Invar effect in fcc-FeCu solid solutions

Pedro Gorria, David Martínez-Blanco, and Jesús A. BlancoDepartamento de Física, Universidad de Oviedo, 33007 Oviedo, Spain

Antonio HernandoInstituto de Magnetismo Aplicado, UCM-RENFE, 28230 Las Rozas, Madrid, Spain

José S. GaritaonandiaDepartamento de Física Aplicada II, UPV/EHU, 48080 Bilbao, Spain

Luis Fernández BarquínDepartamento CITIMAC, F. Ciencias, Universidad de Cantabria, 39005 Santander, Spain

Javier CampoInstituto de Ciencia de Materiales de Aragón, CSIC–Universidad de Zaragoza, 50009 Zaragoza, Spain

Ronald I. SmithISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, United Kingdom

(Received 31 March 2004; published 23 June 2004)

Both Cu and Fe metals, with face-centered cubic(fcc) crystal structures, are nonmagnetic. However, thesubstitution of Cu atoms by Fe in the fcc-Cu lattice leads to the formation of a random solid solution and theappearance of ferromagnetic order, with a value of the magnetic moment per Fe atom in a fcc environmenteven above 2mB. This striking behavior is closely related to magnetovolume effects(Invar), which we havedetected by means of lattice thermal expansion and magnetization measurements in FeCu alloys.

DOI: 10.1103/PhysRevB.69.214421 PACS number(s): 75.50.Bb, 61.12.Ld, 65.40.De, 75.30.Cr

I. INTRODUCTION

Recent reports on the magnetic properties of basic mag-netic systems such as iron have revealed new phenomena,where coexistence of superconductivity andferromagnetism1,2 and spin-glass behavior has beenobserved.3 These phenomena are only found by either usingextreme conditions(such as high-pressure techniques4) ornew synthesis routes[such as mechanical alloying(MA )]. Asis well known, the stable state of Fe at room temperature andatmospheric pressure has a bcc crystal structure with a latticeparametera of about 2.87 Å, the so-calleda-Fe phase. Inthis state, Fe is ferromagnetic up to the Curie temperatureTC=1043 K.5 On heating to the reversible martensite-austensite transition temperature, 1183 K, a structural transi-tion to a face-centered cubic fcc crystal structure takes place5

to form g-Fe, witha<3.54 Å.On the other hand, the understanding of the magnetic

character ofg-Fe at low temperatures is one of the mostinteresting unresolved problems and has been the subject ofdiscussion and controversy from both experimental and the-oretical points of view.6,7 However, the only straightforwardway to stabilize theg-Fe phase is the substitution or inclu-sion of Fe atoms in a stable monatomic fcc crystal latticewhose lattice parameter is similar to that ofg-Fe (around3.5–3.6 Å). Two candidates fulfill this requirement, Nisa<3.52 Åd and Cusa<3.61 Åd but Ni is magnetic and there-fore fcc-FeNi is not a suitable system for studying magne-tism of Fe in a nonmagnetic fcc environment withg-Fe char-acteristics. The other possibility, the fcc-Cu lattice, could

provide the appropriate conditions because Cu is nonmag-netic. However, it has a significant drawback: the miscibilityof Fe in Cu is extremely low, less than 1–2 at.% of Fe canbe mixed with Cu by conventional alloying techniques.Other fcc lattices, such as Pt or Pd, present larger cell param-eterss,3.9 Åd, definitely higher than that ofg-Fe.

Nowadays, Fe-Cu alloys can be prepared across nearlythe whole compositional range using the MA synthesisroute,8–11 displaying either a fcc or bcc structure dependingon the relative starting amounts of each element. The fcccrystal structure is formed forxø70, while a bcc structureforms for xù80.10 Moreover, an unexpected ferromagneticbehavior observed in these materials in the fcc region of theFe-Cu phase diagram reignited the old controversy concern-ing the magnetism ofg-Fe and the evidence for obtainingthis phase with ferromagnetic character. It is worth notingthat fcc-FeCu phases are metastable in nature, because whensamples are submitted to time-controlled heating, segrega-tion of a bcc Fe-rich phase takes place at 500 K, while thefcc-FeCu decomposes completely into nearly pure fcc-Cuand bcc-Fe phases at temperatures above 1000 K.12

There are two open questions still under discussion. First,given that fcc-Cu andg-Fe are nonmagnetic, why does fcc-FeCu show ferromagnetism? Second, it has been observedthat the value of spontaneous magnetization,Ms measured at5 K for the as-milled fcc-FeCu is greater than that of theheat-treated samples,13 in which the measuredMs can comeonly from the segregated bcc-Fe; hence, is then the value ofthe magnetic moment of Fe in a fcc environment(FeCu)enhanced with respect to its value in the bcc state? There is

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no clear and convincing explanation to the first question;only a correlation between the Fe-Fe next-nearest(NN)neighbor distances and ferromagnetic or antiferromagneticcoupling due to changes induced in the Fe 3d band havebeen proposed.12 The second question has been partially an-swered by suggesting two coexisting electronic states withdifferent magnetic moments for fcc-Fe.14,15 The aim of thiswork is to address these two issues properly.

II. EXPERIMENTAL DETAILS

In order to achieve this purpose three FexCu100−x powdersamples, with nominal compositions located at significantpoints of the fcc Fe-Cu phase diagramsx=16,44,and 65d,have been fabricated by MA. We have usedin situ neutronthermodiffraction experiments to follow the temperature de-pendence of their crystal structures up to 1200 K(above thereversiblea-g transformation for Fe) and, together with low-temperature magnetometry up to 5.5 T, a detailed structuraland magnetic characterization has been carried out. The dif-fraction patterns have been fitted using the Rietveld refine-ment method(FULLPROF package16).

III. RESULTS AND DISCUSSION

The most noticeable structural feature that we have ob-served by neutron thermodiffraction is the anomalous tem-perature dependence of the lattice parameter for the threefcc-FeCu samples. As we can see in Fig. 1 the lattice param-eter presents a linear behavior for all of them. However, theslopes are very different as are consequently the estimatedlinear thermal expansion coefficientsaT. For the Fe65Cu35sample[Fig. 1(a)] the calculated value foraT is around 5310−6 K−1, lower than expected, taking into account the val-ues for pure Fes<13310−6 K−1d and pure Cus<17310−6 K−1d in this temperature range. The same figure isobserved in the case of the Fe44Cu56 sample[Fig. 1(b)] be-low 350 K, with aT<3310−6 K−1. A drastic change in theslope takes place above this temperature, leading to an in-crease in the value ofaT up to 16310−6 K−1. For theFe16Cu84 sample[Fig. 1(c)] the calculated value foraT isalso around 15310−6 K−1, in between the values for pure Feand Cu. Along the temperature range of the measurements, ithas to be pointed out that the Fe65Cu35 sample is ferromag-netic, the Fe16Cu84 is paramagnetic, while Fe44Cu56 has itsferro-paramagnetic transition at around 350 K. It is worthnoting that these extremely low values foraT below the mag-netic ordering temperature are typical for Fe Invar-likealloys.17 We show in the inset in Fig. 1(b) the same trend ina conventional FeNi-Invar alloy that we have obtained byMA for comparison. The most striking feature of the Invareffect is that the temperature dependence of the volume mag-netostriction compensates the thermal expansion, over cer-tain ranges. The apparent zero or negative thermal expansionin the ferromagnetic regime, as shown in fcc-FeNi alloys, iscaused by the opposite effects of anharmonic thermal expan-sion and the contraction associated with the decrease of thespontaneous magnetization. The observed thermal variationof the lattice parameter(Fig. 1) indicates clearly the presence

of important magnetovolume effects in these fcc-FeCu ma-terials.

Furthermore, previously reported magnetic moment re-sults are commonly given in terms of magnetic moment permetal atom, giving rise to a linear dependence with respect tothe nominal Fe content.11 From our magnetization measure-ments we have estiamted a Fe magnetic momentmFe ofaround 2mB/Fe for Fe concentrations above 60 at.%, with aslight decrease of this value to 1.5mB observed below30 at.% Fe. The value ofmFe in fcc-FeCu alloys, extrapo-lated to 0 K, can be determined accurately from their mag-netization curves, which were measured at 5 K and underhigh s5.5 Td applied magnetic fields(see Fig. 2). Thesecurves present a clear slope at high fields, indicating that thesamples are not saturated. Using a conventional approach tosaturation law,18 we have performed a fit to obtain the spon-

FIG. 1. (Color online) Temperature dependence of the latticeparameter for the(a) Fe16Cu84, (b) Fe44Cu56, and(c) Fe65Cu35 solidsolutions. The corresponding dependence for a conventional FeNi-Invar alloy is shown in the inset for comparison. The full linesrepresent fits to obtain the value for each thermal expansion coef-ficient (see text for value).

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taneous magnetization value at zero field. The observed largeslope of the curves must be interpreted as a large value forthe high-field susceptibilityxHF. This fact suggests a stronginfluence of magnetovolume effects in the fcc-FeCu system,thus providing further evidence for the Invar character inthese materials. The estimated values ofxHFf,s3–8d310−5 emu g−1 Oe−1g are similar to those obtained in31–40 at.% Ni-containing fcc-FeNi alloysf,s1–6d310−5 emu g−1 Oe−1g.3,17 In Fig. 3 we present the composi-tional dependence ofxHF and mFe (inset) of the fcc-FeCusolid solutions at 5 K, with the values for bcc-Fe, fcc-Ni, andFeNi in the Invar region, also presented for comparison. Wenote that the correlation betweenxHF andm shows the sametrend as in well known FeNi-Invar alloys, that is, the value ofxHF decreases as that form increases in both systems. The

Invar character of fcc-FeCu alloys has been recentlysuggested,19 but direct experimental evidence has not yetbeen reported.

To make further progress with these two main experimen-tal results we must reexamine the basic aspects of the phasestability of fcc g-Fe with respect to the Fe-Fe distances. Aphenomenological model was proposed forty years ago byWeiss20 to explain the ferromagnetism in fcc-FeNi Invar al-loys, recently reinforced by theoretical approaches basedupon band energy calculations for 3d elements.21–23 Thismodel considers two different states for fccg-Fe: one char-acterized by a low atomic volumes,11.09 Å3d and orderedantiferromagnetically below 70 K withmFe<0.5 mB, and an-other state with a high atomic volumes,12.06 Å3d and a Feferromagnetic moment ofmFe<2.8 mB. In addition, the 3dband structure of Fe in weakly ferromagnetic Fe alloys isvery sensitive to slight variations in the atomic volume(orinteratomic Fe-Fe distance).21,24 Therefore, modifications ofthe Fe 3d band via increments in interatomic distances giverise to an increase in the density of states(DOS) at the Fermilevel and thus an enhancement of Fe ferromagnetic character.Changes in the DOS are also provoked by modifications ofthe local symmetry, and/or the number of NN neighbors,and/or the distances between atoms. In our case, the formertwo are expected to be the same in the fcc-FexCu100−x solidsolutions, but the distances between NN neighbors arechanging through the solid solution composition(x=16, 44,and 65) owing to the different atomic sizes of Cu and Fe.

In this way, the occurrence of ferromagnetism in fcc-FeCumetastable alloys could be explained using the same argu-ments. The atomic volume for pure fcc-Cu at 0 Ks,11.6 Å3d is closer to the theoretical one forg2-Fe thanthat forg1-Fe, making theg2-Fe state more stable in the fcc-FeCu system with average atomic volumes around 11.95 Å3.The same figure is also valid for FeNi alloys, but in this casethe atomic volume for the fcc-FeNi phase has a maximumaround 11.6 Å3 (60 at.% in Fe), and then decreases withincreasing Fe content. As a consequence of this, the value ofmFe is lower in the fcc-FeNi system than in the fcc-FeCu one(inset in Fig. 3) and deceases with atomic volume. For Feconcentrations above 70 at.% the atomic volume falls belowthe corresponding one for theg1-Fe state and an antiferro-magnetic behavior is observed in FeNi alloys.17 Moreoverthe energy difference between bothg-Fe states at 0 K is verysmall(around 25 meV), and henceg2↔g1 transitions can beinduced by increases in temperature, which will destroy theferromagnetism in these systems. This fact is seen clearly bythe low values for theTC in fcc-FeCu solid solutions com-pared with the value for bcc-Fe. On the other hand, ferro-magnetism cannot occur for compositions below 10 at.% Febecause the number of NN Fe neighbors of a given atom ina fcc structure is 12, and the probability of one Fe atomhaving a Fe NN neighbor decreases abruptly as shown inpreviously published results.8 In this way, the substitution ofCu atoms by Fe atoms in a fcc crystal, above 10–15 at.%Fe, induces ferromagnetic order in Fe atoms. This ferromag-netic coupling counteracts, via a magnetovolume effect, theexpected decrease in atomic volume associated with thelower values for the Fe ionic radius. Moreover, it gives riseto volume expansion up to values above 12 Å3, near the

FIG. 2. (Color online) Magnetization curves obtained at 5 K andunder applied magnetic fieldssm0Happd up to 5.5 T for the threeFeCu samples. The solid lines are guides for the eyes.

FIG. 3. (Color online) Compositional dependence of the high-field susceptibilityxHF and magnetic momentmFe (inset) for thethree studied fcc-FeCu solid solutions(squares). Values of FeNialloys taken from Ref. 5(circles) in the Invar region and for bcc-Fe(triangles) and fcc-Ni(triangles) are also presented for comparison.The solid lines are guides for the eyes.

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corresponding volume for theg2-Fe state and with values ofmFe that could exceed 2mB.

According to our results we propose the phase diagram ofFig. 4 for the fcc-FeCu Invar solid solutions. The high valuefor mFe in the Fe-rich region(supersaturated solid solution)can be understood only with a lattice parameter close to thetheoretical one forg2-Fe. When the amount of Fe is de-creased, leading to a diluted solid solution,mFe decreases,and hence the lattice parameter must decrease as has alsobeen observed in fcc-FeNi alloys.17 This diagram could beexplained by considering that the introduction of Fe atomsinto the Cu lattice has a two fold effect:(i) the lower Featomic radius produces a volume contraction of the lattice,and(ii ) the ferromagnetic interaction between Fe atoms, en-sured by the high atomic volume of the Cu lattice close tothat for theg2-Fe state, leads to a lattice expansion. For low

Fe dilution (below 10–15 at.%) the absence of Fe NNneighbors does not allow ferromagnetic coupling between Featoms; thus the atomic volume decreases. As the Fe contentincreases, the onset of ferromagnetism takes place, givingrise to an increase in the spontaneous magnetization and alattice expansion due to the magnetovolume effect. However,this picture is only valid for intermediate regions, as purefcc-Fe should not be ferromagnetic because the stable state isg1-Fe. Addition of a small amount of Cu is necessary tomaintain the appropriate atomic volume and thus to stabilizethe g2-Fe state.

IV. CONCLUSION

The origin of the ferromagnetism in FexCu100−x solid so-lutions with a fcc crystal structure is completely determinedby the NN neighbor distance between Fe atoms and the weakferromagnetic character of Fe. Hence, the emergence of fer-romagnetism in the metastable fcc alloys induces magneto-volume effects, such as high-field susceptibility values andalmost zero thermal expansion. In other words, fcc-FeCuconstitutes a new family of Invar alloys. The discovery ofnew intermetallic compounds showing very low values forthe thermal expansion above room temperature, such asFeCu or YbGaGe,25 could open new perspectives in the de-sign and development of new thermomechanical actuatorsthat have to work under variable temperature conditions.

ACKNOWLEDGMENTS

The work was partially supported by the Research GrantsNo. MAT2002-04178-C04 and No. MAT2000-1047 and byEU under IHP programme. We also thank the ILL and theCRG-D1B, together with ISIS for the allocation of neutronbeam time, and the SCT at the University of Oviedo for thehigh resolution XRD facility. D.M.-B. thanks Spanish MCyTfor additional support.

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FIG. 4. (Color online) FexCu100−x magnetic phase diagram at0 K; the atomic volume vs Fe concentration is shown. Atomic vol-umes forg1-Fe andg2-Fe together with that of pure fcc-Cu aremarked with arrows. Red triangles correspond to our data, and adashed line indicates the extrapolated compositional dependence forthe atomic volume in the Invar-ferromagnetic region[ferromagnetic(FM); nonmagnetic(NM)].

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