Amorphous Alloys

Hyperfine Interactions 110 (1997) 51–80 51

Magnetic properties of amorphous alloys

M. Ghafari a and R. Gomez Escoto a,b

a FB 21 – Thin Film Div., Technical University Darmstadt, Petersenstr. 23,D-64287 Darmstadt, Germany

b University of El Salvador, Physics Department, Faculty of Nature Science and Mathematics, 25 Av.Nte., Ciudad Universitaria, San Salvador, El Salvador

The magnetic properties of existing amorphous iron based materials, i.e., Fe–metalloid,Fe–early transition metals and Fe–rare earth alloys, are briefly discussed for some represen-tative alloys. The spin orientation of amorphous Fe–metalloid alloys has been determinedby the angular dependence of hyperfine interactions. It is shown that in iron–early transitionmetals ferromagnetic order is not long-ranged, but determined by magnetic clusters. Themagnetic hyperfine field distributions of Fe-rich iron–early transition metals consist of ahigh and a low field tail. The magnetic structure has been investigated for two represen-tative Fe–RE (RE = Er, Ce) amorphous alloys. For the first time, the magnetic couplingphenomenon in amorphous/crystalline multilayers has been discussed.

1. Introduction

There exist two kinds of amorphous transition metal based alloys with a collectivemagnetic order:

1. Amorphous transition metal–metalloid systems; T–M alloys (T = Transition met-als, Fe, Ni and Co; M = Metalloid, B, P, C, Ge, Si, ...).

2. Amorphous metal–metal systems; T–ET alloys and T–RE alloys; (ET = Earlytransition metals, Y, Zr, Sc, ...; RE = Rare Earth, Er, Gd, Ce, ...).

A schematic of the magnetic structure of two different amorphous systems isshown in figure 1. In this paper, the different magnetic properties of Fe-based amor-phous alloys are discussed. The aim of the present contribution is the summary,completion, and updating of the magnetic properties. The amorphous non-magneticalloys may play an important role in magnetic coupling between magnetic layers ofthe multilayers. The main objectives of this paper are to present:

1. A brief review of basic magnetic properties and Mossbauer parameters of amor-phous Fe–M alloys;

2. A discussion of magnetic structure of amorphous Fe–RE alloys and the effect ofhydrogenation on magnetic properties;

3. A detailed discussion of magnetic behavior of amorphous T–ET alloys;

J.C. Baltzer AG, Science Publishers

52 M. Ghafari, R. Gomez Escoto / Magnetic properties of amorphous alloys

4. A discussion of magnetic coupling phenomenon in amorphous/crystalline multi-layers.

Figure 1. Magnetic structure of amorphous transition metal based alloys.

2. Magnetic properties of amorphous Fe–M, Fe–RE and Fe–ET alloys

2.1. Amorphous Fe–M alloys

Because of the technological potential of amorphous Fe–M alloys as soft mag-netic materials, the magnetic properties have been investigated intensively in the lasttwenty years. Amorphous Fe–M systems with metalloid contents less than 60 at.%show, in general, a ferromagnetic behavior. The disordered, non-periodic structure ofamorphous alloys causes a decrease of the Curie temperature (TC) and magnetic mo-ment. The absence of crystal anisotropy and high resistivity leads to a low hysteresisand low losses of eddy current. These properties combined with high yield stress,corrosion resistance and in some cases a low magnetostriction make amorphous basedFe100−X–MX alloys for many applications as soft magnetic materials preferred to theother magnetic materials.

Depending on the metalloid atoms, two different behaviors of TC as a function ofmetalloid content in the range 15 6 X 6 25 are observed. For example, in amorphousFe–B alloys the TC decreases with increasing iron content. In Fe–P system, however,TC increases linearly with Fe-concentration, figure 2. In both systems, Mossbauer

M. Ghafari, R. Gomez Escoto / Magnetic properties of amorphous alloys 53

Figure 2. Curie temperatures of amorphous Fe100−X–BX and Fe100−X–PX alloys as a function of ironcontent.

Figure 3. Distribution of magnetic hyperfine field of amorphous Fe90B10 alloy.

spectra show a distribution of the hyperfine field, P (Bhf), which displaces towardslarger hyperfine field, Bhf , values at low temperatures. The shape of P (Bhf) showsa broad distribution with a weak, broad low field tail, figure 3. Figure 4 shows theaverage hyperfine field as a function of phosphorous content at room temperature.The decrease of TC as a function of iron content in Fe–B systems is attributed to thecoexistence of antiferromagnetic and ferromagnetic states.

Mossbauer spectroscopy is very suitable for quantitative analysis of magneticanisotropy problems. By using the angular dependence of the magnetic hyperfineinteraction, it is possible to obtain information about the average spin orientation from

Figure 4. Average magnetic hyperfine field, Bhf , as a function of phosphorous concentration at roomtemperature.

Figure 5. Mossbauer spectra of amorphous Fe–P–C alloy at zero and external stress.

the intensity ratio of the second and first lines (I2/I1) or (I5/I6) corresponding to∆m = 0 and ∆m = ±1 nuclear transitions. The relative intensities are given by:I2/I1 = 4 sin2 Θ/(1 + cos2 Θ). Θ is the angle between orientation of spins and thedirection of propagation of γ-rays. For a magnetic spectrum with a six line patternis I2/I1 = 4 or 0 when all spins are aligned perpendicular (Θ = 90◦) or parallel(Θ = 0◦), respectively, to the γ-rays. The ratio of I2/I1 becomes 2 for a randomorientation, Θ ∼= 55◦. The use of the angular dependence of the hyperfine fields for

Figure 6. Mossbauer spectra of amorphous Fe–P–C in external magnetic fields.

amorphous Fe–M ribbons with a positive magnetostriction is demonstrated in a fewexamples:

a) Effect of external stress on spinsMossbauer spectra of amorphous Fe83P5C12 ribbons at room temperature in zero

and an external stress is shown in figure 5. In zero stress I2/I1 is close to 1.5,corresponding to an average value of Θ = 37◦. This indicates a certain preferredorientation of spins perpendicular to the plane of the ribbon. By applying an externalstress parallel to the ribbon, the spins rotate into the plane. This is clearly seen by

Figure 7. The ratio of second and first Mossbauer lines as a function of Bex.

observing the increase in intensity of second and fifth lines. The ratio I2/I1 = 3.5indicates that the spins are preferentially oriented in the stress direction. The magneto-elastic interaction affect soft magnetic properties. Since amorphous Fe–P–C alloy hasa positive magneto-elastic coupling the spins follow the direction of external stress.From this experiment it is possible to determine the magneto-elastic coupling in softmagnetic materials.

b) Effect of external magnetic fields on orientation of spinsBy applying external magnetic fields perpendicular to the ribbon plane of amor-

phous Fe–P–C alloy, the spins rotate first into the plane away from direction of theexternal field, Bex. This is clearly seen by observing the increase in intensity of thesecond and fifth line, figure 6. The maximum value of the second and fifth line isreached by Bex = 4.2 kOe, figure 7. This high value indicates that the spins are prefer-entially oriented along the ribbon plane, this is, perpendicular to the external magneticfield. An explanation of this behavior can be given by the existence of demagnetizingfield. For Bex 6 4.2 kOe, the transverse external magnetic field is completely com-pensated by the demagnetizing field, whereas in the plane direction the demagnetizingfield is negligible and a small component of Bex in the plane of the ribbon becomeseffective and rotates the spins in the direction parallel to the ribbon.

Pankhurst et al. [1] have shown that the atomic moments in soft magnetic amor-phous FeSiB-ribbons do not completely align in the direction of external magneticfields of up to 9 T perpendicular to the ribbon. An a priori model based on frustratedexchange interactions was developed to explain the moment canting in amorphousFeSiB ribbons.

Table 1ZeemanS → ZeemanA. 1, 2, 3, 4, 5 and 6 are six Zeeman lines from absorber (see text). I, II, III, IV,

V and VI are six Zeeman lines from 57Co–αFe source.

(a) 1, 6 2, 5 3, 4

I, VI 9(1− sin2 ω sin2 ψ) 12 sin2 ω sin2 ψ 3(1− sin2 ω sin2 ψ)II, V 12(1− sin2 ω sin2 ψ) 16 sin2 ω cos2 ψ 4(1− sin2 ω cos2 ψ)III, IV 3(1− sin2 ω sin2 ψ) 4 sin2 ω sin2 ψ 3(1− sin2 ω sin2 ψ)

Figure 8. Mossbauer spectra of amorphous Fe80B20 alloy measured with a transversally magnetized 57Cosource in Fe matrix. At the Top spin, the magnetization of the source is parallel to the ribbon direction,

R. At the bottom, the magnetization is perpendicular to R.

c) Determination of spin orientation in the plane of amorphous ribbonBy using linearly polarized γ-rays it is possible to determine the spin direction

of amorphous alloys in the plane of the ribbon.

The six emitted γ-rays of a 57Co in α-Fe matrix are linearly polarized if thesource is magnetized perpendicular to the propagation direction of γ-rays. A magneticabsorber with six lines shown by (1, 2, 3, 4, 5, 6) and six emission lines by (I, II, III,IV, V, VI) has 36 lines. The lines I, III, IV and VI with ∆m = ±1 are parallel andthe lines II and V (∆m = 0) perpendicular to the direction of 57Co spins polarized.The relative intensities of 36 Mossbauer lines are given by the angles ω and ψ. ωis the angle between the spins and the normal to the ribbon plane. ψ is the anglebetween projection of the spins on the ribbon plane and ribbon directions. The relativeintensities are given in table 1. Mossbauer spectra of amorphous Fe–B measured witha transversely magnetized 57Co in α-Fe matrix is shown in figure 8. From the analysisof these measurements the angle ψ = 34◦ (the angle between ribbon direction andspins) was determined. This angle is an average value of preferred orientation of thespins relative to the direction of ribbon.

2.2. Amorphous Fe–RE alloys

Amorphous rare-earth systems show magnetic properties which are different fromthe well known crystalline alloys. An interesting class of magnetic alloys are Fe2REalloys. The X-ray diffraction results show that Fe2RE (RE = La, Pr, Sm, Gd, Dy, Erand Ho) amorphous alloys exhibit similar local short range order [2].

The Fe2RE amorphous alloys, as well as Fe2RE crystalline Laves compounds,are known to be good hydrogen absorbers [3]. Therefore it is interesting to investigatehow hydrogen changes the magnetic properties.

In the present work Fe2Ce and Fe2Er amorphous alloys have been chosen ashydrogenating materials because their structural characteristics are different from eachother [2]. The influence of hydrogen on the magnetic properties for Fe2Ce and Fe2Eramorphous alloys is investigated in detail. The radial distribution functions showdrastic changes on hydrogenation. The effect of hydrogenation on the local shortrange order is much greater for Fe2Ce than for Fe2Er amorphous alloys. These factscan be attributed to an anomalous valence state of cerium into a usual trivalent state.The rare-earth elements are often trivalent, but in amorphous Fe2Ce the Ce atoms arein a mixed valence state [4–6]. Hydrogenation alters an anomalous valence state ofcerium into a usual trivalent state [6]. The hydrogenation leads to significant changes

Table 2Curie temperature and average magnetic hyperfine field of amor-phous Fe–Er, Fe–Er–H, Fe–Ce and Fe–Ce–H alloys. The average

hyperfine field was measured at 4.2 K.

Bhf [T] Tc [K]

Fe2ErH3 28.4 > 550Fe2Er 18.2 164Fe2Ce 16.2 157Fe2CeH4 28.0 > 560

in magnetic properties. For example, the average magnetic hyperfine field Bhf is forFe2CeH4 and Fe2ErH3 amorphous alloys about 60% larger than for Fe2RE amorphousalloys. The average magnetic hyperfine field and the Curie temperature are shown intable 2.

Generally, the magnetic properties of Fe–RE amorphous alloys become complex,compared to the Fe–ET amorphous alloys because RE ion has a large random axialanisotropy which is sensitively reflected in the magnetic properties [7]. Ce atoms inFe2Ce amorphous alloys act as a tetravalent rather than trivalent [8]. Due to the tetrava-lent character of Ce ion in Fe2Ce amorphous alloy, the Ce atoms do not carry largemagnetic moments and show a zero coercive force [9]. Therefore Fe–Ce amorphousalloys are dealt in analogy with Fe–ET amorphous alloys [5]. In a similar manner asthe Fe–ET amorphous alloys [10–12], we found a spin glass like behavior for Fe2Ceamorphous alloys. Ce atoms in Fe2CeH4 amorphous alloys are in trivalent state [4,5].Magnetization measurements show that Er atoms carry a non-zero magnetic momentwhich is anti-parallel to Fe moments.

The onset of decreasing relative transmission in the Mossbauer spectrum uponcooling indicated a Curie temperature of TC = 164 K and 157 K for Fe2Er andFe2Ce amorphous alloys respectively. The values of TC of hydrides of Fe2RE (RE =Ce, Er) alloys are above room temperature. 57Fe Mossbauer spectra and correspondingmagnetic hyperfine field distribution P (Bhf) of amorphous Fe2RE and hydrides areshown in figure 9. P (Bhf) was determined by using a histogram method [13,14]. TheMossbauer parameters show drastic changes by hydrogenation. For the hydrides ofFe2RE amorphous alloys an increase in average hyperfine field of more than 55% wasfound at 4.2 K (table 2). The low temperature (T = 4.2 K) hyperfine field of Fe2Eramorphous alloys shows a broad low field tail down to Bhf = 0 and a high fieldmaximum. The shape of (Bhf) is similar to that found for invar alloys [15,16]. ForFe2Ce amorphous alloy the shape of P (Bhf) shows two maximum, the maximum atlow fields could be as the results of the alternations in line shape in the presence ofquadrupole interactions [17].

P (Bhf) of Fe2Er, Fe2Ce and Fe2ErH3 amorphous alloys consist of only oneP (Bhf), while that of amorphous Fe2CeH4 consists of superposition of two independentdistributions of magnetic hyperfine fields, P1(Bhf) and P2(Bhf). The two distributionsof magnetic hyperfine fields can be ascribed to the two different distributions of in-equivalent Fe-sites in amorphous Fe2CeH4 alloys. Because of the different isomershifts (IS1 = 0.1 mm/s for P1(Bhf); IS2 = 0.5 mm/s for P2(Bhf)), the differentdistributions of magnetic hyperfine field cannot be caused by the different angular ratiobetween the direction of Bhf and the local symmetry axes of atomic structures [18].The existence of two P (Bhf) in Fe2CeH4 was probed one more time by measuring theMossbauer spectrum in an external field (Bex = 5 T). The resulting distributions areshown in figure 10.

In order to understand the magnetic behavior of Fe2ErH3 amorphous alloy, wehave measured the average effective hyperfine field Beff(T ) and the intensity ratio ofthe second and the first line (I2/I1) of Mossbauer spectra as a function of temperature

Figure 9. Mossbauer spectrum of Fe2Er, Fe2ErH3, Fe2Ce and Fe2CeH4 amorphous alloy at 4.2 K.

in an external magnetic field of 5 T, parallel to the γ-ray, figure 11. The averageeffective hyperfine field can be derived from the following equation:

Beff(T ) ={[B2

hf(T ) +B2ex − 2Bhf(T )Bex〈cos θ〉

]}1/2(1)

Beff(T ) is the vector sum of Bhf(T ) and Bex(T ). θ is the angle between Bhf andBex. The value of Beff(T ) shifts (figures 11 and 12) with increasing θ according toequation (1). The angle θ can be determined from the intensity of the second and firstlines (I2/I1) or (I5/I6) corresponding to the ∆m = 0 and ∆m = ±1 nuclear transitions

Figure 10. Mossbauer spectra and magnetic hyperfine field distribution of amorphous Fe2CeH4 in zeroand in an external field of 5 T at 4.2 K. Note that amorphous Fe2CeH4 alloys consist of superposition of

two distributions of magnetic hyperfine fields P1(Bhf) and P2(Bhf).

(see section 2.1). Figure 12 shows the measured Beff and I2/I1 in Bex = 5 T andBex = 0 at different temperatures. The decrease of Beff(T ) in the applied magneticfield indicates the negative hyperfine interaction, the nuclear and atomic momentshave opposing orientation. The spins are almost parallel to the Bex at T > 35 K;the value of Beff is given by Beff(T ) = Bhf(T ) − Bex. The Beff(T ) starts to rotateaway from the direction of Bex upon cooling below 35 K, i.e., grows with decreasingtemperature. Consequently, the observed effective field, Beff(T ), increases with respectto the equation (1). The angle between Beff(T ) and Bex is about θ = 85◦ at T = 4.2 K.

The thermo-magnetization curve given in figure 13 shows a minimum in themagnetization at about T = 30 K. As can be seen from this figure, the change inthe magnetization between T = 4.2 K and T = 30 K is about 25%. Therefore thisminimum cannot be ascribed to the compensation temperature, because the magnetiza-tion increases with increasing temperature up to about 200 K. The magnetic structureof Fe2ErH3 amorphous alloy is mainly determined by the exchange interactions be-tween Fe–Fe, Fe–Er and Er–Er spins, by the applied magnetic field and by the localanisotropy. At T = 4.2 K the iron moments are nearly perpendicular to the direction ofBex = 5 T (figure 11). This led us to assume an anti-ferromagnetic coupling betweenFe and Er moments. The moment direction of Er is determined by the local anisotropyfield. Due to the different arrangements of nearest neighbor ions, the electrostaticfields and with those the local anisotropy fields in Fe2ErH3 are distributed in differ-ent directions. Harris et al. [19] suggested a random axial anisotropy for rare-earth

Figure 11. Mossbauer spectra and magnetic hyperfine field in an external field of 5 T measured atdifferent temperatures.

transition amorphous alloys. This anisotropy tends to align the rare-earth momentsalong random directions. The temperature dependence of magnetization (figure 13)and the Mossbauer results in an external magnetic field suggest the following illustra-tion (figure 14) for the arrangement of Fe and Er moments. The Fe moments are nearlyperpendicular to the direction of Bex at T = 4.2 K and the Er moments rotate towardthe Bex direction with rising temperature (T > 4.2 K). The variance of distribution ofEr moments decreases with increasing temperature (figure 14(b)), because of the tem-perature dependence of anisotropy. The Fe moments and the effective Er moments arenearly parallel to Bex at T > 30 K. Further increase in temperature leads to a decreasein the variance of distribution of Er moments and to an increase in magnetization.

Figure 12. (a) Average magnetic hyperfine field in Bex = 5 T and Bex = 0 as a function of temperature;(b) Relative intensities of second and the first lines, I2/I1, in Bex = 5 T at different temperatures.

The experimental results of magnetization for Fe2Er amorphous alloy in low ex-ternal fields are shown in figure 15. The ZFC (zero field cooled) curves and FC (fieldcooled) curves are different. The FC curves of amorphous Fe2Er increase with in-creasing temperature and at a temperature T > Tf , the magnetization starts to decreaseup to Tc. With increasing Bex, Tf shifts toward lower temperatures. This behaviorcan be understood on the basis of temperature dependence of the magnetic anisotropyenergy. The coercive force of Fe2Er is reported to be of order of 1.3 T at 4.2 K anddecreases rapidly with increasing temperature [8]. Due to the decrease of magneticanisotropy energy with increasing temperature, the ZFC curve increases with risingtemperature. The orientation of spins for the FC curves, however, is achieved at alow magnetic anisotropy energy and therefore the magnetization rises with lowering

Figure 13. Thermo-magnetization curve of Fe2ErH3 amorphous alloy measured in an external field of3 T.

Figure 14. Magnetic structure of Fe2ErH3 amorphous alloy in external magnetic fields.

temperature. Magnetization curves of Fe2Er in an external magnetic field (Bex = 3 T)above the anisotropy field shown in figure 16 indicate the lack of differences betweenthe FC and ZFC curves. An external field of Bex = 3 T overcomes the energy barrierand depresses Tf in figure 15.

A Mossbauer spectrum measured in an external field of 2 T shows (figure 17)that the iron spins are not completely oriented in the direction of Bex. This can beseen from the nuclear transition ∆m = 0, shown by arrows in figure 17. These results

Figure 15. Magnetization as function of temperature for Fe2Er amorphous alloy in Bex = 40 mT andBex = 4 mT.

are in agreement with an asperomagnetic structure type of amorphous Fe2Er [20].Amorphous Fe2Ce has tetravalent character, therefore the magnetic anisotropy

is very weak [9]. These alloys are treated in analogy with amorphous FeZr, FeSc,FeLa, FeHf systems [4]. The ZFC curve increases with increasing temperature andat a temperature T > Tf shows weak temperature dependence up to TC (figure 18).This behavior is similar to that found for re-entrant spin glass alloys: A transitionfrom the paramagnetic to the ferromagnetic state at TC and a spin glass like phase at atemperature Tf below TC. Fukamichi et al. [4] measured the ac and dc susceptibilityof amorphous Fe100−xCex alloys in the range 10 < x < 40. A characteristic spin glassbehavior was found for these alloys at low temperatures. The temperature dependenceof ac susceptibilities exhibits a clear peak. Namely, no magnetic long range order

Figure 16. Magnetization curve for Fe2Er amorphous alloy in an external field of 3 T.

Figure 17. Mossbauer spectra of Fe2Er amorphous alloy in an external field of 3 T.

occurs and the magnetic state transforms from the paramagnetic state to the spin glassstate with decreasing temperature. The magnetization of amorphous Fe2CeH4 alloysmeasured in an external field of 40 mT indicates a non-disappearing Ce momentsin Fe–Ce–H systems. In the range 4.2 K 6 T 6 200 K the magnetization curveshows an increase of magnetization (figure 19). The increases of magnetization can

Figure 18. Magnetization as a function of temperature for Fe2Ce amorphous alloy in an external field of3 T.

Figure 19. Magnetization curve of Fe2CeH4 amorphous alloy in an external field of 40 mT.

be understood if we assume a non-disappearing Ce moment. Investigations on thecubic Laves phase Fe2Ce have shown that the Ce atoms have non-vanishing momentscoupled anti-parallel to the Fe moments [21].

2.3. Amorphous Fe–ET alloys

In amorphous Fe100−XETX alloys with X < 30 at.% the Curie temperatureincreases with iron-content. Above X > 30 at.%, the Curie temperature decreases

Figure 20. Hyperfine field distributions for a representative amorphous Fe92Zr8 alloy in zero and anexternal magnetic field at T = 4.2 K.

monotonically with increasing iron-content.Amorphous Fe–ET (ET = Zr, Sc, Hf) in the range 8 6 X 6 12 received consid-

erable attention because of its unusual magnetic properties at low temperatures [10].In the present paper, we discuss two different systems (Fe–Zr and Fe–Sc) which arerepresentative for the magnetic properties for Fe–ET systems.

2.3.1. Amorphous Fe100−xZrx alloysMain experimental results of 57Fe Mossbauer measurements on magnetically con-

centrated Fe100−xZrx (8 6 x 6 12) are as follows:

(a) At T = 4.2 K, the shape of the distributions P (Bhf) shows a broad low-field taildown to Bhf ≈ 0 and a high-field maximum (figure 20). The relative intensity ofthe low-field tail increases with increasing Fe-content. The high-field maximum atthe peak-hyperfine field (Bp) shifts slightly to larger field values and the averagehyperfine field (Bhf) to smaller field values with increasing Fe-content at T =4.2 K.

(b) The shape of P (Bhf) at 4.2 K in Bex = 0 and Bex = 3 T remains unchanged exceptfor a shift of the distribution as a whole towards lower field values (figure 20).

(c) For X < 12, there is a break in the slope of the temperature dependence of Bhf(T )at a temperature which we denote by Tf (Tf = 35 K for X = 10; Tf = 82 K forX = 9 and Tf = 102 K for X = 8), figure 21.

Figure 21. Average magnetic hyperfine field of amorphous Fe90Zr10 alloy versus temperature in zeroexternal field.

(d) Mossbauer measurements in different external magnetic fields show that for Tf <T < TC the Fe-moments are preferentially aligned parallel to the external field, butare canted away by an angle θ from the external-field direction for T 6 Tf . Thiswas obtained from the relative intensities of the second and fifth Mossbauer lines(corresponding to ∆m = 0 nuclear transitions yielding average values of 〈sin2 θ〉)(figure 22).

(e) The temperature dependence of Bhf(T ) for Tf/2 < T measured at Bex = 0 andBex 6= 0 is consistent with the theoretical results [22,23] for intrinsically ferro-magnetic clusters, figure 3. At T = 0.98TC the plot of (Bhf −Bex) versus 1/Bex

shows a straight line for Bex > 3 T as calculated for non- or weakly interact-ing super-paramagnetic particles with µBex/(kBT ) > 4. From the slope of theselines the average cluster moment at T = 0.98TC was determined for different Feconcentrations, figure 23.

Figure 22. 〈sin2 θ〉 as a function of temperature in an external magnetic field of 3 T.

Figure 23. Average cluster moment versus Fe concentration for amorphous Fe–Zr alloys at T/TC = 0.98.

(f) Excellent fits to the experimental data were achieved with a T 3/2 dependence forthe relative change of Bhf(T ) with temperature at low temperatures for Bex = 0.

The anomalous increase in Bhf(T ) and Bp(T ) below Tf (figure 21) and the in-crease of 〈sin2 θ〉 for T < Tf (figure 3) provide clear microscopic evidence for are-entrant (spin-glass like) state below Tf in amorphous Fe100−xZrx (x < 12). Thespin-canting model attributes the anomalous increase in Bhf(T ) (or Bp) below Tf tothe freezing of the transversal components 〈St〉 of magnetic moments 〈S〉 [24]. Ourobservation (c) of the anomaly in Bhf(T ) as well as in Bp(T ) at Tf indicates that themajority (maybe all) of the Fe moments in the moment distribution (which is reflected

Figure 24. Average magnetic hyperfine field of amorphous Fe90Sc10 alloy versus temperature, measuredin zero external magnetic field.

in the hyperfine-field distribution) participate in the spin-freezing process, particularlythose Fe moments corresponding to the high-field P (Bhf)-maximum. From our results(a) and (b) we conclude that the broad low-field tail at 4.2 K corresponding to static mo-ments (low-spin Fe), is not caused by a distribution in the relaxation rates of thermallyrelaxing spin clusters (relaxing even at low temperature). Our results are consistentwith the model of a “wandering axis ferromagnetic” including individual transversespin freezing [25]: the whole Fe–Zr system consists of an exchange-coupled spincluster with an average cluster moment which is mainly determined by the fractionsof anti-ferromagnetic exchange interaction (competing with ferromagnetic exchange),figure 23.

Using 1.5µB for the average Fe moment our result ((e) and figure 23) leads toaverage cluster dimensions of about 15–20 A near TC in good agreement with neutronresults [26]. Figure 23 shows that with increasing Fe content (i.e., increasing fractionof anti-ferromagnetic exchange) the cluster moment decreases strongly and extrapolatesto zero at X ≈ 96. The results in (c) and figure 21 show also that the transition at Tf

is of microscopic origin, and is not related to domain wall effects.As mentioned in (f), Bhf(T ) decreases rapidly at low temperature and follows a

T 3/2 law with a large value of the B-coefficient (B ≈ 254 × 10−6 K−3/2); thereforewe believe that the magnetic properties of Fe-rich Fe–Zr alloys can be described bythe Heisenberg model.

2.3.2. Amorphous Fe90Sc10 alloysThe experimental results found for Fe90Sc10 are as follows:

(a) Similar to Fe-rich, Fe–Zr alloys, at T = 4.2 K the shape of the distribution P (Bhf)shows a broad low field down to Bhf = 0 and a high field maximum.

Figure 25. B2/3ex against blocking temperature for amorphous Fe90Sc10 alloy.

Figure 26. Relative transmission as a function of temperature.

(b) The slope of the temperature dependence of Bhf(T ), figure 24, shows no break.

(c) The temperature dependence of Bhf measured in Bex > 1 T shows a break inthe slope at a temperature which we denote by Tf . The value of Tf decreaseswith increasing Bex and follows a B2/3

ex law (figure 25) as predicted for super-

Figure 27. Average magnetic hyperfine field and the ratio of the intensities as a function of temperaturemeasured in Bex = 2 T and Bex = 5 T.

paramagnetic alloys [27]. The value of Tf for Bex = 0 was obtained from theB

2/3ex law is in good agreement with the onset of decreasing relative transmission

in the Mossbauer spectrum upon cooling in Bex = 0, figure 26.

Figure 27 shows two representative curves of average hyperfine field (Bhf) andI2/I1 as a function of temperature, measured in Bex = 2 T and Bex = 5 T. AboveT > Tf the average hyperfine fields decrease linearly with increasing temperature

Figure 28. Mossbauer spectra of amorphous Fe90Sc10 alloy measured in an external magnetic field of4 T.

(figure 27). For T < Tf the Fe moments are canted away by an angle θ from theexternal magnetic field direction. This was obtained from the relative intensities of thesecond and first Mossbauer lines (I2/I1), see figure 28.

(d) The temperature dependence of Bhf(T ) for T > Tf at Bex = 0 and Bex 6= 0 isconsistent with the theoretical results [23] for intrinsically ferromagnetic clusters.At T = 100 K the plot of (Bhf−Bex) versus 1/Bex shows a straight line (figure 29)as calculated for non-interacting or weakly interacting super-paramagnetic particleswith µBhf/(kBT ) > 4. From the slope of these lines an average cluster momentof about µ = 200µB at T = 100 K was obtained. Using 1.5µB for the averageFe magnetic moment our results lead to an average cluster dimension of about

Figure 29. Bhf–Bex as a function of 1/Bex for amorphous Fe90Sc10 alloy.

10–12 A at T = 100 K. From the plot of Bhf against 1/Bex it is possible todetermine the static value, when 1/Bex � 0; we obtained 23 T at 100 K. Thesame value is obtained at 4.2 K without a field. From these measurements weconclude that the static value of spins cannot be achieved even at 4.2 K. Forexample, the magnitude of Bhf–Bex measured in Bex = 8 T and 25 K is 25.3 T.This static value is about 5 T higher than that observed without a field. At 4.2 Kthe value of Bhf–Bex measured in Bex = 5 T is about 2.3 T higher than thatobserved without a field. This effect cannot be explained by the existence of ademagnetizing field, which is of the order of 0.9 T.

The Mossbauer results show that the Fe90Sc10 alloys consist of exchange-coupledspin clusters. The average cluster moment is determined by the fraction of anti-ferromagnetic exchange interactions, which competes with ferromagnetic exchange.Below the freezing temperature (T < Tf) the spins show a spin glass type of behavior.Above T > Tf the spins are in a ferromagnetic state. These results are in goodagreement with the model of a “wandering axis ferromagnetic” suggested by Ryan etal. [28].

The lack of anomalous increasing in the Bhf below Tf at Bex = 0 upon coolingdemonstrates the non-appearance of spin-canting in Fe90Sc10 system.

2.4. Magnetic interlayer coupling in amorphous/crystalline multilayers

The magnetic coupling between two magnetic regions separated by non-magneticmetallic regions is, in general, of exchange integral nature (for example, Ruderman–Kittel–Kasuya–Yosida, RKKY interactions) or of dipole nature. The observed couplingbetween the magnetic regions is ferromagnetic, antiferromagnetic or 90◦-type. Thefollowing systems show a magnetic coupling through a non-magnetic material:

(a) multilayers;

(b) discontinuous alloys (for example, Au–Co alloys with a lamellar eutectic structuresimilar to multilayers);

(c) granular alloys (Co–Ag, Co–Cu).

In multilayers, the coupling between magnetic layers apart by non-magnetic layers isdetected in the following systems:

1) magnetic metal/non-magnetic metals/magnetic metal; Fe/Cu/Fe;

2) magnetic metal/semi-conductor/magnetic metal; Fe/Si/Fe, or Fe/Ge/Fe;

3) magnetic metal/insulator/magnetic metals; CoFe/Al2O3/Co;

4) magnetic crystalline metals/non-magnetic crystalline/magnetic amorphous metal;FeB/Cu/FeB;

5) magnetic metal/non-magnetic amorphous metal/magnetic metal; Fe/NiB/Fe.

The interest in coupling phenomenon is motivated by the search of new magneticproperties, for example Giant Magneto Resistance Effect, GMR, as well as fundamentalresearch. In crystalline multilayers, the magnetic coupling oscillates as a function ofnon-magnetic layers. Oscillatory coupling is a general phenomenon in multilayers andcan be interpreted within the RKKY model. The conduction electrons of non-magneticlayers mediate the coupling between the magnetic layers. The RKKY interactions inmultilayers with non-magnetic crystalline layers is given by:

Jeff(Rij) =(Js−d)2

2π2 F (Rij) (2)

F (Rij) = (2kfRij)−4{kfRij cos kfRij − sin kfRij}. (3)

µ and kf are the Fermi energy and wave vector, respectively and Js−d is the interactionbetween the localized spins and conduction electrons. The RKKY interaction oscillatesin sign as a function of interlayer thickness Rij between magnetic layer i and jwith the oscillation period λ = Π/kf as shown in figure 30. Depending on thethickness of the non-magnetic crystalline layers is the coupling between the magneticlayers ferromagnetic or antiferromagnetic. The 90◦-type coupling is found for regionsnear Jeff ≈ 0. The disordered, non-periodic structure of amorphous alloys leads todramatic changes in oscillating coupling. The RKKY interaction in multilayers withnon-magnetic amorphous layers is given by [29]:

F (Rij) =1

(2kfRij)4

a− b√2

{a+ b√

}−(a+ b√

{a+ b√

}]× exp

{−a− b√

}. (4)

Figure 30. Indirect magnetic interactions of amorphous alloys for different Y values (see text).

The a and b parameters are given by:

a= 2kfRij[1 + (Γ/µ)2]1/4

cos{Θ/2} (5)

b= 2kfRij[1 + (Γ/µ)2]1/4

sin{Θ/2} (6)

Θ = tan−1{µ/Γ}.

Γ is the damping factor. Depending on the ratio of Fermi energy to the dampingterm, Y = Γ/µ, the coupling changes the oscillatory form as shown in figure 30. TheFermi wavelength of the amorphous metal–metalloid alloys is about 2.5 A−1 and theminimum value of R is of order 3 A (R is the thickness of non-magnetic amorphousinterlayer). Therefore the value of X = 2kfR > 15 exists in multilayers. For valuesY > 0.1 (figure 30) the dominant interaction between ferromagnetic layers separatedby non-magnetic amorphous alloys is of ferromagnetic nature. The antiferromagneticcoupling is weak. For Y = 1 is the free path of electrons almost equal to the lengthof disorder and the coupling for 2kfR > 15 is of ferromagnetic nature. From thesecalculations we expect for ferromagnetic layers separated by non-magnetic amorphousalloys a ferromagnetic exchange interaction.

The dipole interaction between the magnetic layers through a non-magnetic in-terlayer is possible, too.

In order to investigate the coupling phenomenon via amorphous materials, multi-layers of bcc-Fe/non-magnetic amorphous alloy a-NiB/bcc-Fe were prepared by sput-tering deposition method in an UHV-sputtering system type magnetron. The argonpressure during sputtering was about 10−2 mBar. In order to obtain the NiB layers

Figure 31. Hysteresis loop measured by MOKE for Fe/a-NiB/Fe multilayers.

Figure 32. Magnetoresistance effect in Fe(crystalline)/NiB(amorphous) multilayers.

in amorphous states, the Si-substrate was cooled to liquid nitrogen. The Ni–B alloytarget had a concentration of 75 at.% Ni and 25 at.% B. The deposition rates wereabout 0.5 A/s. Multilayers {Fe(15 A)/NiB(t)}N with 5 < t < 30 A and N = 15 wereprepared. The amorphous structure of films was examined by X-ray grazing incidencemeasurements. The quality of films was controlled by X-ray reflectivity.

The magnetic coupling between Fe layers is through non-magnetic amorphousNiB alloy. The coupling was studied by Magneto-Optical Kerr Effect, MOKE, andresistivity measurements in external magnetic fields. For MOKE measurements a po-

larized laser beam with a wavelength of 7500 A was focused on the surface of sample.The polarization plane of the reflected light is rotated by an angle, Φ, proportionalto magnetization in the plane. By measuring the MOKE in external magnetic fields,the hysteresis loop can be obtained. Figure 31 shows a representative magnetizationcurve, M (H), of Fe/a-NiB/Fe multilayers. The M (H) is typical for layers with ferro-magnetic coupling and low coercive force. The electrical resistivities versus externalfields show small alterations, figure 32.

These results show that the magnetic coupling between iron layers through non-magnetic amorphous NiB interlayers is of ferromagnetic nature. Oscillatory couplingbetween iron layers separated by amorphous NiB alloy is not observed. The resultsare consistent with RKKY interaction theory for amorphous alloys with values ofY > 0.1 as shown in figure 30. In the case of multilayers {Fe(15 A)/NiB(t)}N thevalue of F (X) is almost positive. This means that the indirect interactions betweenthe magnetic layers via non-magnetic amorphous alloy is of ferromagnetic nature.Further measurements (Mossbauer, Brillouin light scattering and Kerr microscope) arein progress to investigate the coupling phenomenon in more detail.

3. Conclusion

This contribution deals with some important magnetic properties of existing amor-phous materials with a collective order. It tries to stress the connections between macro-scopic methods and the Mossbauer effect for understanding the magnetic structures.The magnetic hyperfine field distributions, angular dependence of the hyperfine inter-actions and linearly polarized gamma rays have been used to investigate the magneticproperties. The amorphous materials may play an important role in magnetic couplingbetween magnetic layers of new multilayer systems. For the first time, the magneticcoupling phenomenon in amorphous/crystalline multilayers has been discussed.

References

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L. Eyring (North-Holland, Amsterdam, 1979) p. 575.[9] H. Komatsu and K. Fukamichi, Sci. Rep. RITU A, Vol. 34, No 2, p. 251.

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