Compositional dependence of the giant magnoresistance in ......Compositional dependence of the giant magnetoresistance in FexRh12x thin ﬁlms J. van Driela) Van der Waals-Zeeman Institute,

Compositional dependence of the giant magnoresistancein FexRh1-x thin filmsDriel, van, J.H.; Coehoorn, R.; Strijkers, G.J.; Brück, E.; Boer, de, F.R.

Published in:Journal of Applied Physics

DOI:10.1063/1.369224

Published: 01/01/1999

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Citation for published version (APA):Driel, van, J. H., Coehoorn, R., Strijkers, G. J., Brück, E., & Boer, de, F. R. (1999). Compositional dependence ofthe giant magnoresistance in FexRh1-x thin films. Journal of Applied Physics, 85(2), 1026-1036. DOI:10.1063/1.369224

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JOURNAL OF APPLIED PHYSICS VOLUME 85, NUMBER 2 15 JANUARY 1999

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Compositional dependence of the giant magnetoresistancein FexRh12x thin films

J. van Driela)

Van der Waals-Zeeman Institute, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam,The Netherlands

R. CoehoornPhilips Research Laboratories, Prof. Holstlaan 4, 5656 AA Eindhoven, The Netherlands

G. J. StrijkersDepartment of Physics and COBRA, Eindhoven University of Technology, P.O. Box 513, 5600 MBEindhoven, The Netherlands

E. Bruck and F. R. de BoerVan der Waals-Zeeman Institute, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam,The Netherlands

~Received 31 July 1998; accepted for publication 8 October 1998!

In this article we report on the magnetic and transport properties of FexRh12x thin films, preparedby evaporation in high vacuum, in the composition range 0.41,xFe,0.59. Upon annealing~at atemperature of 870 K or higher! a certain volume fraction transforms to the ordered CsCl-type (a8)FeRh phase. Close to room temperature this phase shows a hysteretic transition between theantiferromagnetic~AF! and the ferromagnetic~F! state for samples withxFe,0.5, which gives riseto a magnetoresistance~MR! effect. Although the magnetic transition was never found to becomplete, it is shown that the full MR ratio can be obtained by extrapolation of the measured MRratio as a function of the relative change of the magnetization at the transition. The AF→F transitionis only observed for films withxFe,0.50560.015, for which thea8 phase with this~fixed!composition is present together with a nonmagnetic Rh-rich fcc-type phase, as is shown from acombination of x-ray diffraction, Mo¨ssbauer spectroscopy, and magnetization studies. Thisobservation, which was not expected from the phase diagrams available from the literature, canexplain our finding that the full MR ratio observed for films in this compositional range isindependent of the Fe content. The full MR ratio is 8566% at room temperature, which is very closeto the MR ratio observed for bulk FeRh, implying a high structural quality of the films grown. X-raydiffraction and transmission electron microscopy were used to quantify microstructural aspects suchas the grain diameter and strain. The highest MR ratio actually observed is 58%, in a 4400 kA/mfield at 275 K. The full MR increases to approximately 150% at 250 K, and, as estimated from theresistivity of F and predominantly AF samples with almost the same composition, to 6806100% at4.2 K. © 1999 American Institute of Physics.@S0021-8979~99!01802-2#

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I. INTRODUCTION

Giant magnetoresistance~GMR! in multilayers and spinvalves has received a great deal of attention after the disery of the effect in 1988.1 However, artificially layered structures are not the only materials to show these large matoresistance~MR! effects, certain intermetallic compoundcan also show a considerable MR effect.2 In this article wefocus on the intermetallic compound Fe–Rh. As early1974 Schinkelet al.3 measured a MR ratio of approximate1700% at 4.2 K for polycrystalline bulk Fe0.505Rh0.495, andAlgarabel et al.4 found for bulk Fe0.5Rh0.5 a MR ratio of690% at room temperature. The change in the resistanclinked to the transition of the compound from the lowtemperature antiferromagnetic~AF! to the high-temperature

a!Present address: Philips Research Laboratories, Postbox WA03, Prof.stlaan 4, 5656 AA Eindhoven, The Netherlands; electronic [email protected]

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ferromagnetic~F! state. For stochiometric FeRh at zero aplied field and at zero pressure, this transition takes placTF–AF5405 K.5 A large number of articles have been pulished treating the magnetic transition of bulk Fe–Rh afunction of either temperature6 or magnetic field7,8 and deal-ing with its dependence on composition,9 heat treatment,10,11

and pressure.12,13The magnetic transition is accompanieda change of the lattice parameters14 and the elastic5,15 andelectrical transport3,4 properties.

According to the phase diagram16 shown in Fig. 1, atroom temperature FexRh12x compounds have the CsCl-typstructure (a8 phase! for xFe.0.485. For 0.33,xFe,0.485there is a two-phase region where both thea8 phase andgphase~fcc solid solution of Fe and Rh! are present. In com-pounds containing between 33 and 55 at. % Fe thea8 phaseshows a transformation between the low-temperaturestate and the high-temperature F state. At high temperatuabout 1600 K forxFe50.5 and 900 K forxFe50.8, there is a

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1027J. Appl. Phys., Vol. 85, No. 2, 15 January 1999 van Driel et al.

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phase transition from thea8 phase to theg phase.Swartzendruber17 has proposed a similar phase diagram,with the boundary between thea8 and thea8/g two-phaseregion shifted toxFe50.47 at room temperature.

Neutron diffraction experiments18–20 indicate that in theAF a8 phase each Fe atom is surrounded by 6 Fe atomsopposite spin direction. For an equiatomic FeRh compothe magnetic moments of the Fe and Rh atoms are 3.30 mB in the AF state, and in the F state they are 3.1 a1.0mB , respectively. Values of magnetic moments forand Rh atoms obtained from self-consistent total-enecalculations21,22 show a good agreement with these expemental results. Mo¨ssbauer spectroscopy23 indicates that ex-cess Fe atoms are positioned on Rh sites in the lattice, haa lower magnetic moment than Fe atoms on Fe sites.

Although the transport and magnetic properties of bFe–Rh are well known today, less research has been donthin films. Lommel observed the AF→F phase transition inFe–Rh thin films that were obtained by annealing Fe–multilayers deposited by evaporation.24 Whereas the temperature hysteresis of the transition is only of the order 1for bulk samples, he found a hysteresis of the order of 10for the thin films. The saturation magnetization abovetransition temperature was observed to be only half of thathe bulk material, whereas well below the transition tempeture part of the magnetization was found to be retained, sgesting that at all temperatures the films consisted of a mture of AF and F phases. The AF→F transition was observeto be accompanied by a decrease of the resistance of appmately 40%, less than half the value~690%! reported in thebulk material.4 Recently Ohtani and Hatakeyama observesimilarly large thermal hysteresis of the magnetic transitin sputter deposited Fe–Rh films, and concluded from intsive structural investigations that it is related to the prese

FIG. 1. Phase diagram for Fe–Rh compound as given by Kubasche~Ref. 16!. Lines separating single phase and two-phase regions are indicwith dashed lines. Magnetic transition temperatures are indicated widashed-dotted line. As discussed in Sec. IV A, the two arrows in the upart of the figure indicate the boundaries between the single phasetwo-phase regions as observed in our thin films.


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of a secondary fcc ~g! phase and to compositionafluctuations.25 In a second publication the same authoshowed that stress in the films, and the stress distributstrongly affect the magnetic transition temperature andhysteresis and steepness of the transition.26 No data on themagnetoresistance are given in Refs. 25 and 26.

In this article we report on a study of the magnetorestance of FexRh12x thin films close to the equiatomic composition, prepared by coevaporation of Fe and Rh and subquent annealing. The purpose of our study was to estabthe relationship between the film composition and the degof completeness of the magnetic transition on the one haand the magnetoresistance on the other hand. This isof the issues that is of interest when assessing the suitabof Fe–Rh films for applications in magnetic field sensoOur experimental results support the earlier finding ofMR ratio that is less than the bulk value. In principlthis could be the result of structural differences in theor AF phases as compared to the bulk compound~e.g.,a difference in the degree of site disorder, or a differescattering rate at grain boundaries!, leading to a differencein the spin dependence of scattering or in the spin flip sctering rate. However, we show that the effect is fully constent with a model within which the MR ratio for films withdifferent Fe content is proportional to the ratio of the manetization change upon the magnetic transition. We wshow that data taken at different alloy compositions extralate to the same~full ! MR ratio, which is found to be essentially the same as that for bulk FeRh. This can be explainfrom the fact that the composition of thea8 phase in thefilms responsible for the AF→F transition, is the same in alcases,xFe50.50560.015. Films with a larger Fe contendo not show the AF→F transition. Films with 0.43,xFe

,0.505 consist of a two-phase mixture ofg and a8 phaseswith the composition mentioned. This result was unexpecas bulk phase diagrams suggest a singlea8 phase showingthe AF→F transition for approximately0.485,xFe,0.55.10,16,17

In Sec. II we give an overview of the experimental prcedure for fabrication and characterization of the thin filmIn Sec. III we will present the results obtained using sevecharacterization techniques after different annealing trements and the results of magnetization and magnetoretance measurements. The influence of the microstructurecomposition of the films on the magnetic and electrical traport properties will be discussed in Sec. IV, in whichestimate of the full MR ratio is given. Finally, we wilpresent a summary and conclusions in Sec. V.

II. EXPERIMENTAL PROCEDURE

The films were fabricated by coevaporation of Fe andonto fused quartz substrates in a HV evaporation chamwith a background pressure of 1026 Pa and a deposition ratof 0.5 nm/s. Deposition took place at room temperature o520 K. The substrates were mechanically polished befdeposition, no predeposition cleaning~sputter-etch, chemicacleaning! was administered. The total thickness of the filmwas 100 nm. The composition of the films was determin

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1028 J. Appl. Phys., Vol. 85, No. 2, 15 January 1999 van Driel et al.

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using Rutherford backscattering spectroscopy~RBS!. The Fecontents of the samples ranged between 41 and 59 awith an accuracy of60.5 at. %.

To obtain the ordereda8 crystal structure from the asdeposited disordered structures, several annealing procedwere used during which the crystallographic transitions wmonitored. The resistance of the films was measured duannealing in vacuum (p,1024 Pa). When annealing in aFaraday balance the magnetization could be measured dthe procedure, with the sample placed in a magnetic field400 kA/m and in a He-atmosphere. For all proceduresheating rate was 10 K/min. The maximum temperature wmaintained from 1 min up to 16 h. The maximum tempetures used were 970 K or lower.

The films were characterized using x-ray diffractio~XRD!, scanning electron microscopy~SEM!, and transmis-sion electron microscopy~TEM!. The amounts of the varioucrystallographically and magnetically distinct phases infilms were determined using57Fe conversion electron Mo¨ss-bauer spectroscopy with a source of57Co in a Rh matrix.

A Faraday balance and a superconducting quantumterference device~SQUID! magnetometer were used to mesure the magnetization as a function of temperature and mnetic field. The resistivity as a function of temperature amagnetic field was measured using a four-point promethod.

III. RESULTS

A. Crystal and grain structure before and after theannealing treatment

The as-deposited FexRh12x films have a disorderedgphase structure forxFe,0.55 and consist of a mixture odisordered bcc~a! and fcc ~g! phases forxFe.0.55. Thedisordereda phase is not present in bulk materials of thcomposition. Thea phase is ferromagnetic at room tempeture and theg phase is paramagnetic.

Figure 2 shows the magnetization~a! and the relativeresistance~b! measured during the annealing proceduretwo samples with 49.0 at. % Fe. When the film is heathere is an upturn in the resistance curve at about 550 Kat the same temperature a finite magnetization develXRD shows a change from the disorderedg to the disordereda phase. This crystallographic transition seems to be omartensitic character, i.e., diffusionless. For films with lethan 51 at. % Fe this transition is not complete, i.e., thersome retainedg phase even after annealing at 970 K forh. The temperature at which theg→a transition takes placeincreases with increasing Rh content. At still higher tempetures thea phase gradually transforms into the ordereda8phase, as is evidenced by the appearance of an~100! super-lattice peak in the XRD spectrum. Annealing temperature870 K or higher are needed to have a largely ordered crystructure. In a film withxFe,0.5, thea8 phase becomes antiferromagnetic at low temperatures. ForxFe50.49 theF→AF transition sets in at 300 K and is completed arou80 K.

SEM shows that there is considerable grain growth ding annealing. For all compositions the as-deposited fi


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have grain sizes<10 nm. After annealing at 970 K for 4 hsamples with 50.9 at. % Fe and 58.8 at. % Fe had avegrain sizes of 80 and 130 nm, respectively~Fig. 3!. Theobservation of an increase of the average grain size withcontent is qualitatively consistent with the analysis of Ohtand Hatakeyama25 for 200 nm-thick sputter-deposited filmsbut the increase in grain size they observe~from 30 nm at46.0 at. % Fe to 400 nm at 54.6 at. % Fe after annealing

FIG. 2. Magnetization~a! and relative resistance~b! during the anneal pro-cedure for two different samples with 49.0 at. % Fe. The arrows showdirection of the temperature cycle.

FIG. 3. SEM surface images for two samples withxFe50.509 ~a! and xFe

50.588~b! after annealing at 970 K for 4 h.


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870 K! is much larger than in our case, which could be dto the difference in deposition techniques.

XRD has been used to determine the lattice parameof the a8 phase, both perpendicular and parallel to the plaof the film ~Fig. 4!. All measurements were performedroom temperature. The samples withxFe.0.49 were in theferromagnetic state. The samples withxFe,0.49 were mea-sured after cooling to 4.2 K and subsequent heating to rotemperature, which results in predominantly antiferromnetic ordering. However, a considerable part of thea8 phaseis still ferromagnetic~as will be explained later in part B othis section!. It is reported that in bulk Fe–Rh samples theis a 0.3% increase in lattice parameter at the AF→Ftransition.7,14 For our thin films only a single spectrumvisible. We note that the difference between the peak ptions of the two spectra is insufficient, with respect to tbroadness of the peaks, to be resolved. This is caused bsmall grain sizes in our thin films.

The in-plane lattice parameter was found to be larthan the perpendicular-to-plane lattice parameter. For fiwith xFe,0.49 the difference is 0.8% and it decreases0.6% for xFe50.588, indicating a considerable tensile strein the film. We will discuss the implications of this stress fthe magnetic transition later in Sec. IV D. Figure 4 alsocludes the bulk lattice parameters as reported inliterature.23 For xFe,0.5 the bulk lattice parameter is focompletely AF samples.

B. Influence of annealing temperature and time onthe magnetic properties

Samples were annealed for different times at sevtemperatures to investigate the influence of the anneaprocedure on the magnetic and transport behavior. Figushows the magnetization as a function of temperature fosample with 49.2 at. % Fe during heating to 570, 720, 8and 970 K. The highest temperature in each case was mtained for no longer than 1 min and the cooling and heatrate were both approximately 10 K/min. Between each teperature cycle the sample is cooled down to 77 K and theated to the next temperature, all in a magnetic field ofkA/m.

After heating to 570 K the sample is ferromagnetic attemperatures, indicating the presence of disordereda phase.

FIG. 4. Compositional dependence of the perpendicular-to-plane~opencircles! and in-plane~closed circles! lattice parameter of thin films at roomtemperature compared with the bulk lattice parameters~Ref. 23! ~crosses!.The dashed lines are only guides-to-the-eye.


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After heating to 720 K a weak F→AF transition is visibleupon cooling and the magnetization has increased indicaa start of the formation of thea8 phase. After heating to 870K the amount ofa8 phase has increased resulting in a highsaturation magnetization and a more pronounced magntransition. Heating to 970 K does not increase the magnzation, but the hysteresis of the magnetic transition hascome larger, so large that a significant part of the samremains ferromagnetic even when approaching 0 K. Ttransition temperature for the AF→F transition, defined asthe temperature at which the change of the magnetizawith temperature shows a maximum, as measured uponcreasing temperature, becomes higher. We have compthe transition temperatures for samples in the range 0,xFe,0.49 after annealing at 920 and 970 K. After anneing at 970 K the average transition temperature is 340610 K,whereas after annealing at 920 K the observed transitemperatures fall in the range 270-340 K. After annealing720 K, other annealing steps no longer have an influencethe Curie temperature of the samples. An average Curie tperature of 69568 K is found for samples in the range 0.,xFe,0.5. For samples with excess Fe the Curie tempeture increases with increasing Fe content, toTC5860 K forxFe50.55.

The time during which the maximum temperature wmaintained, ranged between 1 min and 16 h. No influencannealing time on the magnetic behavior was observedalso XRD did not show a distinct change in microstructu

C. Mossbauer spectroscopy57Fe-Mossbauer spectroscopy can be used to identify

quantify the presence of magnetically and crystallograpcally distinct phases in the films. Shiraneet al.23 have per-formed extensive Mo¨ssbauer spectroscopy on Fe–Rh busamples with different compositions. They observed two dtinct hyperfine fields for samples with 0.5,xFe,0.8, corre-sponding to Fe atoms on Fe sites and on Rh sites inlattice. The latter have a lower magnetic moment, buhigher hyperfine field. It is also possible to distinguish tAF and F phases on the basis of hyperfine spectra. Mrecently Ohtani and Hatakeyama25 have performed Mo¨ss-bauer spectroscopy on sputter-deposited Fe–Rh thin filmthe composition range 0.46,xFe,0.55. They find different

FIG. 5. Magnetization as a function of temperature for a sample with 4at. % Fe during subsequent heating to 570, 720, 870, and 970 K. Betweach heating cycle the sample is cooled down to 77 K and then heated tnext temperature, all in a magnetic field of 400 kA/m. The arrows givedirection of the temperature cycles.


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sextets, which are assigned to Fe atoms with 0, 2–6, andnearest neighbors in thea8 phase. They also find two nonmagneticg phases.

We have performed57Fe-Mossbauer spectroscopy oour films at room temperature, after cooling to 4.2 K aafter heating to 420 K, respectively. The films withxFe

,0.5 have been investigated with predominantly AF ording, as well as with predominantly F ordering. This was doby making use of the hysteresis in the AF-F magnetic trsition with increasing and decreasing temperature. Figushows the spectrum for a film containing 45.4 at. % Fe whhas been heated to room temperature after cooling dow4.2 K. There are two sextets and a singlet present inspectrum. Using the results reported by Shiraneet al.23 thesecan be identified. The singlet belongs to the paramagnetgphase. The two sextets belong to the AF and F phaseshyperfine fields of 25.4 and 27.5 T, respectively.

The amounts ofg, a8~AF! anda8~F! phases are obtainefrom the ratios between the intensities of the singlet andtwo sextets. The magnetization direction in the film candetermined from the ratios of the intensities of the peakssextet. The ratio is 3:j:1:1:j :3, with j54, 0, or 2 for anin-plane, perpendicular, or random magnetization directiFor the film in Fig. 6, we findj53.3 for the F sextet andj51.6 for the AF sextet, indicating that the magnetizationmostly in the plane of the film for the F phase and randfor the AF phase.

When the Mo¨ssbauer spectrum of the same samplemeasured after cooling down from 420 K to room tempe

FIG. 6. Mossbauer spectrum for a film with 45.4 at. % Fe, heated to rotemperature after cooling down to 4.2 K, showing two sextets for thea8~AF!anda8~F! phases and a singlet for the paramagneticg phase.

FIG. 7. Mossbauer spectrum for a film with 58.8 at. % Fe, showing thsextets corresponding to Fe atoms with 0–1, 2–3, and 8 Fe neneighbors.


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ture, only the paramagnetic singlet and the sextet belongto the F phase are found. This implies that at a temperaof 420 K the AF→F transition is complete and that thF→AF transition starts at a temperature below room teperature. This is in agreement with the results from magtization measurements of the same sample.

All samples withxFe,0.5 show the same set of subspetra as the film withxFe50.454~shown in Fig. 6!. The resultsof the fits are summarized in Table I, where the amountsthe respective phases are given. We have measured avhyperfine fields of 25.3 and 27.3 T and isomer shifts of 0.0and 0.035 mm/s for the AF and F phases, respectively. Thvalues do not change significantly with Fe content. Thwas no sextet belonging to Fe atoms on Rh sites visibleany of the samples measured, therefore we conclude thamore than a few percent of the Fe atoms occupy such sThe amount of disorder in these films is therefore very sm

Samples withxFe.0.5 are always ferromagnetic, soheat treatment before the measurements as described adoes not affect the Mo¨ssbauer spectrum. The spectrum osample containing 58.8 at. % Fe is shown in Fig. 7. Thdifferent sextets~I, II, and III! can now be distinguished. Thhyperfine fields are listed in Table II. Making use of thanalysis of the hyperfine field distribution in Fe-rich bucompounds, as given by Shiraneet al.,23 we arrive at thefollowing assignment of local environments to the Fe atogiving rise to these three sextets. Sextets I and II result frFe atoms on Fe sites, with between 0–1 and 2–3 Fe neaneighbors, respectively. Sextet III is related to Fe atomssitioned on the Rh sites of the lattice~with 8 Fe nearest

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TABLE I. Results of Mossbauer spectroscopy on films withxFe,0.5.

Amount of Amount of Amount ofFe content a8 ~AF! phase a8 ~F! phase g ~P! phase Temperature

~at. %! ~%! ~%! ~%! history

45.4 44.2 36.3 19.5 4.2 K, heating0 80.2 19.8 420 K, cooling

45.4 67.4 15.4 17.2 4.2 K, heating

45.9 54.6 28.8 16.6 4.2 K, heating0 82.4 17.6 420 K, cooling

48.3 84.5 0 15.5 4.2 K, heating56.6 30.5 12.9 420 K, cooling

49.0 44.0 47.9 8.1 4.2 K, heating0 87 13 420 K, cooling

TABLE II. Results of Mossbauer spectroscopy on films withxFe.0.5.

Fe content Bh f Amount~at. %! Subspectrum ~T! ~%! Description

51.2 I 27.2 99.3 0 nn. FeIV 0 0.7 paramagnetic

g phase

54.9 I 27.8 100 0–1 nn. Fe

58.8 I 28.6 32.5 0–1 nn. FeII 30.8 53.3 2–3 nn. FeIII 39.9 14.2 8 nn. Fe


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neighbors!. The excess amount of 8.8 at. % Fe in this samshould result in 15% of the total amount of Fe atoms bepositioned on a Rh site. This compares well with the expmental value of 14%.

Two other samples withxFe.0.5 have been investigated; the results are summarized in Table II. The film w51.2 at. % Fe still contains a small amount ofg phase. Thespectra for both samples do not show a well resolved serelated to Fe atoms on Rh sites, though it should be presThis is probably due to the fact that the peaks are too lowbe distinguished above the noise level. The compositiodependence of the hyperfine fields at atoms giving risesextet I~0–1 Fe nearest neighbors! agrees very well with theresults given in Ref. 23.

The amount ofg phase, obtained from Mo¨ssbauer spectroscopy, is plotted in Fig. 8 as a function of the Fe contin the samples. It is clear that the amount ofg phase in-creases when the Fe content decreases.

D. Saturation magnetization

In Fig. 9 the compositional dependence of the saturamagnetization at 300 K is shown. The results for sampwith xFe,0.5 were obtained after heating the sample totemperature where the AF→F transition is completed~about450 K or above! and subsequent cooling to 300 K, whererelatively small field was enough to saturate the magnettion. Samples withxFe.0.5, which show no magnetic transition, were heated from low temperatures to 300 K. Subquently a magnetic field was applied that was large enoto saturate the magnetization.

For our thin films withxFe,0.5 the values can be compared to the values given by Hofer and Cucka for bulk Fe-compounds with excess Rh.9 The values for these bulk compounds and our thin films compare reasonably well. F0.5,xFe,0.6 the few experimental results for the saturatimagnetization reported in the literature are less system~see Table 4 in Ref. 17!. Instead of using these data, wcalculate the saturation magnetization using the magnmoments of the Fe and Rh atoms obtained by Shiraneet al.19

from neutron diffraction experiments at 298 K. For 0.,xFe,0.6 they findmFe53.1mB and mFe52.5mB for Featoms on Fe and on Rh sites of the lattice, respectively.magnetic moment for Rh atoms~on Rh sites! is mRh

FIG. 8. Compositional dependence of the amount of paramagneticg phasedetermined from Mo¨ssbauer spectroscopy. The dashed line is a guide-to-eye.


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51.0mB . The resulting saturation magnetization~dashedline in Fig. 9! compares quite well with our experimentresults in this composition range, from which we can coclude that there is no substantial amount of disorder infilms, since disorder would decrease the saturation magnzation.

E. Magnetization and magnetoresistancemeasurements

Both magnetization and resistance were measuredfunction of magnetic field. Before each measurementfilms were cooled to 4.2 K and then heated to the desitemperature, so as to create a well defined temperaturetory. After stabilization at the desired temperature the mnetic field was varied between 0 and 4400 kA/m. In Fig.the magnetization~a! and resistivity~b! loops for a samplewith 49.0 at. % Fe at different temperatures are given. Tmagnetization curves are compensated for the diamagncontributions from the substrate and the sample holder.cause of the hysteresis in the magnetization versus tempture loops described earlier, part of the sample is ferromnetic even at the lowest temperatures. This F fractionsaturated at low fields, as can be seen in Fig. 10~a! for themagnetization curve at 225 K. Increasing the field causesspins in the AF fraction to rotate over a small angle towathe field direction, resulting in a slow increase of the manetization and the resistance. At a certain magnetic fithere is an upturn in the magnetization curve and the retance starts to decrease. This is the start of the AF→F tran-sition, and with increasing field the film will become moand more ferromagnetic. At 225 K, far below the transititemperature of this film, the maximum available field4400 kA/m is not large enough to have a complete magntransition.

Increasing the temperature decreases the magneticnecessary to start the AF→F transition as can be seen in thresistance versus field curve for 275 K@Fig. 10~b!#, wherethe smallest fields are already enough to start the AF→Ftransition and to decrease the resistance. At 275 K a MRratio of (r02rHmax

)/rHmax558% is obtained, which is the

highest MR ratio we have measured so far in our films.field of 4400 kA/m is still insufficient to fully saturate thsample at this temperature. At 325 K, a temperature abthe transition temperature, the film is mostly ferromagne

e-

FIG. 9. Measured saturation magnetization for thin films~open circles!compared with the result of a model calculation~dashed line! and experi-mental values for bulk samples~closed circles!, all at 300 K.


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FIG. 10. Magnetization~a! and resistivity~b! as a func-tion of applied magnetic field for a thin film withx50.490 at 225~h!, 275 ~d! and 325 K~3!. The ar-rows indicate the direction of the magnetic field chang

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even at low fields. The transition is completed at a magnfield of about 2500 kA/m. Further increase of the magnefield has almost no effect on magnetization and resistivWhen the magnetic field is decreased again, a large hyesis is observed for all temperatures, resulting in a largefraction after the fieldsweep than before. Other films wdifferent compositions were also investigated and showthe same behavior.

IV. DISCUSSION

A. Compositional dependence of phases observed

The results of our measurements of the compositiodependence of the lattice parameters, the Mo¨ssbauer spectrum, and the saturation magnetization of annealed Fethin films lead to the following conclusions regarding toccurrence of the various phases around the equiatomic cposition:

~1! For 0.51<xFe,0.59 the films are single phase, consiing of the ordereda8 phase.

~2! For 0.41,xFe,0.51 the films consist of ana8/g two-phase mixture.

The phase boundary between the single phasea8 region andthe two-phasea8/g region is, from the various experimentresults obtained, located atxFe50.50560.015. The uncer-tainty is in part the result of the uncertainty in the determnation of the composition by RBS~60.005!, but is also re-lated to the measurement accuracies and the samplsample variations observed. From the compositiovariation of the saturation magnetization~Fig. 9! the phaseboundary between the single phaseg region and the two-phasea8/g region is estimated to be located atxFe50.3260.03.

When comparing these results with the bulk Fe–phase diagram one should remember that the films haveannealed at temperatures up to 970 K, and subsequecooled with a relatively high rate. Hence, the phasesserved are expected to be more closely related to the pdiagram at the temperature of annealing than to the phdiagram at room temperature. We have indicated the bouaries between the single phase and two-phase regions, gabove, by arrows in the upper part of the phase diagpresented in Fig. 1. The boundary between the single pha8 region and the two-phasea8/g region is for our filmslocated at an Fe concentration that is approximately 2 ahigher than in the bulk phase diagram given by Ku


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aschewski~Fig. 1, see also Sec. I!. On the other hand, in arecent publication Takahashi and Oshima10 have relocatedthe phase boundary to the Fe-rich side, varying fromxFe

.0.52 for T5700 K to xFe.0.51 for T51000 K. Our re-sults tend to support this latter finding. However, we empsize that one has to be careful when interpreting thin firesults in terms of the phase diagram, in view of the possoccurrence of stress at the temperature of annealing. Acussion of the strain observed in the films is given in parof this section.

The boundary between the single phaseg region and thetwo-phasea8/g region is for our films, within the experimental accuracy, in agreement with the boundary atxFe50.33, asgiven in Fig. 1. Our result is also not significantly differefrom the results given by Swartzendruber,17 who has re-ported a slight temperature dependence of this phase boary: the boundary is positioned atxFe.0.31 for T5700 K,increasing toxFe.0.35 forT51000 K.

B. Stress

In Fig. 4 we have presented evidence for the occurreof tensile stress from the observation of a difference betwthe in-plane lattice parameter (ai) and the perpendicular-toplane lattice parameter (a'). In the absence of measurements of the temperature dependence of the strain, weonly present a limited discussion of its origin. Stress canproduced during the growth of the films, and, upon heatthe samples, it can result from the phase transformationsing place as well as from a difference between the therexpansion coefficients of the film and the substrate. Hoever, if the stress that results from these processes is relas a result of annealing during a sufficiently long periodtime, the strain observed at room temperature is expecteoriginate predominantly from the effect of different thermexpansion coefficients of the film and the substrate upcooling to room temperature.

Assuming that full relaxation has taken place at thenealing temperature, that the strain is homogeneous throout the film and that there is perfect clamping of the filmthe substrate, a first estimate of the strain can be obtafrom literature data of the thermal expansion.15 For the caseof cooling from 970 K to room temperature, bulk FeRshows a linear contraction of approximately 0.54%~neglect-ing the effect of a possible F→AF transition near room temperature!, whereas fused silica glass shows a linear contrtion of only approximately 0.04%.27 At room temperature,ai

is then expected to be approximately 0.5% larger than


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bulk lattice FeRh parameter. Assuming that the elastic prerties of the film are isotropic, it is commonly observed fmetals that the change ofa' is as large, but of the oppositsign as the change ofai . This would result in a differencebetweenai anda' of approximately 1%, and a bulk value othe lattice parameter equal to the average ofai anda' . Theexperimental values of the lattice parameter differencesmaller, 0.8% forxFe,0.49, decreasing to approximate0.6% for xFe50.588~see Fig. 4!. As expected, the bulk lattice parameter (a) is in betweenai and a' for xFe.0.49,although (ai2a) and (a'2a) are dependent on the compsition, and not equal to each other for all compositionsvestigated. We conclude that the strain observed hassame sign and order of magnitude as expected on the basthe simplifying assumptions given above, but that thesesumptions do not give a fully quantitative description of tobservations.

Due to clamping to the substrate the strain will be largin the region close to the substrate–film interface than intop of the film. In the top of the film internal stress can relmore easily, especially at grain boundaries, which will cagaps to appear between grains. A TEM cross-sectional imof a film with xFe50.454, shown in Fig. 11, provides aindication of the formation of such gaps at the film surfaThe resulting relaxation is expected to contribute to the smdiscrepancy between the calculated and experimental dience of the parallel and perpendicular lattice parameters,cussed above.

C. Dependence of the magnetic transition oncomposition

The Mossbauer spectra have revealed that all filmsvestigated, consisting of single phasea8 phase (xFe

>0.505), are ferromagnetic, whereas in the films consisof a two-phasea8/g mixture thea8 phase was observed tshow at a certain temperature an AF→F transition. A firstimplication is that in this system single phase FeRh havthea8 structure and showing an F→AF transition upon cool-ing is not present or not resolved experimentally, whereacontrast, bulk systems of singlea8 phase showing the F→AFtransition are present in an extended compositiorange.10,16,17 A second implication is that for films in themixed-phase region the composition of thea8 phase is inde-pendent of the overall film composition, being equal to t

FIG. 11. Cross section TEM image of a film withx50.454, showing a crackat the film surface and evidence of the presence of strain inside the gr


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composition at the phase boundary. As a result, one expthat, in the absence of effects resulting from microstructudifferences and strain, the temperature or~at a fixed tempera-ture! the applied magnetic field at which the magnetic trasitions take place are not dependent on the overall film coposition.

This conclusion is supported by the observed variatof AF→F transition temperature and of the Curie tempeture, with the overall film composition, as shown in Fig. 1For films annealed at 970 K the transition temperature340610 K, with no significant compositional dependencwhereas for films annealed at 920 K the observed transitemperatures fall in the range of 270–340 K. Although theis a sample-to-sample variation, we again observe no sigcant compositional dependence. Also the observed Ctemperature is constant in the range of 0.4,xFe,0.5.

We cannot exclude the possibility that the tendencyfilms annealed at 920 K to show a lower transition tempeture than that of the films annealed at 970 K results fromcombined effect of a slight difference in the compositionthe a8 phase obtained after annealing at these two temptures ~but still within the range 0.49,xFe,0.52) and astrong compositional dependence of the transition tempture. All reports on bulk systems show indeed a strong copositional dependence of the transition temperature.10,16,17

A dependence of the final composition on the annealtemperature could be a thermodynamic effect, i.e., duedependence of the phase boundary on the temperature,kinetic effect, i.e., due to slow diffusion of Rh atoms towarthe g phase precipitates that are formed at the same tim10

As a result, the Rh concentration across the grains in thewould show a gradient, and the average Rh concentratiothe a8 phase will slowly decrease. Assuming that the trantion temperature is dependent on the Rh concentration,could then explain the observed wide transition with teperature, and the dependence of the transition temperatu

s.

FIG. 12. Compositional dependence of the Curie temperature~d! and thetransition temperature of thea8 phase in Fe-Rh films for two annealintemperatures, 920~h! and 970 K~n!. The dashed line gives the boundabetween the single phasea8 region and the two-phasea81g region atxFe

50.50560.015. Within the experimental accuracy, this line forms alsoborder line between films that are predominantly AF or completely F attemperatures.


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the annealing temperature. For bulk samples, with mlarger grain sizes, an increase of the transition temperatuprolonged annealing is observed.10 For our thin films, we donot see such an effect, although we cannot exclude thatwill be more evident upon employing longer annealing timthan we have used so far.

The absence of consensus about the bulk phase diaand about the compositional dependence of the F to AF tsition temperature, presently make it impossible to givemore detailed discussion. A further complication is the psible effect of strain and of the microstructure. This is tsubject of the next subsection.

D. Effect on the magnetic transition of strain andmicrostructure

Whereas for bulk systems the hysteresis in the transibetween the F and AF state upon a change of temperatuof the applied field is relatively small,3,6,7,9 the hysteresis ismuch larger for thin films. Ohtani and Hatakeyama haveready shown that peeling a Fe-Rh film from a SiO2 substratecauses a decrease of the hysteresis, accompanied by acrease in the transition temperature and a steepening omagnetic transition.26 At the same time they observe a tensstress before peeling~as we have observed in our films! anda volume increase after peeling. The observed decreasthe hysteresis indicates that nucleation and pinning procedepend on strain. The fact that the hysteresis was not cpletely removed indicates that these processes are in addrelated to the occurrence of defects such as, e.g., gboundaries.

High pressure experiments on bulk systems have sha decrease of the hysteresis and a decrease of the A→Ftransition temperature with increasing pressure.12,13 Fromfirst principles band structure calculations also an increastransition temperature has been predicted.21 We note that in amore detailed discussion one has to take into accountboth within the experiments and the calculations the latremains cubic, whereas in the thin films the lattice is epanded as well as deformed.

Evidence for microstructural effects on the magnetransition has been reported by Yokoyamaet al.,28 who havepointed out that the temperature interval in which the AF→Ftransition takes place increases with increasing grain sizeour films the grain sizes vary from 10 to 200 nm, affectithe width of the transition, and possibly~as a result of grain-to-grain variations of the strain! the hysteresis.

E. Magnetoresistance ratio

A number of factors are expected to affect the MR raof our Fe–Rh thin films. First, the MR ratio depends largeon the microstructure and the composition of the film. Finstance, grain boundaries are regions of decreased crylographic ordering and a source of spin-independent scaing. Since the Fe–Rh compound needs to be almost perfeordered to show the magnetic transition it is very likely ththe disordered grain boundaries do not contribute to theeffect. Reduction of the relative contribution of grain bounary scattering to the total resistance by increasing the g


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size will then result in a higher MR ratio. Second, for 0,xFe,0.51 part of the film consists of the paramagneticgphase, as is shown by Mo¨ssbauer spectroscopy, which donot contribute to the change in resistance. The total retance and therefore also the MR ratio are affected byresistance of theg phase and the amount present. Third, tferromagnetic fraction, which remains even after coolingthe lowest temperatures, does not take part in the magntransition. And finally, even at room temperature the mamum available magnetic field of 4400 kA/m is not enoughcompletely saturate the magnetization, which means thatmaximum possible~full ! MR ratio cannot be obtained directly. The full MR ratio can be estimated by correcting fthe two latter effects as described below.

In Fig. 13~a! the MR ratios measured at 300 K are ploted as a function of the relative change of magnetizationseveral samples with different compositions. The changemagnetization (DM ) and resistance (DR) is determined asthe difference between the magnetization and resistancefore and after the field sweep to 4400 kA/m, measured atkA/m ~see Fig. 10!. Hereby the influences of the F and Afractions as described in Sec. III E are removed.DM is di-vided by the saturation magnetization (M sat) as calculatedfrom the values of the magnetic moments given in Ref.and assuming that there is nog phase present~see also SecIII D !. To obtain the MR ratio (DR/R), DR is divided by thelowest resistance for 300 K atH54400 kA/m @see Fig.10~b!#. However, the resistance at total saturation ofmagnetic transition will still be smaller, resulting in a largDR/R. For some samples several data points could betained by making use of the temperature hysteresis. For sa purpose the sample was heated first to different temptures and then cooled down to 300 K. With this method th

FIG. 13. ~a! Magnetoresistance ratio as a function of the relative changmagnetization for several films with different compositions at 300 K. Tstraight line is a least-squares fit through all data points. AtDM /M sat51,DR/R58566%. ~b! The full MR ratio as a function of temperature.


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fraction is varied and different magnetization changesresistance ratios are obtained for the same sample at thetemperature. Before every temperature cycle the sampcooled down to 4.2 K in zero field to remove all effects froprevious temperature or field loops.

A straight line is fitted through all data points and thextrapolated toDM /M sat51, from which an estimate of thefull MR ratio, DR/R58566%, is obtained. Extrapolationwill eliminate the influence of the nonmagneticg phase andthe insufficient magnetic field on the total magnetizatichange. The value ofDR/R for our films is not significantlydifferent from the value obtained by Algarabelet al., 90% at295 K for a bulk sample withx50.50.4 As mentioned beforethe different amounts ofg phase and the different grain sizein the films could have an influence on the total resistaand therefore on the MR ratio, but this is not evident frothis plot, as data points for various compositions fall onsentially the same line. The same procedure can be folloat other temperatures@see Fig. 13~b!#, which shows an in-crease of the full MR ratio with decreasing temperaturelinear extrapolation gives a full MR ratio of approximate400% at 0 K. However, we note that there is no physibasis for this linear extrapolation to 0 K, and the temperatinterval for which data are available is relatively narrow.

Another way to estimate the full MR ratio at low temperatures is by comparing the resistivities of F (xFe.0.5)and predominantly AF (xFe,0.5) samples. We have onlused the results from samples with a small amount ogphase (0.48,xFe,0.5), in order to almost eliminate a posible influence of theg phase on the MR ratio. The effect othe low-resistance F fraction in the predominantly AF filmis corrected for by plotting the low-temperature resistivitythe samples as a function of the magnetization and extralating to zero magnetization~complete antiferromagnetism!.Using this method the resistivity of a completely AF sampis found to be 3965 mV cm. The average resistivity for thesamples (xFe.0.5) is 5mV cm, and a full MR ratio of 6806100% is obtained at 4.2 K. Schinkelet al.3 obtained MRratios in bulk samples of 1700% forxFe50.505 and 700%for xFe50.502 at 4.2 K.

V. CONCLUSIONS

We have shown that there exists a remarkably goagreement between the extrapolated full MR ratio in our tfilms and the measured MR ratio in bulk samples, in partilar around room temperature. An extrapolation method wused for obtaining the full MR ratio because the films studgenerally contain a ferromagnetic fraction that does not ctribute to the resistance change. This is caused by a ltemperature hysteresis in the magnetic transition. So farhave measured a maximum MR ratio of 58% for a thin fiwith x50.49 in a magnetic field of 4400 kA/m at 275 K.

The extrapolated full MR ratio does not depend signcantly on the alloy composition, within the compositionrange studied. This could be explained from the observafrom XRD, Mossbauer spectroscopy, and magnetizatstudies that the composition of the part of the films showthe AF→F transition is independent of the overall Fe co


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tent, viz.xFe50.50560.015. This is the film composition athe phase boundary between the single phasea8 region andthe two-phasea8/g region. Only samples within the twophase region (xFe,0.505) show the AF→F transition. Nomagnetic transition is found for samples with 0.505,xFe

,0.55, in contrast to suggestions from bulk phadiagrams.10,16,17Although it cannot be ruled out that the occurrence of phases as observed in our Fe–Rh films is inenced by the effect of stress or a certain degree of comptional inhomogeneity, our results certainly suggest thatFe–Rh phase diagram should be the subject of a future stInconsistencies between previously published Fe–Rh phdiagrams, in particular concerning the stoichiometry rangewhich a8 FexRh12x is, as a single phase, AF at low tempertures, provide an additional motivation for such a study.

There are differences between the magnetic transitiobulk samples and thin films. The magnetic transition in thfilms takes place in a wider temperature interval and showlarger temperature and field hysteresis. These differencesbe caused by stress present in the film, possibly showgrain-to-grain variations, or by compositional variations dto different amounts of excess Rh still present in thea8phase due to insufficient annealing times.

In principle, intermetallic compounds such as FeRshowing an AF–F transition that is accompanied by a lamagnetoresistance effect could be of interest for applicatiin magnetic field sensors. A potential advantage of intermtallic compounds with respect to giant magnetoresistamultilayer materials such as exchange biased spin valvetheir intrinsic thermal stability. For sensors the use of thfilms is highly preferred, making it possible to make usewafer processing techniques for patterning the material, ein the form of long stripes with a high resistance. Howevwe presently regard Fe–Rh films as unsuitable for suchplications. First, our results confirm the presence of a lathermal and magnetic hysteresis, already reported earliethin film structures that were prepared using differemethods,24–26 and we have no indication at present thatpossible to decrease this effect substantially. Second,magnetic fields required for switching at temperatuaround room temperature are relatively large@see Fig. 10~b!#.However, our finding that the MR ratio is proportional to thratio of the magnetization change to the saturation magnzation in the F phase makes it possible to apply Fe–Rh fiin studies of the fundamental origin of the MR effect. We apresently exploiting this result in a study of the so-callmagnetorefractive effect29 of Fe–Rh, which is the~wave-length dependent! change of the transmission of infrarelight through the films at the AF→F transition.

The observation that the full MR ratio, as obtained fthin films is very close to the value of690% observed forbulk materials4 suggests that in these films, and in the busamples, the MR effect is due to intrinsic spin-dependscattering processes~e.g., electron-phonon and electromagnon scattering!. This finding may stimulate first prin-ciples calculations of the MR effect at room temperatubased on the band structure of perfectly ordered FeRh. Fcalculations, assuming a spin, configuration~F or AF! andband independent relaxation time have been reported by


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mezet al.,30 whose predictions for the MR ratio for diffusivand ballistic transport amount to6600 and 400%, respectively. Our results suggest that the difference with the expmental MR ratio at room temperature is unlikely to be duethe neglect of structural disorder.

We find an increase of the full MR ratio from roomtemperature to 250 K, and~Sec. IV E! a further increase to afull MR ratio of 6806100% at 4.2 K. As at 4.2 K the effecof defects on the scattering probability is much larger thanroom temperature, it is perhaps not very surprising thatlatter result is significantly smaller than the bulk value61700% obtained in Ref. 3. In contrast, results for busystems displayed in Ref. 4 show an unexpected maximof the MR ratio of almost 200% around 250 K, below whicthe MR ratio drops to approximately 85% at 200 K. It woutherefore be of much interest to extend the study of theratio of thin film and bulk systems by performing expements down to 4.2 K in high magnetic fields, of the orderMA/m (B540 T).

ACKNOWLEDGMENTS

The authors would like to thank H.C. Donkersloot, J.MKerkhof, E. Janssen, and R.A.F. van der Rijt for their cotribution to the sample preparation and W.J.A. De CosJ.H.M. Snijders, J.J.T.M. Donkers, M.P.C. Krijn, J.L.CDaams, and P. van der Sluis for helping in the charactertion of the samples. This research has been carried out aPhilips Research Laboratories in Eindhoven and has bsupported by the Dutch Technology Foundation~STW!.

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2V. Sechovsky´, L. Havela, K. Prokesˇ, H. Nakotte, F. R. de Boer, and EBruck, J. Appl. Phys.76, 6913~1994!.


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~1963!.24J. M. Lommel, J. Appl. Phys.37, 1483~1966!.25Y. Ohtani and I. Hatakeyama, J. Appl. Phys.74, 3328~1993!.26Y. Ohtani and I. Hatakeyama, J. Magn. Magn. Mater.131, 339 ~1994!.27Handbook of Materials Science, edited by C. T. Lynch~Chemical Rubber,

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Documents

Compositional dependence of the giant magnoresistance in ......Compositional dependence of the giant magnetoresistance in FexRh12x thin ﬁlms J. van Driela) Van der Waals-Zeeman Institute,