CoFe–Cu granular alloys: From noninteracting particles to magnetic percolation

JOURNAL OF APPLIED PHYSICS VOLUME 85, NUMBER 10 15 MAY 1999

CoFe–Cu granular alloys: From noninteracting particlesto magnetic percolation

Victor Franco,a) Xavier Batlle, and Amılcar Labartab)

Departamento de Fı´sica Fundamental, Facultad de Fı´sica, Universidad de Barcelona, Diagonal, 647,08028 Barcelona, Spain

~Received 27 October 1998; accepted for publication 1 February 1999!

CoFe–Cu granular films with ferromagnetic content ranging from 0.10 to 0.33 by volume wereprepared by radio frequency sputtering. As-cast samples were rapidly annealed at varioustemperatures up to 750 °C to promote the segregation of CoFe particles within the metallic matrix.Magnetic and transport properties suggested that this family of samples may be classified into threegroups:~i! below about 0.20 volume content of CoFe, all samples display the typical features of agranular solid constituted by a random distribution of nanometric CoFe particles within a Cu matrix,and the maximum magnetoresistance is about 20% at low temperature~giant magnetoresistance!;~ii ! for as-cast samples within 0.20 and 0.30 of volume concentration, magnetoresistance andmagnetization display complex bimodal behavior and large metastable effects associated with theinterparticle interactions, which stabilize a domain-like microstructure well below the volumepercolation threshold~0.55!, as already observed in CoFe–Ag~Cu! granular alloys. As aconsequence of the large magnetic correlations, magnetoresistance is very low~1%–3%!. Throughannealing, the microstructure and therefore the transport properties evolve to those of a classicalgiant magnetoresistance system with large particles; and~iii ! above about 0.30 of volume content~and still below the volume percolation threshold!, as-cast samples display both anisotropic andgiant magnetoresistance, as also observed in other granular alloys. Annealing leads to completesegregation and to the formation of large magnetic particles, which results in a transition frommixed behavior of both anisotropic and giant magnetoresistance~GMR! regimes to a giantmagnetoresistance regime, with a maximum GMR of about 7%. ©1999 American Institute ofPhysics.@S0021-8979~99!01810-1#

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I. INTRODUCTION

Nanostructured magnetic materials have been largstudied because of both their technological applicationstheir new challenging magnetic and transport propertThis is the case of granular magnetic alloys consisting onultrafine ferromagnetic~FM! particle distribution embeddein a nonmagnetic metallic matrix, which have been extsively studied in the past few years due to their anomalmagnetotransport properties. In particular, because theyplay negative giant magnetoresistance1 ~GMR!. In these ma-terials, GMR is interpreted within the scope of the spdependent scattering of conduction electrons with the lomagnetic configuration2 either within or at the interfaces othe FM particles embedded throughout the matrix. Somethese materials also show classical anisotropic magnetortance~AMR!.3,4 In this case, the sign of the magnetorestance depends on the angle formed between the appliedand the electrical current.

The purpose of this article is to discuss the physical amagnetic microstructure and the magnetic and transproperties of CoFe–Cu samples with a volume concentraof CoFe (xv) ranging fromxv50.10 to xv50.33. Fe was

a!Electronic mail: [email protected]!Author to whom correspondence should be addressed; electronic

[email protected]

7320021-8979/99/85(10)/7328/8/$15.00

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added to Co~about 5–10 at.%! in the classical CoCu GMRsystem as a minor FM component, in order to increaseGMR effect as previously reported,5 by increasing the magnetic moment of the particles. Although the physical micrstructure is almost the same for all the as-cast samples bthe percolation threshold, magnetic and magnetotransproperties change dramatically withxv . Furthermore, the annealing procedure greatly modifies both the crystal structand the magnetic microstructure, and consequently the mnetotransport properties. Finally, it is shown that the oserved behavior in CoFe–Cu alloys is due to the interpbetween:~i! dipolar interactions between magnetic entiticlosely dispersed in the metallic matrix,~ii ! indirect ferro-magnetic exchange through the metallic matrix due to Coalloying, which disappears with the annealing, and~iii ! out-of-plane uniaxial magnetic anisotropy arising from cryslattice strains, which relaxes and also disappears as a rof annealing.

II. EXPERIMENT

CoFe–Cu thin films with thickness of about 250 nwere radio frequency sputtered onto glass microscope sliThe film thickness was measured using a Tolansky multipbeam interferometer and the composition was determineding energy dispersive x-ray spectrometry and ionic phchemical mass spectrometry. The as-cast samples wereil:

8 © 1999 American Institute of Physics

IP license or copyright; see http://jap.aip.org/jap/copyright.jsp

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7329J. Appl. Phys., Vol. 85, No. 10, 15 May 1999 Franco, Batlle, and Labarta

idly annealed~0.1 s! at 600, 650, and 750 °C in a vacuusystem, in order to promote phase segregation, pargrowth, and strain relaxation. The particle size distributand microstructure were studied by x-ray diffraction~XRD!,atomic force microscopy~AFM!, and transmission electromicroscopy~TEM!. The texture of the samples was studithrough the XRD rocking curves, where the full width at hamaximum ~FWHM! indicates the angular dispersion ofgiven Bragg reflection. XRD rocking curves give informtion on the in-plane crystalline quality, such as the latestructural coherence length and the mosaic spread withinepitaxial film. Magnetic force microscopy~MFM! was usedto study the microscopic magnetic pole distribution perpdicular to the film plane. A magnetic tip consisting ofsingle Si crystal coated with a thin CoCr film~coercive field,Hc536569 Oe) was oscillated 50 nm above the film suface. Magnetoresistance~MR! was measured by an alternaing current four-point probe technique in the temperatrange 2–300 K and in magnetic fields up to 10 kOe. Tmagnetic field was applied in the film plane parallel to tcurrent direction. Hysteresis loops were recorded with abrating sample magnetometer up to 12 kOe and with aperconducting quantum interference device magnetometeto 50 kOe.

III. RESULTS

A. Crystal structure and sample texture

The u/2u XRD spectra for the as-cast samples cleashow the~111! Cu peak at all the concentrations studieOther reflections of the Cu face-centered-cubic~fcc! struc-ture, such as the~222! and the~200! can also be seen, butheir intensities are much lower~see Fig. 1 and inset as aexample!. The spectrum of the amorphous substrate~glass! isobserved at low angles~between 0° and 20°!, and between20° and 40° the amorphous phase of the metallic alloy is aobserved. These results indicate that the as-cast samplesa low degree of crystallinity, because of the rapid quenchproduced during deposition. Besides, the Cu crystallitesmostly oriented along the111& direction, which is perpen-dicular to the film plane. However, this texture is not coplete since a small peak corresponding to the~200! Cu re-flection is also present. The rocking curves for the~111! Cu

FIG. 1. @~a! and inset# XRD spectra for a Co23Fe11Cu66 sample as-cast andannealed at~b! 600, ~c! 650, and~d! 750 °C. Vertical lines represent bulvalues for~111! Cu, ~111! Co, and~200! Cu reflections, respectively.


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peak for Co11Fe6Cu83 show an angular dispersion~with re-spect to the film normal! of 26.6° and 17.9° for the as-casand 750 °C annealed samples, respectively. The degretexture increases slightly with both Cu concentration andnealing temperature, as expected~see Table I!. CoFe forms afcc solid solution at all the concentrations studied. Thecrystals, display similar texture although the peaksweaker since the degree of crystallinity is lower. In the acast samples, CoFe crystals are not large~or well crystal-lized! enough to be easily observed in conventionalu/2uspectra. Specially detailed spectra were recorded to lothe CoFe peaks position. This is also supported by thethat magnetic and transport properties are closer to thoseCoFeCu alloy. To verify the fcc structure and the texturethe samples, otheru/2u spectra were recorded at differentxangles~by tilting the sample with respect to an axis paralto the film plane!, in such a manner that by rotating thsample 35°~expected angle between the^111& and the 100&cube directions!, the relative intensity of the~200! Cu reflec-tion becomes maximal with respect to the~111! reflection,confirming the sample texture and crystal structure~Fig. 2!.All the peaks are shifted from their corresponding bulk vues~Fig. 1! because of strains during deposition due todifferences between thermal expansion coefficients ofglass substrate and the sample film, and to the presencmetal coherent interfaces~MCIs! and CoFe–Cu alloying. Asshown by the shifting of the peaks, the lattice spacingsdhkl

of the bulk fcc CoFe and Cu are modified. Furthermore,d111

is shorter than expected, while thed200 is longer~see Fig. 3!.This leads to a deformed cubic cell squeezed in the direc

FIG. 2. XRD spectra for a Co11Fe6Cu83 as-cast sample atx50° and x535°.

TABLE I. FWHM of the rocking curves for the~111! Cu and~111! Coreflections for samples Co11Fe6Cu83 and Co23Fe11Cu66 , as-cast and at threeannealing temperatures~in brackets!.

Sample ~111! Cu ~111! Co

Co11Fe6Cu83 as-cast 26.6° ¯

Co11Fe6Cu83~600 °C! 21.2° 29.8°Co11Fe6Cu83~650 °C! 19.5° 23.4°Co11Fe6Cu83 ~750 °C! 17.9° 21.2°Co23Fe11Cu66 as-cast 35.1° ¯

Co23Fe11Cu66~600 °C! 24.9° 32.1°Co23Fe11Cu66~650 °C! 17.8° 24.4°Co23Fe11Cu66~750 °C! 16.1° 22.3°


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7330 J. Appl. Phys., Vol. 85, No. 10, 15 May 1999 Franco, Batlle, and Labarta

normal to the film plane and stretched in the parallel dirtion. This is because when atoms are deposited onto the gsubstrate, the film cools down and the mean atomic distantend to shrink, but the glass substrate, with a lower therexpansion coefficient, avoids film contraction. Thus, tmean in-plane distances are larger than expected, whileperpendicular ones are shorter. Thus, it has been foundthe unit cell that best fits the XRD spectra is a rombohedone with angles of 90.5° and 89.5° for all as-cast sampirrespective of the FM content. By adding CoFe, the lattspacings of Cu tend to decrease due to CoFe–Cu alloand MCI strains. However, while the substrate–samstrains are anisotropic, the deformation due to the preseof CoFe are isotropic and equally affects all thedhkl spacingsas can be observed in Fig. 3, where thed111 andd200 versusxv slopes are parallel. With annealing, the spacings evolvthe expected bulk values so the crystal structure goes frorombohedric to a cubic symmetry. The same happens wthe fcc CoFe crystals, for which these slight deformatiomight be enough to produce a uniaxial magnetoelasticisotropy as shown in Ref. 6, where an axial deformationabout 0.01% in a fcc crystal is enough to induce uniaxanisotropy. This uniaxial anisotropy is perpendicular tofilm plane due to the sample texture. Uniaxial anisotropare found in cubic systems and considered to be causethe stress which might be produced by a difference in thmal expansion coefficients between film and substrate oan epitaxial misfit.7 Thus, perpendicular anisotropy has albeen observed in a variety of fcc thin films grown onsingle-crystal substrate, such as fcc PtMnSb grown on Mn2O~see for example Ref. 8!, where the lattice mismatch betweethe sample and the substrate is responsible for the perdicular anisotropy.

Through annealing the microstructure evolves tohigher degree of crystallinity and phase segregation,strain relaxation occurs. Thus, as particles grow with anning, peaks shift to their expected bulk values and theycome narrower, increasing their intensities~Fig. 1! and the~111! reflection corresponding to the fcc CoFe particlewhich is also textured normal to the film, becomes cleaobservable. No extra reflections appear for the Cu phaseit remains textured along the111& direction, as the rockingcurves confirm. XRD spectra indicate that the size of the

FIG. 3. Interplanar lattice spacingdhkl for the ~111! and~200! ~a! CoFe and~b! Cu reflections as a function of the FM concentration for several as-samples.


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particles varies from 15 to 30 nm for the as-cast samplesfrom 25 to 45 nm for the 750 °C annealed samples, bdepending on the Cu concentration~the higher the concentration, the larger the particles before and after annealin!.The CoFe particles segregated after soft annealing~at600 °C! have a mean size of 10 nm irrespective of the Fconcentration, which increases to 30–35 nm for the 750annealed samples, depending on the CoFe concentraAFM and bright field TEM images show a narrow Cu paticle size distribution in the as-cast samples and a widerin the annealed ones. Figures 4~a! and 4~b! show an exampleof these images for as-cast Co12Fe7Cu81, from which thegranular nature of the samples is observed, being the surroughness about 3065 nm. The granular nature of thsamples is also evidenced by dark field TEM; the size ofCu and CoFe particles deduced from this method is content with the XRD results. In Fig. 4~c!, the dark field ofCoFe-rich pseudoamorphous particles is shown, the msize of the particles is 81/25 nm. The matrix surroundingthese particles consists of Cu crystals with 10% of Coalloyed. This microstructure is of the greatest importanceexplain magnetotransport properties.

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FIG. 4. ~a! AFM image of the surface of a Co19Fe8Cu73 as-cast sample,~b!bright field TEM picture of a Co12Fe7Cu81 as-cast sample,~c! dark fieldTEM picture of the CoFe crystals in a Co12Fe7Cu81 as-cast sample.


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B. MFM images

For all as-cast samples with FM content above 20MFM images show long range magnetic domain microstrtures~Fig. 5!. These MFM images evidence the existencea magnetic microstructure perpendicular to the film plaThe magnetic moments of neighboring grains tend to beranged parallel in an out-of-plane direction, leading to strilike magnetic domains that are themselves aligned antipalel, which leads to an overall demagnetized state. Thmagnetic domains, much larger than the particle sizes,stabilized due to the interplay of:~i! dipolar interactions,which tend to flux closure of neighboring magnetic domaof opposite magnetization,~ii ! indirect FM interactionsthrough the matrix, which tend to form large FM domainand ~iii ! perpendicular anisotropy, arising from crystal dtortion, as observed in CoFe–Ag~Cu! granular alloys.9,10 Theorigin of these terms in the Hamiltonian of the present gralar media can be justified as follows. Dipolar interactionsintrinsic to small particle systems. It is suggested that inrect FM exchange among particles takes place throughmatrix, since the matrix itself is ferromagnetic for all as-casamples due to CoFe–Cu alloying. The degree of alloyinconstant, i.e., the Cu matrix is CoFe saturated from the lest FM composition studied (xv;0.10). Thus, the stripedlike domains may only appear when the interparticle distais short enough (xv>0.20).11 Finally, the origin of theuniaxial perpendicular anisotropy, responsible for the out-plane component of the magnetization, is found in the crycell deformation. MFM images of the as-cast samples shthat the width of the domains increases with increasingFM content, from about 105 nm forxv50.26 to 125 nm forxv50.33. The intensity of the recorded signal and the shaness of the domains also increase withxv , suggesting alarger out-of-plane component of the magnetization, aspected when decreasing the mean distance between theparticles. However, belowxv50.20, MFM images do noshow any additional contrast with respect to the AFM iages, indicating that no magnetic domains are present sinteractions are weaker due to the fact that FM particlesfurther apart. Through annealing, particles grow leadingthe formation of large FM clusters with the magnetic mment lying in the film plane.9,10 Hysteresis loops show thathe perpendicular anisotropy disappears, due to stress ration. Moreover, as the particles segregate, the matrix islonger FM, and the out-of-plane magnetic microstructurelost.

FIG. 5. MFM pictures of a Co19Fe8Cu73 as-cast sample and a Co23Fe11Cu66

as-cast samples at room temperature and at remanent state.


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C. Transport properties

Taking into account the magnetotransport propertithis family of samples can be classified in three differegroups. Belowxv;0.20, annealed samples display the tycal features of a granular solid constituted by a randomtribution of nanometric CoFe particles within the Cmatrix.5,12,13 The maximum magnetoresistance observedthis family is about 20% at low temperature (T520 K andH510 kOe) for anxv50.16 sample annealed at 600 °C. Tchange in magnetoresistance is defined as,

DMR5@R~T,H50!2R~T,H !#

R~T,H50!. ~1!

The curves corresponding to the as-cast samples~Fig. 6!display low values of MR~below 4%! because CoFe ismainly alloyed with the Cu matrix, thus the scattering rsponsible for GMR is not very effective because of the laof sharp interfaces and the dilution of the magnetic momein the Cu matrix.14 As a consequence, with annealing Mincreases, the material becomes magnetically softer, andteresis effects appear due to the growth of relatively lar(.10 nm! CoFe particles~see Fig. 6!.

For xv50.20– 0.30, MR for the as-cast samples displacomplex bimodal behavior and large metastable effewhich are associated with high magnetic correlations10 ~Fig.7!. The inner peaks correspond to all the irreversible conbutions, such as domain wall motion and those arising frgranularity ~isolated FM particles and uncompensated mments of the antiparallel arrangement!, while the outer broadmaxima are attributed to the progressive rotation of the mnetic domains structure towards the field axis. There is alsthird contribution at intermediate fields arising from th

FIG. 6. DMR vs applied in-plane field in parallel geometry at 20 K forCo11Fe6Cu83 sample,~a! as-cast and~b! annealed at 600 °C.

FIG. 7. DMR vs in-plane applied field in parallel geometry at 20 K forCo22Fe8Cu70 sample as-cast.


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CoFe alloyed in the matrix, giving place to an AMR, whicis responsible for the slight increase in MR at fields of a fhundred Oersteds in the parallel geometry. The high mnetic correlations lead to small values of MR~;2%! andanomalous magnetic training behavior in as-cast sampWe use the expression ‘‘training behavior’’ to refer to tfact that the MR curves change as the magnetic field ispeatedly cycled, i.e., each time a610 kOe field is applied,the resistivity decreases~Fig. 7!. After few loops, trainingeffects disappear and a new~metastable! state is achievedwhich remains stable while further measurements areformed. This new metastable state is lost after about 24zero field and then, the training behavior can be repeatedthese findings reveal the coexistence of highly degenerremanent states due to magnetic correlations and disoThe observed decrease in the resistance might be due tfact that as the magnetic field is cycled, magnetic mometend to be in plane, forming large in-plane domains leadto a reduction of the electron scattering in the domain waas shown in CoFe–Ag~Cu! samples.10 A more detailed ex-planation may be found in Ref. 15.

Stripe-like domains and particles do not show the sathermal behavior because of differences in magnetic sThus, while at low temperature the inner peaks of the MRhigher than the outer peaks, the opposite is observed at rtemperature~Fig. 8!, probably because small magnetic enties tend to become superparamagnetic and no longer papate in the MR, while the outer maxim associated withantiparallel stripe structure is stable at room temperatureshown by MFM. As a consequence of the annealing,characteristic GMR behavior of a granular solid is recove~Fig. 9!. In the samples with lower FM content particlegrow slowly with annealing,16 then the bimodal behavior remains after soft annealing, while for samples with higher F

FIG. 8. DMR vs in-plane applied field in parallel geometry at room temperature for Co22Fe8Cu70 as-cast sample.

FIG. 9. DMR vs in-plane applied field in parallel geometry at 20 K fCo22Fe8Cu70 sample annealed at 750 °C.


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content this behavior rapidly disappears even at soft annings, due to the precipitation of large particles.

Above xv;0.30 ~and still below the volume percolatiothreshold!, as-cast samples show both AMR and GMR,previously observed in Co–Ag alloys.4 However, the anneal-ing procedure leads to the complete segregation of thecontent, which results in a transition from the AMR–GMregime to the normal GMR regime, with a maximum GMof about 7%~Fig. 10!. Therefore, in the as-cast samples tCoFe–Cu alloy is rich enough in FM content to displAMR, as other ferromagnetic alloys do. In fact, both phnomena coexist, e.g., for Co23Fe11Cu66, the as-cast sample~inset of Fig. 10! displays AMR at low fields, while GMRdominates above;1000 Oe. This sample presents AMR uto 765 Oe with a variation of the resistance about 0.3%,above 765 Oe GMR dominates, displaying a low valueMR ~0.5%!. AMR is no longer observable after the first anealing~600 °C!, and the value of GMR grows to 2.3%. MRincreases with annealing up to 4.10% for 650 °C and 7.3for 750 °C. The bimodal behavior observed in the range frxv50.20 to 0.30 is not detected for larger FM concenttions. However, for the as-cast samples, the inner peak stture is probably hidden by the AMR effect@we note that insome CoFe–Ag~Cu! alloys, AMR coexists with the bimodapeak structure#.

D. Magnetic properties

The magnetization curves for as-cast samples withFM content (xv,20%) only display hysteresis below abo10 K, showing superparamagnetic behavior at higher teperatures due to the absence of large magnetic particlessides, in the as-cast samples with a high FM contentxv.30%), hysteresis decreases from 5 to 150 K~the coercivefield Hc decreases from 200 to 25 Oe!, and remains almosconstant from 150 to 300 K (Hc;25 Oe). These facts maindicate the formation of magnetic domains~.100 nm!, dueto FM exchange through the FM matrix, which are stableroom temperature, as MFM shows. For samples withxv50.20– 0.30, the in-plane magnetization curves for as-csamples seem to arise from the superimposition of two hteresis loops:10 ~i! the inner loop corresponds to all the irreversible contributions, such as the domain wall motion adomain rotation, and other contributions coming from tgranularity, such as those corresponding to both isolamagnetic particles and uncompensated moments of the

FIG. 10. DMR vs in-plane applied field in parallel geometry forCo23Fe11Cu66 sample at 20 K~a! ~detail in inset! as-cast, annealed at~b!600 °C and~c! 750 °C.


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parallel stripe-like domain arrangement, and~ii ! the outerloop corresponds to the progressive rotation of the antipalel domain arrangement towards the field axis, leading tquasilinear field dependence of the magnetization~Fig. 11!.The field dependence of the magnetization curves is content with the main features observed in the MR curves~Fig.11!. The inner relative maxima of the MR, occur at the cercive field of the hysteresis loop~;100 Oe! and the outerones occur at about the field at which irreversibility disapears~1500–2000 Oe!. We note that the irreversible contrbution ~inner loops! is larger for the parallel hysteresis loothan for the perpendicular one, since in the latter, the rotaof the cluster moments towards the field axis is not affecby the random topological distribution of stripe-like domaiin the film plane. Forxv.0.30 hysteresis loops display thsame features. No discontinuity suggesting the nucleatiomagnetic bubbles is observed in the hysteresis loop forperpendicular geometry~Fig. 12!, in contrast with results forCo thin films,17 since we are dealing with a granular systeso domain inversion does not take place continuously.these facts suggest that granular alloys displaying long radomain-like structures share some features of both contous and discontinuous magnetic systems. Through anneathe magnetic hysteresis and the saturation magnetizatiocrease as CoFe particles precipitate and grow, and theversibility and the squareness of the hysteresis loopscreases as the crystals anisotropy evolves from uniaxiacubic. The bimodal behavior disappears and the maximthe MR curves occur atHc ~about 500 Oe!, having a lowthermal dependence.

The remanent-to-saturation magnetization ra(Mr /Ms) increases with annealing, approaching 0.823low temperature: the expected value for a cubic symmewith the easy axis in the100& direction ~Fig. 13!. For the

FIG. 11. DMR and hysteresis loop for a Co22Fe8Cu70 as-cast sample at 20 Kwith the field applied in the plane direction in parallel geometry.

FIG. 12. Parallel and perpendicular normalized hysteresis loops at rtemperature for a Co26Fe5Cu69 as-cast sample.


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as-cast samples, the uniaxial anisotropy coming from theformed fcc cell leads to aMr /Ms value tending to 0.5 at lowtemperature~Fig. 13!, as expected for uniaxial anisotropy.18

However, for some as-cast samples, this value is greater0.5, which might be due to the coexistence of axial distorand cubic fcc crystals. In fact, the deformations nearsubstrate must be much greater than those far from it,cause there is stress relaxation due to plastic deformat~dislocations, vacancies, . . . ! as the film grows. Thus, for theas-cast sample withxv50.18, the thickness is 355 nm anMr /Ms ~5 K! is ;0.6 and for the as-cast sample withxv50.33, the thickness is 240 nm andMr /Ms ~5 K! is ;0.5.Assuming that the mean blocking temperature,^TB&, may beapproximated as:KV525kBTB , whereV is the particle vol-ume, andkB the Boltzmann constant, it is found thatTB forparticles with a diameter of 10 nm is 46 K. Thus, at rootemperature, all the as-cast and soft annealed samples~allthese samples present particles with a mean diameter b10 nm! should be superparamagnetic and theMr /Ms valueshould be zero. However, in the samples with high FM cotent (xv.0.20), magnetic correlations keep theMr /Ms ratioconstant withT since these correlations overcome the thmal decrease ofMr /Ms . For samples annealed at 750 °^TB& should be about 1000 K for the samplexv50.18~meanparticle diameter, 28 nm! and about 1900 K for the samplxv50.33 ~mean particle diameter, 35 nm!. Thus, the weaktemperature dependence of theMr /Ms ratio of the 750 °Cannealed samples has to be attributed to the large size oFM particles rather than to interparticle interactions.

The orientation of the anisotropy axes in the sampmay be calculated using simple energy arguments by cparing parallel and perpendicular hysteresis loops19 ~Fig. 12!.The u angle of the resulting uniaxial anisotropyK with re-spect to the film normal is found through the expressions19

Hs i1Hs'54pMs12K

Ms,

Hs i52K cos2 u

Ms, ~2!

whereHsi is the parallel saturation field,Hs' is the perpen-dicular saturation field, andMs is the saturation magnetization. This procedure is valid for an uniaxial system, but malso be applied to mixtures of uniaxial and cubic systemsexplained by Dormann, Fiorani, and Tronc in Ref. 20 w

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FIG. 13. Mr /Ms ratio for a Co12Fe7Cu81 sample~a! as cast, annealed at~b!650 °C and annealed at~c! 750 °C and for a Co23Fe11Cu66 sample~d! as castand annealed at~e! 750 °C.



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TABLE II. Angle of the magnetic anisotropy (u) with respect to the film normal and anisotropy constant(K)for different FM contents and annealing temperatures.Ms is the saturation magnetization,Hsi is the parallelsaturation field andHs' is the perpendicular saturation field.

Sample xv Ms (emu/cm3) Hsi ~Oe! Hs' ~Oe! K(erg/cm3!106 u°

Co7Fe4Cu89 as-cast 0.10 180 2150 2250 0.19 0Co12Fe7Cu81 as-cast 0.18 282 1500 3500 0.20 0Co12Fe7Cu81 750 °C 0.18 348 2800 8200 1.6 54Co22Fe9Cu69 as-cast 0.30 420 1500 5400 0.34 0Co22Fe9Cu69 750 °C 0.30 544 2600 10000 2.39 56Co23Fe11Cu66 as-cast 0.33 490 980 5000 0.19 0Co23Fe11Cu66 600 °C 0.33 568 1500 5800 0.62 34Co23Fe11Cu66 650 °C 0.33 631 2300 7800 1.80 52Co23Fe11Cu66 750 °C 0.33 631 2700 9500 2.40 54

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the particularity that the calculatedK corresponds to an effective average of the different uniaxial and cubic~first andsecond order! contributions. Furthermore, the anisotropythese systems is the result of the combination of the magtoelastic, surface, and shape contributions, and the interticle interactions, in such a manner that the resultingK val-ues can hardly be attributed to one precise origin. Thuangles obtained as a function of the FM concentrationthe annealing temperature are showed in Table II. FrTable II, the following conclusions may be drawn:~i! irre-spective of the FM content, the magnetic anisotropy stperpendicular to the film plane~u50!, as the crystal structureof the as-cast samples remains basically the same,~ii ! whenparticles become larger through annealing, and the crysevolve from distorted cubes to fcc cells, the angle ofmagnetic anisotropy moves from 0° towards 54.7°~anglebetween the 111& and ^100& cube directions!, which is theexpected value for an~111! fcc textured crystal,~iii ! K foras-cast samples is almost constant~experimental values varybetween 0.23106 and 0.43106 erg/cm3) since the crystaldeformation is independent ofxv , and ~iv! with annealingMs increases and the saturation fields also increase leadinlarger values ofK. The values corresponding to the cubcase are larger than those corresponding to the uniaxial cand larger than 0.83106 erg/cm3, which corresponds to anoninteracting distribution of Co fcc FM particles.21 Thismay be due to high magnetic interactions in the CoFe aggates resulting from the annealing procedure~direct ex-change!. However, it is difficult to compare these situatiosince in the as-cast samples there is a ferromagnetic mwith diluted magnetic moments and slight uniaxial deformtion, while after annealing the matrix is no longer FM andthe CoFe is well precipitated and crystallized in large~up to100 nm! particle clusters.

IV. CONCLUSIONS

As the FM content is increased, transport propertevolve from GMR to AMR, with an intermediate region iwhich high magnetic correlations strongly affect the magtotransport properties, leading to low values of GMR. Forsamples withxv,0.20, GMR values of 20%~T520 K,H510 kOe! are found after moderate annealing. WhenFM concentration increases (xv50.20– 0.30) magnetic interactions become stronger and MR decreases. Whenxv

2010 to 161.116.168.169. Redistribution subject to A

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.0.30, the CoFe–Cu alloy present in the as-cast samdisplays AMR behavior. Through annealing CoFe particgrow and normal GMR with moderate strength~7% atT520 K andH510 kOe, forxv50.33) is observed. Structural and magnetic characterization is consistent with thresults. In the as-cast samples, CoFe particles, Cu partiand a FM CoFeCu alloy coexist setting up complex dipoand exchange interactions. Furthermore, due to residual gsubstrate–film stress, there is a perpendicular magnuniaxial anisotropy. When the CoFe particles dispersedthe Cu~CoFe! matrix are close enough (xv.0.20), and be-low the percolation threshold, stripe-like magnetic domastabilize.10 The annealing procedure segregates the CoFeloyed in the matrix, the particles grow and become moseparated, and the crystal strains relax. Therefore, thechange interactions through the matrix and the uniaxialisotropy disappear and the out-of-plane magnetic domstructures are lost. A variety of ferromagnetic/nonmagnegranular alloys based on Co display this complex magnand transport behavior, the crossover FM contents witthose different regimes being the only difference amothem, since those values depend on the relative immiscibof the components of each particular granular alloy.9 A de-tailed study of the FeNi–Ag and CoFe–Ag~Cu! granular al-loys also showed similar features.

ACKNOWLEDGMENTS

The authors would like to thank Dr. M. L. Watson fosupplying the facilities to synthesize the samples. Finansupport of both the Spanish CICYT through the MAT-90404 project and the Catalonian CIRIT through the SGR1project are largely recognized. The Spanish–British JoAction HB 1996-0066 is also acknowledged.

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3T. R. McGuire and R. I. Potter, IEEE Trans. Magn.11, 1018~1975!.4J. A. Mendeset al., J. Appl. Phys.81, 5208~1997!.5S. R. Teixeiraet al., J. Phys.: Condens. Matter6, 5545~1994!.6C. H. Lee, Hui He, F. J. Lamelas, W. Vavra, C. Uher, and R. Clarke, PhRev. B42, 1066~1990!.

7S. Chikazumi,Physics of Magnetism~R. E. Krieger, Malabar, FL, 1964!.8R. Carey et al., Seventh Intermag-MMM Conference, San Francisc1998.


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11V. Franco, X. Batlle, and A. Labarta Phys. Rev. B~submitted!.12A. Milner, A. Gerber, B. Groisman, M. Karpovsky, and A. Gladkikh

Phys. Rev. Lett.76, 475 ~1996!.13H. Sato, Y. Kobayashi, Y. Aoki, and H. Yamamoto, J. Phys.: Conde

Matter 7, 7053~1995!.14K. Ounadjelaet al., Phys. Rev. B17, 12252~1996!.


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17J. F. Gregget al., Phys. Rev. Lett.77, 1580~1996!.18E. C. Stoner and E. P. Wohlfarth, Philos. Trans. R. Soc. London, Se

240, 599 ~1948!.19J. Q. Xiao, C. L. Chien, and A. Gavrin, J. Appl. Phys.79, 5309~1997!.20J. L. Dormann, D. Fiorani, and E. Tronc, Adv. Chem. Phys.98, 283

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CoFe–Cu granular alloys: From noninteracting particles to magnetic percolation

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