Phase transitions in ferrimagnetic and ferroelectric ceramics by ac measurementsA. Peláiz-Barranco, M. P. Gutiérrez-Amador, A. Huanosta, and R. Valenzuela Citation: Applied Physics Letters 73, 2039 (1998); doi: 10.1063/1.122360 View online: http://dx.doi.org/10.1063/1.122360 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/73/14?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Microstructure and ferroelectric properties of Mn O 2 -doped bismuth-layer ( Ca , Sr ) Bi 4 Ti 4 O 15 ceramics J. Appl. Phys. 98, 064108 (2005); 10.1063/1.2058174 Grain boundary electric characterization of Zn 7 Sb 2 O 12 semiconducting ceramic: A negative temperaturecoefficient thermistor J. Appl. Phys. 93, 5576 (2003); 10.1063/1.1566092 Doping effect in layer structured SrBi 2 Nb 2 O 9 ferroelectrics J. Appl. Phys. 90, 5296 (2001); 10.1063/1.1413236 Erratum: “Two distinct dielectric relaxation mechanisms in the low-frequency range in (K 0.50 Na 0.50 ) 2 (Sr0.75 Ba 0.25 ) 4 Nb 10 O 30 ceramics” [Appl. Phys. Lett. 73, 1442 (1998)] Appl. Phys. Lett. 73, 2222 (1998); 10.1063/1.122441 Two distinct dielectric relaxation mechanisms in the low-frequency range in (K 0.50 Na 0.50 ) 2 (Sr 0.75 Ba 0.25 )4 Nb 10 O 30 ceramics Appl. Phys. Lett. 73, 1442 (1998); 10.1063/1.122379

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

138.251.14.35 On: Thu, 18 Dec 2014 02:53:07

Phase transitions in ferrimagnetic and ferroelectric ceramicsby ac measurements

A. Pelaiz-Barranco,a) M. P. Gutierrez-Amador, A. Huanosta, and R. Valenzuelab)

Institute for Materials Research, National University of Mexico, Mexico D.F., 04510 Mexico

~Received 18 May 1998; accepted for publication 6 August 1998!

Ac conductivity measurements were carried out on polycrystalline samples of a ferrimagnetic spinel(Zn0.44Mn0.56Fe2O4) and a ferroelectric perovskite (Sr0.25Bi4Ti3.25O12.75), in the temperature range20–160 and 20–660 °C, respectively, and in the frequency range 5 Hz–13 MHz. The impedanceresponse in both cases could be resolved into two contributions, associated with the bulk~grains!and the grain boundaries. An analysis by means of the ac conductivity power law showed evidenceof a critical temperature of 132 and 536 °C, for the ferrimagnetic and the ferroelectric samples,respectively, which corresponds to the Curie temperature for each type of material. These results areinterpreted in terms of the disorder increase approaching the phase transition. ©1998 AmericanInstitute of Physics.@S0003-6951~98!04640-3#

Impedance spectroscopy1 ~IS! is a measuring techniquewhich is becoming a powerful characterization methodologyfor a wide range of materials. In the case of polycrystallineceramics, the electrical properties of grains can be separatedfrom the other sources of impedance, i.e., grain boundariesand electrodes, by using the complex impedance formalismsand other related formalisms. In ferroelectric materials, acmeasurements can, therefore, separate the ferroelectric per-mittivity and provide an accurate image of polarizationphenomena.2 IS has also been used in polycrystalline ferritesto study the effects of additives,3 for instance, by analyzingthe changes introduced in the grain and grain-boundary im-pedance response. To our knowledge, however, no directevidence of the Curie transition has been observed in ac con-ductivity experiments.

A convenient formalism to investigate the frequency be-havior of conductivity in a variety of materials is based onthe power relation proposed by Jonscher,4

sT~v!5s~0!1Avs, ~1!

where sT is the total conductivity,s~0! is the frequency-independent conductivity, and the coefficientA and exponents are temperature and material dependent.5 The termAvs

contains the ac dependence and characterizes all dispersionphenomena. The exponents has been found to behave in avariety of forms:6–9 a constant, decreasing with temperature,increasing with temperature, etc., but always within 0,s,1.

In this letter, a study of the thermal behavior of thepower-law frequency dependence, of Zn–Mn ferrites andSr–Bi–Ti ferroelectrics is presented. It is found that both thecoefficient A and the exponents exhibit a critical point~aminimum and a maximum, respectively! at the order–disorder ~from ferrimagnetic to paramagnetic in the firstcase, and from ferroelectric to paraelectric, in the second!transition temperature. An interpretation in terms of the dis-order involved in the phase change is proposed.

ZnxMn12xFe2O4 ferrites in the compositionx50.44were prepared by the usual ceramic methods, fromhigh-purity, reagent-grade ~Johnson Matthey GmbH!a-Fe2O3, MnCO3, and ZnO. Samples of ferroelectricSrxBi4Ti31xO1213x , with x50.25 were prepared also fromhigh-purity, reagent-grade~Johnson Matthey GmbH! SrTiO3

and Bi2O3 oxides, by the ceramic technique.Impedance measurements were carried out in the fre-

quency range 5 Hz–13 MHz in a system including a HP4192A impedance analyzer controlled by a PC. The measur-ing software, created in our laboratory, allows the measure-ment of 94 discrete frequencies in about 3 min.

Initial magnetic permeability as a function of tempera-ture was measured in an apparatus10,11 where the sample,with a toroidal shape, is used as a transformer core.

We first present the IS results for the MnZn ferritesample. Complex impedance plots,Zi5 f (Zr), whereZi andZr are the imaginary and real components of impedance,respectively, showed two well-resolved semicircles over thewhole measured temperature range, Fig. 1. These results can

a!On leave from Facultad de Fı´sica, University of Havana, Cuba.b!Corresponding author. Electronic mail: monjaras@servidor.unam.mx

FIG. 1. Complex impedance plot at room temperature. Inset, the Arrheniusplot of grains and grain-boundary conductivity.

APPLIED PHYSICS LETTERS VOLUME 73, NUMBER 14 5 OCTOBER 1998

20390003-6951/98/73(14)/2039/3/$15.00 © 1998 American Institute of Physics This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

138.251.14.35 On: Thu, 18 Dec 2014 02:53:07

be modeled by an equivalent circuit formed by twoRC par-allel arms in series, inset of Fig. 2. The value of each equiva-lent resistor can be extracted from the diameter of semi-circles. A relaxation frequency is observed for each arm, Fig.2; at this frequency, the conditionZi5Zr occurs and it ispossible to calculate the corresponding value of equivalentcapacitors fromC51/(vR), where v is the angular fre-quency (v52p f ).

The values of capacitors provide a criterium to relatethese semicircles with the pertinent microstructural feature atthe origin of specific impedance contribution.12 One of thearms, RgCg , is, therefore, associated with the impedanceresponse of the bulk~or grains!, and the other one,RgbCgb,with the response of grain boundaries. As the measuringtemperature increases,Rg and Rgb decrease following avariation of Arrhenius type. A linear relationship is observedwhen these data are plotted in the form logs vs 1/T, wheres is the electrical conductivity, as shown in the inset of Fig.1.

The ac conductivity power law of Eq.~1! can be used toanalyze the obtained results.sT(v) is obtained form the realpart of admittanceYr as

sT~v!5gYr5gZr /@~Zr !21~Zi !

2#, ~2!

whereg is the geometrical factor.

The variations ofsT(v) with frequency, for selectedtemperatures, are shown in Fig. 3 in log–log form. Afrequency-independent plateau appears for the low-frequency range, associated with the terms~0!. As frequencyincreases, two dispersion regions appear for all temperatures.If the low-frequency dispersion is associated with grainboundaries~since it is associated with the larger capacitancevalue! and the high-frequency one with grains~smaller ca-pacitance value!, Eq. ~1! can be modified as13

sT~v!5s~0!1A1vs11A2vs2, ~3!

to describe these different contributions to conductivity. Thebehaviors ofA1 , A2 , s1, ands2 with temperature appear inFigs. 4 and 5.

The exponentss1 ands2 exhibit a quite different depen-dence with temperature, Fig. 4.s1, associated with the grain-boundary conductivity, shows a small decrease with tem-perature, with no particular feature. In contrast,s2, whichdepends on grain~or bulk! conductivity, shows a steep in-crease and then a maximum at aboutT5132 °C, followedby a decrease to values close to the room-temperature ones.In the case of theA terms,A2 , which is grain related, exhib-its a clear minimum value for the same temperature wheres2showed a maximum.A1 , on the other hand, shows a con-tinuous increase, with no special feature for any temperature.

In order to obtain some insight about the critical behav-ior of the A2 ands2 parameters, the initial magnetic perme-

FIG. 3. Dependence of total conductivitysT(v) with frequency for selectedtemperatures.

FIG. 2. Dependence of imaginary impedance on frequency. Inset, theequivalent circuit.

FIG. 4. Thermal behavior of the exponentss1 ~grains! ands2 ~grain bound-aries! in the modified power relation of Jonscher.

FIG. 5. Thermal variations of theA1 ~grains! and A2 ~grain boundaries!terms in the power relation.

2040 Appl. Phys. Lett., Vol. 73, No. 14, 5 October 1998 Pelaiz-Barranco et al.

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

138.251.14.35 On: Thu, 18 Dec 2014 02:53:07

ability of the ferrite sample was measured as a function oftemperature, Fig. 6. This property shows an increase as thetemperature increases, and an almost vertical drop at the Cu-rie temperatureTc , where the sample changes from a long-range ordered ferrimagnetic arrangement to a disorderedparamagnetic structure. The observed value, Fig. 6, isTc

5132 °C, which coincides quite well with the maximum inthe s2 vs T plot ~Fig. 4!, and the minimum in the thermalvariations ofA2 , Fig. 5. In other words, themagneticphasechange is associated with a critical behavior in theelectricalconductivity parametersA ands.

In order to verify the generality of these results, a similarmethodology was followed on the ferroelectric sample. Afterfrequency measurements, which resulted also in a clear reso-lution of the bulk and grain-boundary contributions to theimpedance, theA ands terms were calculated and are shownin Fig. 7. A similar behavior is observed, with a maximumfor the s exponent, and a minimum for theA term, both forthe ferroelectric Curie temperatureTc5563 °C. It, therefore,turns out that the critical behavior ofs and A is associatednot only with magnetic phase transitions, but also with ferro-electric phase transitions.

The ac conductivity power law seems to be originated byrelaxation processes with a wide distribution of time con-stant; ‘‘parallel’’ and ‘‘series’’ relaxation processes havebeen used9 to propose a general explanation in highly disor-dered materials such as glasses. While a direct correlationbetween the observedA and s values is still lacking, someform of disorder seems to be essential for a system to exhibita power-law behavior. Also, variations in the exponents canbe expected if the polarizability of the involved material de-pends on the energy barrier for a simple hopping processbetween two sites.

In the present case, it appears that in the temperature-

increasing process, the proximity to the phase transition isassociated with an increase in disorder. In the case of mag-netic transitions, the significant increase in specific heat closeto the Curie temperature effectively appears to be consistentwith this view. An important point to note is that while mostferroelectric–paraelectric transitions are considered first-order transitions from a thermodynamic point of view,ferrimagnetic–paramagnetic phase changes account forsecond-order transitions. Our results would, therefore, pointto a more general feature of conductivity behavior. Electri-cally based methods can effectively lead to a detailed char-acterization of a wide range of materials.

This study was partially funded by DGAP-UNAM~Grant No. IN 100996!. One of the authors~A.P-B.! ac-knowledges partial support from the University of Mexico~IIM-UNAM and DGIA-UNAM ! and the Third World Acad-emy of Sciences~TWAS!, for a leave of absence; and one ofthe authors~M.P.G-A.! thanks DGAPA-UNAM for a Ph.D.fellowship.

1J. R. MacDonald,Impedance Spectroscopy~Wiley, New York, 1987!.2N. Hirose and A. R. West, J. Am. Ceram. Soc.79, 1633~1996!.3H-F. Cheng, J. Appl. Phys.56, 1831~1984!.4A. K. Jonscher, Nature~London! 264, 673 ~1977!.5A. P. Almond, A. R. West, and R. J. Grant, Solid State Commun.44, 277~1982!.

6A. K. Jonscher,Dielectric Relaxation in Solids~Chelsea Dielectric, Lon-don, 1983!.

7H. Jain and J. N. Mundy, J. Non-Cryst. Solids91, 315 ~1987!.8K. Funke, Prog. Solid State Chem.22, 111 ~1993!.9S. R. Elliott, Solid State Ionics70/71, 27 ~1994!.

10E. Cedillo, J. Ocampo, V. Rivera, and R. Valenzuela, J. Phys. E13, 383~1980!.

11R. Valenzuela, J. Mater. Sci.15, 3173~1980!.12A. R. West,Solid State Chemistry and its Applications~Wiley, New York,

1984!, p. 483.13F. Salam, J. C. Guintini, S. Sh. Soulayman, and J. V. Sanchetta, Appl.

Phys. A: Mater. Sci. Process.63A, 447 ~1996!.

FIG. 7. Exponents and coefficientA in the case of the ferroelectric sample.FIG. 6. Thermal variations in the relative initial magnetic permeability ofthe MnZn ferrite sample.

2041Appl. Phys. Lett., Vol. 73, No. 14, 5 October 1998 Pelaiz-Barranco et al.

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

138.251.14.35 On: Thu, 18 Dec 2014 02:53:07