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390 Brazilian Journal of Physics, vol. 31, no. 3, September, 2001

Static Magneto Optical Birefringence ofNew Electric Double Layered Magnetic FluidsJ. Depeyrot+l G. J. da Silva", C. R. Alves", E. C. Sousa", M. Magalhaes",

A. M. Figueiredo Neto2, M. H. Sousa", and F. A. Tourinho"1Complex Fluids Group, Instituto de Fisico;

Universidade de Brasilia, Caixa Postal 04455, 70919-970, Brasilia (DF), Brazil2Instituto de Fisica, Universidade de Sao Paulo,

Caixa Postal 66318, Sao Paulo (SP), Brazil3Complex Fluids Group, Instituto de Quimica,

Universidade de Brasilia, Caixa Postal 04478, 70919-970 Brasilia (DF), BrazilReceived on 27 May, 2001

Magnetic birefringence measurements are performed under a static field on Electric Double LayeredMagnetic Fluids based on copper and zinc ferrite nanostructures. The optical birefringence isrelated to a single-particle effect and well described by a Langevin model which includes a log-normal distribution of particles. By the field-induced birefringence level, these new magnetic fluidsare comparable to usual ones, a result which could offer a new way for biological applications.

I IntroductionNowadays, Magnetic Fluids (MF) or Ferrofluids arestable colloidal suspensions of magnetic mono domainnanosized particles dispersed in a specific liquid carrier[1]. Due in part to the coexistence of a strong magneti-zation with fluidity properties and also to the versatil-ity of molecular liquids carrier which can be employed,such artificial systems leads to numerous technologicalapplications [2] . Fundamental studies are generally per-formed in electric double layered magnetic fluids (EDL-MF) [3 ] where the stabilization is achieved by intro-ducing, between particles, electrostatic repulsive forcesobtained by an adjustable surface charge density.

MF have long been investigated using magneto-optical birefringence measurements. For instance, mag-netic colloidal sols based on Fe304 [4] , ,),-Fe203 [5],CoFe204 [6]and NiFe204 [7]nanoparticles are opticallyactive and exhibit strong optical birefringence undermagnetic fields. In diluted solutions (typically of theorder of 1016 particles per em"), the magneto-opticalbehavior of MF can be well described by a Langevinformalism that includes a log-normal size distributionof roughly spherical particles [4 , 8].

Nevertheless, until now, the origin of the MFmagneto-optical birefringence is not well understood. A

*Fax:+55 61 307 23 63; e-mail:[email protected]

possible field-induced effect on the particle material, thecubic (spinel) crystal structure and the nearly sphericalparticle shape observed by electron microscopy do notexplain the optical anisotropy. Optical birefringenceand dichroism of surfacted MF have been interpreted interms of orientation or aggregation in the presence of amagnetic field of particle aggregates already present inthe solution in the absence of the field [9]. However, inEDL-MF, recent Small Angle X-ray scattering measure-ments performed on a large number of samples show atzero field a low degree of particle aggregation [10]. For-mation of chain-like aggregates in the applied field hasalso been proposed to account for the magneto-opticalbehavior of MF [11]. Nevertheless, such model resultsin considerable deviation from experiments at low field.Furthermore, a field induced aggregation of particles inEDL-MF is rejected by Small Angle Neutron Scatteringresults if the ionic strength of the solutions is less than0.05 mol L-1with particles of surface charge densityabout 0.2 C m-2 [12].

More recently, static magneto-optical birefringenceof size sorted ,),-Fe203 nanoparticles indicated [13 ] , onthe contrary, that the optical anisotropy observed inEDL-MF is not due to cooperative process of particleagglomeration in the field but to a particle surface mag-netic anisotropy, coming from the discontinuity of mag-
mailto:e-mail:[email protected]:e-mail:[email protected]

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netic interactions between individual spins which resideat the particle surface, coupled to a slight ellipticity ofthe particles.

The aim of the present work is to investigate thestatic magneto-optical birefringence of new EDL-MFbased on copper and zinc ferrite nanoparticles. Thechemical synthesis of these ferrofluids as well as theirmagnetic properties have already been presented in aprevious paper [14]. Such MF could offer a new alter-native for biological applications since their iron con-tent is reduced and they would therefore be notablyeasier to titrate in biological in vivo experiments. Insuch a context, it is essential to check their optical bire-fringence level since optical birefringence measurementshave shown to be a useful tool in testing the grafting ofmagnetic nanoparticles by antibodies [15].

The current work is divided as follows. In sectionII, we give a brief description of the EDL-MF chemicalsynthesis as well as a chemical and structural analysisof the synthesized nanoparticles. Parts of our previousmagnetization data obtained at 300 K are reviewed insection III. Then, in section IV, static magneto-opticalmeasurements are presented and discussed within theframework of the Langevin model.

II Chemical synthesis and par-ticle characterization

EDL-MF synthesis. The EDL-MF elaboration is car-ried out on three basic steps [14]: firstly, the fer-rite nanoparticles synthesis, then the chemical surfacetreatment, and finally the peptization of the particlesin a stable aqueous colloidal solution. CuFe204 andZnFe204 oxide nanoparticles were prepared using hy-drothermal coprecipitating aqueous solution of CuCh-FeC13 and ZnCh-FeC13 mixtures, respectively, in alka-line medium. After the coprecipitation step, the pre-cipitate is washed in order to suppress the high ionicstrength of the medium and the particle surface iscleaned by a (2 mol L-1) HN03 solution. Moreover, toensure the thermodynamical stability of the particles anempirical process has been proposed: the precipitatedis boiled with a 0.5 mol L-1 Fe(N03h solution. Then,the particles are conveniently peptized in acid mediumby the adjustment of the ionic strength, resulting in astable sol of high quality.

Chemical analysis. Once the EDL-MF synthesis hasbeen performed, the sample composition is controlledby chemical analysis: iron(III) titration is determinedby dichromatometry. Copper (II) titration is done by

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volumetric analysis with iodine and zinc (II) is quan-tified using plasma emission spectroscopy. Then, eachMF precursor solution is diluted at two volume frac-tion of magnetic nanomaterial, = 0.73% and =0.15% for Cu-based samples and = 0.75% and =0.16% for Zn-based ones. These volume fraction valueshave been chosen in order to perform magnetizationand magneto-optical measurements on sufficiently di-lute samples where the inter-particles interactions canbe considered as negligible and the independent particlemodel well works.

Magnetic material yield. The experimental proce-dure used to determine the best value in divalent metalmolar fraction is an adaptation of the method of contin-uous variation or "Job's method". A series of solutionsof equal total concentration in metal [M2+ + Fe3+] isprepared with different relative amounts of M2+ andFe3+ reacting in excess of sodium hydroxide in orderto obtain the ferrite nanoparticles. For each solution,the corresponding magnetic material yield is measuredusing an adaptation of the Gouy method, where an ap-parent increase in mass Llm can be detected when thesolution is submitted to a magnetic field gradient. Fig.1displays the variations of the normalized value of themagnetic material yield as a function of the divalentmetal molar fraction XM2+ . As it can be seen, ourmeasurements show a very good agreement with thetheoretical curve deduced from the chemical reaction offerrite formation [14]. The maximum yield correspondsto that provided by the exact ferrite stoichiometry witha value of XM2+ equal to 0.33.

X-rays diffraction. In order to characterize the crys-talline structure of our magnetic nanoparticles, X-raysdiffraction measurements were performed on powdersamples obtained after evaporation of the liquid car-rier, using a RigakujDenki X-rays diffractometer andthe CuKo: radiation at 1.54 A . We present in Fig. 2 atypical powder diffraction pattern which exhibits sev-eral lines corresponding to the characteristic interpla-nar spacing [220], [311], [400], [422], [511], [440] and[533] of the spinel structure [16]. Table 1 compares forboth kind of nanomaterial the measured peak intensi-ties with the American Society for Testing and Materi-als (ASTM) values [17] and also gives the cubic latticecell deduced from the peak position with average val-ues of 0.828 nm and 0.832 nm to be compared to theASTM ones 0.835 nm and 0.844 nm for CuFe204 andZnFe204 respectively.

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[311]

[440][511]

800 30 60 700 502ec )Figure 1. X-ray powder difratograms of copper and zinc fer-rite nanoparticies. The characteristic diffracted directions[220], [311], [400], [422], [511], [440] and [533] of the spinelstructure are indexed.

l:!. CuFe,04D ZnFe,O.

-_ Theoreticalcurve

0,0 0,2 0,4 0,6 0,8 1,0Molar Ratio XM,.

Figure 2. Normalized mass variation /::;.m/ /::;.mrnax or mag-netic material yield as a function of the divalent metal molarratio, XM2+ .

Moreover, the observed line width arises from thefinite dimension of the crystal (polycrystalline speci-mens) and is related to the roughly spherical particle di-ameter. Additional sources of broadening, arising fromthe experimental setup and instrumentation, were dis-counted here using a Si standard monocrystal. Then,using the Scherrer equation [18]it yields a mean diame-

Brazilian Journal of Physics, vol. 31, no. 3, September, 2001

ter dXR = 8.4 nm in the case of Cu-based nanoparticlesand dXR = 6.3 nm in the case of Zn-based ones.Table 1: Crystallographic analysis of Fig. 1 forCuFe204 and ZnFe204 nanoparticles. The interpla-nar spacing dhkl is calculated from the line posi-tion by using the Bragg law and the correspondingcubic lattice cell a is deduced. The experimentalpeak intensities Iexp are compared to the ASTM ones.

CuFe,O, ZnFe,O,hkl dhkl (A) a {run} lap lASTM dhkl (A) a (run) lap l4STM220 2.898 0.820 26 42 2.903 0.82, 29 30311 2.485 0.824 100 100 2.508 0.83, 100 100400 2.065 0.826 19 30 2.080 0.83, 18 17422 1.695 0.830 1.697 0.83, 14 12511 1.598 0.830 31 40 1.609 0.836 33 30440 1.470 0.832 45 60 1.479 0.837 62 60533 1.274 0.835 II 20 1.274 0.835 10 9

III Magnetization resultsMagnetic properties of Magnetic Fluids arise from thedispersion of magnetic nanoparticles in a liquid carrier.In spinel-type nanoparticles, the exchange interactionsbetween ions of the tetrahedral and the octahedral siteslead to a global ferrimagnetic order in the particles coreand due to their small size, each magnetic particles be-haves as a single magnetic domain of volume V bearinga permanent magnetic moment /1 of modulus msV, msbeing the nanomaterial magnetization. Then, at 300 Kand for enough dilute solutions (for a volume fraction < 2%) , the magnetic fluid response to an appliedfield H results from the progressive orientation in thefield of an ensemble of non interacting magnetic mo-ment which are free to rotate in the solvent. This super-paramagnetic behavior is well described by a Langevinformalism including a log normal size distribution totake into account the size polydispersion of particles[19,20]. Thus, at T = 300 K and at zero field the mag-netization is zero due to thermal fluctuations; as themagnetic field increases, the solution magnetization in-creases too and does not present any hysteresis. In thelimit of small fields, the magnetization is proportionalto H and at large magnetic fields, all the magnetic mo-ment are aligned in the field direction and the magne-tization saturates scaling a linear law as a function ofI/H. Such a model well works at room temperature

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for magnetic fluids based on 10 nm sized ,),-Fe203 par-ticles, using a nanomaterial magnetization about 75%of the bulk one. Nevertheless, as the proportion of spinslocated in the neighborhood of the particle surface in-creases when the particle size is reduced, the magneticproperties of very small particles (typically inferior to 5nm) is strongly influenced by the spin arrangement ofthe particle surface. The lower coordination of surfaceions does modify the exchange interactions and it hasbeen shown the existence of a superficial shell wherethe spin configuration can be disordered resulting thenin a reduced average net moment [21, 22]. EDL-MFbased on 4.4 nm sized NiFe204 nanoparticles exhibit asubstantial particle surface disorder and the resultingmagnetization does not follow a simple single-domainparticle model [23]. Evidence for spin-glass-like behav-ior of surface spins in ,),-Fe203 particles has also beenreported using quasi-elastic neutron scattering [ 24 ] andFMR [25 ] measurements.

However, the magnetic behavior of Cu- and Zn-based samples exhibited in Fig. 3 shows that, inboth cases the solution magnetization tends toward andnearly reaches the saturation. This typical superparam-agnetic behavior allows the use of the independent mo-ment model since the magnetization is proportional tothe volume fraction of magnetic nanomaterial. Fur-thermore, in the limit of high fields, a simple estimationof the saturation magnetization of the magnetic parti-cles can be made. Then, from the complete analysisof these curves, it has been deduced [14] , the particlesmean magnetic size and polydispersion. The results arelisted in Table 2.

100

H (kA rn')

10

o

10 100 1000

Figure 3. Log-log representation of the normalized magne-tization M / if! as a function of the applied magnetic field H.The full line is the best fit obtained by using the Langevinformalism coupled with a log-normal distribution (see Table2 for the resulting parameters size distribution).

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Table 2: Mean nanoparticle size deduced from X-raydiffraction DxR, magnetic size D~ag and polydisper-sity smag deduced from magnetization measurementsand compared to the respective birefringence ones D 8 irand shir. D t} and D'lIF are the sizes determined fromthe low field analysis and the high field one.

DX R (run) D~,g (nm) r= D~i ' (run) Dr ~ (nm) Dm (nm) SCuFeZ04 8.4 6.0 0.45 11.8 13.9 0.5.9ZnFe,04 6. 3 5.9 0.3 8.5 8.8 0.3.5

IV Magneto-optical behaviorBirefringence Langevin formalism. Isotropic at zero ap-plied field, magnetic fluid solutions become opticallyactive when the field is turned on, due to some opticalanisotropy along the magnetic easy axis of particles.For a magnetic solution of volume fraction of inde-pendent polydisperse particles, the Langevin formalismgives the static field-induced birefringence at a temper-ature T as [6, 8, 13] :

D..n(H) 1 0 00 D3 L2 (~ (D) )P (D) dDD..no 1 0 00 D3 P (D )dD

where ~ = p,H/ k BT is the Langevin parameter, L 2 (~ ) =1-3L1 (~)/ ~ is the second Langevin function, L1 (~) be-ing the well known first Langevin function. D..no cor-responds to the optical anisotropy (shape anisometryand/or magnetic anisotropy) of one particle in suspen-sion and slightly depends on the particle size [13 ] .Theparticles diameters distribution is generally well de-scribed by a log-normal law:

(1 )

P (D) = 1 exp[[_ln2(D/Do)] ,V2JrDs 2S2where D is the particle diameter, s is the standard devi-ation and In Do corresponds to the mean value of In D .The moments of the log-normal size distribution func-tion are defined by:

(2 )

r o o ( ~ ~ )< tr: >= io tr:P(D)dD = Dg exp -2- . (3 )Since ms is determined by magnetization measure-ments, the curve D..N(H)/ therefore reduces to a func-tion of two parameters Do and s if D..no can be evalu-ated. Moreover, following the analyses made in refer-ences [4 ] and [13 ] , a crossing of the results obtained by

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using the whole birefringence curve with those obtainedby using both the limits of low and high fields allows agood determination of the size distribution parameters.For high fields, 1- 3[LI(~)/~l = 1- (3/~) and the solu-tion birefringence can be linearly written as a functionof l/H as:

Lln = Llno _ ( 18kBT ) _ _ ! _ . (4 ) ms7r < D 3 > H

For low fields, 1- 3[LI(~)/~l = e /15 and the solu-tion birefringence is proportional to H 2 :

Both equations show that the high field diameteris related to the third moment of the log-normal sizedistribution whereas the low field one corresponds to ahigher moment of the distribution. Furthermore, thehigh fields analysis allows a simple determination ofLlnoBirefringence measurements. The external-field in-duced birefringence is measured up to a magnetic fieldabout 1.5 x 103 kA m:", by encapsulating magneticfluid samples in non-birefringent glass cells a few hun-dred micrometers thick and using the conventional setup well described in references 13 and 26. When themagnetic field is switched on, the ferrofluid cell behavesas a birefringent plate characterized by a phase-lag iprelated to the birefringence of the sample of thicknesse by ip = 27reLln/ A . where A . is the wavelength of theincident light. In our experiments, the detection deviceincludes a photoelastic optical modulator and a lock-inamplifier which compares the detected signal from thephotocell to the reference signal from the modulator.Then, the component at pulsation w of the transmittedlight intensity Iw is proportional to sino. If the samplethickness and the volume fraction of nanomaterialare well chosen, several oscillations occur as it can beseen on Fig. 4 which shows the variations of Iw as afunction of the applied field in the case of Zn- basedmagnetic fluid sample ( = 0.75%).

The corresponding birefringence variations can eas-ily be deduced from such measurements and the bire-fringence data are plotted in linear coordinates in Fig.5a and Fig. 5b for Cu- and Zn-based samples respec-tively. The same qualitative behavior is observed forall our samples: Lln is an increasing function of theapplied field and tends toward the saturation at ourmaximum field value. Moreover, as it can be seen onthe insets of Figs. 5a and 5b, the birefringence is pro-portional to showing, as expected for the values of used in our experiments, that the measured birefrin-gence is related to a single-particle effect. Indeed the

Brazilian Journal of Physics, vol. 31, no. 3, September, 2001

(5 )

coincidence of the data when normalized by the volumecontent of nanoferrite confirms the applicability of theindependent particle model described in the beginningof this section. To determine the saturation behaviorof Lln, the results are exhibited in Fig. 6a and Fig. 6bin double-logarithmic coordinates where the full line isthe result of a best fit obtained by using equations 1and 2. Fig. 7a and 7b present, in linear coordinates,the high field data (H > 500 kA m:") in such a man-ner that Llno is determined by the value of Lln/ when1/ H tends toward zero. Furthermore, the insets of bothFigures illustrate, in log-log representation, the low fieldbehavior (H < 10 kA m :") of Lln proportional to H 2.This H 2 variations also indicates that at low fields, thebirefringence samples comes from individual particles.

Using both the limits of low and high fields, onecan also obtain the size distribution parameters. Thena crossing of these results with those obtained by us-ing the whole birefringence curve allows a good deter-mination of the nanoparticle size and the polydisper-sion. In such a context, the analysis of our birefrin-gence curves gives the results summarized in Table 3,where we compare D g i r , the mean value of D deducedfrom the whole curve, with D J _ l c = D g i r exp(6s2) andD 'J j p = D g i r exp(Lfis''}, the averaged values of D ob-tained from the low-field and high-field analyses respec-tively. As it can be seen, the standard deviations sbirare close to those found from magnetization measure-ments (smag) whereas is significantly larger than show-ing as expected that the optical birefringence is moresensible to large particles. In the case of Cu-based sam-ples, the difference between the deduced averaged val-ues of the nanoparticle sizes is larger due to the quitebroad size distribution (s = 0.5) when compared to Zn-based ones (s = 0.3) and is directly related to the syn-thesis process.

IO J (a.u.) f \\ \~o

6,OX103

3,OX103

10 10' 102 103Figure 4. Component Iw at pulsation w of the transmittedlight intensity as a function of the applied field for Zn-basedsample. Iw is proportional to senrp.

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1,8x104

oooooo9oo6,Ox10s g

1,2x10""'

0,0

n0000c 9

IQo

o 0 o o

o 00 D00 0 cD

o 0 o o

o 0= 0,73 %

CuFe 0 :::: r ' ~ " 02 4

0,009B

0,000u_----4~OO~--~.0~0----'~200~~

0,0 5,Ox102

H(kAm)

o o o = 0,15%

Figure 5a. Birefringence ~n and normalized birefringence ~n/if! (inset) of copper ferrite samples as a function of the appliedmagnetic field. (0, if! = 0.73 % ; D, if! = 0.15 %).

o

1,5x103

1,4x10-4

7,Ox10-S

o!} ZnFep.fj

o{j8

oo (J) 0 0 0 00 0o 0 = 0.75%

o 0

o

0,00,0

o = 0,16%

1,2x103 1,8x1036,Ox102Figure 5b. Birefringence ~n and normalized birefringence ~n/if! (inset) of zinc ferrite samples as a function of the appliedmagnetic field. (0, if! = 0.75 % ; D, if! = 0.16 %).

100 10'

CuFep.

102 103

10-2

ZnFe20.

H (kA rn')

103

Figure 6a. Log-log representation of the normalized bire-fringence ~n/if! of Cu-based samples as a function of theapplied magnetic field. The full line is the best fit obtainedby using eq. (1) (see Table 2 for the resulting parameterssize distribution).

Figure 6b. Log-log representation of the normalized bire-fringence ~n/if! of Zn-based samples as a function of theapplied magnetic field. The full line is the best fit obtainedby using eq. (1) (see Table 2 for the resulting parameterssize distribution).

10-4

100 10'

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396 Brazilian Journal of Physics, vol. 31, no. 3, September, 2001

2,6x102

2,6x102

1,Ox104Figure 7a. High field analysis of birefringence data for Cu-based samples. The inset illustrates the low field behavior~n IXH2 .

2,Ox104

2,4x102

2,4x10'",2x10'"Figure 7b. High field analysis of birefringence data for Zn-based samples. The inset illustrates the low field behavior~n IXH2 .

Table 3: Saturation magnetization and opticalanisotropy of ferrite nanoparticles (chemically copre-cipitated) with their relevant references.

ms (kA m ) [14] 270 305 261 270' 153 122MnFe,04 NiFe204'" CuFe,04 ZnFe204

0.01 0.065 0.01 0.029 0.026

Finally, Table 3 summarizes the saturation mag-netization and the optical anisotropy values of ferritenanoparticles, all obtained by the same coprecipitationmethod in order to compare the birefringence levels ofcorresponding ferrofluid solutions. As it can be seen,our new EDL-MF samples present a comparable opti-cal level to that of more common magnetic fluids show-ing that they also could represent good precursors forapplied biological purposes.

v ConclusionEDL-MF based on copper and zinc ferrite nanoparti-cles have been successfully synthesized. The particlescrystallographic structure has been checked by using X-rays diffraction and identified as spinel-type. The mag-netic behavior of such ferrofluid solutions is typicallysuperparamagnetic and can be readily interpreted, inthe low concentration range investigated here, using asimple single-domain particle Langevin model. In thesame way, their magneto-optical birefringence has beenmeasured in the dilute regime and is related to a singleparticle effect. In the investigated range of magneticfields, the Langevin birefringence formalism well worksand it has been possible to determine the parameters ofthe size distribution as well as the optical anisotropy ofone particle in solution. Our results show that by the

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field-induced birefringence level, copper and zinc ferritebased MF are comparable to usual ones. Due to theirreduced iron content, such magnetic colloids would rep-resent a new alternative for biological applications. Infuture, it will be interesting to investigate their opticalproperties from a dynamic point of view. In addition,optical birefringence measurements performed on Ni-,Cu- and Zn-based EDL-MF samples synthesized withnanoparticles of different sizes are in progress.

AcknowledgmentsThe authors are greatly indebted to Dr. Itri (USP)

for X-ray diffraction measurements. They also thankthe Brazilian agencies CNPq/Pronex, CAPES, FAPDFand FAPESP for their financial support.

References[1 ] R. E. Rosensweig, Ferrohydrodynamics, (Cambridge

University Press, New York, 1985).[2] Magnetic Fluids and Applications Handbook, edited by

B. Berkovski (Begell House Inc. Pub!., New-York, 1996).[3] F. A. Tourinho, J. Depeyrot, G. J. da Silva, M. C. F. L.

Lara, Braz. J. Phys. 28, 413 (1998).[4] H. W. Davies, J. P. Llewellyn, J. Phys. D12, 311 (1979).[5] J. -C. Baeri, R. Perzynski, D. Salin, V. Cabuil, R. Mas-

sart, J. Magn. Magn. Mater. 62, 36 (1986).[6] S. Neveu-Prin, F. A. Tourinho, J. -C. Baeri, R. Perzyn-

ski, Colloids Surf. A80, 1 (1993).[7] E. Hasmonay, J. Depeyrot, M. H. Sousa, F. A. Tour-

inho, J. -C. Baeri, R. Perzynski, J. Magn. Magn. Mater.201, 195 (1999).

[8] J. -C. Baeri, V. Cabuil, R. Massart, R. Perzynski, D.Salin, J. Magn. Magn. Mater. 65, 285 (1987).

[9] P. C. Scholten, IEEE Trans Mag. 16, 221 (1980).[10] R. Itri, J. Depeyrot, F. A. Tourinho, M. H. Sousa, Eur.

Phys. J. E 4, 201 (2001).[11] S. Taketomi, Jpn. J. App!. Phys.22, 1137 (1983).

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[12] E. Dubois, Ph. D. thesis, Universite Pierre et MarieCurie, Paris (1997).

[13] E. Hasmonay, E. Dubois, J. -C. Baeri, R. Perzynski,Yu. L. Raikher, V. I. Stepanov, Eur. Phys. J. B 5, 859(1998).

[14] M. H. Sousa, F. A. Tourinho, J. Depeyrot, G. J. daSilva, M. C. F. L. Lara, J. Phys. Chern. B 201, 1168(2001).

[15] A. Halbreieh, J. Roger, J.-N. Pons, M. F. Da Silva,E. Hasmonay, M. Roudier, M. Boynard, C. Sestier, A.Amri, D. Geldweth, B. Fertil, J.-C. Baeri, D. Sabolovic,in Scientific and Clinical Applications of Magnetic Car-riers, U. Hafeli, W. Sehiit, J. Teller, M. Zborowski (Eds) ,Plenum Press, New York, 1997, p 399.

[16] International Tables for X-ray Crystallography(Kynoeh Press, Birmingham, England, 1968).

[17] ASTM ne;>25-0283 (CuFe204) and 22_1012 (ZnFe204).[18] C. Hammond, The Basics of Crystallography and

Diffraction (Oxford University Press, New York, 1997),p 145.

[19] R. W. Chantrell, J. Popplewell, S. W. Charles, Physica86, 1421 (1977).

[20] J. -C Baeri, R. Perzynski, D. Salin, V. Cabuil, R. Mas-sart, J. Magn. Magn. Mater. 62, 36 (1986).

[21] R. H. Kodama, J. Magn. Magn. Mater. 200, 359(1999).

[22] R. H. Kodama, A. E. Berkowitz, E. J. McNiff Jr., S.Foner, Phys. Rev. Lett. 77, 394 (1996).

[23] E. Hasmonay, J. Depeyrot, M. H. Sousa, F. A. Tour-inho, J. -C. Baeri, R. Perzynski, Yu. L. Raikher, I Rosen-man, J. App!. Phys. 88, 6628 (2000).

[24] F. Gazeau, E. Dubois, M. Hennion, R. Perzynski, Yu.L. Raikher, Europhys. Lett. 40, 575 (1997).

[25] F. Gazeau, J. -C. Baeri, F. Gendron, R. Perzynski, Yu.L. Raikher, V. I.Stepanov, E. Dubois, J. Magn. Magn.Mater 186, 175 (1998).

[26] C. Y. Matuo, A. Bourdon, A. Bee, A. M. FigueiredoNeto, Phys. Rev. E 56, 1310 (1997).

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