Magnetic random anisotropy model approach on nanocrystalline Fe88Sm9Mo3 and Fe88Sm9Mo3C alloys

Journal of Alloys and Compounds 584 (2014) 352–355

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Review

Magnetic random anisotropy model approach on nanocrystalline Fe88Sm9Mo3 and Fe88Sm9Mo3C alloys Z. Yamkane a,⇑, H. Lassri a, A. Menai a, S. Khazzan b, N. Mliki b, L. Bessais c a

LPMMAT, Université Hassan II – Ain Chock, Faculté des Sciences, B.P. 5366 Maarif, Casablanca, Morocco Laboratoire Matériaux Organisation et Propriétés, Faculté des Sciences de Tunis, Université de Tunis El Manar, 2092 Tunis, Tunisia c CMTR, ICMPE, UMR7182, CNRS  Université Paris Est, 2-8 rue Henri Dunant, F-94320 Thiais, France b

a r t i c l e

i n f o

Article history: Received 18 May 2013 Received in revised form 8 August 2013 Accepted 9 August 2013 Available online 7 September 2013 Keywords: Nanocrystalline alloy Magnetization Random magnetic anisotropy

a b s t r a c t The structure and magnetic properties of nanocrystalline Fe88Sm9Mo3 and Fe88Sm9Mo3C alloys have been investigated by means of X-ray diffraction coupled with magnetic measurements. We report here our study of approach to saturation magnetization. The results have been interpreted in the framework of random magnetic anisotropy model. From such analysis, some fundamental parameters have been extracted. We have determined the local magnetic anisotropy constant KL which are found to be 2.1  107 erg/cm3 for the nanocrystalline Fe88Sm9Mo3 alloy at 10 K. Carbon insertion leads to a decrease of the KL and magnetization. Ó 2013 Published by Elsevier B.V.

Contents 1. 2. 3.

4.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Structure and microstructure analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Magnetic properties and hyperfine parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. Random magnetic anisotropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1. Introduction Among the recently discovered nanocrystalline magnetic materials, Rare-earth-Iron (R-Fe) based intermetallics have attracted much interest. Rare earth brings high anisotropy and iron offers high Curie temperature and saturation magnetic moment. This combination corresponds to the basal ingredients required for high performance permanent magnets. It is well known that the net anisotropy in rare earth-Fe intermetallics is determined by the sum of the Fe sublattice and rare earth sublattice anisotropies. The anisotropy of the rare earth sublattice can be described by the product of the second-order crystal parameter and the second order Stevens coefficient on the basis of the single-ion model [1]. ⇑ Corresponding author. Tel.: +212 522 23 06 80/84; fax: +212 522 23 06 74. E-mail address: [email protected] (Z. Yamkane). 0925-8388/$ - see front matter Ó 2013 Published by Elsevier B.V. http://dx.doi.org/10.1016/j.jallcom.2013.08.065

352 353 353 353 354 354 355 355

These permanent magnets materials are attractive for several applications in the electro-technology hence much attention is being given to them. Moreover, after the insertion of light elements such as N, H, or C in the aforementioned intermetallics, it was found that most of fundamental characteristics are drastically modified. Then, the anisotropy field and the Curie temperature (TC) are enhanced. Nanocrystalline R-Fe materials could be obtained by melt-spinning, high energy ball milling and thin films prepared either by sputtering or by evaporated deposition techniques. There is a plethora of publications on such materials dealing with the preparation and study of their magnetic properties [2–5]. Herzer has shown that the random magnetic anisotropy model (RAM) explains the effective anisotropy energy even in nanocrystalline systems and predicted that the coercivity (HC) varies as the sixth power of the grain size (D) in the range of D is lower than the ex-

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2500 2000

Intensity (arb. units)

change correlation length (Lex) [6–8]. Since Herzer’s first application of the RAM to nanocrystalline Fe–Si–B–Nb–Cu alloy, this model has been employed widely to explain the origin of the magnetic softness in various nanocrystalline systems [7]. However, the original RAM only deals with single-phase systems. The properties of the nanomaterials are found to be different from their bulk counterpart. It is generally observed that for nanomaterials, both magnetization and the Curie temperature show a decrease. In this work, we present in detail our study on nanocrystalline Fe88Sm9Mo3 and Fe88Sm9Mo3C alloys and also discuss the magnetic properties. In their bulk state, these materials could be saturated with moderate applied fields of the order of 0.5 teslas, whereas in their nanostate, they do not show saturation even at 2 teslas. This has been reported by many authors working on nanogranular compounds who invoke several models to explain the small but definite positive slope in the M–H curve near the saturation point [9,10]. This slope is termed as high field susceptibility and some authors have analyzed this it to some extent. In this paper we would like to focus on this slope and discuss the anisotropy that it causes this. We also calculate, based on the existing models, some fundamental parameters of the nanocrystalline Fe88Sm9Mo3 and Fe88Sm9Mo3C alloys.

1500 1000 500 0 -500 -1000 36

40

44

48

52

56

60

64

2θ angle (deg) Fig. 1. Rietveld analysis of X-ray diagram of the carburated Fe88Sm9Mo3 annealed at 875 °C. Observed (black line), calculated (continuous red line) and difference patterns (blue line). Vertical marks from above to the bottom indicate the hkl positions of respectively P6/mmm and a-Fe phases. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

2. Experiment The samples were prepared by the technique of high energy ball milling and subsequent annealing. A mixture of high purity powders of Sm (99.99%) and prealloyed Sm2Fe17 were handled inside a glove box under high purity argon gas. Sm excess was added in order to maintain an overpressure of samarium on the samples. It is also necessary to compensate Sm loss during handling. Sm amount is optimized to get the final stoichiometry of Fe88Sm9Mo3. Mo powder is introduced with Sm2Fe17 and Sm powder. All powders were carefully weighed inside the box to give Sm–Fe–Mo mixtures and placed immediately into stainless steel containers. Next, the powders were ball milled in a high energy planetary ball mill Fritsch P7. The as-milled powder were wrapped in tantalum foil and sealed into silica tubes under vacuum, and then they were annealed at the appropriate temperature. Carbonation was achieved after reacting Fe–Mo–Sm powders with an appropriate amount of C14H10 powders. The mixtures of alloys and C14H10, in stoichiometric proportion, were annealed at 420 °C under vacuum for 48 h to ensure a good homogeneity of the carbon distribution. Mg chips, previously placed inside the reacting tube, absorbed the hydrogen overpressure resulting from the cracking of hydrocarbon [11]. X-ray diffraction (XRD) was carried out with Cu Ka radiation on a Brucker diffractometer. The data treatment was carried out by a Rietveld refinement as implemented in the FULLPROF computer code. This refinement gives the weight percentage of each of the coexisting phases, the line broadening leads to the autocoherent domain size D owing to Scherrer formula. In order to explore the microstructure of Fe88Sm9Mo3 alloys, transmission electron microscopy (TEM) studies were used. The observations were made using a JEOL 2010 FEG microscope operating at 200 kV. A slow scan Camera on a Gatan Imaging Filter was employed for image recording. The composition of the grains was analyzed using the EDX system attached to the microscope. Specimens for TEM were thinned using a Focused Ion Beam (FIB) type FEI Helios 600 Nanolab dual beam. The hysteresis loops were carried out in the temperature range 10–300 K, using a PPMS9 Quantum Design equipment and a maximum applied field of 90 kOe on powder in epoxy resin. The Mössbauer spectra were collected using a conventional 512 channel spectrometer with a source of 57Fe. The spectra were least-square fitted in assumption of lorentzian lines. The estimated errors are ±1 kOe for hyperfine field HHF, ±0.005 mm/s for isomer shift d and quadrupole interaction 2e.

3. Results and discussion 3.1. Structure and microstructure analysis The X-ray diffraction patterns of Fe88Sm9Mo3 and Fe88Sm9Mo3C alloys reveal a well crystalized phase. As an example, the Rietveld analysis of the carburated Fe88Sm9Mo3 phase and annealed at 875 °C is presented in Fig. 1. The Rietveld analysis of the XRD data using the FullProff program gives the density of studied phase to be 7.87 g/cm3. The X-ray diagram of the Fe88Sm9Mo3 shows a major phase (around 98%) typical of the hexagonal P6/mmm structure as ob-

Fig. 2. The local environment for carbon 3f octahedral site for Fe88Sm9Mo3. Mo atoms are located in 2e site in the P6/mmm structure [14].

tained previously [12,13]. a-Fe is only observed for Fe88Sm9Mo3C. It may result from a small decomposition of the Fe88Sm9Mo3 phase occurring during the carbonation process because no a-Fe was observed, neither on the X-ray diagram nor on the Mössbauer spectra before carbonation. The lattice parameters of the Fe88Sm9Mo3C alloys were determined from the corresponding Rietveld refinements for their nominal composition, according to the atomic distribution used previously to describe the P6/mmm unit cell of the noncarbonated alloys with one C randomly distributed (see Fig. 2) over all three 3f positions (1/2, 0, 0), (0, 1/2, 0), (1/2, 1/2, 0). Mo atoms are located in 2e site in the P6/mmm structure [14]. The structure has been refined on the basis of the vacancy model [13,15]. Rietveld refinement reveals a single phase: The structure results performed for the carbureted FeSmMo based alloy shows the presence of a main phase with the hexagonal P6/mmm space group. No iron-based additional phase is observed. Upon carbonation, the unit-cell volume increases. The results of the structure refinement performed for Fe88Sm9Mo3 and its carbide are listed in Table 1 with 0.72 Fe atom in 2e (0, 0, z) position, 2 Fe atoms in the 6l position (x, 2x, 0) and the 3g site (1/2, 0, 1/2)

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Table 1 a and c cell parameters, grain size volume V, RB and v2 factors from Rietveld fit for Fe88Sm9Mo3 and Fe88Sm9Mo3C alloys.

v2 x (6l) z (2e)

Fe88Sm9Mo3C

4.9103(2) 4.2006(3) 87.71 4.57 1.57 0.286 0.275

4.9942(3) 4.2355(5) 91.49 1.38 1.83 0.289 0.273

100 80 60

M (emu/g)

a (Å) c (Å) V (Å3) RB

Fe88Sm9Mo3

120

40 20 0 -20 -40 -60 -80 -100 -120 -15

-12

-9

-6

-3

0

3

6

9

12

15

H (kOe) Fig. 4. The hysteresis loop of the Fe88Sm9Mo3.

Fig. 3. HREM micrograph of the carburated Fe88Sm9Mo3.

occupied totally by Fe. The samarium site (0, 0, 0) is occupied by 0.64 atom. The grain size of the sample was determined from XRD patterns using Rietveld method by the Scherrer formula. It was found to be equal to about 11 nm. In order to investigate the nanostructure of the Fe88Sm9Mo3C alloy, transmission electron microscopy was performed. A HRTEM image corresponding to the sample is shown in Fig. 3. It is estimated from a series of TEM images that the mean grain size of the nanocrystalline alloy is about ten nanometers, which is close to the value calculated from the XRD.

Fig. 5. The 293 K Mössbauer spectrum of the Fe88Sm9Mo3.

used respectively for Sm, Fe, Mo. The mean hyperfine field for Fe88Sm9Mo3 phase and the mean isomer shift were, respectively 21.52 T, and 0.101 mm/s. 3.3. Random magnetic anisotropy

3.2. Magnetic properties and hyperfine parameters Fig. 4 shows, as an example, the hysteresis loop of the nanocrystalline recorded at 300 K. It can be seen that the nanocrystalline SmFeMo alloy has a relatively high saturation magnetization as MS = 980 emu/cm3. According to our studies on the relationship between the coercivity and the grain size [16], the coercivity is found to be closely related to the microstructure. The Mössbauer spectrum relative to the Fe88Sm9Mo3C alloy obtained at room temperature, together with the fits, is shown in Fig. 5. The atomic arrangements are rather complex due to the statistical distribution of Mo. Consequently, the experimental spectrum results from the convolution of numerous sextets. For the Mössbauer analysis, it takes into account the following from two criteria: (i) The most pertinent solution is the one which uses the smallest number of magnetic sites required to fit the spectra. (ii) The assignment of the hyperfine parameter set of a given sextet to its crystallographic site obeys the relationship between the isomer shift and the Wigner–Seitz Cell (WSC) volumes. The WSC volumes have been calculated by means of Dirichlet domains and coordination polyhedra for each crystallographic family [14,15]. The radius values of 1.81, 1.26, 1.39 Å have been

Let’s remember that Random Magnetic Anisotropy (RMA) was first proposed by Harris et al. [17] to explain the anisotropy found in some amorphous alloys and particularly those containing rare earth. They attributed this anisotropy to the topological disorder. The random anisotropy according to this model arises out of crystal field effects of local sites. Since there is a topological disorder the symmetry axis of the sites are randomly oriented. Thus, there is no single direction of either easy or hard axis. These axis are spread in all directions making it difficult to saturate. Based on their Hamiltonian, Chudnovsky et al. [18–20] proposed a model to analyze the approach to saturation. This model was applied successfully to explain the results by several authors. We had used this model to analyze our results on several rare earth based amorphous alloys and obtained various fundamental parameters such as local anisotropy and the correlation lengths [21]. We propose to apply similar ideas to the nanomaterials. The application of this random anisotropy model to nanomaterials could be justified as follows. The nanograins due to their low dimension have a lower symmetry in the regions particularly near the surface, resulting in a kind of uniaxial anisotropy. As the grains are oriented at random, there is no alignment of this axis which

Z. Yamkane et al. / Journal of Alloys and Compounds 584 (2014) 352–355

Table 2. In the nanocrystalline alloys, the magnetic anisotropy constant calculated from the law of approach to saturation (Table 2) is near than that obtained for the Sm2Fe17xGax compounds [22]. According to the single ion anisotropy model, the magnetic anisotropy of Fe88Sm9Mo3, KL is the sum of the Sm sublattice anisotropy, KSm, and the Fe sublattice anisotropy KFe. The small reduction of local magnetic anisotropy in Fe88Sm9Mo3C alloy can be attributed to the presence of the small amount of soft magnetic a-Fe phase, detected by XRD, which results from the small decomposition of the Fe88Sm9Mo3 phase occurring during the carbonation process. Beside the magnetovolumic and electronic effects on the magnetic properties due to the insertion of carbon, the small amount of soft magnetic a-Fe phase yields enhancement of the Curie temperature and intergrain exchange coupling strength.

1000

M(emu/cm3)

800

600

Fe 88 Sm 9 Mo3 Fe 88 Sm 9 Mo3C

400

200

0 0

20

40

60

80

100

H (kOe)

4. Conclusion

Fig. 6. The magnetization versus magnetic field for the Fe88Sm9Mo3 and Fe88Sm9Mo3 alloys at 10 K.

Table 2 Some magnetic parameters of Fe88Sm9Mo3 and Fe88Sm9Mo3C compounds at 10 K.

Fe88Sm9Mo3 Fe88Sm9Mo3C

MS(emu/cm3)

Hr (kOe)

Hu + Hex (kOe)

KL (107 erg/cm3)

980 690

43 54

17.4 21.7

2.1 1.86

then leads to a spread in their direction. This is then analogous to the amorphous materials where the topological disorder leads to a spread in the axis of symmetry. The essential difference of course is that in the amorphous alloys the structural correlation length is of the order of 1 or 2 nm whereas in nanomaterials the grain size is an order of magnitude bigger. This would result in some differences in details and could affect the magnitude of the anisotropy. We briefly describe below the model we have used. We can describe the approach to magnetic saturation by the formula [18–20]:

MðHÞ ¼ MS 1 

a2 ¼

a2 ðH þ Hu þ Hex Þ2

 2 H2r 1 2K L ¼ 15 15 M S

355

!

We have prepared the nanocrystalline Fe88Sm9Mo3 and Fe88Sm9Mo3C alloys by ball milling technique and carried out magnetization study. We have shown that it is possible to extend the application of random magnetic anisotropy model originally developed for amorphous alloys to the nanocrystalline materials. The model gives a good fit of the experimental M(H). Besides the M(H) calculation, we have also determined some fundamental parameters such as random anisotropy fields and local random anisotropy constant. References [1] [2] [3] [4] [5] [6] [7] [8] [9]

ð1Þ

[10] [11] [12]

ð2Þ

where H is the applied magnetic field in (kOe), MS is the saturation magnetization in emu/g, Hu is the coherent field, Hex is the exchange field, Hr is the random magnetic anisotropy field and a2 is a constant which is a function of the local magnetic anisotropy constant KL and MS. The magnetization curves for all samples are found to fit well Eq. (1) as shown in Fig. 6. The values of the parameters MS and a2, obtained from the fitting at 10 K, are listed in Table 2. These values of MS, and a2 obtained were used to determine KL using Eq. (2). Values of the parameters obtained by this way are also displayed on

[13] [14] [15] [16] [17] [18] [19] [20] [21] [22]

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