to decreases for x'1.2. The small values of k and its strong temperature-dependence (exponential relation) indicate that the hopping conduction mechanism is predominant at high temperatures in region III. In region II, the band conduction mechanism shares in electric conduction process beside the hopping conduction mechanism. The band conduction mechanism is predominant in region I. 1999 Elsevier Science B.V. All rights reserved. Keywords: DC electrical conductivity; Thermoelectric power; Magnetic permeability; Carrier concentration; Activation energies
1. Introduction The chemical composition, type and amount of additives, preparation conditions such as sintering temperature, sintering time and pressing pressure of the sample [1] control the physical properties of ferrites. According to their crystal structure, hexaferrites are classi"ed into "ve main groups [2]: M-type or BaFe O , W-type or BaMe Fe O , * Corresponding author.
X-type or Ba Me Fe O , Y-type or Ba Me Fe O and Z-type or Ba Me Fe O . Where Me represents a divalent metal ion from the "rst transition series or it may represent Zn or Mg. The Curie temperature and anisotropy were studied for Y-type Ba Zn Fe O [3] while the structure [4] and complex magnetic permeability [5] were studied for the hexaferrites Ba Ni Zn Fe O . The study of electrical con \V V ductivity, thermoelectric power, carriers concentration, activation energies, and drift mobility give much more valuable information on the behavior
0304-8853/99/$ - see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 9 9 ) 0 0 1 2 0 - 1
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of free and localized electric charge carriers. This leads to good explanation and understanding of the mechanism of electric conduction in the studied samples. Therefore, the authors aimed to study the e!ect of temperature and composition on the thermoelectric power, DC electrical conductivity, carrier concentration, drift mobility, Fermi energy and magnetic permeability for a series of Ba Ni Zn Fe O Y-type hexaferrites pre \V V pared by the usual ceramic technique. Fig. 1. Resonance circuit used for the determination of magnetic permeability k .
2. Experimental A series of samples of the Y-type Ba Ni Zn Fe O hexaferrite system (with \V V x"0, 0.4, 0.8, 1.2, 1.6 and 2) were prepared in the form of discs (of thickness h and cross-sectional area A) using the usual ceramics technique as mentioned earlier [4]. The surfaces of the disc-shaped samples were polished well, then coated with silver paste as contact materials for the electrical measurements. Owing to Ohm's law, DC electrical conductivity p was determined from the DC cur"! rent}voltage relation for all samples from room temperature up to about 850 K using the twoprobe method. The thermoelectric power a was determined form the resulted thermovoltage *< under a temperature di!erence *¹ between the two surfaces as a"*
(1)
C is a variable capacitance, C is the stray capacitance and ¸ is the self-inductance of the coil wound around the sample. On drawing the relation between 1/f and C, the values of ¸ could be cal culated from the slope of the lines as a function of temperature and composition. The initial magnetic permeability k was calculated from the values of ¸ using the following relation: D k" 10¸, BS
(2)
where B"(b!a)h and D"(b#a)/2 are the area and average radius of the toroidal sample; a and b are the internal and external radii of the toroid. The magnetic permeability k was studied below room temperature (from 110 K using liquid nitrogen cooling) up to 950 K (using an electric heater around the samples). The temperature of the samples was measured and controlled using a Ni}NiCr thermocouple in contact with the samples. The experimental measurements were carried out under vacuum to avoid moisture absorption on surfaces of the samples and to reduce the loss of heat. This work was carried out at the Physics Department, Faculty of Science, Tanta University, Egypt. 3. Results and discussion 3.1. Temperature dependence For semiconductors, the temperature dependence of the DC electrical conductivity p is simply "!
M.A. El Hiti, A.M. Abo El Ata / Journal of Magnetism and Magnetic Materials 195 (1999) 667}678
controlled by the following Arrhenius relation:
E , p "p exp ! "! k¹
(3)
where p is a pre-exponential constant of conduct ivity unit ()\ cm\), E is the activation energy for electric conduction and k is Boltzmann's constant. The logarithmic representation of Eq. (3) (ln p "! versus 1/¹) is given in Fig. 2a. According to Eq. (3) and to the theory of magnetic semiconductors of Irkhin and Turov [11], Fig. 2a must represent a straight line (for each sample) whose slope increases on passing from the ferrimagnetic to the paramagnetic region. Generally, Fig. 2a shows three regions with two breaks at di!erent temperatures. This behavior of the di!erent regions with di!erent activation energies was observed before for each of Cu}Ti [12], NiZn}Cu [13], Li}Ti [14], Li}Ni [15], Cu}Ni [16] and Cu}Co [17] ferrites. Region I appears at low temperatures (from room temperature), it is characterized with low electrical conductivity values (from 6;10\ up to 2.5;
10\ )\ cm) and low activation energy values (from 0.056 up to 0.098 eV). The conduction in this region is attributed mainly to impurities, defects and interstitial which generally appear in ferrites at low temperatures. The low values of electrical conductivity in region I is attributed mainly to the very low concentration of impurities. The small values of activation energy for electric conduction E in re gion I are related to the fact that the charge carriers from impurities are free and not localized. The conductivity and activation energy slightly increases in the region II from 1.5;10\ up to 1.2;10\ )\ cm\; and from 0.32 to 0.67 eV, respectively. The conduction mechanism in region II may be a!ected either by phase transition [16] or may be related to some type of impurity phase still present in the samples. Region III is characterized by high conductivity (from 1.8;10\ up to 0.14 )\ cm\) and low activation energy (from 0.048 up to 0.086 eV). The conduction is attributed to the change in magnetic order or magnetic transition from the ferrimagnetic to the paramagnetic state. Two transition temperatures, the "rst (¹ ) and second (¹ ) temperatures, separate the three regions in Fig. 2a. In many ferrites, where the hopping conduction mechanism (small polaron) is dominant, the DC electrical conductivity p was theoretically pre"! dicted in the following form [18}20]:
E p "A ¹ exp ! , "! k¹
Fig. 2. Temperature dependence of the DC electrical conductivity p for samples with composition x"(䊐) 0.0, (䉬) 0.4, (#) "! 0.8, (*) 1.2, (*) 1.6 and (䉭) 2 for: (a) ln p versus 1/¹ and "! (b) ln p ¹ versus 1/¹. "!
669
(4)
where A is a pre-exponential constant. The semilogarithmic representation of Eq. (4) as given in Fig. 2b shows the same behavior as in Fig. 2a. The e!ect of temperature on the thermoelectric power a is illustrated in Fig. 3 for all samples. Fig. 3 shows that a is negative for all samples over the whole temperature range. This indicates that the majority of electric charge carriers are electrons, therefore the studied samples are extrinsic semiconductors of n-type. Fig. 3 shows that a increases on increasing the temperature. This could be related to the fact that the hopping or/and number of charge carrier increases as temperature increases (due to the thermal activation or enhancement). Fig. 3 shows
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M.A. El Hiti, A.M. Abo El Ata / Journal of Magnetism and Magnetic Materials 195 (1999) 667}678
Fig. 3. E!ect of temperature ¹ on the thermoelectric power a for samples in Fig. 2.
cusp-like minima at certain temperatures ¹ . A similar behavior was observed earlier for Cu}Ti [12], MgCu}Al [21], Cu [22] and MgZn}Zr [23] ferrites. These cusp-like minima were related to the "lling of oxygen vacancies at these temperatures, this reduces the concentration of mobile electrons [12]. The temperatures ¹ at these cusp-like min ima are determined from Fig. 3 as a function of composition. The carrier concentration n and the thermoelectric power a are controlled by the following expression [24,25]:
a n"N exp ! , k
(5)
where N"10 cm\ for low-mobility semiconductors like ferrites of localized energy levels [26,27]. The carrier concentration n is calculated at di!erent temperatures from the experimental values of a using Eq. (5) for all samples. The calculated values of n are represented in Fig. 4 as a function of temperature ¹ in the semilogarithmic form (ln n versus 1/¹). Generally, Fig. 4 shows that n increases on increasing the temperature due to the thermal liberation (generation) of electrons. The temperature dependence of charge carries n is con-
trolled by the following expression [28]:
E n"N exp ! , k¹
(6)
where E is the activation energy for the generation of charge carrier and N is a pre-exponential con stant. The activation energy E was calculated from Fig. 4 as a function of composition and listed in Table 1. When only one type of charge carrier is predominant and is responsible for electric conduction (electrons for the present samples), then the Fermi energy E in terms of temperature ¹ and ther$ moelectric power a is given by the following expression [29,30]: E "ea¹!B k¹. (7) $ Using the experimental values of a and corresponding temperatures ¹ in Eq. (7), the Fermi energy E could be calculated for all samples as a function $ of temperature (for B "0 and 2). E is represented $ in Fig. 5 as a function of temperature ¹ that shows a linear relationship above ¹"450 K. E de$ creases as the temperature increases. This is due to the fact that, the charge carriers at higher temperatures occupy energy levels (Fermi levels) nearer to the bottom of conduction band (at donor level).
M.A. El Hiti, A.M. Abo El Ata / Journal of Magnetism and Magnetic Materials 195 (1999) 667}678
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Fig. 4. E!ect of temperature on the charge carrier concentration n for samples in Fig. 2.
Table 1 Compositional dependence of activation energies for electric conduction (E , E and E ); for hopping E , for carrier generation E and at & donor level E " X
Composition
E
E
E
E
E &
E "
0.0 0.4 0.8 1.2 1.6 2.0
Ba Ni Fe O Ba Ni Zn Fe O Ba Ni Zn Fe O Ba Ni Zn Fe O Ba Ni Zn Fe O Ba Zn Fe O
0.060 0.061 0.056 0.070 0.086 0.098
0.527 0.490 0.404 0.326 0.595 0.667
0.071 0.054 0.048 0.061 0.077 0.086
0.130 0.116 0.107 0.132 0.154 0.187
0.120 0.108 0.096 0.111 0.141 0.172
0.097 0.125 0.142 0.138 0.128 0.117
Fig. 5 shows a non-linearity below ¹"450 K, this is due to the predominance of impurity conduction in the low temperature region. The Fermi energy E in terms of temperature ¹, energy at donor level $ E , and concentration of acceptors N and donors " N and (for the present samples N 'N '0) is " " given by the following expression [31,32]:
E "E #k¹ ln $ "
N !N " . N
(8)
The relation between E and ¹ sometimes repres$ ents a straight line at high temperatures and a curve at low temperatures as was observed in the case of
the present samples, Cu}Ti [12] and Cu [22] ferrites. Sometimes, this relation is linear at low temperatures and non-linear at high temperatures as was observed for MgZn}Zr [23] ferrites. Extrapolating the linear part to ¹"0, where E "E $ " according to Eq. (8). The values of E are calculated " from Fig. 5 as a function of composition and listed in Table 1. The drift mobility k in terms of p and n is "! given by p "nek . (9) "! The experimental results of p and calculated "! values on n were used in Eq. (9) to calculate the drift
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Fig. 5. Temperature dependence of Fermi energy E for the $ same samples in Fig. 2 for: (a) B "0 and (b) B "2.
mobility k as a function of temperature for all samples. The drift mobility k is controlled by the following relationship [33]:
k E k " exp ! & , k¹ ¹
(10)
where k "eld/k is a pre-exponential constant of units cm V\ s\ K\, E is the activation energy & for hopping, l is the vibration phonon frequency, d"a(2/4 is the jumping length for charge carriers and a is the lattice constant. The logarithmic representation of Eq. (10) for all samples as shown in Fig. 6 gives straight lines with di!erent slopes. Fig. 6 indicates that the drift mobility k increases as the temperature increases, and this is related to the thermal enhancement of the hopping of charge carriers between the adjacent sites. The values of drift mobility k for the present samples are in the range 10\}10\ cm V\ s\ K\ which is in agreement with the reported values 10\ cm V\ s\ K\ for oxidic ferrites [34,35].
The activation energy for hopping E is calculated & from slopes of the lines (Fig. 6) for each sample and listed in Table 1. In region I (from room temperature to about 400 K in Fig. 2), the temperature coe$cient of carrier concentration (1/n)(dn/d¹) changes from 0.012 up to 0.058 K\. The temperature coe$cient of drift mobility (1/k )(dk /d¹) changes from 0.011 up to 0.015 K\. It was found that (1/n)(dn/d¹) is higher than (1/k )(dk /d¹); therefore, the band con duction mechanism (by impurities) is predominant in region I. In region II (from 400 K to about 500 K in Fig. 2), (1/n)(dn/d¹) changes from 0.002 to 0.094 K\ while (1/k )(dk /d¹) changes from 0.0013 to 0.0077 K\. Therefore, both the band and hopping conduction mechanisms are responsible for electric conduction in region II. The value of (1/n)(dn/d¹) changes from 0.0013 to 0.058 K\ and is lower than that for (1/k )(dk /d¹) which changes from 0.016 to 0.093 K\ (in region III above 500 K in Fig. 2). This means that the hopping conduction mechanism is dominant in region III (electron hopping between Fe> and Fe> ions at adjacent octahedral (B)-sites). The electron exchange between Fe> and Fe> ions [17,36,37] and hole transfer between Ni> and Ni> ions [36] at the equivalent crystallographic sites (specially B-sites) are responsible for electric conduction in ferrites according to Verwey de Boer mechanism [17,37]. The Ni> [36] and Fe> [38] ions could be formed during the sintering process of the samples and/or according to the following reaction, which is predominant in ferrites containing Ni> ions [36]: Ni>#Fe>&Ni>#Fe>.
(11)
The electric charge carriers (electron at 3d> in Fe> and hole at 3d in Ni> ions) are generally localized in the 3d shell. Therefore, the electric conduction takes place by the hopping of charge carriers between the occupied and unoccupied sites or between ions of di!erent valences at equivalent crystallographic positions. The localized ions come close enough due to the lattice (thermal) vibrations; as a result small polarons are induced. The e!ect of temperature on the initial magnetic permeability k is illustrated in Fig. 7a and Fig. 7b) for all samples in the temperature range from 110
M.A. El Hiti, A.M. Abo El Ata / Journal of Magnetism and Magnetic Materials 195 (1999) 667}678
673
Fig. 6. E!ect of temperature on drift mobility k of charge carriers for samples in Fig. 2.
ature ¹ for all samples except for the sample with x"2 (Ba Zn Fe O ferrite). This peak is related to the transition from the ferrimagnetic to the paramagnetic state. The second peak ¹ appears below room temperature for all samples; this peak is related to a magnetic phase transition. This secondary peak ¹ was observed before for Fe O [8], Mn ferrites [39,40], Mn}Zn ferrite [41] and Mn}Ni ferrites [42]. The height of this peak may be limited not only by some inhomogeneity of the samples but also by the shape and stress anisotropy still present [2]. The initial magnetic permeability k for the hex agonal ferrites in terms of rotational processes of saturation magnetization M and e!ective mag netocrystalline anisotropy constant K (K is a linear combination of K , K ,2) is given in the following form [2]: Fig. 7. E!ect of temperature on initial magnetic permeability k for samples in Fig. 2 for composition: (a) x"0, 0.4 and 0.8; (b) x"1.2, 1.6 and 2.
up to 950 K. Fig. 7 indicates that k increases as the temperature increases. Two peaks were observed in Fig. 7, the "rst peak nearly appears above room temperature, it is the well-known Curie temper-
M k" . (12) K Since the magnetization vector M decreases mono tonically with increasing temperature, therefore it is expected that all anomalies in the k }¹ curve could be related to the behavior of the magnetocrystalline anisotropy constant or to the orientation process of the magnetization vector with respect to C-axis. The values of ¹ and ¹ are determined as a
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M.A. El Hiti, A.M. Abo El Ata / Journal of Magnetism and Magnetic Materials 195 (1999) 667}678
function of composition from Fig. 7 and listed in Table 2. 3.2. Compositional dependence The e!ect of composition on the DC electrical conductivity p and thermoelectric power a; and "! the carrier concentration n and drift mobility k (at selected temperatures of 350, 400, 450 and 500 K) are represented in Fig. 8a and Fig. 8b; and Fig. 9a and Fig. 9b, respectively. Fig. 8a indicates that the studied samples have high electrical conductivity Table 2 Compositional dependence of the transition temperatures ¹ and ¹ (from k }¹ curves); ¹ and ¹ (from p }¹ curves) "! and ¹ (from a}¹ curves) in Kelvin degree X
¹
¹
¹
¹
¹
0.0 0.4 0.8 1.2 1.6 2.0
158 211 228 240 254 202
840 775 691 513 407 }
480 450 435 420 410 400
565 545 580 480 560 550
588 555 455 } 476 444
Fig. 8. Compositional dependence (at temperatures of: (#) 350, (䊏) 400, (£) 450 and (*) (500 K) for: (a) p and (b) a. "!
Fig. 9. Compositional dependence (at the same temperatures in Fig. 8) for: (a) n and (b) k .
p values (from 10\ up to 10\ )\ cm\). This "! could be attributed to the high concentration of Fe ions (which are the source of electronic charge carriers) as the present chemical formula Ba Ni Zn Fe O indicates. At low temper \V V atures in region I, the electric conduction is mainly by band conduction mechanism (free electrons from impurities). In region III at high temperatures, the conduction is by the hopping of localized electrons in the 3d shell between Fe> and Fe> ions (small polaron) according to Verwey mechanism [17,43] and the hopping of localized holes in 3d shell between Ni> and Ni> ions [36]. Sometimes, the free charges from impurity atoms share in the conduction process, i.e. the band conduction mechanism takes part in the conduction process besides the hopping conduction mechanism especially in region II at intermediate temperatures. Each of p "! (Fig. 8a), a (Fig. 8b), n (Fig. 9a) and k (Fig. 9b) increase as Zn> ions substitution to Ni> ions increases reaching maximum at x"1.2 and start to decrease for x'1.2. The e!ect of Zn> ions substitution on the initial magnetic permeability k and Fermi energy E (at $
M.A. El Hiti, A.M. Abo El Ata / Journal of Magnetism and Magnetic Materials 195 (1999) 667}678
selected temperatures) is given in Fig. 10a and Fig. 10b, respectively. Fig. 10a shows that the value of k decreases as Zn> ion substitution increases. This may be related to the increase in the replacement of non-magnetic Zn> ions to magnetic Ni> ions. It is suggested that the exchange interaction between the di!erent allowed seven magnetic sublattices (which leads to the parallel alignment magnetic vector to the direction perpendicular to Caxis) is stronger than that between ions in the same magnetic sub-lattice. The strength of this exchange interaction decreases when a magnetic (Ni>) ion is replaced by non-magnetic (Zn>) ion. This leads to an instability of the parallel alignment between ions and changes the magnetic state of the material. This explains the decrease in k as Zn> ion replacement to Ni> ion increases as shown in Fig. 10a. The behavior of initial magnetic permeability k (Fig. 10a) with composition is the reverse of that for DC conductivity p (Fig. 8a), thermoelectric power "! a (Fig. 8b), carrier concentration n (Fig. 9a) and drift mobility k (Fig. 9b). This behavior was ob served before for Ni Mn Fe O ferrites [42]. >V V \V It was reported that the decrease in k and increase
Fig. 10. Compositional dependence (at the same temperatures in Fig. 8) for: (a) k and (b) E . $
675
in p are related to the superparamagnetic behav"! ior of Fe> ions as in the case of ZnNi}Mn [44] and Li}Ti [45] ferrites. Fig. 10b shows that the Fermi energy E in$ creases as Zn> ion substitution increases, reaching a maximum at x"1.2 and decreasing for x'1.2. The increase in Fermi energy E (Fig. 10b) for $ x(1.2, raises the donor level E (Table 1) nearer " to the bottom of the conduction band. The e!ect of Zn> ions substitution on the activation energies for electric conduction (E , E and E in regions I, II and III from Fig. 2); for carrier generation E (from Fig. 4), at donor level E (from " Fig. 5) and for hopping E (from Fig. 6), respective& ly, are listed in Table 1. The results in Table 1 indicate that the activation energy for electric conduction E (in region II) is higher than E (in region I) and E (in region III). This could be related to the conduction by impurities (in region I which needs a small energy to move the free charge) and to the hopping conduction mechanism of localized electric charge carriers (in region III). The conduction in region II is due to both the hopping and band conduction mechanism therefore needs activation energies more than those needed in regions I and III. The activation energies for electric conduction (E , E and E ), for carrier generation E and hopping E decreases as Zn> & ion substitution increases for x(1.2 and increase for x'1.2. On the contrary, p (Fig. 8a), carriers "! concentration n (Fig. 9a) and drift mobility k (Fig. 9b) increase as Zn> ion increases for x(1.2 and decrease for x'1.2. This result is in good agreement with the conclusion that the higher electrical conductivity and drift mobility (for higher values of Zn> ions substitution) are associated with lower values of activation energies for electric conduction (E , E and E ), and hopping E , and vise versa. & The temperatures at the "rst (Curie temperature ¹ ) and secondary peaks (¹ ) observed on k }¹ curves in (Fig. 7) are listed in Table 2 as a function of Zn> ion substitution. Table 2 also shows the e!ect of Zn> ion substitution on the transition temperatures (¹ and ¹ ) on p }¹ curves (in Fig. "! 2) and the temperature ¹ at cusp-like minima observed on a}¹ plot (in Fig. 3). Table 2 shows that the values of Curie (¹ ) and secondary (¹ ), transition (¹ and ¹ ) and ¹ temperatures
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M.A. El Hiti, A.M. Abo El Ata / Journal of Magnetism and Magnetic Materials 195 (1999) 667}678
decrease as Zn> ion substitution increases. This may be attributed to the replacement of non-magnetic Zn> ions to magnetic Ni> ions, which will a!ect the magnetic order and reduce the exchange interaction; consequently this reduces the transition temperatures. No magnetic transition temperature was observed above room temperature (Curie temperature ¹ ) for samples with x"2 (Ba Zn Fe O ) when the non-magnetic Zn> ions completely replace magnetic Ni> ions. The neutron di!raction studies for Zn -Y-type materials [46] identi"ed that the basal plane is the preferred plane of magnetization from room temperature up to ¹ . Neutron di!raction [46] and MoK ssbauer [47] studies for Zn -Y-type identi "ed the presence of a phase angle between Fe ions below room temperature. The reorientation of magnetization vector from the preferred basal plane to a preferred cone of magnetization occurs at a certain temperature ¹ below room temperature. Therefore, the sharp decrease in k below room temperature may be corresponding to a transition from the preferred plane to the preferred cone (as shown in Fig. 7). This transition temperature ¹ depends on the concen tration of Ni> ion content in the samples as listed in Table 2. It has been reported that the magnetic Ni> ions preferentially occupy the B-sites [44,48}50], magnetic Fe ions partially occupy tetrahedral (A)-sites as well as B-sites [48,49,51}55]. The non-magnetic Zn> ions strongly prefer the occupation of A-sites [44,48,52,54}58]. When the replacement of Zn> ions (at A-sites) for Ni> ions (at B-sites) increases, some of Fe ions at A-sites will migrate to B-sites to balance the decrease in B-sites population [45,50,54]. As a result, the number of Fe ions at B-sites increases leading to a marked increase in p (Fig. 8a), a (Fig. 8b), (Fig. 9a) and k (Fig. 9b) for "! x(1.2. As the Zn> ions substitution increases, the concentration of Fe> and Fe> at B-sites increases more and more. As a consequence, the conduction mechanism takes place by the hopping of electrons and holes in accordance with Eq. (11). The presence or generation of large numbers of electrons and holes (at higher x) leads to the occurrence of some type of compensation between them. Therefore, the total number of charge carriers n de-
creases leading to a marked decrease in each of p "! (Fig. 8a), a (Fig. 8b), n (Fig. 9a) and k (Fig. 9b). The decrease in p for x'1.2 may be due to the "! decrease in the probability of Fe> formation, where Zn> ions start replacing Ni> ions at Bsites.
4. Conclusions (1) The DC electrical conductivity p , ther"! moelectric power a, drift mobility k and car rier concentration increase whereas the Fermi energy E decreases on increasing the temper$ ature. The increase in p , a, n, k with temper"! ature is related mainly to the thermal enhancement (activation) and/or thermal liberation of electric charge carriers. The decrease in E with temperature is due to the fact that the $ thermal energy (from heating) raises the energy (Fermi) level or donor level of electronic charge carriers for n-type semiconductors. (2) The relations between ln p and 1/¹, and "! ln p ¹ and 1/¹ represent the same behav"! ior. The variation of the electrical conductivity with temperature shows three di!erent regions. The electric conduction is due to impurities in region I which is characterized with low conductivity and low activation energy E . In re gion II which follows region I, the electrical conductivity and activation energy E increase due to thermal activation of both the drift mobility and impurities. The electric conduction is by the hopping and band conduction mechanism. Region III at high temperature is characterized with high conductivity and low activation energy E . The electric conduction in region III is related mainly to the hopping conduction mechanism. (3) The thermoelectric power a was found to be negative for all samples over the whole temperature range. This indicates that the studied samples are extrinsic semiconductors of n-type where the majority of charge carriers are electrons. Cusp-like minima are observed in a}¹ curves; these minima are related to the "lling of oxygen vacancies.
M.A. El Hiti, A.M. Abo El Ata / Journal of Magnetism and Magnetic Materials 195 (1999) 667}678
(4) The initial magnetic permeability k increases on increasing the temperature, reaching a maximum nearly at the Curie point ¹ and de creases rapidly after ¹ . The sample with x"2, did not show any magnetic transition temeprature above room temperature or Curie temperature ¹ . Another peak (¹ ) was ob served for all samples below room temperature. (5) The values of ¹ decrease on increasing Zn> ion substitution. This is due to the replacement of the magnetic Ni> ion by the non-magnetic Zn> ion. (6) The DC electrical conductivity p , ther"! moelectric power a, carriers concentration n and drift mobility k increase as Zn> ion substitution increases reaching maxima at x"1.2, and decreases for x'1.2. (7) The Fermi energy E and activation energies $ (E , E and E for electric conduction, E for carrier generation, and E for hopping) de& crease on increasing the substitution of nonmagnetic Zn> ions for magnetic Ni> ions for x(1.2 and increase for x'1.2.
Acknowledgements The authors would like to thank Dr. S.M. Attia, Physics and Chemistry Department, Faculty of Education-Kafr El Shiekh, Tanta University, for his help during the experimental measurements for the present work.
References [1] E.J.W. Verwey, P.W. Haaijman, F.C. Romeyn, G.W. van Oosterhout, Philos. Mag. Rep. 5 (1950) 173. [2] J. Smit, H.B.J. Wijn, Ferrites, Cleaver-Hume Press, London, 1959, p. 202 (Chapter IX). [3] G. Albanese, A. Dariu, F. Licci, S. Rinaldi, IEEE Trans. Magn. MAG-14 (1978) 710. [4] M.K. El Nimr, M.A. Ahmed, M.A. El Hiti, A.M. Abo El Ata, J. Mater. Sci. Lett. 1999, in press. [5] H.J. Kown, J.Y. Shin, J.H. Oh, J. Appl. Phys. 75 (1994) 6109. [6] M.A. El Hiti, A.M. Abdeen, Mater. Sci. Tehcnol. 14 (1997) 417. [7] W.D. Kingery, H.K. Bowen, D.R. Uhlmann, Introduction to Ceramics, 2nd ed., Wiley, New York, 197.
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[8] A.G. Awad, M.A. Ahmed, J. Phys. (France) 38 (1977) 237. [9] Z. Simsa, Czech. J. Phys. B 16 (1966) 919. [10] B.G. Gri!ths, D. Elwell, R. Parker, Philos. Mag. 22 (1970) 163. [11] Yu.P. Irkhin, E. Turov, Sov. Phys. JETP 33 (1957) 673. [12] B.L. Patil, S.R. Sawant, S.A. Patil, Phys. Stat. Sol. A 133 (1992) 147. [13] G.K. Joshi, A.Y. Khot, S.R. Sawant, J. Mater. Sci. 22 (1987) 1694. [14] R. Manjula, V.R.K. Murthy, J. Sobhanadri, J. Appl. Phys. 59 (1986) 2929. [15] P.V. Reddy, J. Appl. Phys. 63 (1988) 3783. [16] A.A. Ghani, A.I. Eatah, A.A. Mohamed, Proceedings of the International Conference on Ferrites, Kyoto, Japan, 1980, p. 216. [17] E.J.W. Verwey, J.H. de Boer, Red. Trav. Chim. Phys. Bas. 55 (1936) 531. [18] T. Holstein, Ann. Phys. (NY) 8 (1959) 345. [19] L. Erildman, T. Holstein, Ann. Phys. (NY) 21 (1963) 4929. [20] D. Emin, T. Holtstein, Ann. Phys. (NY) 53 (1969) 439. [21] N.V. Mulay, K.B. Reddy, V.D. Reddy, P.V. Reddy, Phys. Stat. Sol. (a) 130 (1992) 397. [22] A.A. Ghani, S.A. Mazen, A.H. Ashour, Stat. Sol. (a) 184 (1984) 337. [23] N. Nanba, S. Kobayashi, Jpn. J. Appl. Phys. 17 (1978) 1819. [24] F.J. Morin, H. Geballe, Phys. Rev. 99 (1955) 467. [25] A.A. Samokhavlov, A.G. Rustamov, Sov. Phys. Solid State 7 (1964) 749. [26] F.J. Morin, Phys. Rev. 93 (1953) 1195. [27] P.V. Reddy, T.S. Rao, Phys. Stat. Sol. (a) 92 (1985) 303. [28] C. Cropichka, Ferrite Physics and its Magnetic Oxides, Mir Publisher, Moscow, (Chapter VII) (in Russian). [29] A.E. Lo!e, Physics of Semiconductors, Iforscarch Limited, London, 1960. [30] A.J. Bosman, C. Crevecoeur, J. Phys. Chem. Solids 30 (1969) 1151. [31] J.S. Blakemore, Semiconductor Statistics, Pergamon Press, New York, 1962. [32] A.A. Ghani, S.A. Mazen, A. Ashour, Phys. Stat. Sol. (a) 84 (1984) 337. [33] R.R. Heikes, W.D. Johnason, J. Chem. Phys. 26 (1957) 582. [34] P.S. Jain, V.S. Darshane, Nucl. Phys. Solid State Symp. 24 (1981) 529. [35] M.N. Kahn, A. Venkatachalam, A. Ahmed, V.S. Darshane, J. Mater. Sci. 25 (1990) 595. [36] L.G. van Uitert, J. Chem. Phys. 23 (1955) 1883. [37] E.J. Verwey, P.W. Haaijman, F.C. Romeyn, C.W. Oostenhout, Philips Res. Rep. 9 (1954) 428. [38] F.K. Lotering, J. Phys. Chem. Solids 25 (1964) 95. [39] A. Goldman, Modern Ferrite Technology, Marcel Dekker, New York, 1993. [40] U. Enz, Physica 24 (1958) 609. [41] D. Stoppels, J. Appl. Phys. 52 (1981) 2432. [42] A.I. El Shora, M.A. El Hiti, M.K. El Nimr, M.A. Ahmed, A.M. El Hasab, J. Magn. Magn. Mater., accepted for publication.
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[43] E.J. Verwey, P.W. Haaijman, F.C. Romyen, G.W. Oosterhout, Philps Res. Rep. 9 (1954) 428. [44] B.V. Bhise, M.B. Dongar, S.A. Patil, S.R. Sawant, J. Mater. Sci. Lett. 10 (1991) 922. [45] P. Kishan, C. Prakash, J.S. Bijal, K.K. Laroia, Phys. Stat. Sol. (a) 84 (1984) 533. [46] E.E. Ymzin, Y. Lecvich, Crystal 15 (1970) 280. [47] G. Ablanese, G. Asti, C. Lamborizio, J. Appl. Phys. 39 (1968) 1198. [48] G. Joshi, S. Deshpande, A. Khot, S.R. Sawant, Solid State Commun. 65 (1988) 1593. [49] T.E. Whall, N. Salerno, Y.G. Proykova, V.A. Babers, Philos. Mag. Lett. B 53 (1986) L67. [50] B.V. Bhise, M.B. Dongar, S.A. Patil, S.R. Sawant, Phys. Rev. 122 (1962) 1447.
[51] J.S. Bijal, S. Phanjouban, D. Kothari, C. Prakash, P. Kishan, Solid State Commun. 83 (1972) 679. [52] M.N. Kahn, A.A. Ahmed, V.S. Darshane, J. Mater. Sci. 24 (1989) 163. [53] R. Bauminger, S.G. Cohen, A.M. Arinov, S. Ofer, E. Segal, Phys. Rev. 122 (1962) 1497. [54] G.K. Joshi, S.A. Deshpande, A.Y. Khot, S.R. Sawant, Ind. J. Phys. A 61 (1987) 241. [55] R.B. Jotania, R.V. Upadhay, R.G. Kulkarni, IEEE Trans. Magn. 28 (1992) 1889. [56] H. Patil, R. Upadhyay, N. Shamkuwar, R. Kulkarni, Solid State Commun. 81 (1992) 1011. [57] M. Arshed, M. Butt, M. Siddique, A. Anwar, T. Abbas, H. Ahmed, Solid State Commun. 84 (1992) 717. [58] E. Grandjean, A. Gerard, Solid State Commun. 25 (1978) 679.
Semiconductivity in Ba Ni Zn Fe O Y-type hexaferrites \V V M.A. El Hiti, A.M. Abo El Ata* Faculty of Science, Physics Department, Tanta University, Tanta, Egypt Received 7 July 1998; received in revised form 18 December 1998
Abstract The electric, thermoelectric and magnetic properties were studied as a function of temperature and composition for a series of Ba Ni Zn Fe O Y-type hexaferrite samples (with x"0, 0.4, 0.8, 1.2, 1.6 and 2) prepared using the usual \V V ceramic technique. The experimental results indicated that the DC electrical conductivity p , thermoelectric power a, "! di! mobility k , carrier concentration n and initial magnetic permeability k increase whereas the Fermi energy E decreases as the temperature increases. a has a negative sign for all samples indicating that the majority of electric $ charge carriers are electrons. The study of initial magnetic permeability showed two peaks on k }¹ curves. The "rst peak nearly appears at Curie temperature ¹ for all samples except for the sample with x"2 while the second peak ¹ appears below room temperature for all samples. ¹ decreases due to the replacement of non-magnetic Zn> ions to magnetic Ni> ions. k , activation energies for hopping E , for carrier generation E and for electric conduction (E , E and E in & regions I, II and III) decreases to reach minimum at x"1.2 and start to increase for x'1.2. Each of p , a, n, k and "! energy at donor level E increase as the substitution of non-magnetic Zn> ions to magnetic Ni> ions increase reaching " maximum at x"1.2 and start to decreases for x'1.2. The small values of k and its strong temperature-dependence (exponential relation) indicate that the hopping conduction mechanism is predominant at high temperatures in region III. In region II, the band conduction mechanism shares in electric conduction process beside the hopping conduction mechanism. The band conduction mechanism is predominant in region I. 1999 Elsevier Science B.V. All rights reserved. Keywords: DC electrical conductivity; Thermoelectric power; Magnetic permeability; Carrier concentration; Activation energies
1. Introduction The chemical composition, type and amount of additives, preparation conditions such as sintering temperature, sintering time and pressing pressure of the sample [1] control the physical properties of ferrites. According to their crystal structure, hexaferrites are classi"ed into "ve main groups [2]: M-type or BaFe O , W-type or BaMe Fe O , * Corresponding author.
X-type or Ba Me Fe O , Y-type or Ba Me Fe O and Z-type or Ba Me Fe O . Where Me represents a divalent metal ion from the "rst transition series or it may represent Zn or Mg. The Curie temperature and anisotropy were studied for Y-type Ba Zn Fe O [3] while the structure [4] and complex magnetic permeability [5] were studied for the hexaferrites Ba Ni Zn Fe O . The study of electrical con \V V ductivity, thermoelectric power, carriers concentration, activation energies, and drift mobility give much more valuable information on the behavior
0304-8853/99/$ - see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 9 9 ) 0 0 1 2 0 - 1
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of free and localized electric charge carriers. This leads to good explanation and understanding of the mechanism of electric conduction in the studied samples. Therefore, the authors aimed to study the e!ect of temperature and composition on the thermoelectric power, DC electrical conductivity, carrier concentration, drift mobility, Fermi energy and magnetic permeability for a series of Ba Ni Zn Fe O Y-type hexaferrites pre \V V pared by the usual ceramic technique. Fig. 1. Resonance circuit used for the determination of magnetic permeability k .
2. Experimental A series of samples of the Y-type Ba Ni Zn Fe O hexaferrite system (with \V V x"0, 0.4, 0.8, 1.2, 1.6 and 2) were prepared in the form of discs (of thickness h and cross-sectional area A) using the usual ceramics technique as mentioned earlier [4]. The surfaces of the disc-shaped samples were polished well, then coated with silver paste as contact materials for the electrical measurements. Owing to Ohm's law, DC electrical conductivity p was determined from the DC cur"! rent}voltage relation for all samples from room temperature up to about 850 K using the twoprobe method. The thermoelectric power a was determined form the resulted thermovoltage *< under a temperature di!erence *¹ between the two surfaces as a"*
(1)
C is a variable capacitance, C is the stray capacitance and ¸ is the self-inductance of the coil wound around the sample. On drawing the relation between 1/f and C, the values of ¸ could be cal culated from the slope of the lines as a function of temperature and composition. The initial magnetic permeability k was calculated from the values of ¸ using the following relation: D k" 10¸, BS
(2)
where B"(b!a)h and D"(b#a)/2 are the area and average radius of the toroidal sample; a and b are the internal and external radii of the toroid. The magnetic permeability k was studied below room temperature (from 110 K using liquid nitrogen cooling) up to 950 K (using an electric heater around the samples). The temperature of the samples was measured and controlled using a Ni}NiCr thermocouple in contact with the samples. The experimental measurements were carried out under vacuum to avoid moisture absorption on surfaces of the samples and to reduce the loss of heat. This work was carried out at the Physics Department, Faculty of Science, Tanta University, Egypt. 3. Results and discussion 3.1. Temperature dependence For semiconductors, the temperature dependence of the DC electrical conductivity p is simply "!
M.A. El Hiti, A.M. Abo El Ata / Journal of Magnetism and Magnetic Materials 195 (1999) 667}678
controlled by the following Arrhenius relation:
E , p "p exp ! "! k¹
(3)
where p is a pre-exponential constant of conduct ivity unit ()\ cm\), E is the activation energy for electric conduction and k is Boltzmann's constant. The logarithmic representation of Eq. (3) (ln p "! versus 1/¹) is given in Fig. 2a. According to Eq. (3) and to the theory of magnetic semiconductors of Irkhin and Turov [11], Fig. 2a must represent a straight line (for each sample) whose slope increases on passing from the ferrimagnetic to the paramagnetic region. Generally, Fig. 2a shows three regions with two breaks at di!erent temperatures. This behavior of the di!erent regions with di!erent activation energies was observed before for each of Cu}Ti [12], NiZn}Cu [13], Li}Ti [14], Li}Ni [15], Cu}Ni [16] and Cu}Co [17] ferrites. Region I appears at low temperatures (from room temperature), it is characterized with low electrical conductivity values (from 6;10\ up to 2.5;
10\ )\ cm) and low activation energy values (from 0.056 up to 0.098 eV). The conduction in this region is attributed mainly to impurities, defects and interstitial which generally appear in ferrites at low temperatures. The low values of electrical conductivity in region I is attributed mainly to the very low concentration of impurities. The small values of activation energy for electric conduction E in re gion I are related to the fact that the charge carriers from impurities are free and not localized. The conductivity and activation energy slightly increases in the region II from 1.5;10\ up to 1.2;10\ )\ cm\; and from 0.32 to 0.67 eV, respectively. The conduction mechanism in region II may be a!ected either by phase transition [16] or may be related to some type of impurity phase still present in the samples. Region III is characterized by high conductivity (from 1.8;10\ up to 0.14 )\ cm\) and low activation energy (from 0.048 up to 0.086 eV). The conduction is attributed to the change in magnetic order or magnetic transition from the ferrimagnetic to the paramagnetic state. Two transition temperatures, the "rst (¹ ) and second (¹ ) temperatures, separate the three regions in Fig. 2a. In many ferrites, where the hopping conduction mechanism (small polaron) is dominant, the DC electrical conductivity p was theoretically pre"! dicted in the following form [18}20]:
E p "A ¹ exp ! , "! k¹
Fig. 2. Temperature dependence of the DC electrical conductivity p for samples with composition x"(䊐) 0.0, (䉬) 0.4, (#) "! 0.8, (*) 1.2, (*) 1.6 and (䉭) 2 for: (a) ln p versus 1/¹ and "! (b) ln p ¹ versus 1/¹. "!
669
(4)
where A is a pre-exponential constant. The semilogarithmic representation of Eq. (4) as given in Fig. 2b shows the same behavior as in Fig. 2a. The e!ect of temperature on the thermoelectric power a is illustrated in Fig. 3 for all samples. Fig. 3 shows that a is negative for all samples over the whole temperature range. This indicates that the majority of electric charge carriers are electrons, therefore the studied samples are extrinsic semiconductors of n-type. Fig. 3 shows that a increases on increasing the temperature. This could be related to the fact that the hopping or/and number of charge carrier increases as temperature increases (due to the thermal activation or enhancement). Fig. 3 shows
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Fig. 3. E!ect of temperature ¹ on the thermoelectric power a for samples in Fig. 2.
cusp-like minima at certain temperatures ¹ . A similar behavior was observed earlier for Cu}Ti [12], MgCu}Al [21], Cu [22] and MgZn}Zr [23] ferrites. These cusp-like minima were related to the "lling of oxygen vacancies at these temperatures, this reduces the concentration of mobile electrons [12]. The temperatures ¹ at these cusp-like min ima are determined from Fig. 3 as a function of composition. The carrier concentration n and the thermoelectric power a are controlled by the following expression [24,25]:
a n"N exp ! , k
(5)
where N"10 cm\ for low-mobility semiconductors like ferrites of localized energy levels [26,27]. The carrier concentration n is calculated at di!erent temperatures from the experimental values of a using Eq. (5) for all samples. The calculated values of n are represented in Fig. 4 as a function of temperature ¹ in the semilogarithmic form (ln n versus 1/¹). Generally, Fig. 4 shows that n increases on increasing the temperature due to the thermal liberation (generation) of electrons. The temperature dependence of charge carries n is con-
trolled by the following expression [28]:
E n"N exp ! , k¹
(6)
where E is the activation energy for the generation of charge carrier and N is a pre-exponential con stant. The activation energy E was calculated from Fig. 4 as a function of composition and listed in Table 1. When only one type of charge carrier is predominant and is responsible for electric conduction (electrons for the present samples), then the Fermi energy E in terms of temperature ¹ and ther$ moelectric power a is given by the following expression [29,30]: E "ea¹!B k¹. (7) $ Using the experimental values of a and corresponding temperatures ¹ in Eq. (7), the Fermi energy E could be calculated for all samples as a function $ of temperature (for B "0 and 2). E is represented $ in Fig. 5 as a function of temperature ¹ that shows a linear relationship above ¹"450 K. E de$ creases as the temperature increases. This is due to the fact that, the charge carriers at higher temperatures occupy energy levels (Fermi levels) nearer to the bottom of conduction band (at donor level).
M.A. El Hiti, A.M. Abo El Ata / Journal of Magnetism and Magnetic Materials 195 (1999) 667}678
671
Fig. 4. E!ect of temperature on the charge carrier concentration n for samples in Fig. 2.
Table 1 Compositional dependence of activation energies for electric conduction (E , E and E ); for hopping E , for carrier generation E and at & donor level E " X
Composition
E
E
E
E
E &
E "
0.0 0.4 0.8 1.2 1.6 2.0
Ba Ni Fe O Ba Ni Zn Fe O Ba Ni Zn Fe O Ba Ni Zn Fe O Ba Ni Zn Fe O Ba Zn Fe O
0.060 0.061 0.056 0.070 0.086 0.098
0.527 0.490 0.404 0.326 0.595 0.667
0.071 0.054 0.048 0.061 0.077 0.086
0.130 0.116 0.107 0.132 0.154 0.187
0.120 0.108 0.096 0.111 0.141 0.172
0.097 0.125 0.142 0.138 0.128 0.117
Fig. 5 shows a non-linearity below ¹"450 K, this is due to the predominance of impurity conduction in the low temperature region. The Fermi energy E in terms of temperature ¹, energy at donor level $ E , and concentration of acceptors N and donors " N and (for the present samples N 'N '0) is " " given by the following expression [31,32]:
E "E #k¹ ln $ "
N !N " . N
(8)
The relation between E and ¹ sometimes repres$ ents a straight line at high temperatures and a curve at low temperatures as was observed in the case of
the present samples, Cu}Ti [12] and Cu [22] ferrites. Sometimes, this relation is linear at low temperatures and non-linear at high temperatures as was observed for MgZn}Zr [23] ferrites. Extrapolating the linear part to ¹"0, where E "E $ " according to Eq. (8). The values of E are calculated " from Fig. 5 as a function of composition and listed in Table 1. The drift mobility k in terms of p and n is "! given by p "nek . (9) "! The experimental results of p and calculated "! values on n were used in Eq. (9) to calculate the drift
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Fig. 5. Temperature dependence of Fermi energy E for the $ same samples in Fig. 2 for: (a) B "0 and (b) B "2.
mobility k as a function of temperature for all samples. The drift mobility k is controlled by the following relationship [33]:
k E k " exp ! & , k¹ ¹
(10)
where k "eld/k is a pre-exponential constant of units cm V\ s\ K\, E is the activation energy & for hopping, l is the vibration phonon frequency, d"a(2/4 is the jumping length for charge carriers and a is the lattice constant. The logarithmic representation of Eq. (10) for all samples as shown in Fig. 6 gives straight lines with di!erent slopes. Fig. 6 indicates that the drift mobility k increases as the temperature increases, and this is related to the thermal enhancement of the hopping of charge carriers between the adjacent sites. The values of drift mobility k for the present samples are in the range 10\}10\ cm V\ s\ K\ which is in agreement with the reported values 10\ cm V\ s\ K\ for oxidic ferrites [34,35].
The activation energy for hopping E is calculated & from slopes of the lines (Fig. 6) for each sample and listed in Table 1. In region I (from room temperature to about 400 K in Fig. 2), the temperature coe$cient of carrier concentration (1/n)(dn/d¹) changes from 0.012 up to 0.058 K\. The temperature coe$cient of drift mobility (1/k )(dk /d¹) changes from 0.011 up to 0.015 K\. It was found that (1/n)(dn/d¹) is higher than (1/k )(dk /d¹); therefore, the band con duction mechanism (by impurities) is predominant in region I. In region II (from 400 K to about 500 K in Fig. 2), (1/n)(dn/d¹) changes from 0.002 to 0.094 K\ while (1/k )(dk /d¹) changes from 0.0013 to 0.0077 K\. Therefore, both the band and hopping conduction mechanisms are responsible for electric conduction in region II. The value of (1/n)(dn/d¹) changes from 0.0013 to 0.058 K\ and is lower than that for (1/k )(dk /d¹) which changes from 0.016 to 0.093 K\ (in region III above 500 K in Fig. 2). This means that the hopping conduction mechanism is dominant in region III (electron hopping between Fe> and Fe> ions at adjacent octahedral (B)-sites). The electron exchange between Fe> and Fe> ions [17,36,37] and hole transfer between Ni> and Ni> ions [36] at the equivalent crystallographic sites (specially B-sites) are responsible for electric conduction in ferrites according to Verwey de Boer mechanism [17,37]. The Ni> [36] and Fe> [38] ions could be formed during the sintering process of the samples and/or according to the following reaction, which is predominant in ferrites containing Ni> ions [36]: Ni>#Fe>&Ni>#Fe>.
(11)
The electric charge carriers (electron at 3d> in Fe> and hole at 3d in Ni> ions) are generally localized in the 3d shell. Therefore, the electric conduction takes place by the hopping of charge carriers between the occupied and unoccupied sites or between ions of di!erent valences at equivalent crystallographic positions. The localized ions come close enough due to the lattice (thermal) vibrations; as a result small polarons are induced. The e!ect of temperature on the initial magnetic permeability k is illustrated in Fig. 7a and Fig. 7b) for all samples in the temperature range from 110
M.A. El Hiti, A.M. Abo El Ata / Journal of Magnetism and Magnetic Materials 195 (1999) 667}678
673
Fig. 6. E!ect of temperature on drift mobility k of charge carriers for samples in Fig. 2.
ature ¹ for all samples except for the sample with x"2 (Ba Zn Fe O ferrite). This peak is related to the transition from the ferrimagnetic to the paramagnetic state. The second peak ¹ appears below room temperature for all samples; this peak is related to a magnetic phase transition. This secondary peak ¹ was observed before for Fe O [8], Mn ferrites [39,40], Mn}Zn ferrite [41] and Mn}Ni ferrites [42]. The height of this peak may be limited not only by some inhomogeneity of the samples but also by the shape and stress anisotropy still present [2]. The initial magnetic permeability k for the hex agonal ferrites in terms of rotational processes of saturation magnetization M and e!ective mag netocrystalline anisotropy constant K (K is a linear combination of K , K ,2) is given in the following form [2]: Fig. 7. E!ect of temperature on initial magnetic permeability k for samples in Fig. 2 for composition: (a) x"0, 0.4 and 0.8; (b) x"1.2, 1.6 and 2.
up to 950 K. Fig. 7 indicates that k increases as the temperature increases. Two peaks were observed in Fig. 7, the "rst peak nearly appears above room temperature, it is the well-known Curie temper-
M k" . (12) K Since the magnetization vector M decreases mono tonically with increasing temperature, therefore it is expected that all anomalies in the k }¹ curve could be related to the behavior of the magnetocrystalline anisotropy constant or to the orientation process of the magnetization vector with respect to C-axis. The values of ¹ and ¹ are determined as a
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M.A. El Hiti, A.M. Abo El Ata / Journal of Magnetism and Magnetic Materials 195 (1999) 667}678
function of composition from Fig. 7 and listed in Table 2. 3.2. Compositional dependence The e!ect of composition on the DC electrical conductivity p and thermoelectric power a; and "! the carrier concentration n and drift mobility k (at selected temperatures of 350, 400, 450 and 500 K) are represented in Fig. 8a and Fig. 8b; and Fig. 9a and Fig. 9b, respectively. Fig. 8a indicates that the studied samples have high electrical conductivity Table 2 Compositional dependence of the transition temperatures ¹ and ¹ (from k }¹ curves); ¹ and ¹ (from p }¹ curves) "! and ¹ (from a}¹ curves) in Kelvin degree X
¹
¹
¹
¹
¹
0.0 0.4 0.8 1.2 1.6 2.0
158 211 228 240 254 202
840 775 691 513 407 }
480 450 435 420 410 400
565 545 580 480 560 550
588 555 455 } 476 444
Fig. 8. Compositional dependence (at temperatures of: (#) 350, (䊏) 400, (£) 450 and (*) (500 K) for: (a) p and (b) a. "!
Fig. 9. Compositional dependence (at the same temperatures in Fig. 8) for: (a) n and (b) k .
p values (from 10\ up to 10\ )\ cm\). This "! could be attributed to the high concentration of Fe ions (which are the source of electronic charge carriers) as the present chemical formula Ba Ni Zn Fe O indicates. At low temper \V V atures in region I, the electric conduction is mainly by band conduction mechanism (free electrons from impurities). In region III at high temperatures, the conduction is by the hopping of localized electrons in the 3d shell between Fe> and Fe> ions (small polaron) according to Verwey mechanism [17,43] and the hopping of localized holes in 3d shell between Ni> and Ni> ions [36]. Sometimes, the free charges from impurity atoms share in the conduction process, i.e. the band conduction mechanism takes part in the conduction process besides the hopping conduction mechanism especially in region II at intermediate temperatures. Each of p "! (Fig. 8a), a (Fig. 8b), n (Fig. 9a) and k (Fig. 9b) increase as Zn> ions substitution to Ni> ions increases reaching maximum at x"1.2 and start to decrease for x'1.2. The e!ect of Zn> ions substitution on the initial magnetic permeability k and Fermi energy E (at $
M.A. El Hiti, A.M. Abo El Ata / Journal of Magnetism and Magnetic Materials 195 (1999) 667}678
selected temperatures) is given in Fig. 10a and Fig. 10b, respectively. Fig. 10a shows that the value of k decreases as Zn> ion substitution increases. This may be related to the increase in the replacement of non-magnetic Zn> ions to magnetic Ni> ions. It is suggested that the exchange interaction between the di!erent allowed seven magnetic sublattices (which leads to the parallel alignment magnetic vector to the direction perpendicular to Caxis) is stronger than that between ions in the same magnetic sub-lattice. The strength of this exchange interaction decreases when a magnetic (Ni>) ion is replaced by non-magnetic (Zn>) ion. This leads to an instability of the parallel alignment between ions and changes the magnetic state of the material. This explains the decrease in k as Zn> ion replacement to Ni> ion increases as shown in Fig. 10a. The behavior of initial magnetic permeability k (Fig. 10a) with composition is the reverse of that for DC conductivity p (Fig. 8a), thermoelectric power "! a (Fig. 8b), carrier concentration n (Fig. 9a) and drift mobility k (Fig. 9b). This behavior was ob served before for Ni Mn Fe O ferrites [42]. >V V \V It was reported that the decrease in k and increase
Fig. 10. Compositional dependence (at the same temperatures in Fig. 8) for: (a) k and (b) E . $
675
in p are related to the superparamagnetic behav"! ior of Fe> ions as in the case of ZnNi}Mn [44] and Li}Ti [45] ferrites. Fig. 10b shows that the Fermi energy E in$ creases as Zn> ion substitution increases, reaching a maximum at x"1.2 and decreasing for x'1.2. The increase in Fermi energy E (Fig. 10b) for $ x(1.2, raises the donor level E (Table 1) nearer " to the bottom of the conduction band. The e!ect of Zn> ions substitution on the activation energies for electric conduction (E , E and E in regions I, II and III from Fig. 2); for carrier generation E (from Fig. 4), at donor level E (from " Fig. 5) and for hopping E (from Fig. 6), respective& ly, are listed in Table 1. The results in Table 1 indicate that the activation energy for electric conduction E (in region II) is higher than E (in region I) and E (in region III). This could be related to the conduction by impurities (in region I which needs a small energy to move the free charge) and to the hopping conduction mechanism of localized electric charge carriers (in region III). The conduction in region II is due to both the hopping and band conduction mechanism therefore needs activation energies more than those needed in regions I and III. The activation energies for electric conduction (E , E and E ), for carrier generation E and hopping E decreases as Zn> & ion substitution increases for x(1.2 and increase for x'1.2. On the contrary, p (Fig. 8a), carriers "! concentration n (Fig. 9a) and drift mobility k (Fig. 9b) increase as Zn> ion increases for x(1.2 and decrease for x'1.2. This result is in good agreement with the conclusion that the higher electrical conductivity and drift mobility (for higher values of Zn> ions substitution) are associated with lower values of activation energies for electric conduction (E , E and E ), and hopping E , and vise versa. & The temperatures at the "rst (Curie temperature ¹ ) and secondary peaks (¹ ) observed on k }¹ curves in (Fig. 7) are listed in Table 2 as a function of Zn> ion substitution. Table 2 also shows the e!ect of Zn> ion substitution on the transition temperatures (¹ and ¹ ) on p }¹ curves (in Fig. "! 2) and the temperature ¹ at cusp-like minima observed on a}¹ plot (in Fig. 3). Table 2 shows that the values of Curie (¹ ) and secondary (¹ ), transition (¹ and ¹ ) and ¹ temperatures
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decrease as Zn> ion substitution increases. This may be attributed to the replacement of non-magnetic Zn> ions to magnetic Ni> ions, which will a!ect the magnetic order and reduce the exchange interaction; consequently this reduces the transition temperatures. No magnetic transition temperature was observed above room temperature (Curie temperature ¹ ) for samples with x"2 (Ba Zn Fe O ) when the non-magnetic Zn> ions completely replace magnetic Ni> ions. The neutron di!raction studies for Zn -Y-type materials [46] identi"ed that the basal plane is the preferred plane of magnetization from room temperature up to ¹ . Neutron di!raction [46] and MoK ssbauer [47] studies for Zn -Y-type identi "ed the presence of a phase angle between Fe ions below room temperature. The reorientation of magnetization vector from the preferred basal plane to a preferred cone of magnetization occurs at a certain temperature ¹ below room temperature. Therefore, the sharp decrease in k below room temperature may be corresponding to a transition from the preferred plane to the preferred cone (as shown in Fig. 7). This transition temperature ¹ depends on the concen tration of Ni> ion content in the samples as listed in Table 2. It has been reported that the magnetic Ni> ions preferentially occupy the B-sites [44,48}50], magnetic Fe ions partially occupy tetrahedral (A)-sites as well as B-sites [48,49,51}55]. The non-magnetic Zn> ions strongly prefer the occupation of A-sites [44,48,52,54}58]. When the replacement of Zn> ions (at A-sites) for Ni> ions (at B-sites) increases, some of Fe ions at A-sites will migrate to B-sites to balance the decrease in B-sites population [45,50,54]. As a result, the number of Fe ions at B-sites increases leading to a marked increase in p (Fig. 8a), a (Fig. 8b), (Fig. 9a) and k (Fig. 9b) for "! x(1.2. As the Zn> ions substitution increases, the concentration of Fe> and Fe> at B-sites increases more and more. As a consequence, the conduction mechanism takes place by the hopping of electrons and holes in accordance with Eq. (11). The presence or generation of large numbers of electrons and holes (at higher x) leads to the occurrence of some type of compensation between them. Therefore, the total number of charge carriers n de-
creases leading to a marked decrease in each of p "! (Fig. 8a), a (Fig. 8b), n (Fig. 9a) and k (Fig. 9b). The decrease in p for x'1.2 may be due to the "! decrease in the probability of Fe> formation, where Zn> ions start replacing Ni> ions at Bsites.
4. Conclusions (1) The DC electrical conductivity p , ther"! moelectric power a, drift mobility k and car rier concentration increase whereas the Fermi energy E decreases on increasing the temper$ ature. The increase in p , a, n, k with temper"! ature is related mainly to the thermal enhancement (activation) and/or thermal liberation of electric charge carriers. The decrease in E with temperature is due to the fact that the $ thermal energy (from heating) raises the energy (Fermi) level or donor level of electronic charge carriers for n-type semiconductors. (2) The relations between ln p and 1/¹, and "! ln p ¹ and 1/¹ represent the same behav"! ior. The variation of the electrical conductivity with temperature shows three di!erent regions. The electric conduction is due to impurities in region I which is characterized with low conductivity and low activation energy E . In re gion II which follows region I, the electrical conductivity and activation energy E increase due to thermal activation of both the drift mobility and impurities. The electric conduction is by the hopping and band conduction mechanism. Region III at high temperature is characterized with high conductivity and low activation energy E . The electric conduction in region III is related mainly to the hopping conduction mechanism. (3) The thermoelectric power a was found to be negative for all samples over the whole temperature range. This indicates that the studied samples are extrinsic semiconductors of n-type where the majority of charge carriers are electrons. Cusp-like minima are observed in a}¹ curves; these minima are related to the "lling of oxygen vacancies.
M.A. El Hiti, A.M. Abo El Ata / Journal of Magnetism and Magnetic Materials 195 (1999) 667}678
(4) The initial magnetic permeability k increases on increasing the temperature, reaching a maximum nearly at the Curie point ¹ and de creases rapidly after ¹ . The sample with x"2, did not show any magnetic transition temeprature above room temperature or Curie temperature ¹ . Another peak (¹ ) was ob served for all samples below room temperature. (5) The values of ¹ decrease on increasing Zn> ion substitution. This is due to the replacement of the magnetic Ni> ion by the non-magnetic Zn> ion. (6) The DC electrical conductivity p , ther"! moelectric power a, carriers concentration n and drift mobility k increase as Zn> ion substitution increases reaching maxima at x"1.2, and decreases for x'1.2. (7) The Fermi energy E and activation energies $ (E , E and E for electric conduction, E for carrier generation, and E for hopping) de& crease on increasing the substitution of nonmagnetic Zn> ions for magnetic Ni> ions for x(1.2 and increase for x'1.2.
Acknowledgements The authors would like to thank Dr. S.M. Attia, Physics and Chemistry Department, Faculty of Education-Kafr El Shiekh, Tanta University, for his help during the experimental measurements for the present work.
References [1] E.J.W. Verwey, P.W. Haaijman, F.C. Romeyn, G.W. van Oosterhout, Philos. Mag. Rep. 5 (1950) 173. [2] J. Smit, H.B.J. Wijn, Ferrites, Cleaver-Hume Press, London, 1959, p. 202 (Chapter IX). [3] G. Albanese, A. Dariu, F. Licci, S. Rinaldi, IEEE Trans. Magn. MAG-14 (1978) 710. [4] M.K. El Nimr, M.A. Ahmed, M.A. El Hiti, A.M. Abo El Ata, J. Mater. Sci. Lett. 1999, in press. [5] H.J. Kown, J.Y. Shin, J.H. Oh, J. Appl. Phys. 75 (1994) 6109. [6] M.A. El Hiti, A.M. Abdeen, Mater. Sci. Tehcnol. 14 (1997) 417. [7] W.D. Kingery, H.K. Bowen, D.R. Uhlmann, Introduction to Ceramics, 2nd ed., Wiley, New York, 197.
677
[8] A.G. Awad, M.A. Ahmed, J. Phys. (France) 38 (1977) 237. [9] Z. Simsa, Czech. J. Phys. B 16 (1966) 919. [10] B.G. Gri!ths, D. Elwell, R. Parker, Philos. Mag. 22 (1970) 163. [11] Yu.P. Irkhin, E. Turov, Sov. Phys. JETP 33 (1957) 673. [12] B.L. Patil, S.R. Sawant, S.A. Patil, Phys. Stat. Sol. A 133 (1992) 147. [13] G.K. Joshi, A.Y. Khot, S.R. Sawant, J. Mater. Sci. 22 (1987) 1694. [14] R. Manjula, V.R.K. Murthy, J. Sobhanadri, J. Appl. Phys. 59 (1986) 2929. [15] P.V. Reddy, J. Appl. Phys. 63 (1988) 3783. [16] A.A. Ghani, A.I. Eatah, A.A. Mohamed, Proceedings of the International Conference on Ferrites, Kyoto, Japan, 1980, p. 216. [17] E.J.W. Verwey, J.H. de Boer, Red. Trav. Chim. Phys. Bas. 55 (1936) 531. [18] T. Holstein, Ann. Phys. (NY) 8 (1959) 345. [19] L. Erildman, T. Holstein, Ann. Phys. (NY) 21 (1963) 4929. [20] D. Emin, T. Holtstein, Ann. Phys. (NY) 53 (1969) 439. [21] N.V. Mulay, K.B. Reddy, V.D. Reddy, P.V. Reddy, Phys. Stat. Sol. (a) 130 (1992) 397. [22] A.A. Ghani, S.A. Mazen, A.H. Ashour, Stat. Sol. (a) 184 (1984) 337. [23] N. Nanba, S. Kobayashi, Jpn. J. Appl. Phys. 17 (1978) 1819. [24] F.J. Morin, H. Geballe, Phys. Rev. 99 (1955) 467. [25] A.A. Samokhavlov, A.G. Rustamov, Sov. Phys. Solid State 7 (1964) 749. [26] F.J. Morin, Phys. Rev. 93 (1953) 1195. [27] P.V. Reddy, T.S. Rao, Phys. Stat. Sol. (a) 92 (1985) 303. [28] C. Cropichka, Ferrite Physics and its Magnetic Oxides, Mir Publisher, Moscow, (Chapter VII) (in Russian). [29] A.E. Lo!e, Physics of Semiconductors, Iforscarch Limited, London, 1960. [30] A.J. Bosman, C. Crevecoeur, J. Phys. Chem. Solids 30 (1969) 1151. [31] J.S. Blakemore, Semiconductor Statistics, Pergamon Press, New York, 1962. [32] A.A. Ghani, S.A. Mazen, A. Ashour, Phys. Stat. Sol. (a) 84 (1984) 337. [33] R.R. Heikes, W.D. Johnason, J. Chem. Phys. 26 (1957) 582. [34] P.S. Jain, V.S. Darshane, Nucl. Phys. Solid State Symp. 24 (1981) 529. [35] M.N. Kahn, A. Venkatachalam, A. Ahmed, V.S. Darshane, J. Mater. Sci. 25 (1990) 595. [36] L.G. van Uitert, J. Chem. Phys. 23 (1955) 1883. [37] E.J. Verwey, P.W. Haaijman, F.C. Romeyn, C.W. Oostenhout, Philips Res. Rep. 9 (1954) 428. [38] F.K. Lotering, J. Phys. Chem. Solids 25 (1964) 95. [39] A. Goldman, Modern Ferrite Technology, Marcel Dekker, New York, 1993. [40] U. Enz, Physica 24 (1958) 609. [41] D. Stoppels, J. Appl. Phys. 52 (1981) 2432. [42] A.I. El Shora, M.A. El Hiti, M.K. El Nimr, M.A. Ahmed, A.M. El Hasab, J. Magn. Magn. Mater., accepted for publication.
678
M.A. El Hiti, A.M. Abo El Ata / Journal of Magnetism and Magnetic Materials 195 (1999) 667}678
[43] E.J. Verwey, P.W. Haaijman, F.C. Romyen, G.W. Oosterhout, Philps Res. Rep. 9 (1954) 428. [44] B.V. Bhise, M.B. Dongar, S.A. Patil, S.R. Sawant, J. Mater. Sci. Lett. 10 (1991) 922. [45] P. Kishan, C. Prakash, J.S. Bijal, K.K. Laroia, Phys. Stat. Sol. (a) 84 (1984) 533. [46] E.E. Ymzin, Y. Lecvich, Crystal 15 (1970) 280. [47] G. Ablanese, G. Asti, C. Lamborizio, J. Appl. Phys. 39 (1968) 1198. [48] G. Joshi, S. Deshpande, A. Khot, S.R. Sawant, Solid State Commun. 65 (1988) 1593. [49] T.E. Whall, N. Salerno, Y.G. Proykova, V.A. Babers, Philos. Mag. Lett. B 53 (1986) L67. [50] B.V. Bhise, M.B. Dongar, S.A. Patil, S.R. Sawant, Phys. Rev. 122 (1962) 1447.
[51] J.S. Bijal, S. Phanjouban, D. Kothari, C. Prakash, P. Kishan, Solid State Commun. 83 (1972) 679. [52] M.N. Kahn, A.A. Ahmed, V.S. Darshane, J. Mater. Sci. 24 (1989) 163. [53] R. Bauminger, S.G. Cohen, A.M. Arinov, S. Ofer, E. Segal, Phys. Rev. 122 (1962) 1497. [54] G.K. Joshi, S.A. Deshpande, A.Y. Khot, S.R. Sawant, Ind. J. Phys. A 61 (1987) 241. [55] R.B. Jotania, R.V. Upadhay, R.G. Kulkarni, IEEE Trans. Magn. 28 (1992) 1889. [56] H. Patil, R. Upadhyay, N. Shamkuwar, R. Kulkarni, Solid State Commun. 81 (1992) 1011. [57] M. Arshed, M. Butt, M. Siddique, A. Anwar, T. Abbas, H. Ahmed, Solid State Commun. 84 (1992) 717. [58] E. Grandjean, A. Gerard, Solid State Commun. 25 (1978) 679.