Magnetic moment arrangement in amorphous Fe0.66Er0.19B0.15

Journal of Magnetism and Magnetic Materials 251 (2002) 271–282

Magnetic moment arrangement in amorphous Fe0.66Er0.19B0.15 ! a,*, B. Kalskab,c,1, D. Satu"aa, L. Dobrzynski ! a,c, A. Broddefalkd, K. Szymanski b d R. W.appling , P. Nordblad a

Institute of Experimental Physics, University of Bia!ystok, Lipowa 41, Bia!ystok 15-424, Poland b Department of Physics, Uppsala University, Box 530, Uppsala 751 21, Sweden c ! The Soltan Institute for Nuclear Studies, 05-400 Otwock-Swierk, Poland d Department of Material Science, Uppsala University, Box 534, Uppsala 751 21, Sweden Received 4 April 2002; received in revised form 1 August 2002

Abstract . Magnetization measurements and Mossbauer spectroscopy with and without a monochromatic circularly polarized . Mossbauer source (MCPMS) have been performed in order to determine the magnetic properties of the amorphous alloy Fe0.66Er0.19B0.15. The system is found to order ferrimagnetically at TC ¼ 330 K and to show a compensation temperature (Tcomp ) at 120 K. A reorientation of the magnetic moments of iron and erbium during sample cooling through the compensation point in magnetic field is clearly displayed in the MCPMS data. The orientation of the net magnetic moment is due to the orientation of Fe moments above Tcomp and to Er moments at low temperatures. The results are compatible with a model of predominantly antiferromagnetic Fe–Er coupling accompanied by random local anisotropy acting on the Er moments. r 2002 Elsevier Science B.V. All rights reserved. PACS: 76.80; 75.50.K; 75.50.G . Keywords: Mossbauer polarimetry; Er–Fe alloys; Amorphous alloys; Spin structure

1. Introduction Amorphous materials exhibit a variety of magnetic structures. If the material includes both 3d and 4f elements, the inter-elemental coupling between the two species can be negative, as e.g. has been observed in amorphous Gd–Fe and Gd–Co

*Corresponding author. Fax: +48-85-457223. ! E-mail address: [email protected] (K. Szymanski). 1 Present address: Freie Universit.at Berlin, Institut fur . Experimentalphysik, Arnimallee 14, 14195 Berlin.

systems [1]. In such systems the different magnetic elements form subnetworks, which correspond to the sublattices of ferrimagnetic crystalline materials. The magnetic moments of the 3d-elements are, in general, parallel to each other. In some cases, depending on the local surroundings of individual atoms, the easy direction of the magnetic moments of the 4f-elements varies randomly throughout the material. This causes the directions of their moments to be distributed over space with a resultant moment being antiparallel to the 3d moments, as observed e.g. in DyCo3.4 [2] and ErCo2 [3].

0304-8853/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 2 ) 0 0 6 9 6 - 0

272

! K. Szymanski et al. / Journal of Magnetism and Magnetic Materials 251 (2002) 271–282

Iron–erbium alloys can be stabilized in amorphous states by an addition of boron as a glass former. In most cases, these materials show a longrange magnetic order in spite of the lack of longrange atomic order. Hyperfine interactions in amorphous Er–Fe alloys have been reported in [4]. The interaction between the 3d and 4f moments has been found to be antiferromagnetic, both in the Fe–Er–B–Si [5,6] and the Co–Er–B systems [7]. This paper presents results from experimental investigations of the ordered magnetic phase of an amorphous Fe0.66Er0.19B0.15 alloy by means of magnetization measurements, conventional M. ossbauer spectroscopy and monochromatic circu. larly polarized mossbauer spectroscopy (MCPMS) [8–11]. An attempt is made to determine the actual configuration of the magnetic moments in this alloy.

2. Experimental The samples in the form of thin ribbons were prepared in a conventional manner by rapid quenching in an inert atmosphere (melt spinning). The thickness of the prepared ribbons was about 40 mm. Part of the ribbons were ground to a powder, which was checked by X-ray diffraction for the existence of crystalline phases. The microscopic magnetic properties were stu. died by conventional Mossbauer spectroscopy using a set-up working in constant acceleration mode with pure a-Fe as a reference and 57Co:Rh as a source. A randomly oriented absorber was made in the form of a pellet containing about 12 mg of Fe0.66Er0.19B0.15 powder per cm2. The lack of preferential orientation in the absorber was checked by measurements at the so-called ‘‘magic angle’’ geometry [12,13]. To investigate the direction and alignment of the iron moments with respect to an applied magnetic field, MCPMS measurements were performed on the same absorber in an applied field of 8  105 A/ m at three different temperatures (12, 250 and 295 K). The polarized radiation was obtained by introducing a filter between the source (57Co:Cr) and the absorber. The filter resonantly absorbs

photons with only one helicity. The remaining photons, after passing through the filter, were used . for Mossbauer measurements in which the magnetization of the absorber was oriented by an external longitudinal field of 8  105 A/m. For details of the experimental method, see Refs. [8,9]. The magnetization measurements were carried out in a Quantum Design MPMS 5.5T SQUID magnetometer. Magnetization vs. temperature curves were recorded between 10 and 400 K in applied fields of 8  103 and 8  105 A/m employing both zero field cooled (ZFC) and field cooled (FC) procedures. Hysteresis loops were recorded in fields up to 4  106 A/m at several temperatures between 5 and 293 K. The applied field was always directed along the length of the ribbon sample used in these experiments. Chemical analysis showed that, within an estimated error of 1%, the composition of the amorphous material was Er=45.8%, Fe=52.7% and B=2.4% wt (corresponding to 19.0, 65.6 and 15.4 at%, respectively).

3. Results No narrow lines corresponding to crystalline phases were detected by X-ray diffraction, showing that the material is amorphous. The magnetization vs. temperature curves in applied fields of 8  103 and 8  105 A/m are shown in Fig. 1. Some features of these curves are worth noting. The overall behaviour in the larger field (8  105 A/m) resembles the temperature dependence of the net spontaneous magnetization of an N-type ferrimagnet [14], with a compensation temperature Tcomp of about 120 K. For the lower applied field (8  103 A/m), there is a large difference between the ZFC and FC magnetization curves at temperatures below Tcomp ; which reflects that a larger coercivity develops at temperatures below Tcomp : The large negative magnetization that appears below Tcomp in the FC curve also reflects the large coercivity and implies that the antiferromagnetically coupled Er and Fe subnetworks remain locked in the direction established at high temperature and are unable to flip the net magnetization to align along the weak

! K. Szymanski et al. / Journal of Magnetism and Magnetic Materials 251 (2002) 271–282

273

30 20

σ (Am2/kg)

10 0 -10

8 kA/m, ZFC 8 kA/m, FC 0.8 MA/m, ZFC 0.8 MA/m, FC

-20 -30 0

100

200

300

400

500

T (K) Fig. 1. The ZFC and FC magnetization in applied fields of 8  103 and 8  105 A/m.

40

σ (Am 2/kg)

20

0

-20

-40 -5×106

-2.5×10 6

0

2.5×106

5×10 6

H (A/m) Fig. 2. The hysteresis curve measured at 5 K.

applied field. The magnetic ordering temperature can be estimated to be TC ¼ 330 K from the low field curves. In Fig. 2, the hysteresis curve measured at 5 K is shown. The magnetization curve attains a certain saturation at a rather high field, followed by a weak almost linear increase at even higher fields. The net magnetization in a field of 8  105 A/m (where the saturation level has been established) is 27.5 Am2/kg. The coercive force is quite large,

HC=3.7  105 A/m. It is also seen that the domain structure is removed at a field of 8  105 A/m. This certifies that the magnetization vs. temperature curves measured at this field rather accurately reflects the net spontaneous magnetic moment of the system at all temperatures except at temperatures close to TC and Tcomp : With increasing temperature, the spontaneous magnetization rapidly decreases towards zero at the compensation temperature (cf. Fig. 1). As

! K. Szymanski et al. / Journal of Magnetism and Magnetic Materials 251 (2002) 271–282

274

4

5

Hc (10 A /m)

3 2 1 0 0

50

100 T (K)

150

200

Fig. 3. The temperature dependence of the coercivity.

T=295K

a

T=295K

b

illustrated in Fig. 3, the coercive field first decreases, but then shows a minimum followed by a sharp maximum as Tcomp is approached. Around the compensation temperature the coercive field becomes experimentally poorly defined because of the vanishing net magnetic moment. Ideally, a divergence of the coercive field is expected to occur at Tcomp [15]. On further increasing the temperature, HC rapidly decreases to reach very small values at high temperatures. . Fig. 4 shows standard Mossbauer spectra that have been recorded at different temperatures. All spectra show broad sextets, typical for amorphous materials. Within the experimental accuracy, no differences revealed between the standard and the ‘‘magic angle’’ measurements (see Fig. 4a and b), indicating that the sample has no magnetic texture, at room temperature.

transmission [arb. unit]

4. M.ossbauer spectra analysis T=295K

c

T=250K

d

The magnetic texture in the sample can be extracted from the transition probabilities in a . standard Mossbauer spectrum: i1 : i2 : i3 : i4 : i5 : i6 ¼ 3 : z : 1 : 1 : z : 3; where theD z value allows an E ~ Fe Þ2 ; of the estimate of the average square ð~ gm cosine of the angle between the direction of the photon ~ g and the direction of the Fe hyperfine ~ Fe : magnetic field m 4z ~ Fe Þ2 S ¼ : ð1Þ /ð~ gm 4þz

T=12K

e

-6

-4

-2 0 2 velocity [mm/s]

4

6

. Fig. 4. Mossbauer spectra measured on a powdered absorber in standard transmission geometry (a) and on a ribbon in ‘‘magic angle’’ geometry (b). Spectra measured in an applied field Hext ¼ 8  105 A/m at the indicated temperatures (c), (d) and (e). The spectra displayed in (d) and (e) are sums of the spectra measured with two opposite polarizations and correspond to the experiment with unpolarized radiation.

The brackets /S denotes an average over the hyperfine field orientations in the sample and ~ g ~ Fe are unit vectors. and m The MCPMS spectra exhibit a characteristic asymmetry, see Fig. 5. Defining the asymmetry in intensities for lines 3 and 4 (or 1 and 6) as i4  i3 i1  i6 a¼ ¼ ; ð2Þ i4 þ i3 i1 þ i6 ~ Fe S (the one can express the average cosine /~ gm projection of the iron moment on the field direction) by [8,9] 4a ~ Fe S ¼ ; ð3Þ /~ gm ð4 þ zÞp

! K. Szymanski et al. / Journal of Magnetism and Magnetic Materials 251 (2002) 271–282

M Fe

M Fe

Er

250K

M Fe

α-Fe

transmission [arb. unit]

transmission [arb. unit]

α-Fe

Er

M Fe

Fe

M Er

250K

M Er

Fe

275

12K 12K -6 (a)

-4

-2 0 2 velocity [mm/s]

4

6

-6 (b)

-4

-2 0 2 velocity [mm/s]

4

6

Fig. 5. a-Fe (10 mg of Fe powder per cm2) and amorphous Fe0.66Er0.19B0.15 measured in an axial magnetic field of Hext ¼ 8  105 A/m . using a monochromatic circularly polarized Mossbauer source. Here M denotes the direction of the net magnetization, Fe the direction of Fe atomic moment and Er the direction of Er atomic moment. (a) and (b) correspond to measurements with opposite polarizations.

where p is the degree of circular polarization of the beam. The direction of the projection of the iron moments onto the field direction lies along the field if the intensity of line 1 is larger than that of line 6 (and is reversed in the opposite case). The Standard Normos package was used to fit . the Mossbauer spectra and obtain the distribution of the hyperfine field. In a first attempt, the spectra were fitted with a single Zeeman component broadened by a Gaussian distribution of the hyperfine magnetic field (h.m.f.). However, using this approach the shape of the measured spectra could not be fully reproduced. Thus, a second Zeeman component with a Gaussian distribution was added in order to better reproduce the asymmetric shape of the h.m.f. distribution (see top of Fig. 6).

Since the absorption peaks in the spectra are strongly overlapping, the results of the fits are ambiguous, [16–18]. In our case, the main problem concerns an ambiguity in estimating an acceptable range of values for the z and a parameters. A procedure used to estimate z is described below. We focus on the measurements performed at room temperature, where the overlap of the lines is most pronounced. Reasonable fits of the experimental data and hyperfine field distributions PðB; Hext ; zÞ can be obtained with z in the range 1.5–2.5 for the zero field experiment (Hext ¼ 0) and with z ¼ 020:7 for the in field experiment (Hext ¼ 8  105 A/m), see Figs. 4 and 6. It is further assumed that the applied field induces a reorientation of the magnetic moments, but that the shape of the h.m.f. distribution PðB; Hext ; zÞ

! K. Szymanski et al. / Journal of Magnetism and Magnetic Materials 251 (2002) 271–282

P(B)

P(B)

276

0

10

z 2 =1 .8

z 1 =0 .0

z 2 =2 .0

z 1 =0 .2

z 2 =2 .2

z 1 =0 .4

20

0

10

B [T]

20 B [T]

2.4

z2

2.2

2.

1.8

1.6

0

0.1

0.2

0.3

0.4

0.5

z1 Fig. 6. Top: examples of the hyperfine field distribution obtained from the best fits to the experiment in zero field (left) and in external field (right) collected at room temperature. Bottom: contour plot of the similarity (D2 ) between the distributions of the hyperfine magnetic field obtained from the best fits (see Eq. (4)).

remains intact. Based on this assumption we plot the parameter D2 ; which is a measure of the similarity between the distributions: D2 ðz1 ; z2 Þ Z N ¼ ðPðB; Hext ; z1 Þ  PðB; 0; z2 ÞÞ2 dB:

ð4Þ

0

A contour plot of D2 is shown in Fig 7. The minimum of D2 was found for z1 ¼ 0:2 and z2 ¼

2:0; the latter value is expected for a randomly oriented powder. It has been reported from measurements on a texture free metglass, that the z parameter differs from the expected 2 by about 7% [19]. We thus assume that a possible range for the z2 parameter is z2 ¼ 1:8C2:2: It then follows from Fig. 6 that one can accept values of z1 o0:3: From measurements on in-field oriented a-Fepowders, the minimal value which could be experimentally accepted for z1 was found to be

! K. Szymanski et al. / Journal of Magnetism and Magnetic Materials 251 (2002) 271–282

277

datuni.axs, axg 1.0

T=295 K

0.8

T=250 K

<(γ⋅mFe)2>

T=12K

0.6

0.4

-1.0

-0.5

0.0

0.5

1.0

<γ⋅mFe> Fig. 7. The correlation between the average cosine and the average cosine square of the angle between the Fe hyperfine field and the direction of photon. The solid line represents Eqs. (4) and (5). The dotted lines cross at a point which corresponds to an isotropic distribution of the directions of the hyperfine magnetic fields. The error bars correspond to the limits given in Table 1.

about 0.05 [8]. We think that the angular disorder is larger in our Fe0.66Er0.19B0.15 than in a-Fe, and hence conclude that 0.05oz1o0.3. The derived values of z and the square cosines are quoted in Table 1 (for fully isotropic orientation of Fe moments z ¼ 2). The in-field measurements on the powdered sample indicate a substantial alignment of the iron moments along the magnetic field applied parallel to ~ g : The MCPMS spectra were fitted simultaneously with the standard spectra. The fitted lines are shown together with experimental points in Figs. 5 and 6. The most difficult point in the analysis is to obtain the transition probabilities i1 : i2 : i3 : i4 : i5 : i6 from the relative areas under the absorption peaks whose integrated intensity ratios are denoted by I1 : I2 : I3 : I4 : I5 : I6 : The relative area under the absorption peaks does not directly correspond to the transition probability. An example illustrating this is the calibration spectrum measured on a-iron in Fig. 5. Indeed, the area ratios I1 =I4 and I6 =I3 are smaller than the transition probability (which is equal to 3) because of three main causes (a) thickness effects [20], (b) influence of accidental acoustic noise and vibra-

Table 1 Results of magnetization (line 2) and MCPMS measurements (lines 3,4) of powdered sample in external field of Hext ¼ 8  105 A/m at temperatures given in first line. Lines 5 and 6—averages of Fe magnetic moment angular distributions determined from Eqs. (1) and (3) y—the angle of a Fe-cone (Eqs. (13) and (14)), d—minority fraction (Eq. (15)), BFe average hyperfine field, mFe —magnetic moment of Fe determined from Eq. (16), Line 10 Contribution of average Er moment to total magnetization (per atom, see Eq. (18)) given in the last line. A minus sign in lines 6 and 11 indicate antiparallel orientation of the average moment with respect to net magnetization 1 2 3 4 5 6 7 8 9 10 11

T (K) m (mB Þ i1 =i6 Z ~ Fe Þ2 S /ð~ gm ~ /~ g  m Fe S yFe (deg) d BFe (T) mFe (mB) ~ Er S (mB) gm mEr /~

12 0.296 3.2(3) 0.40(8) 0.82(3) (0.79–0.59) 36(3) 0.08–0.19 20.2(2) 1.7(2)0 5.0–6.2

250 0.245 0.30(3) 0.31(6) 0.86(3) 0.62–0.83 31(4) 0.07–0.17 12.3(2) 1.1(2) (1.1–1.9)

295 0.228 0.23(3) 0.18(12) 0.92(6) 0.75–0.99 22(10) 0–0.1 9.3(2) 0.9(1) (1.1–1.9)

tions introduced by the drive system working at the constant acceleration mode and (c) inhomogeneity of the thickness distribution. The thickness

278

! K. Szymanski et al. / Journal of Magnetism and Magnetic Materials 251 (2002) 271–282

distribution arises due to the way the absorber is prepared. In order to reach saturation of the calibration absorber, the a-iron powder was oriented in an externally applied magnetic field, perpendicular to the absorber plane. One may expect that all the elongated a-Fe particles were oriented due to the shape anisotropy and thus increases the inhomogeneity in the density distribution seen by the ~ g -beam. In order to get the average cosine (Eq. (3)) one has to correct the relative areas Ii and derive the probabilities ii : In some cases the correction is easy. All three aforementioned factors can be corrected to a reasonable level in the case of the aFe spectrum when the transmission integral is used and the intensity ratios i1 =i4 and i6 =i3 are fixed equal to 3, see Ref. [8]. Such a procedure can be considered as a kind of calibration of the absorption scale of the spectra. In contrast, an analogous procedure can hardly be applied to the measured Er–Fe–B spectra because the presence of a wide h.m.f. distribution and quadrupole interaction result in unknown i1 =i4 and i6 =i3 ratios. However, below we propose a convenient method to estimate reasonable limits for the average cosine (Eq. (3)). Let us estimate the systematic errors introduced by using I instead of i (we omit indices for short notation). It is a reasonable assumption that the three discussed factors cause changes of the observed amplitudes in such a way that the large amplitudes are attenuated more than the small ones. This can be written for the integrated intensities I (area under the absorption line) as

sion integral [20] (for small t the expression Eq. (5) corresponds to the thin absorber approximation). Using Eq. (5), replacing i by I in Eq. (3) and expanding in a (small) parameter C we have 4A 4A ~ Fe S ¼ ð1 þ 2CÞ > ; ð6Þ /~ gm ð4 þ zÞp ð4 þ zÞp

I ¼ b  Dv hð1  c  htÞ;

The width Dv in Eq. (8) for the absorption peaks 1 and 6 may be related to the FWHM of the h.m.f. distribution, DB : 1 Dv ¼ ðg1=2  3g3=2 ÞDB ; ð11Þ 2 where coefficients g3=2 and g1=2 are nuclear gyromagnetic factors for the excited and ground states of the 57Fe [21] nucleus, and 1=2ðg1=2 23g3=2 Þ ¼ 0:1613 mm/s/T. The FWHM of the h.m.f. distribution is about 12.8 T, (see top of Fig. 6). From the width of the calibration lines (0.25 mm/s) we derive Dv =D* v ¼ 7:7 and from the sample thickness and composition we find t=*t ¼

ð5Þ

where b is a positive normalization constant of no interest in the actual considerations, c is a small positive coefficient and t is the effective thickness of the sample [20]. The parameters Dv and h are the width and height of the absorption peak, broadened by the distribution of the hyperfine parameters. Without a distribution of the hyperfine interactions, the broadening Dv is of the order of the natural width. In our notation the product Dv  h is proportional to the transition probability denoted already by i: Eq. (5) is approximately true for the thickness effects described by the transmis-

where A is the experimentally measured asymmetry defined conveniently as I1  I6 A¼ ; ð7Þ I1 þ I6 and the small parameter ct I1  I6 : C¼ bDv I1 þ I6

ð8Þ

The right-hand side of Eq. (6) thus serves as an upper limit for the average cosine. A lower limit for the average cosine in the Fe– Er–B sample can be estimated using the spectrum of a-Fe measured under the same conditions. Since the second and fifth lines are almost absent, we ~ Fe Þ2 S and may assume that both averages /ð~ gm ~ Fe S are equal to 1 and from Eq. (3) we have /~ gm * þ 2CÞ: * p ¼ a ¼ Að1 ð9Þ The symbols on the right-hand side of Eq. (9) correspond to the a-Fe spectrum, and are marked by tilde. Inserting the polarization degree (Eq. (9)) expressed by the parameters of the calibration spectrum into the average cosine (Eq. (3)) of the investigated sample and expanding in the parameter C we have 4 A * ~ Fe S ¼ /~ gm ð1 þ 2C  2CÞ: ð10Þ ð4 þ zÞ A*

! K. Szymanski et al. / Journal of Magnetism and Magnetic Materials 251 (2002) 271–282

* 0:845: Finally we can estimate C=CE0:1; which allows a safe estimate of the lower limit of Eq. (10): 4 A ~ Fe So /~ gm : ð12Þ ð4 þ zÞ A* The upper and the lower limit for the average cosine based on Eqs. (6) and (12) are included in the uncertainties given in the Table 1.

5. Magnetic structure To describe the actual spin structure let us assume that the magnetic moments are homogeneously distributed within a cone of angle y (e.g. y ¼ p=2 correspond to a half-sphere) and that the symmetry axis of the cone is along the ~ g direction. In such a case ~S ¼ /~ gm

1 þ cos y ; 2

~ Þ2 S ¼ /ð~ gm

1 þ cos y þ cos2 y : 3

ð13Þ ð14Þ

~ Þ and /ð~ ~ Þ2 S is The correlation between ð~ gm gm shown in by the solid line in Fig. 7. After a little of algebra we find that the Fe spin structure at room temperature can roughly be considered as distributed homogeneously in a cone with an angle y ¼ 227101: At lower temperatures the experimental points and their error bars are located too far from the solid line to justify our assumptions on the directions of the magnetic moments. The discrepancy can be accounted for if we assume that a minority part d of the Fe atoms are oriented antiparallel with respect to the ones of the majority part. Antiparallel reversal does not change the ~ Þ2 S while it reduces the /~ ~S value of /ð~ gm gm value, and in our simple model of homogeneously distributed cone we have ~ S ¼ ð1  2dÞ /~ gm

1 þ cos y : 2

ð15Þ

An estimate of d at different temperatures is given in Table 1. In order to estimate magnetic moment of the iron atom one can inspect published data for the . hyperfine field of iron determined by Mossbauer

279

spectroscopy and the magnetic moment of iron determined by neutron diffraction or saturation magnetization measurements. In Fig. 8 we show data from different intermetallic compounds [19–29] and some XFe2 Laves phases (X is a Rare Earth or a light 4d element) [27–33] for which the average magnetic moments and the average hyperfine fields for given sites (sublattices) were determined. It is seen from the figure that, for well defined families of alloys, e.g. Fe–Si, Fe–P, Fe-B and Fe–C, Fe–Sn, the experimental points are located along lines with nearly the same slope dB=dmFe ¼ ð13:672:0Þ T=mB ; which is close to the already published value 12:5 T=mB [34]. The lines corresponding to different families are however somewhat shifted vertically with respect to each other. We would like to find a linear relation between the hyperfine field and the magnetic moment corresponding to our Fe0.66Er0.19B0.15 alloy. Since this composition is close to the 0.6Fe2Er+0.4FeB, we choose a vertical shift which corresponds approximately to weighted average of the shifts of the Fe2Er and FeB compounds and obtain T B ¼ ð13:672:0Þ mFe  ð2:370:7ÞT; ð16Þ mB which corresponds to the line in Fig. 8. The iron magnetic moments determined by Eq. (16) are shown in Table 1. Using the magnetic moment of Fe and its component projected on the direction of the field one can estimate the magnetic moment of Er. The average magnetic moment per atom from magnetization measurement can be expressed as X ~ i S; m¼ ci mi /~ gm ð17Þ i

where ci is concentration of the ith element, mi the atomic magnetic moment, and /S is average cosine between the direction of the magnetic ~ i Þ and the direction of the moment ð~ m i ¼ mi  m average magnetization, which in our case coincides with the direction of the g-ray. The contribution to the magnetization per single Er atom is then given by ~ Er S ¼ mEr /~ gm

~ Fe S m  cFe mFe /~ gm : cEr

ð18Þ

280

! K. Szymanski et al. / Journal of Magnetism and Magnetic Materials 251 (2002) 271–282

mome.axs, axg Fe3Si [20] DyFe2 [27,28,30]

hyperfine magnetic field [T]

Fe3P [21]

HoFe2 [27,29,30]

30

ErFe2 [27,28,30]

Fe3P [21]

TmFe2 [22,27,28,30] ZrFe2 [25,26] YFe2 [27,28,30]

Fe2B [19] Fe3Sn2 [23]

Fe3Si [20]

20

Fe5Sn3 [20]

Fe3P [21]

Fe3C [19] FeSn [23,24] FeSn2 [22,23]

FeB [19]

10

0 0.0

0.5

1.0

1.5

2.0

magnetic moment of Fe [µΒ] Fig. 8. Experimental values of magnetic moments and hyperfine magnetic fields of iron. The dashed line is used for estimation of the Fe moment for amorphous Fe0.66Er0.19B0.15.

The numerical results are given in Table 1. From Eq. (18) and the assumption that the atomic moment of Er is 9 mB, we obtain that the angle y of the cone in which the Er moments are distributed is in-between 721 and 861. Our results clearly demonstrate that Er provides the dominating contribution to the magnetization at temperatures below Tcomp and a small antiparallel contribution (with respect to the net magnetization) at higher temperatures.

6. Discussion Combining the temperature dependence of the net spontaneous magnetization, derived from the magnetization measurements, with the component of the average magnetic moment of the iron atom . from Mossbauer spectroscopy, it was possible to estimate the magnitude and temperature dependence of projection of the Er and Fe moments

along the net magnetization (always using data measured in an applied field of 8  105 A/m). Using the low temperature results for the hyperfine field and published data for iron moments and the hyperfine fields for this class of systems, the zero temperature iron moment is estimated to be 1.7(2) mB, a value that is smaller than the 2.2 mB characteristic for elemental metallic iron. Such a reduction of the average moment of a 3d atom is typical for amorphous metals. The MCPMS data show that the iron moments are aligned along the magnetic field at high temperatures, and become antiparallel with respect to the applied field at temperatures below the compensation temperature, implying, as just mentioned, that the net magnetization is dominated by the Er subnetwork magnetization at low temperatures and the Fe subnetwork at higher temperatures. Our results indicate that the iron moments exhibit a certain misalignment with respect to the external ~ Fe SE0:7 at T ¼ 12 K, which reduces field, /~ gm the magnitude of the iron moment contribution to

! K. Szymanski et al. / Journal of Magnetism and Magnetic Materials 251 (2002) 271–282

the net magnetization from 1.7 to 1.2 mB per Fe atom. The Fe contribution to magnetization is positive at T ¼ 250 and 295 K. The values of ~ Fe S show that the alignment of the iron /~ gm moments increases when the temperature is approaching to TC : The derived component of the Er moment along the magnetic field is about 5 mB/atom at low temperature, which is much smaller than the expected 9 mB/atom calculated from Hund’s rules. However, accounting for a random distribution of the directions of the these moments within the hemisphere, due to the random anisotropy of the 4f-moments in the material, the component antiparallel to the Fe moment is expected to amount to 1/2 the free erbium moment, i.e. 4.5 mB. The value of the Er moment estimated from the present data is slightly larger, supporting that the Er moments form part of a half-sphere. At these low temperatures, the magnetization is dominated by the Er moments that are strongly confined to their local anisotropy directions. In this situation the pinning forces for spin flip become substantial as is reflected in the large and temperature dependent coercive field (cf. Fig. 3). The observed results indicate a dominating antiferromagnetic exchange interaction of the Er (orbital) magnetic moment and the Fe 3d-spin moment. This strong exchange energy and the strong random local anisotropy of the Er moments dominate the ferromagnetic interaction of the Fe atoms at low temperatures and cause substantial canting also of the Fe-moments. As to the spin structure, we have concluded that the Er moment directions uniformly fill almost a half-sphere, while the iron moments at average exhibit a smaller canting. In addition, a small fraction of iron moments seems oriented parallel to the average direction of Er moments. A schematic picture of the magnetic structure is shown in Fig. 9. Whether this description is the unique solution to the magnetic structure of our amorphous Fe0.66Er0.19B0.15 material remains an open question, since our element sensitive technique only measures two types of spatial averages: the cosine and its square. We also conclude that the use of a circular . polarized Mossbauer source provides richer and

281

Fig. 9. Schematic representation of a possible spatial arrangement of the Er and Fe magnetic moments which are homogeneously distributed within the 3D-cones. Longer and shorter arrows correspond to Er and Fe atomic magnetic moments, respectively.

less ambiguous information about the magnetic structure of this type of amorphous systems than . conventional Mossbauer spectroscopy.

Acknowledgements We would like to thanks for Dr. Jean Pettersson for preforming the chemical analysis and LarsErik Tergenius for helping in sample preparation. One of authors (K.S.) thanks Prof. H. Figiel and Prof. Pszczo"a for supplying RE metals at initial stage of investigations.

References [1] S. Chikazumi, Physics of Ferromagnetism, 2nd Edition, Oxford University Press, Oxford, 1997. [2] J.M.D. Coey, J. Chappert, J.P. Rebouillat, Phys. Rev. Lett. 36 (1976) 1061. [3] B. Boucher, A. Lienard, J.P. Rebouillat, J. Schweizer, J. Phys. F 9 (1979) 1421; B. Boucher, A. Lienard, J.P. Rebouillat, J. Schweizer, J. Phys. F 9 (1979) 1433.

282

! K. Szymanski et al. / Journal of Magnetism and Magnetic Materials 251 (2002) 271–282

[4] M. Ghafari, R. Gomez Escato, Hyperfine Interact. 110 (1997) 51. [5] R. Krishnan, H. Lassri, J. Teillet, J. Magn. Magn. Mater. 98 (1991) 155. [6] J. Teillet, H. Lassri, R. Krishnan, A. Laggoun, Hyperfine Interact. 55 (1990) 1083. [7] R. Krishnan, H. Lassri, Sol. State Commun. 69 (1989) 803. ! [8] K. Szyma!nski, L. Dobrzynski, B. Prus, M.J. Cooper, Nucl. Instrum. Methods B 119 (1996) 438. ! [9] K. Szyma!nski, D. Satu"a, L. Dobrzynski, J. Phys.: Condens. Matter 11 (1999) 881. [10] K. Szyma!nski, Nucl. Instrum. Methods B 134 (1998) 405. ! [11] K. Szymanski, J. Phys.: Condens. Matter 12 (2000) 7495. [12] T. Ericsson, R. W.appling, J. Phys. C 6 (12) (1976) 719. [13] J.M. Greneche, F. Varret, J. Phys. 43 (1982) L-233. [14] L. N!eel, Ann. Phys. 3 (1948) 137. [15] P. Hansen, in: K.H.J. Buschow (Ed.), Handbook of Magnetic Materials, Vol. 6, Elsevier Science Publishers BV, Amsterdam, 1991 (Chapter 4). [16] G. Le Caer, J.M. Dubois, H. Fischer, I.U. Gonser, H.G. Wagner, Nucl. Instrum. Methods B 5 (1984) 25. [17] G. Le Caer G, R.A. Brand, Hyperfine Interact. 71 (1992) 1507. ! [18] K. Szyma!nski, D. Satu"a, L. Dobrzynski, J. Phys.: Condens. Matter 11 (1999) 881. [19] J.M. Greneche, F. Varret, Sol. State Commun. 54 (1985) 985. [20] S. Margulies, J.R. Ehrman, Nucl. Instrum. Methods 12 (1961) 131.

[21] J.M. Trooster, M.P.A. Viegers, in: J.W. Robinson (Ed.), Handbook of Spectroscopy, Vol. III, CRC Press. Inc., Boca Raton, FL, 1981. [22] T. Shinjo, F. Ito, H. Takaki, Y. Nakamura, N. Shikazono, J. Phys. Soc. Japan 19 (1964) 1252. [23] W.A. Hines, A.H. Menotti, J.I. Budnick, T.J. Burch, T. Litrenta, V. Niculescu, K. Raj, Phys. Rev. B 13 (1976) 4060. . [24] L. H.aggstrom, P. James, O. Eriksson, Hui-ping Liu, M. ! ! Trosko, K. Szymanski, L. Dobrzynski, Phys. Rev. B 61 (2000) 6798. [25] W. Nicholson, E. Friedmann, Bull. Am. Phys. Soc. 8 (1963) 43. [26] G. Trumpy, E. Both, C. Djega-Mariadassou, P. Lecocq, Phys. Rev. B 2 (1970) 3477. [27] K. Yamaguchi, H. Watanabe, J. Phys. Soc. Japan 22 (1967) 1210. [28] G.K. Wertheim, V. Jaccarino, J.H. Wernick, Phys. Rev. 136 (1964) A151. [29] Y. Muraoka, M. Shiga, Y. Nakamura, J. Phys. F 9 (1979) 1889. [30] E. Burzo, Z. Angew. Phys. 32 (1971) 127. [31] G.K. Wertheim, J.H. Wernick, Phys. Rev. 125 (1962) 1937. [32] M. van der Kraan, P.C.M. Gubbens, J. Phys. Colloq. C 6 (suppl.) (1974) 469. [33] D. Barb, E. Burzo, M. Morariu, Fifth International . Conference on Mossbauer Spectroscopy, Bratislava, September 3–7, 1973, Czechoslovak Atomic Energy Commission Nuclear Information Centre, Bratislava. [34] P. Panissod, J. Durand, J.I. Budnick, Nucl. Instrum. Methods 199 (1982) 99.