Investigation of static and dynamic magnetic properties of Joule heated granular Co10Cu90 ribbons

*Correponding author. Tel.: #39-06-9067-2553; fax: #39-06-9067-2270.

E-mail address: "[email protected] (D. Fiorani)

Journal of Magnetism and Magnetic Materials 202 (1999) 123}132

Investigation of static and dynamic magnetic propertiesof Joule heated granular Co

10Cu

90ribbons

D. Fiorani!,*, A.M. Testa!, E. Agostinelli!, P. Imperatori!, R. Caciu!o", D. Rinaldi",P. Tiberto#, F. Vinai#, P. Allia$

!ICMAT, CNR, Area della Ricerca di Roma, Via Salaria Km29.500-C.P. 10; 00010 Monterotondo Stazione, Roma, Italy"INFM, Dip. di Scienze dei Materiali e della Terra, Univ. di Ancona, Ancona, Italy

#Istituto Elettrotecnico Nazionale Galileo Ferraris, Torino, Italy$INFM, Dip. di Fisica, Politecnico di Torino, Torino, Italy

Received 6 August 1998; received in revised form 4 January 1999Dedicated to the memory of J.L. Dormann

Abstract

The magnetic properties of a granular Co}Cu alloy (Co10

Cu90

) produced by melt-spinning and annealed by Jouleheating at di!erent DC current densities have been investigated by magnetization, DC and AC susceptibility measure-ments. The increase of the heating current density has been found to promote grain growth and to enhance the strength ofintergrain interactions, determining a change of magnetic behavior: from a collective freezing in random directions ofmoments of nanosized Co particles to an inhomogeneous and progressive blocking of moments of particles withincreasing size. The e!ects of Joule heating on microstructure and magnetic properties are discussed in relation to thegiant magnetoresistance properties exhibited by the system, which con"rm the development of interparticle correlationswith increasing the heating current density. ( 1999 Elsevier Science B.V. All rights reserved.

PACS: 75.20.En; 75.40.Cx; 75.60.Ej; 75.60.Jp

Keywords: Granular materials; Alloys; Giant magnetoresistance; Superparamagnetism

1. Introduction

The interest in magnetotransport properties ofgranular metals [1] and granular ferromagnets[2,3], investigated both experimentally and theor-etically since the early 1970s, has been recently

renewed by the discovery of the so-called &giantmagnetoresistance' (GMR) e!ect [4}6] inheterogeneous metallic alloys, in which nanosizedferromagnetic grains (e.g. Fe, Co, Fe}Ni) are em-bedded in a non-magnetic matrix (e.g. Ag, Cu, Au)[7,8].

Because of the relatively large surface-to-volumeratio of small particles, spin dependent scattering atthe interfaces between the grains and the matrixwas suggested to be the main source of the GMRe!ect [7,8], although the role of the scattering

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 3 0 3 - 0

inside the ferromagnetic particles should not beneglected [9}12]. The spin dependent scattering isstrongly a!ected by the particle microstructure andmorphology (particle size and shape, defects, inter-facial roughness, etc.) as well as by interparticleinteractions (expected to be dipolar or RKKY).

Since the concentration of magnetic grains in thematrix has also been found to strongly a!ect theGMR response [13}16], a great deal of interestrecently has been devoted to the study of the in#u-ence of interparticle magnetic coupling on theGMR response. Indeed, the interparticle interac-tions have been found to be responsible for thedeviation [17}19] in the low "eld region from thequadratic dependence of the fractional GMR(*R/R) on the square of the reduced magnetization(M/M

4, where M

4is the saturation magnetization)

which has been predicted for an assembly of non-interacting grains [2,3]. For such reasons, a deeperunderstanding of the dependence of the magneticproperties on the particle microstructure and inter-particle interactions has become necessary. Indeed,depending on the preparation method and anneal-ing conditions (thermal annealing, Joule heating),di!erent kinds of magnetic behavior have beenreported in the literature, including blocking ofmoments of superparamagnetic particles [17}19],spin-glass [20] and reentrant ferromagnetictransitions [21].

In this context, the dependence of the macro-scopic magnetic properties of a rapidly solidi"edCo

10Cu

90granular ribbon on the particle size dis-

tribution and on interparticle interactions has beeninvestigated in order to get a better insight intotheir correlation with the GMR e!ect. The sampleswere submitted to a Joule heating treatment withdi!erent DC current densities [22] to producea variation of grain size and interparticle interac-tions and hence optimize the GMR response. Themagnetic investigation was performed by magneti-zation, DC and AC susceptibility measurements inthe temperature range 4.2}300 K.

2. Experimental

Continuous ribbons of CoxCu

100~x(x"

5, 10, 15) were obtained by planar #ow casting on

a CuZr wheel rotating at high velocity in a Heatmosphere, as reported elsewhere [23,24]. In orderto induce the precipitation of Co particles, di!erentribbon strips (width"5 mm; thickness 40}60 lm)of a selected composition (x"10) were annealed invacuum by Joule heating at di!erent DC currentdensity values (0)J)3.4]107 A/m2) for a "xedtime of t"60 s.

X-ray di!raction measurements were performedon a Seifert XRD 3000P di!ractometer, in theBragg}Brentano geometry, using Cu K

aradiation.

Spectra were collected in the h}2h scan mode.The magnetic properties (static and dynamic) of

both as quenched and annealed samples werestudied by means of a commercial SQUID mag-netometer (2}300 K; H

.!9"55 kOe) and an AC

susceptometer (15}300 K), operating with an oscil-lating "eld H"H

0cos 2p ft (H

0"4 Oe; 5 Hz(

f(10 kHz). The magnetoresistance measurements(results have been reported elsewhere [23,24]) wereperformed up to H"20 kOe at 10 K and roomtemperature by the conventional four probes tech-nique, applying the "eld in the sample plane (per-pendicular to the bias current).

3. Results and discussion

3.1. X-ray diwraction measurements

The X-ray di!raction pattern of the as-cast rib-bon is shown in Fig. 1a. Peaks match with those ofa face-centered-cubic (FCC) phase. From the analy-sis of peak intensities there is no evidence of texture.The lattice spacing, determined from the angularposition of di!raction peaks through a least-squares re"nement process, is 0.3608 nm. Sucha value is intermediate between those of bulk FCCCo and Cu (0.3545 and 0.3615 nm, respectively), inagreement with the lattice parameter calculated bythe Vegard's law for a Co

10Cu

90alloy. This result

clearly indicates the formation of a FCC alloyphase.

The di!raction patterns of ribbons Joule heatedup to J"2.9]107 A/m2 are similar to the as-cast one and the calculated lattice spacings arethe same. However, such a result cannot excludethe presence of Co nanocrystals with coherent

124 D. Fiorani et al. / Journal of Magnetism and Magnetic Materials 202 (1999) 123}132

Fig. 1. X-ray di!raction pattern of as-cast (a) and3.4]107 A/m2 Joule heated (b) ribbons. Stars indicate the smallbumps due to the Co-rich phase.

Fig. 2. FC and ZFC susceptibility (H"10 Oe) versus temper-ature for the as-cast sample and di!erent annealing currentdensities.

interfaces with the Cu matrix, and extremely smallcrystallite size which would lead to very broadpeaks, almost impossible to detect.

As the annealing current is increased up to3.4]107 A/m2, the di!raction peaks shift to lower2h angles and small bumps on the high side of the(1 1 1) and (2 0 0) peaks become visible, as shown inFig. 1b. These bumps indicate the presence of a sec-ond FCC phase beginning to segregate: their posi-tions correspond to a lattice parameter larger thanthat of bulk Co, so they are probably due to a Co-rich phase. An average crystallite size of 12 nm hasbeen estimated for the Co-rich nanoparticles fromthe half value widths of the di!raction pro"les byusing the Scherrer equation and taking into ac-count the correction of the instrumental factors.The formation of a Co-rich phase during the an-nealing process induces an increase of the latticeconstant of the alloy phase (0.3611 nm), evidencedby the shifts to lower 2h angles of the (1 1 1) and(2 0 0) peaks.

3.2. Static magnetic properties

Low "eld (H"10 Oe) DC susceptibility wasmeasured as a function of temperature followingthe standard zero-"eld cooling (ZFC) and "eldcooling (FC) procedures. The behavior observedfor the as-cast sample and for heating currentsJ(2.9]107 A/m2 is reported in Fig. 2a.

The maximum observed in the sZFC

curves ischaracteristic of both an assembly of super-paramagnetic particles [25] and of spin-glass sys-tems [26]. In the latter case ¹

.!9is the freezing

temperature, whereas in the former ¹.!9

is relatedto the average blocking temperature by a relation-ship which depends on the type of volume distribu-tion function.

On the other hand, a di!erent temperature de-pendence of the s

FCsusceptibility is expected for the

two types of system. At high temperature sFC

, cor-responding to an equilibrium state, follows a Curie(or Curie}Weiss) law for both systems, since the

D. Fiorani et al. / Journal of Magnetism and Magnetic Materials 202 (1999) 123}132 125

regime is paramagnetic in the spin-glass case andsuperparamagnetic for a "ne particle system. Onthe other hand, below ¹

.!9, s

FCshows either a pla-

teau or a small maximum for spin-glasses, whereasit is expected to increase according to a Curie lawfor an assembly of non-interacting "ne particles. Insuch a case, as the temperature decreases, s

FC"rst

increases according to a Curie}Weiss law, then itdeviates downwards and shows a weak maximumat a temperature below ¹

.!9. Therefore, the behav-

ior of sFC

(Fig. 2a) suggests the existence of inter-particle interactions, which can determine acollective freezing of particle moments leading toa cluster glass like state. Indeed, the collective lowtemperature state is expected to be characterized bya disordered arrangement of moments, due to therandom distribution of anisotropy axes and therandom coupling between cobalt particles througheither dipole}dipole or RKKY interactions via thecopper matrix.

For the as-cast sample, the splitting occurs ata temperature ¹

41much higher than ¹

.!9, sugges-

ting that a progressive blocking of nanosized par-ticles occurs with decreasing temperature,according to the distribution of anisotropy energybarriers (E

B) for magnetization reversal (deter-

mined by the distribution of particle size andshape), followed by a collective freezing in randomdirections, due to interparticle interactions. Indeed,the splitting temperature, indicating the beginningof the blocking process, corresponds to the highestblocking temperature ¹

Bof particle moments. On

the other hand, for J"2.4]107 A/m2, sZFC

andsFC

split at the maximum of sZFC

, as in canonicalspin-glasses, suggesting a cooperative freezing ofmagnetic moments.

The collective behavior of nanosized particles atlow temperature, implying the predominance of theinteraction energy on the single particle anisotropyenergy, is coherent with the results of X-ray di!rac-tion, which indicate alloying between Co and Cufor J(2.9]107 A/m2. Actually, the cluster glassstate should arise in such a case from interactionsbetween moments of Co particles too small to bedetected by X-ray di!raction. This is in agreementwith the very low measured magnetoresistance(5}10% at 10 K; 1% at room temperature; [23,24]),implying that the alloying is not complete and that

a small fraction of nanosized particles is indeedsegregated from the Cu matrix.

For J"2.9]107 A/m2 (Fig. 2b), a di!erent be-havior is observed: the maximum becomes broader,¹

.!9increases up to +25 K and s

FCincreases with

decreasing temperature, unlike spin-glasses. Thisbehavior indicates a progressive blocking of singleparticle moments. The single particle behavior be-comes dominant when the anisotropy energy(E

B"K

!<, for uniaxial anisotropy) becomes larger

than the interaction energy. Indeed, the observedbehavior re#ects the increase of particle size andindicates a broadening of their size distribution.However, even in this case interparticle interactionsare not negligible, as indicated by the deviation ofsFC

from the Curie}Weiss law at low temperature.These data, suggesting a phase separation forJ"2.9]107 A/m2, with formation of a large frac-tion of nanosized Co particles (although still toosmall to be detected by X-ray di!raction) are inagreement with the strong observed increase ofmagnetoresistance (25% at 10 K; 7% at room tem-perature, reported in Refs. [23,24]).

Finally, for J"3.4]107 A/m2, a second changeoccurs: the ZFC susceptibility curve becomes ex-tremely broad and the maximum is no longer well-de"ned, whereas the FC susceptibility saturates atlow temperature. This gives evidence of a rapidincrease of particle size for currents J*2.9]107 A/m2, the tendency of particles to coalesce andthe development of stronger and stronger interac-tions between the moments of ferromagnetic par-ticles for such high values of J. Such picture iscoherent with the modi"cation of X-ray di!ractionpatterns, which gives evidence of Co rich phasesegregation, and with the strong decrease of mag-netoresistance (10% at 10 K; 1% at room temper-ature [23,24]), con"rming the further growth of thegrain size and the increase of interparticle interac-tions.

Magnetization versus "eld curves show hystere-tic behavior up to temperatures much higher than¹

.!9and ¹

41. Such a behavior re#ects a distribu-

tion of blocking temperatures, due to a distributionof particle sizes and shapes. The particle size distri-bution for di!erent heating currents was deter-mined by "tting the high temperature (¹*300 K)anhysteretic magnetization curves by a weighted


Fig. 3. Magnetization versus "eld at 20 K for the as-cast sampleand di!erent current densities.

Fig. 4. Coercive "eld at 20 K versus annealing current density.

sum of Langevin functions, assuming a sphericalshape of particles [23,24]. The maximum density ofsmallest grains (S fT+3 nm) was found forJ"2.9]107 A/m2 [23,24] at which the sampleexhibited the highest GMR value at room temper-ature. For the as-cast sample the M versus H curvesat 77(¹(300 K were "tted by a Langevin func-tion whose argument, mH

0/K¹, was modi"ed

including a molecular "eld interaction termH

*¸(mH

0#H

*)/K¹. The negative value of H

*indicates that antiferromagnetic-like interparticleinteractions are dominant [27]. This is also coher-ent with the negative h value (!112 K), deducedfrom the Curie}Weiss law s"C/(¹!h), where thesusceptibility was determined by the initial slope ofthe M versus H curves at di!erent temperatures[27].

Hysteresis cycles (Fig. 3) were also performed atlow temperature (¹"20 K) on di!erent samplesand the coercive "elds (H

#) and the saturation mag-

netization (M4) were extracted. H

#was found to

increase with increasing current density (Fig. 4),re#ecting the increase of the size of single domainmagnetic particles. A previous study on samplesannealed with conventional heat treatment [28],showed an increase of H

#(¹"10 K) for

¹!//

)673 K and then a decrease for higher an-nealing temperatures, revealing the growth of par-ticles bigger than those obtained by Joule heatingtreatment.

For all the samples, the saturation "eld is large(Fig. 3), due to the disorder and canting of momentson the surface of nanosized particles. It decreaseswith increasing J, re#ecting the increase of theaverage particle size. The saturation magnetizationM

4"rst increases with J, as expected for an in-

creased size of ferromagnetic particles and thendecreases for J"3.4]107 A/m2. Such behavior,also observed in some cases for conventional an-nealing performed at high temperature, may be dueto the back di!usion of Co atoms into the Cumatrix [21].

For J(2.9]107 A/m2, the ratio M3/M

4;0.5,

whereas for J*2.9]107 A/m2, M3/M

4+0.5, as

expected for an assembly of particles with uniaxialanisotropy and random distribution of anisotropyaxes. This supports the existence of two di!erentmagnetic regimes.

3.3. Dynamic magnetic properties

3.3.1. AC susceptibility measurementsIn order to investigate the e!ect of Joule heating

on the dynamic properties, the AC susceptibilityhas been measured as a function of temperature atdi!erent frequencies (5)f)104 Hz) (Fig. 5). Thecomparison of the temperature dependence of thein phase component (s@) of the susceptibility fordi!erent annealing current densities supports theidea of the onset of a di!erent magnetic regime forJ*2.9]107 A/m2. The frequency dependence of


Fig. 5. (a) Real part of the AC susceptibility versus temperatureat 1000 Hz for the di!erent annealing current densities (L:J"0.8]107 A/m2; ]"2.4]107 A/m2; # "2.6]107 A/m2;n"2.9]107 A/m2). (b) Real part of the AC susceptibility ver-sus temperature at di!erent frequencies for the as-cast sample.(L: 5 Hz; ]: 100 Hz; #: 1000 Hz).

Fig. 6. Arrhenius plot of the frequency dependence of ¹.!9

forthe as-cast sample (L) and for J"2.9]107 A/m2 (m).

s@ was also analyzed in detail and reported in Fig.5b, which shows, as expected, the increase of¹

.!9with the frequency. For an assembly of non-

interacting superparamagnetic grains the relax-ation time (q) of single particle moments is given byan Arrhenius law, q"q

0exp(E

B/k¹) (E

Bis the en-

ergy barrier for magnetization reversal). The block-ing temperature ¹

B, is indeed de"ned as the

temperature ¹ at which q is of the order ofthe measuring time t

.("1/f ), that is ¹

B"

(EB/k)/ln(t

./q

0), which increases with decreasing the

measuring time. Although the data are linear ifplotted on a semilog scale (Fig. 6), the values of thecharacteristic relaxation time q

0deduced from such

a plot (e.g. 10~24 s for the as-cast sample) arewithout physical meaning, suggesting the existenceof inter-particle interactions [29]. Nevertheless, theincrease of the slope d(1/f )/d(1/¹) with the heatingcurrent (e.g. 54 K for as-cast and 139 K forJ"2.9]107 A/m2; Fig. 6) indicates, at least quali-tatively, an increase of the total energy barrier, dueto the increase of particle size and inter-particleinteractions. The Vogel}Fulcher law (VF),q"q

0exp[E

B/k(¹!¹

0)] [30], proposed in order

to account for interparticle interactions throughthe temperature ¹

0(proportional to the interaction

energy), gives a satisfactory description of the fre-quency dependence of ¹

.!9for all the samples, with

a meaningful value of q0(10~11 s). However, the VF

law is phenomenological and it does not allow us todistinguish between spin-glasses and "ne particlesdynamics. Spin-glasses dynamics are known to becharacterized by a critical divergence of the relax-ation time according to a power law [26]:q/q

0+mz+[(¹!¹

#)/¹

#]~zl. This law gives a very

satisfactory description of the data for the as-castsample (Fig. 7), with very reasonable values of para-meters: q

0"10~11 s, ¹

#"14 K (corresponding to

the low "eld static value of ¹.!9

, zl"7 (corre-sponding to the value obtained by Monte Carlosimulations and reported for spin-glasses [26]).


Fig. 7. Temperature dependence of the relaxation time (1/f) forthe as-cast sample: the solid line is a "t with the power law (seetext).

Fig. 8. Temperature dependence of remanent magnetization(after applying a "eld of 100 Oe) for the as-cast sample andJ"3.4]107 A/m2.

Fig. 9. Time decay of the remanent magnetization (after ap-plying a "eld of 100 Oe) at di!erent temperatures forJ"2.4]107 A/m2.

Such results support the existence of a spin-glasslike collective freezing of particle moments (clus-ter-glass). Recently, the same critical dynamicalbehavior has also been observed in stronglyinteracting magnetic nanoparticles [31,32]. More-over, for J*2.9]107 A/m2 the power law is notfollowed, consistent with the other evidence whichcan point to a blocking of moments of non-interac-ting or weakly interacting superparamagnetic par-ticles, whose behavior is dominated by the singleparticle anisotropy energy barrier.

3.3.2. Remanent magnetization measurementsThe remanent magnetization (M

3) was measured

after cooling the samples in a "eld of 100 Oe andwaiting 60 s at the measurement temperature be-fore switching o! the "eld (thermoremanent mag-netization). Both temperature and time dependenceof M

3were analyzed. Fig. 8 shows the remanent

magnetization as a function of temperature for theas-cast sample and for the sample annealed atJ"3.4]107 A/m2. In the former case, the re-manence persists well above ¹

.!9(+16 K), pro-

viding evidence of progressive blocking of particlemoments with a large distribution of blocking tem-peratures. However, a large increase of M

3is ob-

served below ¹+¹.!9

, entering the cluster-glass

regime. On the other hand, for J"3.4]107 A/m2,a slower and regular increase with decreasing tem-perature is observed, as expected for an assembly ofparticles whose moments block progressively.

The time decay of TMR is reported in Fig. 9 forthe sample annealed at J"2.4]107 A/m2. Therelaxation is essentially logarithmic, except forsmall deviations at short measuring times; there-fore, a normalized logarithmic relaxation rate canbe de"ned as S"d(¹RM)/d ln t.


Fig. 10. Magnetoresistance at 10 K and relaxation rates S at 30and 50 K versus current density.

Fig. 11. Reduced GMR versus M/M4for (a) an ideal ensemble of

non-interacting magnetic moments; (b) as-cast material; (c)sample annealed at J"3.4]107 A/m2. The reduced height h isindicated for case (b).

Fig. 12. Reduced height (h) of #at-top parabolas (see text) versusannealing current density.

In order to investigate the correlation betweenthe magnetic viscosity of the samples and theirmagnetotransport characteristics, GMR at 10 Kand relaxation rates at ¹"30 K and at ¹"50 Kare plotted in Fig. 10 as a function of the annealingcurrent density. Indeed, both GMR and the relax-ation rate show a maximum at approximately thesame value of the annealing current density, locatedin the region of the change of magnetic regime. Thiscon"rms the existence of an optimum grain sizewhich maximizes the GMR value and the detri-mental e!ect of increasing interparticle interac-tions, since they tend to favour the polarization ofthe moments in preferred directions, therefore re-ducing the magnetic disorder in zero or low mag-netic "elds.

Further evidence of the presence of magneticinterparticle correlations is given by the reductionof the experimental GMR with respect to the idealcase (i.e., non-interacting particles), which can beusefully monitored by reporting the reduced heightof #at-top parabolas (h) in the so-called reduced-GMR representation [23,24]. The parameter h liesbetween zero and one, the two limits representingthe case of complete parallel alignment and com-plete independency of adjacent magnetic moments,respectively. As an example, two reduced GMRcurves (b: as-cast material; c: sample annealed at

J"3.4]107 A/m2) are reported in Fig. 11, to-gether with the perfect parabola representing theideal system of non-interacting magnetic moments.The room temperature behavior of h with the an-nealing current density is shown in Fig. 12: thedegree of magnetic correlation is found to be al-most constant up to J values comparable to the onecorresponding to the maximum GMR. For higher


J values, h drops down to a very small value,corresponding to particularly strong interparticlecorrelations. Interestingly, there is good agreementbetween the conclusions drawn from the presentresults, obtained at room temperature, and thoseobtained from the low-temperature analysis per-formed in the previous sections. This supports a selfconsistent description of the nature and role ofmagnetic interactions in granular Co

10Cu

90, main-

taining its validity in an extended temperaturerange.

4. Conclusions

The results of magnetization and susceptibilitymeasurements on Co}Cu granular ribbons showthat their macroscopic magnetic properties arisefrom the combination of both grain size distribu-tion and interparticle interactions, which are modi-"ed by Joule heating treatment at di!erent currentdensities. Such treatment has been found to pro-duce a change of magnetic behavior: froma cooperative freezing in random directions of mo-ments of very small particles (cluster-glass-likestate), to a progressive blocking of moments ofnanoparticles whose size increases with the currentdensity. At the same time, the strength of the inter-action between ferromagnetic particles increaseswith the current density. This is con"rmed by theGMR dependence on the heating current, showinga strong reduction with respect to the ideal caseof non-interacting particles. Furthemore, incorrespondence with the change of magnetic be-havior, the GMR reaches a maximum. This hasbeen related to the presence of an optimum grainsize (+3 nm) and weak interparticle inter-actions.

Acknowledgements

We would like to thank Mrs. Pasquale Filaci andClaudio Veroli for magnetization and X-ray dif-fraction measurements, respectively. This work was"nancially supported by &Progetto Finalizzato Ma-teriali' of National Research Council (CNR).

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Investigation of static and dynamic magnetic properties of Joule heated granular Co10Cu90 ribbons