Mossbauer effect studies of Tb0.27 Dy$_{0.73} $ (Fe_{1−x} Co_{x })_{2}2$ intermetallics at 295 K

— physics pp. 537–548

M¨ ossbauer effect studies of Tb

Dy

(Fe

Co

)

intermetallics at 295 K

W BODNAR¹, M SZKLARSKA-ÃLUKASIK¹, P STOCH^2,3, P ZACHARIASZ², J PSZCZOÃLA^1,∗ and J SUWALSKI²

1Faculty of Physics and Applied Computer Science, AGH, Al. Mickiewicza 30, 30-059 Krak´ow, Poland

2Institute of Atomic Energy, 05-400 ´Swierk-Otwock, Poland

3Faculty of Material Science and Ceramics, AGH, Al. Mickiewicza 30, 30-059 Krak´ow, Poland

∗Corresponding author. E-mail: pszczola@agh.edu.pl

MS received 18 September 2009; revised 22 March 2010; accepted 06 April 2010

Abstract. The synthesis of materials and the studies of crystal structure and ⁵⁷Fe M¨ossbauer effect were performed for Tb0.27Dy0.73(Fe1−xCox)2 intermetallics. Terfenol- D (Tb0.27Dy0.73Fe2) is the starting compound of this Fe/Co-substituted series. X-ray measurements showed evidence of a pure cubic Laves phase C15, MgCu2-type, and unit cell parameters were determined across the series. A Co substitution introduced local area, at sub-nanoscale, with random Fe/Co neighbourhoods of the⁵⁷Fe atoms.

M¨ossbauer effect spectra for the Tb0.27Dy0.73(Fe1−xCox)2 series at room temperature are composed of a number of locally originated subspectra due to the random distrib- ution of Fe and Co atoms in the transition metal sublattice, and due to [1 1 1] an easy axis of magnetization. Isomer shift, magnetic hyperfine field and quadrupole interaction parameter were obtained from the spectra, both for the local area and for the bulk sample.

As a result of Fe/Co substitution, a Slater–Pauling-type curve for the average magnetic hyperfine field vs. Co content was observed. It was found that the magnetic hyperfine fields corresponding to the local area also create a dependence of the Slater–Pauling-type vs. Co contribution in the Fe/Co neighbourhoods.

Keywords. Intermetallics; crystal structure; Laves phase; M¨ossbauer effect; hyperfine interaction; Slater–Pauling dependence; easy axis of magnetization.

PACS Nos 76.80.+y; 61.10.Nz; 71.20.Lp; 71.20.Eh; 75.50.Gg

1. Introduction

Heavy rare earth (R)–transition metal (M) ferrimagnets of the RM2-type are widely studied because of their practical applications [1–4]. The ferrimagnetism of R–

M compounds is a result of the coexistence of the rare earth’s 4f(5d) electron magnetism and transition metal’s 3d magnetism [5]. RM2 intermetallics exhibit

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a variety of interesting and practically useful properties. For instance, RFe2-type materials have strong magnetostriction [6–8]. Compounds of the TbxDy1−xFe2

series have been studied and high magnetostriction has been observed especially in the Tb0.27Dy0.73Fe2 compound (commercially known as Terfenol-D) [6–8]. Re- cently, Terfenol-D and other intermetallics of the Tb0.27Dy0.73(Fe1−xCox)2 series have been widely used as strongly magnetostrictive constituents of composites with piezoceramics, which present strong magnetoelectric effect [9–12].

It is known that Fe/Co substitution in RFe₂-type compounds strongly changes their physical properties [13–16]. It was previously found from ⁵⁷Fe M¨ossbauer effect studies of the Dy(Fe1−xCox)2 pseudobinaries [13,14] that the⁵⁷Fe magnetic hyperfine fieldHhf, treated as a function of the average numbernof 3delectrons calculated per transition metal atom, resembled a Slater–Pauling plot.

It has been found that the magnetic hyperfine field scales approximately the magnetic moment averaged per atom in the transition metal sublattice. Moreover, it was found that Curie temperatureTc(n) of the Dy(Fe1−xCox) series changed in some degree analogously to the magnetic hyperfine fieldHhf(n) [15]. As a result of Fe/Co substitution, maximal values ofHhf and Tc have been obtained for the Dy(Fe0.7Co0.3)2compound [13–15].

Fe/Co substitution in RFe₂-type compounds changes the number n of 3d elec- trons in the M sublattice, strongly influences the 3d-band and thus magnetism, and hyperfine interactions. Therefore it is interesting to study the influence of the 3d band population on the magnetism of the 3d-sublattice and especially on the hyperfine interaction parameters in Terfenol-D-type Co-substituted compounds.

Thus, it is interesting to study by M¨ossbauer effect, the Tb0.27Dy0.73(Fe1−xCox)2

intermetallics with Terfenol-D as the starting compound of the series, which can be treated as potential constituents of composite and laminate magnetoelectric materials [9–12].

2. Materials and X-ray studies

Polycrystalline intermetallics Tb0.27Dy0.73(Fe1−xCox)2 (x= 0,0.1,...,0.9 and 1.0) were synthesized by arc melting with contact-less ignition in a high-purity argon atmosphere using appropriate amounts of Tb (99.9%), Dy (99.9%), Fe and Co (99.99% purity) [17]. To homogenize, the obtained ingots were annealed in vacuum at 1200 K for 12 h and then cooled down along with the furnace (cooling: ∼250 K h⁻¹.

The post-annealed compounds were micromilled and their phase homogeneity and crystal structure were studied by standard X-ray powder diffraction measurements using MoKαradiation with an angle step of 0.05^◦.

The X-ray patterns (figure 1) obtained for these compounds were analysed using a Rietveld-type procedure adopting both the K_α1 (wavelength λ₁ = 0.70930 ˚A) and Kα2 (wavelength λ2 = 0.71359 ˚A) lines [18,19]. The powder pattern of the studied Tb0.27Dy0.73Co2 compound is not presented in the figure. For the closely situated neighbouring X-ray peaks a pair of sticks (corresponding toKα1 andKα2

lines), not necessarily well separated, is presented below the experimental (open dots) and fitted (solid line) Roentgenograms. Very weak X-ray reflexes are not

described by the Miller indexes. Additionally, a differential pattern is added at the bottom of each Roentgenogram. Rietveld reliability factors [18] of the exemplary compound Tb0.27Dy0.73(Fe0.5Co0.5)2 are equal: Rp = 13.2, Rwp = 16.1,Re = 8.6 and the convergence testχ²= 3.47. TheR-factors and theχ² values for the other compounds of the studied series are comparable to the presented example.

A clean cubic, Fd3m, MgCu2-type C15 crystal structure was observed for all the compounds studied. The C15-Laves phase structure has been described in detail elsewhere [20]. As it was impossible to fit additional X-ray lines even with a low intensity, it can be deduced that Fe and Co atoms are randomly distributed in the transition metal sublattice.

It can be added that in the C15 crystal structure, each transition metal atom is surrounded by six transition metal atoms as its nearest neighbours.

Because the atomic radius of Fe (rFe = 1.72 ˚A) is higher when compared with the corresponding radius of Co (rCo = 1.67 ˚A), the unit cell parameter described by the following numerical formula,a(x) = (−0.104x²−0.029x+ 7.337) ˚A, decreases softly non-linearly with cobalt content x (figure 2) [21]. This formula is used to follow the experimental points and is obtained by a least squares fitting procedure.

The border line values of the studied series coincide well with the existing literature data (open points) [22–27]. The observed convex deviationa(x) from Vegard’s rule, i.e. linear dependence, is typical of R–M intermetallics [15,22,24,28].

3. Results and discussion

3.1Spectra and analysis

The⁵⁷Fe M¨ossbauer patterns, presented in figure 3, were collected at room tem- perature by using a standard transmission technique with a⁵⁷Co in Pd source [29].

After a number of different fitting trials, it was found that it is necessary to consider not only the random distribution of the Fe/Co atoms but also the direction of the easy axis of magnetization.

Actually, as a result of the random distribution of the Fe/Co atoms in the tran- sition metal sublattice, the probed iron atom can have different neighbourhoods;

it can be surrounded by (6−k) iron atoms andk cobalt atoms (k= 0,1,2, ...,6).

Each Fe/Co surrounding introduces its own subspectrum locally into the resulting M¨ossbauer effect pattern and thus its own set of hyperfine interaction parameters, with probability

P(6;k) = 6!

(6−k)!k!(1−x)^6−kx^k (1)

is described by Bernoulli distribution adapted for the intermetallic formula Tb0.27Dy0.73(Fe1−xCox)2 [30]. During the fitting procedure it was assumed that amplitudeA(k) of a particular subspectrum follows the probability P(6;k). The surroundings with probabilities less than 0.1 of maximal probability are not con- sidered. For this reason, the remaining probabilities were normalized again.

Moreover, it was assumed that all subspectra originated by the random distri- bution of Fe and Co atoms can be ascribed to the [1 1 1] direction of the easy

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Figure 1. X-ray powder diffraction patterns of the Tb0.27Dy0.73(Fe1−xCox)2

intermetallics (300 K). Fitted differential pattern is added below each Roentgenogram.

axis of magnetization. In this case the [1 1 1] direction introduces two magnetically inequivalent iron sites (site 1 : site 2) with a population ratio 0.75 : 0.25 and as a re- sult introduces two component subspectra for analogous neighbourhood. It can be

Figure 2. The unit cell parameters of the Tb0.27Dy0.73(Fe1−xCox)2 inter- metallic system (300 K). Open circles are taken from [22–27].

seen that for Tb0.27Dy0.73(Fe0.1Co0.9)2 withk= 6 cobalt atoms as nearest neigh- bours there is no magnetic hyperfine interaction at the studied iron nuclei and only the quadrupole doublet is observed. The problem of fitting this kind of complex M¨ossbauer spectra is described elsewhere [29,31–35].

3.2Local hyperfine magnetic fields

The magnetic hyperfine fields Hhf corresponding to different subspectra of the Tb0.27Dy0.73(Fe1−xCox)2 series obtained from numerical analysis, grouped in a bundle for site 1 and a bundle for site 2, treated as functions of numberk, are pre- sented in figure 4. The dependencies are labelled with thex-parameter. Addition- ally, figure 5 shows arithmetically averaged magnetic hyperfine fieldsHhfagainst the numberkof Co atoms in the nearest neighbourhood. At both the iron places (sites 1 and 2), a Slater–Pauling-type dependence for the average magnetic hyperfine field as a function ofkis observed. TheHhf dependencies in figure 5 are described by the following numerical formulae: Hhf(k) = (6.2k+ 223) kOe (line 1.1) and H_hf(k) = (−14.7k + 260.1) kOe (line 1.2) both for site 1,H_hf(k) = (7.9k+ 206.7) kOe (line 2.1) andHhf(k) = (−14.8k+ 248.1) kOe (line 2.2) both for site 2.

It is interesting to present the fitted magnetic hyperfine field data again in figure 6. The dependencies of the localHhf fields, the bundle for site 1 and the bundle for site 2, ascribed to the correspondingkvalues treated as functions of the composition parameterxare presented in figure 6. The dashed lines present the averages of the magnetic hyperfine fields calculated using Bernoulli distribution [30].

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Figure 3. ⁵⁷Fe transmission M¨ossbauer spectra of the Tb0.27Dy0.73

(Fe1−xCox)2 intermetallics (300 K). Coloured lines represent particular sub- spectra.

Figure 4. The local magnetic hyper- fine fields Hhf labelled by x (for sites 1 and 2) as functions of k for the Tb0.27Dy0.73(Fe1−xCox)2 series.

Figure 5. The magnetic hyperfine field Hhf as a function of k (for sites 1 and 2) averaged arithmetically across the Tb0.27Dy0.73(Fe1−xCox)2 series.

3.3Average hyperfine interaction parameters

The average hyperfine interaction parameters weighted by subspectra amplitudes, which follow the Bernoulli distribution, i.e. the isomer shift IS (with respect to iron metal, at 300 K), the magnetic hyperfine fieldHhf and the quadrupole inter- action parameter QS [32], obtained for the Tb0.27Dy0.73(Fe1−xCox)2series at room temperature, are presented in figure 7.

The isomer shift IS is described by the numerical formula IS(x) = (−0.189x²+ 0.128x−0.110) mm s⁻¹(figure 7, line 1).

The averageHhf dependence for site 1 can be divided into three sections described by the numerical formulae: Hhf(x) = (76.4x+ 210.2) kOe (figure 7, line 2.1), Hhf(x) = (−93.7x+ 266.3) kOe (figure 7, line 2.2), Hhf(x) = (−749x+ 785) kOe (figure 7, line 2.3). Analogously, for site 2 the next formulae have been fitted:

Hhf(x) = (99.0x+ 191.9) kOe (figure 7, line 3.1),Hhf(x) = (−93.7x+ 253.2) kOe (figure 7, line 3.2), H_hf(x) = (−813.0x+ 819.6) kOe (figure 7, line 3.3). Figure 7 also contains literature data [22,36].

For both sites 1 and 2, a Slater–Pauling-type dependence is observed. At first, a weak ferromagnetic-type behaviour of theM-sublattice is observed. Two 3dsub- bands with opposite spin are not filled up [37]. The magnetic hyperfine field in the Tb0.27Dy0.73(Fe1−xCox)2series grows withxand the maximum value of the field is

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Figure 6. The local magnetic hyper- fine fields Hhf labelled by k (for sites 1 and 2) as functions of x for the Tb0.27Dy0.73(Fe1−xCox)2 series.

Figure 7. Hyperfine interaction parame- ters of the Tb0.27Dy0.73(Fe1−xCox)2series.

Dependence 1 corresponds to average val- ues, dependencies 2,4 correspond to site 1 and dependencies 3,5 correspond to site 2.

Pluses denote literature data [22,24,36].

approached for the Tb0.27Dy0.73(Fe0.7Co0.3)2 compound. At this composition the filling up of the majority 3dsubband by 3delectrons is terminated.

For higher Co-substitution strong ferromagnetic-type behaviour of the M- sublattice appears [37]. The filling-up of the minority 3d subband still proceeds and the observed field decreases gradually with x. Because, for almost all the Tb0.27Dy0.73(Fe1−xCox)2 series Curie temperatures are relatively high, magnetic moments are not specially distanced from magnetic saturation [24]. This is not the case for cobalt-rich compounds. As a consequence, the magnetic hyperfine field (figure 7, lines 2.3 and 3.3) decreases considerably when compared with the previous line segments (figure 7, lines 2.2 and 3.2).

The quadrupole parameter QS changes slightly withxand can be described by the numerical formulae: QS(x) = (0.029x+ 0.064) mm s⁻¹ (figure 7, line 4 – site 1), QS(x) = (0.032x−0.127) mm s⁻¹ (figure 7, line 5 – site 2).

The determined hyperfine interaction parameters coincide well with such frag- mentary data as already shown in [36,38,39].

Figure 8. Correlations between magnetic hyperfine fieldsHhf(k) andHhf(x), for both sites 1 and 2. Line segments are numbered as in figure 6.

3.4Local and average magnetic fields

It is interesting to compare the average local magnetic hyperfine field Hhf as a function ofk(figure 5) andHhf as a function ofx, the bulk type average magnetic hyperfine field (function ofx, figure 7). The correlations betweenH_hf(x) andH_hf(k) for both sites 1 and 2 are presented in figure 8. The points in the figure are described by numbersxandk.

The k-values, the local composition parameters in the nearest neighbourhood, are calculated using the proportionx: 1 =k: 6 where, as mentioned previously, six denotes the number of nearest neighbours surrounding the studied Fe atom and k is the average number of Co atoms in the neighbourhood [1,2,20]. The k-value used imitates locally bulk composition parameterxof the Tb0.27Dy0.73(Fe1−xCox)2

series.

The Hhf(k) dependence for site 1 correlated with Hhf(x) dependence can be divided into three sections (sections numbered as in figure 7) described by numer- ical formulae: H_hf(k) = (0.5H_hf(x) + 124.4) kOe (figure 8, line 2.1), H_hf(k) = (0.9Hhf(x) + 21.8) kOe (figure 8, line 2.2), Hhf(k) = (0.1Hhf(x) + 168) kOe (figure 8, line 2.3). Analogously for site 2 the next formulae have been fitted:

Hhf(k) = (0.4Hhf(x) + 122.6) kOe (figure 8, line 3.1),Hhf(k) = (0.8Hhf(x) + 28.8) kOe (figure 8, line 3.2),Hhf(k) = (0.1Hhf(x) + 158.7) kOe (figure 8, line 3.3). The

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Hhf(k)-values used to construct figure 8 are determined from figure 5. Considering figures 5 and 7 it can be seen that, section by section, a linear correlation between Hhf(k) andHhf(x)-values appears (figure 8). Line segments 2.1, 3.1 correspond to weak ferromagnetic-type behaviour and line segments 2.2, 2.3 and 3.2, 3.3 corre- spond to strong ferromagnetic-type behaviour of the transition metal sublattice.

4. Conclusion

Co substitution in the Tb0.27Dy0.73(Fe1−xCox)2 series introduces a number of es- sential changes. That is, it introduces an additional 3d electron per atom into the transition metal sublattice, it decreases the lattice parameter with x and thus decreases the average distance between the nearest neighbour 3d atoms.

These changes strongly influence the band structure, especially the 3dband struc- ture, and consequently all the observed physical properties, including hyperfine interactions.

Here it is interesting to consider the following aspect of Co-substitution. That is, Co substitution leads to differences in the surroundings of the probed iron atoms.

As a result, the local character of the magnetic hyperfine field is demonstrated and each Fe/Co neighbourhood of the probed Fe atom introduces its own localHhf(x) dependence resembling the Slater–Pauling curve (figure 6). Moreover, the magnetic hyperfine fieldsHhf(k) ascribed to the different Fe/Co neighbourhoods also create a local-type Slater–Pauling dependence againstk(figure 4). Thus, considering the above data, the local character of the 3dmagnetic moment and consequently of the 3dband can be deduced.

As a result, the average value of magnetic hyperfine fieldHhftreated as a function of the composition parameterx, calculated for the bulk sample, creates a Slater–

Pauling dependence (figure 7).

It is interesting to see that the correlation between the average value of Hhf(k) (taken from figure 5) and the average value ofHhf(x) (taken from figure 7) con- stitute, segments by segments, linear dependencies, as presented in figure 8. This correlation can be treated as additional support because the locally originated mag- netic hyperfine fields ascribed to the sub-nanoscale area follows a Slater–Pauling dependence.

Both the magnetic fields, averageHhfas a function ofxandHhfas a function ofk, exhibit weak ferromagnetic behaviour (x≤0.3 andk≤2) and strong ferromagnetic behaviour (x >0.3 andk >2) in the transition metal sublattice. This result can be helpful for both band-type calculations and practical applications of Terfenol-D type Tb0.27Dy0.73(Fe1−xCox)2compounds, potential constituents of the magnetoelectric composites.

Acknowledgements

This work is supported partially by The Polish Ministry of Science and Higher Edu- cation, Project No. R015000504 and partially by AGH, Projects Nos 10.10.220.476 and 11.11.220.01.

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