Finite size effects and spin transition in ball-milled γ-(FeMn)30Cu70 nanostructured alloys

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Physica B 354 (2004) 174–182 www.elsevier.com/locate/physb

Finite size effects and spin transition in ball-milled g-(FeMn)30Cu70 nanostructured alloys J. Restrepoa,, J.M. Grenecheb, J.M. Gonza´lezc a Grupo de Estado So´lido, Instituto de Fı´sica, Universidad de Antioquia, A. A. 1226, Medellı´n, Colombia Laboratoire de Physique de l’Etat Condense´, UMR CNRS 6087, Universite´ du Maine, 72085 Le Mans, Cedex 9, France c Instituto de Magnetismo Aplicado, P.O. Box 155. 28230 Las Rozas, Madrid, Spain

b

Abstract Fe15Mn15Cu70 alloys were prepared by high-energy ball milling over a wide range of grinding times from 15 min to 72 h. The corresponding magnetic properties were followed by means of vibrating sample magnetometry, magnetic susceptibility and Mo¨ssbauer spectroscopy. By using a Rietveld structural analysis of high-resolution X-ray diffraction data, lattice parameter and grain size correlations with magnetization and coercive force were carried out. Results revealed a strong microstructural dependence of the magnetic properties with the grain size, resembling a finite sizedriven magnetic transition at a critical crystallite value of around 8.5 nm. This behavior is endorsed by a partial low- to high-spin transition according to isomer shift results, at a critical unit-cell volume of around 50 A˚3 at 77 K attributed to strong local variations of the interatomic spacing as a consequence of the employed ball-milling procedure. Finally, as concerns to temperature behavior, samples exhibited a freezing temperature at around 61 K and a wide distribution of relaxation times ascribed to the presence of interacting CuMn and FeMnCu clusters. r 2004 Elsevier B.V. All rights reserved. PACS: 75.50.Bb; 76.80.+y; 81.40.Rs Keywords: Nanostructured alloys; Mo¨ssbauer; Spin transition

1. Introduction g-Fe has been the subject of several theoretical and experimental investigations since it can be Corresponding

author. Tel.: +54 4 210 5630; fax: +54 4 233 0120. E-mail address: jrestre@fisica.udea.edu.co (J. Restrepo).

found in different electronic and magnetic states within a very narrow energy range [1–8]. Concretely it has been established that FCC iron can exist in two states with energies slightly different: a low-volume, low-spin, antiferromagnetic or nonmagnetic state and a high-volume, high-spin, ferromagnetic state. On the other hand, the presence of a copper matrix helps to stabilize the

0921-4526/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2004.09.043

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FCC structure despite the low solubility with iron which can be easily overcome trough techniques like mechanical alloying [9–11]. This technique in addition provides the possibility of having different unit-cell volumes as a consequence of millingdriven strain effects. Concretely, ball-milling gives rise to a lattice expansion as high as 0.6% respective to the Cu lattice parameter as it has been already reported for FCC Fe30Cu70 [10]. This fact is important as the g-Fe magnetic moment is strongly volume dependent and it can even change discontinuously in the vicinity of a critical volume. On the other hand, in g-Mn–Cu alloys, lattice expansion goes up to 3.7% upon alloying with Mn below the martensitic transformation [12], providing in this way a much wider range of unit-cell volumes. These features have motivated us to consider the proposed ball-milled alloy in order to elucidate the magnetic behavior of iron in a g matrix, where the effect of interatomic spacing can be addressed.

2. Experimental (Fe50Mn50)30Cu70 samples were prepared by alloying pure (499.99%) elemental powders in a planetary ball mill under inert atmosphere. Continuous milling times of 0.25, 0.5, 1, 2, 4, 6, 12, 21, 48 and 72 h were considered and the average sample-balls weight ratio was 1:7. Every sample for every milling time was prepared separately in order to preserve the sample to balls weight ratio. Magnetic characterization was performed by means of (i) vibrating sample magnetometry in the temperature range from 5 up to 300 K with an external applied field of 3 T below 300 K and 0.9 T at room temperature, (ii) AC susceptibility with temperatures ranging from 10 to 120 K and using alternating field frequencies from 40 to 2500 Hz, and (iii) 57Fe Mo¨ssbauer transmission spectrometry at 77 and 4.2 K by using a 57Co source in a Rh matrix. Isomer shift (d) values are quoted relative to a-Fe at room temperature. Structural analysis was carried out by means of highresolution X-ray diffraction (XRD) using a Phillips X’pert diffractometer (with monochro( Diffracmatic Cu–Ka radiation, l ¼ 1:54056 A).

175

tion patterns were fitted with the MAUD program (http://www.ing.unitn.it/luttero/maud/) based on the Rietveld method from which the Popa anisotropic size-strain model [13] describing the asymmetric broadenings of Bragg peaks was employed.

3. Results and discussion Fig. 1 shows the fitting results for the 48-h sample with and without considering crystallite anisotropy. The remarkable improvement in the fitting procedure when considering first-order anisotropy suggests the occurrence of plastic deformation attributed to the milling procedure. In fact, severe dislocations and lattice distortions at nanometric scale responsible for crystallite anisotropy have been already reported to occur in the mechanically alloyed Fe50Cu50 system [14]. In the first milling stages below some few hours, both XRD peaks and Mo¨ssbauer spectra reveal the presence of precursor elements, which progressively become alloyed coherently with the g-Cu matrix, reaching a steady state after around 21 h. Diffraction peaks are also progressively broadened and shifted toward lower 2y values according to alloy consolidation and lattice expansion. This latter is shown in Fig. 2, where the lattice parameter increases with milling time and becomes practically constant beyond 21 h of milling. This increase, around 10% in unit-cell volume respect to pure copper, constitutes a surprisingly large expansion and a suitable scenario for confirming theoretical predictions about spin transitions controlled by unit-cell volume. As it has been already reported for similar systems like FeCu [10,15] and CuMn [12], the expansion upon alloying can be attributed to magnetovolume and mechanically induced strain effects like the introduction of defects which in turn favor solubility enhancement [10,15]. As the lattice parameter increases before reaching the steady state the grain size decreases rapidly as shown in Fig. 2, and then it becomes stable at around 8.5 nm. Mo¨ssbauer spectra at 77 K, recorded in the velocity range of 72 mm/s, are shown in Fig. 3, where the chosen fitting procedure is based on the

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Intensity (counts)

104

103

40

60

80

100

120

100

120

1000 0 -1000 (a)

2θ (degrees)

Intensity (counts)

104

103

40

60

80

1000 0 -1000

(b)

2θ (degrees)

Fig. 1. X-ray diffractograms for the 48 h sample and fitting results corresponding to an (a) isotropic crystallite scheme and (b) firstorder anisotropy in the Popa size-strain model. Insets show how it looks like the average crystallite in each case. The bottom part shows the difference between the experimental data and those of the fitting procedure.

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3.70 12 3.69 (FeMn)30Cu70 11

3.67 3.66 2.2 %

10

3.65 3.64

Grain Size (nm)

Lattice Parameter (Å)

3.68

9

3.63 3.62

8 Pure Cu

3.61 0

20

40 60 80 Milling Time (hours)

100

120

Fig. 2. Lattice parameter dependence and grain size dependence on the milling time.

asymmetry of the doublet and Mo¨ssbauer data collected at 4.2 K. The observed results evidence a spin transition of one of the components at around 3.675 A˚ from 0.44 to 0.14 mm/s, almost two times greater than that observed in FeNi alloys at the Invar composition undergoing a high-spin (HS) to low-spin (LS) transition [16,17]. Isomer shift results revealing this phenomenology are summarized in Fig. 4. These results are also in agreement with theoretical predictions [2,6,7] about the magnetic behavior of iron in FCC matrices. AC magnetic susceptibility measurements reveal a wide distribution of relaxation times tð¼ 1=nÞ as well as a weak dependence on frequency with a sensitivity DT f =ðT f Dlog nÞ ¼ 0:015 in the steady state (with Tf=61 K), typical of several spin glasses [18]. Freezing temperatures (Tf) were computed from the maximum of the in-phase susceptibility component, and they are shown in Fig. 5. On the other hand, the non-linear behavior of the natural logarithm of t according to the employed frequencies, as a function of the reciprocal freezing temperature as shown in Fig. 6, suggests that the Arrhenius law predicted for isolated particles would not be a suitable representation of our system, implying the occurrence of at least weakly interacting nanograins [18].

Moreover, a linear fit of data in Fig. 6 would give an activation energy of around 9000 K and a frequency of 1066 s1, without physical meaning. Hence, a Fulcher-type law for magnetically interacting particles would be a more suitable representation [18]. In the case, for example, of the 72-h sample, Fig. 7 shows the reciprocal susceptibility w1 as a function of temperature. From this figure, data obey a Curie–Weiss law above Tf as shown by the linear fit, endorsing effectively the occurrence of interparticle interactions with Y ¼ 13 K; and a Curie constant C=0.058 emu K/g. The observed spin glass-type behavior can be ascribed to the presence of CuMn clusters accordingly with the negative enthalpy of mixing of these elements. In Fig. 8, we have carried out a compilation of the freezing temperatures of this canonical Cu100xMnx spin glass. Hence and below the concentration of the martensitic transformation [12], data follow a relationship of the form log T f ¼ 0:76ð2Þlog x þ 0:94ð2Þ; with x=at% Mn and a correlation factor of 0.995, from which the obtained freezing temperature in the steady state (61 K) leads to the composition Cu87Mn13. On the basis of this stoichiometry, we have computed the effective magnetic moment per Mn atom meff ; according to m2eff ¼ 3 kB wM ðT  YÞ=N A m2 ; where

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α-Fe non-alloyed

1.000

(2) 22% δ(1) = 0.23 m m/s Γ(1) = 0.35 m m/s ∆(1) = 0.45 m m/s

0.995

δ(2) = 0.43 m m/s Γ(2) = 0.27 m m/s ∆(2) = 0.41 mm/s

(1) 73%

2h

0.999 0.996 0.993

δ(1) = 0.24 m m/s τ(1) = 0.32 m m/s ∆(1) = 0.45 m m/s

(2) 26% (1) 74%

4h

δ(2) = 0.43 m m/s Γ(2) = 0.29 m m/s ∆(2) = 0.43 m m/s

0.990 0.999

Relative Transmission

0.996 0.993

δ(1) = 0.26 m m/s Γ(1) = 0.38 m m/s ∆(1) = 0.43 m m/s δ(2) = 0.36 m m/s Γ(2) = 0.29 m m/s ∆(2) = 0.39 m m/s

(2) 12%

6h (1) 88%

0.990 0.999 0.996 0.993

δ(1) = 0.30 m m/s Γ(1) = 0.38 m m/s ∆(1) = 0.43 m m/s δ(2) = 0.12 m m/s Γ(2) = 0.31 m m/s ∆(2) = 0.51 m m/s

(2) 16%

12 h (1) 84%

0.990 0.999

0.996

0.993 1.000 0.996 0.992 0.988

δ(1) = 0.30 m m/s Γ(1) = 0.33 m m/s ∆(1) = 0.44 m m/s

(2) 26% (1) 74%

21 h

δ(2) = 0.14 m m/s Γ(2) = 0.29 m m/s ∆(2) = 0.50 m m/s

δ(1) = 0.32 m m/s Γ(1) = 0.43 m m/s ∆(1) = 0.50 m m/s

(2) 24%

δ(2) = 0.14 m m/s Γ(2) = 0.32 m m/s ∆(2) = 0.53 m m/s

-2

-1

48 h

(1) 76%

0

1

2

Velocity (mm/s) Fig. 3. Mo¨ssbauer spectrum at 77 K for different milling times. The shown parameters d; G and D correspond to the isomer shift, the full-width at half-maximum (FWHM) and the quadrupolar splitting, respectively.

wM is the molar susceptibility, and mð¼ mB Þ is the Bohr’s magneton. The result is 4.95 mB, which corresponds well to what would be expected for this composition below the percolation threshold as is shown in Fig. 9, which is also a compilation of effective magnetic moments for this system [19–24]. Consequently, we assume that the formation of Curich–Mn clusters can presumably take place in our system. Although the occurrence of these CuMn clusters can not be resolved by the employed Mo¨ssbauer technique, the presence of others Fe-based clusters however can be elucidated. Fig. 10 shows the Mo¨ssbauer spectrum at 4.2 K for the 48 h sample and the corresponding hyperfine field distribution (HFD) of the magnetic component. The well-defined doublet and the magnetic contribution are attributed to iron moments in a non-blocked and a blocked state, respectively. On the other hand, the broadening of the HFD, ranging from around 2 to 30 T, reveals clearly the presence of many Fe environments consistent with atomic and structural disorder, being more probable those Fe sites with lower hyperfine fields. This situation endorses firstly the alloying of the constituent elements at atomic level, and secondly the occurrence of very diluted Fe sites, i.e. surrounded mainly by copper according to nominal stoichiometry, as the most probable ones. In this respect, from a binomial point of view, the first five most probable atomic configurations are (9,1,2), (9,2,1), (8,2,2), (10,1,1) and (8,1,3), where the nomenclature (k; l; m) accounts for k atoms of Cu, l atoms of Mn and m atoms of Fe in the first coordination shell. The presence of Mn atoms in the first Fe coordination shell is expected, since they provoke an abrupt decrease in the hyperfine magnetic field in the g phase [25,26]. However the presence of isolated FeMn clusters is discarded due to the obtained isomer shifts values. Concretely, in the mechanically alloyed Fe1xMnx system, a FCC single phase is obtained in the range x=20–70 at% Mn, and the Mo¨ssbauer spectra are characterized by a paramagnetic signal with isomer shifts, relative to a-Fe, negative and close to zero [25,27,28]. This fact is a consequence of the close electronic configurations of these elements, [Ar]3d64s2 for Fe and [Ar]3d54s2 for Mn, and therefore no large variations in the

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0.50 0.32

0.45 0.40

Isomer Shift (mm/s)

0.30

LS 0.35

0.28

0.30 0.25

0.26 0.20

HS 0.24

0.15 0.10

0.22 3.64

3.65

3.66 3.67 3.68 Lattice Parameter (Å)

3.69

3.70

Fig. 4. Lattice parameter dependence of the isomer shift. LS and HS correspond to the low- and high-spin states, respectively.

-3 40 Hz -4 64 175 Hz

-5 62

ln τ

Freezing temperature (K)

66

-6 60

1 kHz -7

58 -8 0

10

20 30 40 50 Milling time (hours)

60

72 h 2.5 kHz

70 0.0162

0.0164

0.0166

0.0168

1/Tf (K-1)

Fig. 5. Milling time dependence of the freezing temperature obtained from the peak position of the real part of the susceptibility at 175 Hz. For other frequencies in the considered range the variation of the peak position is less than 1 K.

Fig. 6. Variation of the freezing temperature in the classical plot of ln t versus 1=T f for the 72 h sample.

isomer shift are expected. However, such d values are considerably different to what we have found (see Fig. 3) in our system under similar milling conditions, suggesting the absence of pure and

isolated FeMn clusters. Concerning the formation of isolated FeCu clusters, a previous work on FeCu alloys prepared by vapor deposition over the entire range of composition [29], show an increase

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2.2

Effective Magentic Moment (µB)

Reciprocal Susceptibility x 103 (emu/g)-1

6 2500 Hz 40 Hz Linear fit

2.4

2.0 1.8 1.6 72 h

4 3

Banerjee Morris Morgownik Mulder Harders Cowlam This work

2 1

1.4 30

40

50

60

70

80

90

100 110 120

Fig. 7. Inverse susceptibility as a function of temperature for two different frequencies corresponding to the 72 h sample.

100

Mulder Banerjee Morgownik Clad Gray Wohlfarth Gibbs-Aged Gibbs-Quenched Ketelsen Tsunoda This work Linear fit

10 Cu100-xMnx

0.1

1 10 Mn Concentration (at.%)

0 1

Temperature (K)

Freezing Temperature (K)

5

100

Fig. 8. Log–log plot of the freezing temperature as a function of the Mn concentration.

of the isomer shift at 4.2 K up to a maximum value of 0.18 mm/s as the copper content increases, whereas in mechanically alloyed Fe25Cu75 [30], authors report an average isomer shift of 0.225 mm/s at 300 K after 24 h of milling in agreement with reported values in other diluted FeCu alloys [31]. Differently from this, our best estimate of the average isomer shift is 0.28(1) mm/s at 77 K in the steady state. Therefore, the

10 Mn Concentration (at.%)

100

Fig. 9. Semilog plot of the effective magnetic moment as a function of the Mn content.

occurrence of FeCurich clusters does not seem to be a predominant feature in our system. On the other hand, the presence of intermediate compositions like Fe50Cu50 does not take place since the reported mean hyperfine field value of 22.3 T at 300 K [32] contrasts with our well-defined paramagnetic scenario at 77 K. Finally, the room temperature hysteretic behavior and the specific magnetization at 0.9 T as a function of grain size are shown in Figs. 11 and 12, respectively. The obtained results suggest a grain size driven transition at around 8.5 nm characterized by a smooth decrease of the magnetization attributable to short-range magnetic interactions. Concomitantly, such a transition coincides with a sharp decrease of the coercive force resembling the occurrence of a superparamagnetic state for grain sizes below 8.5 nm. The observed hysteretic behavior was confirmed through low-temperature measurements (above the freezing temperature) with an external applied field of 3 T.

4. Conclusions Firstly, Mo¨ssbauer results at 77 K and the observed asymmetric doublet suggest a crossover between two well-distinguishable iron sites. One of

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0.998

12

0.996

10

Probability (a.u)

Relative Transmission

1.000

0.994

8 6 4 2 0

0.992

0

-8

5

-6

10 15 20 Hyperfine Field (T)

-4

25

30

-2 0 2 Velocity (mm/s)

4

6

8

Fig. 10. Mo¨ssbauer spectrum at 4.2 K of the 48 h sample and the corresponding Hfd of the magnetic component.

0.35

Specific Magnetization at 1 T (emu/g)

3.5

Coercive Field (kOe)

0.30

0.25

0.20

0.15

0.10

3.0 2.5 2.0 1.5 1.0 0.5 0.0

8.0

8.5

9.0

9.5

10.0 10.5

11.0 11.5 12.0

Grain Size (nm)

8.0

8.5

9.0

9.5

10.0

10.5 11.0

11.5

12.0

Grain Size (nm) Fig. 11. Coercive field as a function of grain size.

them undergoing a LS to HS transition at a critical unit-cell volume around 50 A˚3 (3.67 A˚oa o3.68 A˚) corresponding to a grain size of around 8.5 nm, which is in turn consistent with theoretical predictions [6,7]. Contrary to this, those iron sites exhibiting a linear increase of isomer shift with the average lattice parameter, presumably belong to

Fig. 12. Grain size dependence of the specific magnetization at 0.9 T.

the core of the grains where lattice expansion should be ruled out smoothly compared to grain boundaries where larger local distortions, a greater density of defects, and consequently greater volume instabilities are expected. Both iron sites

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are characterized by atomic and structural disorder with some few Mn atoms in the first neighborhood and mainly surrounded by Cu atoms. This fact is endorsed by the obtained broadenings of HFDs and microstructural data. Moreover, the positive FeCu enthalpy of mixing should limit the spatial extent of FeCu-rich clusters leading to stoichiometric gradients of the considered FeMnCu alloy and consequently to a non-homogeneous random solution. On the other hand, the negative CuMn enthalpy of mixing suggests the presence of CuMn clusters responsible for spin glass behavior. Secondly, magnetometric results allow proposing a scenario of weakly coupled and diluted magnetic clusters in the steady state. Such a state is characterized by large interatomic spacings with a unit-cell volume almost 10% larger than that of pure copper, and small grains of some few nanometers. Results revealed also a grain size-driven magnetic transition, presumably a multi-domain to single-domain transition in agreement with coercive results, at around 8.5 nm where short-range magnetic interactions play an important role.

Acknowledgments This work was supported by Universidad de Antioquia (Project Sostenibilidad-GES 20032004), ECOS-Nord and the COLCIENCIAS Project No. 1115-05-12409. One of the authors (J.R.) would like to thank the one year postdoctoral fellowship provided by Re´gion Pays de la Loire at the Universite´ du Maine-Le Mans (France), and to the Instituto de Ciencia de Materiales at Madrid where samples were prepared. We are very grateful to A.M. Mercier from Laboratoire des Fluorures of Universite´ du Maine UMR CNRS 6010 for performing XRD measurements. References [1] H.C. Herper, E. Hoffmann, P. Entel, Phys. Rev. B 60 (1999) 3839.

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