Tln(t/τ0) scaling approach and fluctuation field analysis in interacting particulatesystemsM. García del Muro, X. Batlle, A. Labarta, J. M. González, and M. I. Montero Citation: Journal of Applied Physics 81, 7427 (1997); doi: 10.1063/1.365442 View online: http://dx.doi.org/10.1063/1.365442 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/81/11?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Distributions of dipolar interaction fields in nano-granular magnetic systems J. Appl. Phys. 110, 023902 (2011); 10.1063/1.3609061 Experimental studies of fluctuation field and temperature coefficient of coercivity in advanced data backup tapes J. Appl. Phys. 101, 123904 (2007); 10.1063/1.2747220 Characteristic correlations between the Δm * interaction curves and the Preisach diagram in particulate media J. Appl. Phys. 91, 8733 (2002); 10.1063/1.1447487 Interparticle interactions in perpendicularly and longitudinally oriented Ba-ferrite particulate media J. Appl. Phys. 91, 4418 (2002); 10.1063/1.1453491 The effect of magnetic interaction in barium hexaferrite particles J. Appl. Phys. 81, 3812 (1997); 10.1063/1.364778

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T–ln( t /t0) scaling approach and fluctuation field analysisin interacting particulate systems

M. Garcıa del Muro,a) X. Batlle, and A. LabartaDepartament de Fı´sica Fonamental, Universitat de Barcelona, Diagonal 647, 08028 Barcelona,Catalonia, Spain

J. M. Gonzalez and M. I. MonteroDepartamento de Propiedades O´ pticas, Magne´ticas y de Transporte, Instituto de Ciencia de Materiales deMadrid (C.S.I.C.), Campus de la U.A.M., Cantoblanco, 28049 Madrid, Spain

~Received 3 June 1996; accepted for publication 7 March 1997!

The time dependence of the magnetization in samples having a different degree of interparticleinteractions is analyzed. The selected compound was a nanocrystalline powder of the compositionBaFe10.4Co0.8Ti0.8O19 with and without an admixture of nanosized SiO2 particles. Two differentapproaches were considered for the analysis of the thermally activated demagnetization: theT• ln(t/t0) scaling of the thermomagnetic relaxation in zero applied field, and the classicalfluctuation field and activation volume analysis. The energy barrier distribution obtained from theformer approach shows that the occurrence of larger demagnetizing interactions leads to a relativeenhancement of the lowest energy barriers with respect to the largest barriers. Activation volumesare found to increase with demagnetizing interactions and the leading demagnetizing mechanismappears to shift from an individual particle mode~coherent or nucleation! to a collective one. Bothanalyses are suggested to be taken into account in order to ascertain the influence of interactions onthe magnetic properties of nanocrystalline particles. ©1997 American Institute of Physics.@S0021-8979~97!08011-0#

I. INTRODUCTION

The time dependence of the magnetization has beenlargely discussed for almost five decades.1 Most of the stud-ies are based on the logarithmic approximation, which con-sists by assuming that, at any given temperature and during asuitable time interval, the relaxation law is logarithmic. Fromthis logarithmic description, the magnetic viscosity (S) isobtained, i.e., the slope of theM versus ln(t) curves. How-ever, this approach is only strictly valid when either the en-ergy barrier distributionf (E) is uniform ~which is not veryrealistic! or when the contribution of those particles havingenergy barriers close to the maximum off (E) dominates therelaxation during the experimental time window. The mainproblem concerning this kind of analysis arises from the factthat the relaxation curves, corresponding to a given experi-mental time window and obtained at different temperatures,reflect the relaxation of different regions off (E). Recently,Labartaet al.2 have shown that time-dependent thermorema-nence data collapse onto a single master curve with a scalingvariable of the typeT• ln(t/t0). This master curve corre-sponds to the whole relaxation curve at the lowest measuredtemperature and spans a time range as large as 10340 s ~whichis a time range experimentally inaccessible!. Furthermore,the derivative of the master curve provides the effective dis-tribution function of energy barriersf (E).3 The analysis ofthe thermoremanence data carried out following this proce-dure has been successfully applied to different small particlesystems.2–4 A conclusion from those studies was the factthat, when the overall interparticle dipolar interactions weredemagnetizing, the amount of low-energy barriers was larger

than what was expected for a log–normal distribution of par-ticle diameters. Also, demagnetizing interactions lead to anenhancement of the relaxation rate at low temperatures,4

which was also observed in numerical simulation studies.5 Itwas suggested that care should be taken when analyzingthermoremanent data at low temperature, in order not to con-fuse these experimental findings with the signature of mac-roscopic quantum tunneling.

The aim of this work is to gain further information aboutthe effect of interactions on the magnetic relaxation. Ther-moremanence measurements were carried out for an assem-bly of nanocrystalline substituted barium–hexaferrite par-ticles before and after milling them with a nanosized SiO2

powder. The milling process effects the aggregation stateand, thus, the interparticle interactions. As has been previ-ously published,6 the dM (H) analysis of the remanencecurves~isothermal remanent magnetization and dc demagne-tizing remanence! suggests that the substituted barium ferritepowders prepared with the SiO2 admixture, display largerdemagnetizing interactions than the powder without the ad-mixture. The time dependence of the thermoremanence wasanalyzed in terms of theT• ln(t/t0) scaling and also follow-ing the ‘‘classical’’ treatment in terms of the fluctuation fieldand activation volumes,7–9 so as to show that both ap-proaches are complementary concerning the relaxation of anassembly of small particles displaying dipolar interactions.

II. EXPERIMENT

Nanocrystalline BaFe10.4Co0.8Ti0.8O19 particles ~CoTisample! with a mean particle volume of 105 and 90 nm3, asdetermined from transmission electron microscopy~TEM!and x-ray diffraction, respectively,4 were prepared by usinga!Corresponding author. Electronic mail: montse@hermes.ffn.ub.es

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the glass crystallization method.10 A detailed magnetic char-acterization of this powder can be found in Ref. 4. The pow-der was compacted by cold pressing in order to avoid par-ticle rotations during magnetic measurements. A secondsample was prepared by milling for 5 min the magneticnanocrystalline powder together with a 3 nm SiO2 powder~CoTi1SiO2 sample! in a 60% volume fraction of silica. Themilling was carried out by means of a planetary ball mill,using hardened stainless steel jars and balls in a weight ofballs-to-weight sample ratio of 40:1. The mixed powder wasalso compacted by cold pressing.

Magnetization measurements were carried out with a su-perconducting quantum interference device~SQUID! magne-tometer in the temperature range 4.2–300 K and under mag-netic fields up to 50 kOe. Low-field susceptibility wasrecorded under a field of 25 Oe. Isothermal hysteresis loopswere measured at several temperatures to obtain both thecoercive force,Hc , and critical field,Hcr ~the latter standsfor the field at which the differential susceptibility corre-sponding to the demagnetization branch of the hysteresisloop presents the maximum value, and gives, in isotropicsamples, a reliable measure of the field for which the maxi-mum rate of irreversibilities occurs!. The time dependence ofthe thermoremanence in the temperature range 9–250 K wasmeasured at zero field after field cooling the sample at 200Oe from room temperature. These results were analyzed interms of theT• ln(t/t0) scaling.2–5 In order to obtain thefluctuation field and the activation volume, the time depen-dence of the magnetization was measured under several ap-plied demagnetizing fields in the region of the demagnetiza-tion curve corresponding to the critical field, after zero-fieldcooling the sample from room temperature and saturating itin a 50 kOe field at the measuring temperature.

III. RESULTS AND DISCUSSION

A. Low-field susceptibility

We show in Fig. 1 the temperature dependence of themagnetization after zero-field-cooling~ZFC! and field-cooling ~FC! processes recorded at 25 Oe for both the CoTiand CoTi1SiO2 samples. The curves display all the typicalfeatures of a small particle system with a distribution of par-ticle volumes and anisotropies, leading to an effective distri-bution of energy barriers~see Ref. 4 and 11 for details!.dM (H) plots6 show that interactions are demagnetizing inboth samples, but they do not show conclusive differences~see the inset in Fig. 1!. Also, the low-field susceptibility forthis sample shows the following differences with respect tothe CoTi sample: the temperature of the ZFC maximum(TM) is about 20 K higher and the FC magnetization remainsconstant as the temperature decreases below 80 K. This be-havior may be understood taking into account that the mill-ing process enhances demagnetizing interactions. This factintroduces additional disorder in the CoTi1SiO2 samplewith respect to the CoTi sample~and the larger the disorder,the higher the thermal energy necessary to reach the super-paramagnetic regime, and the flatter the FC at low tempera-tures!.

B. Coercive force

For an assembly of randomly oriented particles, thecoercive field in the blocked state is expected to dependon temperature asHc5Hc(0)(12AT0.77),12 with A5(bkB )/^E&0.77. b is given by the relation between the ex-perimental measuring time and the characteristic attemptingtime, which governs the Arrhenius law for magnetic relax-ation @b5 ln(tm /t0)#. Although t0 is usually taken as1029 s, in the present case, we use 10212 s ~see the nextsection and Ref. 4!, leading tob;32 for SQUID measure-ments. The coercive force is plotted againstT0.77 for bothsamples in Fig. 2. TheT0.77 law is verified below 30 K~therelationship is lost as the amount of superparamagnetic par-

FIG. 1. Temperature dependence of the magnetization after zero-field-cooling ~ZFC! and field-cooling~FC! processes recorded at 25 Oe for boththe CoTi and CoTi1SiO2 samples. Inset:dM plots for both samples, wheredM (H)5md(H)2(122mr(H)), md(H) being the reduced dc demagnetiz-ing remanance andmr(E) the isothermal remanence magnetization.

FIG. 2. Coercive field plotted versusT0.77 for both samples. Solid linesrepresent the fitting of experimental data according toHc5Hc(0)(12AT0.77).The arrow indicates the temperature above which experimentalvalues deviate from the fitting.

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ticles increases!. The coercive forces at 0 K obtained fromthe fit are Hc(0)56388 Oe ~CoTi sample! andHc(0)55950 Oe~CoTi1SiO2 sample!. The mean value ofthe energy barrier distribution is the same for the twosamples within the experimental error:^E&52.7310213 ergand ^E&52.8310213 erg for the CoTi and the CoTi1SiO2

samples, respectively. According to these results, by mixingthe ferrite nanoparticles with SiO2, the mean height of theenergy barrier does not change, but the sample demagnetizesmore easily~see theHc values in Fig. 2!. We, thus, under-stand that in the CoTi1SiO2 sample, demagnetizing interac-tions have been enhanced with respect to the CoTi one.

C. Relaxation of the thermoremanence: T– ln( t /t0)scaling

The time dependence of the thermoremanence was ana-lyzed in terms of theT• ln(t/t0) scaling. We show in Fig. 3the reduced magnetizationM /M0 versus the scaling variable,for t0510212 s. The scaling procedure consists of choosingthe t0 that makes all experimental relaxation curves corre-sponding to the different temperatures scale onto a singlemaster curve that stands for the whole relaxation curve at thelowest temperature. Although the suitablet0 is the same forthe two samples, larger relaxation rates at low and at verylarge T• ln(t/t0) values are observed for the CoTi1SiO2

sample. In addition, the derivatives of the two master curves~which are proportional to the effective distribution of en-ergy barriers! evidence a larger~lower! density of low-~high-! energy barriers in the CoTi1SiO2 sample than in theCoTi sample~Fig. 4!. This transference of energy barriers isa consequence of the milling process, which breaks the par-ticle stacks,4 and produces an enhancement of the demagne-tizing interactions at the expense of those that were magne-tizing. The maximum of the energy barrier distribution isattained at similar energy values in both samples, as ex-pected from theHc versusT0.77 curves. Considering thestructure of the energy barrier distributions~Fig. 3! we havefitted the master curves to an expression of the type3

M ~ t !5M0E0

`

dE•@p• f 1~E!1~12p!• f 2~E!#

3exp@2t/t~E!#, ~1!

corresponding to two log–normal distributions of energybarriers,f 1(E) and f 2(E). The best fits of the experimentalmaster curves to Eq.~1! are obtained with the followingparameters:~a! the CoTi sample: blocking temperatures as-sociated with the peaks of the distributionsTB01538 K andTB025121 K, widthss150.74 ands250.40, and relativeweightp50.19; and~b! the CoTi1SiO2 sample:TB01552 Kand TB025136 K, s150.66 ands250.34, andp50.40.TB01 describes the extra contribution of the low-energy bar-riers ~demagnetizing interactions!, while theTB02 is linked tothe second contribution centered at higher energies and de-scribes those noninteracting particles and/or particles withmagnetizing interactions.

It is not possible to attain a good fitting of the experi-mental values below aboutT• ln(t/t0)51300 ~see Fig. 3!,but this is not relevant concerning the present discussionsince the differences between both curves, which we inter-pret as due to interaction effects, were observed above thisvalue of the scaling variable. The fitting of the master curvein the case of the CoTi1SiO2 sample has been recorded upto T• ln(t/t0)56800, because, above this value, it decaysfaster than a log–normal distribution function does. The sec-ond energy distributionf 2(E) is comparable to the blockingtemperature distributionF(TB) derived for the CoTi samplefrom thermoremanent data, and to the volume distributionobtained from the fitting of the high-temperatureM (H)curves to a distribution of Langevin functions,4 since in thissample the overall magnetic behavior is dominated byf 2(E) ~p is only 0.19!. The total distribution of energy bar-riers f (E)5p f1(E)1(12p) f 2(E) ~Fig. 4! is in good agree-ment with the derivative of the experimental master curve,]M /]@T• ln(t/t0)#, for the CoTi sample. For the CoTi1

FIG. 3. Master curves. Magnetization vsT• ln(t/t0), with t0510212 s, for26 temperatures within 11 and 220 K for the CoTi sample~d! and theCoTi1SiO2 sample~j!. The fittings according to Eq.~1! are represented bysolid lines. FIG. 4. Effective distribution of energy barriers, obtained through the nu-

merical derivative of the master curves~Fig. 3! with respect to the scalingvariable, for the CoTi sample~d! and CoTi1SiO2 sample~s!. Solid linesrepresent the total energy barrier distributionsp f1(E)1(12p) f 2 obtainedby fitting the master curve to Eq.~1!.

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SiO2 sample, the experimental master curve is also fitted byassuming thatf (E) may be described through two log–normal distributions. However, when demagnetizing interac-tions are enhanced, the effective distribution of the energybarrier deviates from this assumption, as numerical simula-tion evidences.5 This is the reason why for this sample thederivative of the experimental master curve deviates fromp f1(E)1(12p) f 2(E), although the difference is not crucialconcerning our purpose.

D. Fluctuation field and activation volume

The time dependence of the magnetization was recordedfor several applied demagnetizing fields ranging from0.85Hcr up to 1.15Hcr . The experimental procedure used todetermine the fluctuation field and the activation volume wasproposed by Givordet al.,13 and is compatible with the mag-netic equation of state proposed by Estrinet al..14 The mag-netic viscosityS5dM/dLnt was evaluated in the time rangegoing from 500 up to 1500 s~Fig. 5!. The coefficient ofmagnetic viscositySv ~which is directly related with the fluc-tuation field! is given by15

Sv5S~12Dx rev!

x irr, ~2!

wherex irr andx rev are the irreversible and reversible suscep-tibilities of the material, andD is the demagnetizing factor.In the present work,x irr was evaluated from the slope ofirreversible demagnetization curvesm0M irr versusm0Ha ~ap-plied field!. The (m0M irr , m0Ha) values were determinedfrom the conditiondm0M /dt5const in thedm0M /dt versusm0M curves ~Fig. 5, inset!, corresponding to the differentfields applied in the measurements. In the present case,Dx rev is always lower than 0.07x irr , and Eq.~2! transformsinto S5x irrSv . The error associated with this assumption is

in all cases below one order of magnitude of the value of theexperimental error. The obtainedSv value can be related to aso-called activation volume defined through the expression

va5kBT/m0MsSv , ~3!

wherem0Ms is the saturation magnetization of the bulk ma-terial, andva represents the volume of material involved in asingle activation process.8 The fluctuation field is related toSv as Hf5Sv• ln(tm /t0), so, for our measurements,Hf

;32Sv .The temperature dependence of the fluctuation field is

shown in Fig. 6 for the two studied samples. TheHf valuesare significantly lower in the CoTi1SiO2 sample than in theCoTi sample. According to Eq.~3!, we show in Fig. 7 thetemperature dependence of the activation volume of bothsamples. A clear increase ofva with temperature is observed.In general, the interpretation of the measured values forHf

and va is complex.16 Commonly, va is understood as thevolume that is able to overcome the energy barrier whenHf is applied~or, conversely,Hf is the field at which thebarrier forva is equal to the thermal energy!. As we increase

FIG. 5. Typical measurements recorded to obtain the coefficient of magneticviscosity (Sv5S/x irr! and the activation volume given by Eq.~3!. The timevariation of the magnetization is measured at diverse inversion fields aftersaturating the sample at the measuring temperature.S is extracted from theslope of them0(M2M0) vs ln(t) curves.x irr is the slope of them0M irr vsm0Ha plots, where the values ofm0M irr correspond to the different valuesresulting for the used fields, consideringdm0M /dt constant~as shown in theinset!. These examples correspond to the CoTi sample recorded at 43 K.

FIG. 6. Fluctuation field (Hf532Sv) vs temperature for both samples. Theerror barrs come from the different field dependence ofxirr andS.

FIG. 7. Activation volume vs temperature for both samples. The arrowshows the mean particle volume for the CoTi sample obtained by TEM~1.05310225 m3!.

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the temperature, the same field is able to reverse bigger vol-umes. Concerning the CoTi sample,va ranges within aboutone-third and three times the mean particle volume. The par-ticle size distribution obtained from TEM indicates a non-negligible amount of particles with this largest volume. Wealso note that the ratiova~CoTi1SiO2 sample!/va~CoTisample! is about 3 in the studied temperature range~withinthe experimental error!, which suggests that the mechanismresponsible for the variation ofva in temperature is the samefor both samples. The fact that the activation volume isclearly larger for the CoTi1SiO2 sample indicates that de-magnetizing interactions are more important in this samplewith respect to the CoTi sample. Only at the lowest tempera-ture is va for the CoTi1SiO2 sample of the order of theparticle volume obtained by TEM and x-ray diffraction~thearrow in Fig. 7!, and at the highest temperature,va is abouteleven times the mean particle volume~this volume is muchlarger than the maximum volume detected by TEM!. Theseresults suggest that the demagnetization process goes froman individual mechanism~coherent rotation or nucleation!for the CoTi sample to a collective mechanism for theCoTi1SiO2 sample due to demagnetizing interactions.

IV. CONCLUSIONS

The aim of the work was to clarify the role of the de-magnetizing interactions on the magnetic relaxation of anassembly of nanocrystalline particles. According to previousresults,4,6 barium–hexaferrite nanoparticles are a suitablesystem for this purpose because of their resulting demagne-tizing interactions in the blocked regime. We had previouslyshown that, according to theT• ln(t/t0) scaling, an enhance-ment of the lowest energy barriers was detected when de-magnetizing interactions are present.4 By milling the par-ticles with SiO2, we have modified the dipolar interactionsby breaking the particle aggregates,~which results in a largermagnitude of the stray fields!. TEM micrographs17 show thatparticles tend to pile up, leading to stacks where interactionsare magnetizing, although particle clusters are also observed,where interactions are demagnetizing~see Ref. 6, and refer-ences therein!. Interstack interactions are also expected to bedemagnetizing.18

The parameters obtained from the two different ap-proaches@T• ln(t/t0) scaling and fluctuation field# suggestthat demagnetizing interactions have increased after milling.By breaking the stacks and particle clusters, we understandthat either the importance of magnetizing interactions has

diminished or that of demagnetizing interactions has in-creased. The activation volume analysis suggest that we gofrom an individual inversion mechanism to a collective one.All in all, these facts lead to an enhancement of the lowestenergy barriers~and to the consequent decrease in the larg-est! as shown by theT• ln(t/t0) scaling, and is reflected asbigger thermally unstable volumes according to the fluctua-tion field approach.

ACKNOWLEDGMENTS

The authors are indebted to Professor P. Go¨rnert and Dr.W. Schuppel for providing the barium–hexaferrite nanocrys-talline powder, and wish to thank Dr. C. de Julia´n for assis-tance in some of these measurements and helpful discus-sions. This work has been funded by the Spanish C.I.C.Y.T.through Project No. MAT94-1024-CO2-02. The financialsupport of the Catalan C.I.R.I.T. through Project No.GRQ1012 is also acknowledged.

1L. Neel, Ann. Geophys.5, 99 ~1949!.2 A. Labarta, O. Iglesias, Ll. Balcells, and F. Badı´a, Phys. Rev. B48,10 240~1993!.

3O. Iglesias, F. Badı´a, A. Labarta, and Ll. Balcells, J. Magn. Magn. Mater.140-144, 399~1995!; O. Iglesias, F. Badı´a, A. Labarta, and Ll. Balcells, Z.Phys. B.100, 173 ~1996!.

4X. Batlle, M. Garcı´a del Muro, A. Labarta, and P. Go¨rnert, J. Magn.Magn. Mater.157-58, 191 ~1996!; X. Batle, M. Garcı´a del Muro, and A.Labarta, Phys. Rev. B~to be published!.

5R. Ribas and A. Labarta, J. Magn. Magn. Mater.157-58, 351 ~1996!; R.Ribas and A. Labarta, J. Appl. Phys.80, 5192~1996!.

6M. El-Hilo, H. Pfeiffer, K. O’Grady, W. Schu¨ppel, E. Sinn, P. Go¨rnert, M.Rosler, D. P. E. Dickson, and R. W. Chantrell, J. Magn. Magn. Mater.129, 339 ~1994!.

7R. Street and J. C. Woolley, Proc. Phys. Soc. London, Sec. A62, 562~1949!.

8E. P. Wohlfart, J. Phys. F14, L155 ~1984!.9R. Street, R. K. Day, and J. B. Dunlop, J. Magn. Magn. Mater.69, 106~1987!.

10P. Gornert, E. Sinn, and M. Ro¨sler, Key Eng. Mater.58 129 ~1991!.11X. Batlle, M. Garcı´a del Muro, J. Tejada, P. Go¨rnert, and E. Sinn, J. Appl.Phys.74, 3333~1993!.

12H. Pfeiffer and W. Schu¨ppel, Phys. Status Solidi A119, 259 ~1990!.13D. Givord, A. Lienard, P. Tenaud, and T. Viadieu, J. Magn. Magn. Mater.67, L281 ~1987!; D. W. Taylor, thesis, Institut National Politechnique deGrenoble~1992!.

14Y. Estrin, P. G. McCormick, and R. Street, J. Phys., Condens. Matter.1,4845 ~1989!.

15L. Folks and R. Street, J. Appl. Phys.76, 6391~1994!.16A. M. de Witte, K. O’Grady, G. N. Coverdal, and R. W. Chantrell, J.Magn. Magn. Mater.88, 183 ~1990!.

17T. Ido, O. Kubo, and H. Yokoyama, IEEE Trans. Magn.MAG-22, 704~1986!.

18Y. J. Chen and M. H. Kryder~unpublished!.

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