Magnetic random anisotropy model approach on nanocrystalline Fe88Sm9Mo3 and Fe88Sm9Mo3C alloys

Review

Magnetic random anisotropy model approach on nanocrystalline Fe 88 Sm 9 Mo 3 and Fe 88 Sm 9 Mo 3 C 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

b

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

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 Fe

88

Sm

9

Mo

3

and Fe

88

Sm

9

Mo

3

C 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 K

L

which are found to be 2.1 10

⁷

erg/cm

³

for the nanocrystalline Fe

88

Sm

9

Mo

3

alloy at 10 K. Carbon insertion leads to a decrease of the K

L

and magnetization.

Ó 2013 Published by Elsevier B.V.

Contents

1. Introduction . . . 352

2. Experiment . . . 353

3. Results and discussion . . . 353

3.1. Structure and microstructure analysis . . . 353

3.2. Magnetic properties and hyperfine parameters . . . 354

3.3. Random magnetic anisotropy . . . 354

4. Conclusion . . . 355

References . . . 355

1. Introduction

Among the recently discovered nanocrystalline magnetic mate- rials, 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].

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 (T

C

) are enhanced.

Nanocrystalline R-Fe materials could be obtained by melt-spin- ning, 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 prepa- ration and study of their magnetic properties [2–5]. Herzer has shown that the random magnetic anisotropy model (RAM) ex- plains the effective anisotropy energy even in nanocrystalline sys- tems and predicted that the coercivity (H

_C

) varies as the sixth power of the grain size (D) in the range of D is lower than the ex- 0925-8388/$ - see front matter

Ó

2013 Published by Elsevier B.V.

http://dx.doi.org/10.1016/j.jallcom.2013.08.065

⇑ Corresponding author. Tel.: +212 522 23 06 80/84; fax: +212 522 23 06 74.

E-mail address: zinebyamkane@yahoo.fr (Z. Yamkane).

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

Contents lists available at ScienceDirect

Journal of Alloys and Compounds

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / j a l c o m

change correlation length (L

ex

) [6–8]. Since Herzer’s first applica- tion of the RAM to nanocrystalline Fe–Si–B–Nb–Cu alloy, this mod- el has been employed widely to explain the origin of the magnetic softness in various nanocrystalline systems [7]. However, the origi- nal RAM only deals with single-phase systems. The properties of the nanomaterials are found to be different from their bulk coun- terpart. It is generally observed that for nanomaterials, both mag- netization and the Curie temperature show a decrease.

In this work, we present in detail our study on nanocrystalline Fe

₈₈

Sm

₉

Mo

₃

and Fe

₈₈

Sm

₉

Mo

₃

C alloys and also discuss the mag- netic properties. In their bulk state, these materials could be satu- rated 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 nano- granular compounds who invoke several models to explain the small but definite positive slope in the M–H curve near the satura- tion point [9,10]. This slope is termed as high field susceptibility and some authors have analyzed this it to some extent. In this pa- per 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 Fe

88

Sm

9

Mo

3

and Fe

88

Sm

9

Mo

3

C alloys.

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 preal- loyed Sm

2

Fe

17

were handled inside a glove box under high purity argon gas. Sm ex- cess 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 Fe

88

Sm

9

Mo

3

. Mo powder is introduced with Sm

2

Fe

17

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 C

14

H

10

powders. The mixtures of alloys and C

14

H

10

, 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, ab- sorbed the hydrogen overpressure resulting from the cracking of hydrocarbon [11].

X-ray diffraction (XRD) was carried out with Cu K a radiation on a Brucker dif- fractometer. The data treatment was carried out by a Rietveld refinement as imple- mented in the FULLPROF computer code. This refinement gives the weight percentage of each of the coexisting phases, the line broadening leads to the auto- coherent domain size D owing to Scherrer formula.

In order to explore the microstructure of Fe

88

Sm

9

Mo

3

alloys, transmission elec- tron 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 ana- lyzed 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 spec- trometer with a source of

⁵⁷

Fe. The spectra were least-square fitted in assumption of lorentzian lines. The estimated errors are ±1 kOe for hyperfine field H

HF

,

±0.005 mm/s for isomer shift

d

and quadrupole interaction 2 e .

3. Results and discussion

3.1. Structure and microstructure analysis

The X-ray diffraction patterns of Fe

88

Sm

9

Mo

3

and Fe

88

Sm

9

Mo

3

C alloys reveal a well crystalized phase. As an example, the Rietveld analysis of the carburated Fe

88

Sm

9

Mo

3

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/cm

³

.

The X-ray diagram of the Fe

88

Sm

9

Mo

3

shows a major phase (around 98%) typical of the hexagonal P6/mmm structure as ob-

tained previously [12,13]. a -Fe is only observed for Fe

88

Sm

9

Mo

3

C.

It may result from a small decomposition of the Fe

88

Sm

9

Mo

3

phase occurring during the carbonation process because no a -Fe was ob- served, neither on the X-ray diagram nor on the Mössbauer spectra before carbonation.

The lattice parameters of the Fe

88

Sm

9

Mo

3

C alloys were deter- mined from the corresponding Rietveld refinements for their nom- inal 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 mod- el [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 Fe

88

Sm

9

Mo

3

and its car- bide 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)

36 40 44 48 52 56 60 64

-1000 -500 0 500 1000 1500 2000 2500

In te n s it y (a rb . u n its)

2 θ angle (deg)

Fig. 1.

Rietveld analysis of X-ray diagram of the carburated Fe

88

Sm

9

Mo

3

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.)

Fig. 2.

The local environment for carbon 3f octahedral site for Fe

88

Sm

9

Mo

3

. Mo atoms are located in 2e site in the P6/mmm structure [14].

Z. Yamkane et al. / Journal of Alloys and Compounds 584 (2014) 352–355 353

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 Fe

88

Sm

9

Mo

3

C alloy, transmission electron microscopy was performed. A HRTEM image corresponding to the sample is shown in Fig. 3. It is esti- mated 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.

3.2. Magnetic properties and hyperfine parameters

Fig. 4 shows, as an example, the hysteresis loop of the nanocrys- talline recorded at 300 K. It can be seen that the nanocrystalline SmFeMo alloy has a relatively high saturation magnetization as M

S

= 980 emu/cm

³

. According to our studies on the relationship be- tween the coercivity and the grain size [16], the coercivity is found to be closely related to the microstructure.

The Mössbauer spectrum relative to the Fe

88

Sm

9

Mo

3

C alloy ob- tained at room temperature, together with the fits, is shown in Fig. 5. The atomic arrangements are rather complex due to the sta- tistical distribution of Mo. Consequently, the experimental spec- trum 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 spec- tra. (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

used respectively for Sm, Fe, Mo. The mean hyperfine field for Fe

88

Sm

9

Mo

3

phase and the mean isomer shift were, respectively 21.52 T, and 0.101 mm/s.

3.3. Random magnetic anisotropy

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] pro- posed 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 param- eters 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 nanomate- rials 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

Table 1

a and c cell parameters, grain size volume V, R

B

and v

²

factors from Rietveld fit for Fe

88

Sm

9

Mo

3

and Fe

88

Sm

9

Mo

3

C alloys.

Fe

88

Sm

9

Mo

3

Fe

88

Sm

9

Mo

3

C

a (Å) 4.9103(2) 4.9942(3)

c (Å) 4.2006(3) 4.2355(5)

V (Å

³

) 87.71 91.49

R

B

4.57 1.38

v

²

1.57 1.83

x (6l) 0.286 0.289

z (2e) 0.275 0.273

Fig. 3.

HREM micrograph of the carburated Fe

88

Sm

9

Mo

3

.

-15 -12 -9 -6 -3 0 3 6 9 12 15

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

M (emu/ g)

H (kOe)

Fig. 4.

The hysteresis loop of the Fe

88

Sm

9

Mo

3

.

Fig. 5.

The 293 K Mössbauer spectrum of the Fe

88

Sm

9

Mo

3

.

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

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 M

S

1 a

2

ðH þ H

u

þ H

ex

Þ

²

!

ð1Þ

a

2

¼ H

²_r

15 ¼ 1

15 2K

L

M

S

2

ð2Þ

where H is the applied magnetic field in (kOe), M

S

is the saturation magnetization in emu/g, H

u

is the coherent field, H

ex

is the exchange field, H

_r

is the random magnetic anisotropy field and a

₂

is a constant which is a function of the local magnetic anisotropy constant K

L

and M

S

. The magnetization curves for all samples are found to fit well Eq. (1) as shown in Fig. 6. The values of the parameters M

S

and a

2,

obtained from the fitting at 10 K, are listed in Table 2. These values of M

S

, and a

2

obtained were used to determine K

L

using Eq. (2). Val- ues of the parameters obtained by this way are also displayed on

Table 2. In the nanocrystalline alloys, the magnetic anisotropy con- stant calculated from the law of approach to saturation (Table 2) is near than that obtained for the Sm

2

Fe

17x

Ga

x

compounds [22].

According to the single ion anisotropy model, the magnetic anisot- ropy of Fe

88

Sm

9

Mo

3

, K

L

is the sum of the Sm sublattice anisotropy, K

Sm

, and the Fe sublattice anisotropy K

Fe

.

The small reduction of local magnetic anisotropy in Fe

88

Sm

9

Mo

3

C 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 Fe

88

Sm

9

Mo

3

phase occurring during the carbonation process. Beside the magnetovol- umic 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 ex- change coupling strength.

4. Conclusion

We have prepared the nanocrystalline Fe

88

Sm

9

Mo

3

and Fe

88

Sm

9

Mo

3

C 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] K.H.J. Buschow, Rep. Prog. Phys. 54 (1991) 1123.

[2] M.D. Coey, D. Givord, A. Lienard, J. Rebouillat, J. Phys. F 11 (1981) 2707.

[3] E. Burzo, Rom. Rep. Phys. 60 (2008) 701.

[4] E. Burzo, A. Chelkovski, H.R. Kirchmayr, vol. 19d2 (Landolt-Börnstein Handbuch, 1990).

[5] C. Djega-Mariadassou, L. Bessais, A. Nandra, E. Burzo, Phys. Rev. B 68 (2003) 024406.

[6] G. Herzer, IEEE Trans. Mag. 25 (1989) 3327–3329.

[7] G. Herzer, IEEE Trans. Mag. 26 (1990) 1397–1402.

[8] H.Q. Guo, T. Reininger, H. Kronmüller, M. Rapp, K.V. Skumrev, Phys. Status Solidi A 127 (1991) 519–527.

[9] J. Dash, S. Prasad, N. Venkataramani, R. Krishnan, P. Kishan, N. Kumar, S.D.

Kulkani, S.K. Date, J. Appl. Phys. 86 (1999) 3303.

[10] L. Bessais, C.D. Mariadassou, H. Lassri, N. Mliki, J. Appl. Phys. 106 (2009) 3904.

[11] L. Bessais, S. Sab, C. Djega-Mariadassou, J.M. Grenèche, Phys. Rev. B 66 (2002) 054430.

[12] L. Bessais, C. Djega-Mariadassou, A. Nandra, M.D. Appay, E. Burzo, Phys. Rev. B 69 (2004) 64402.

[13] S. Khazzan, N. Mliki, L. Bessais, J. Appl. Phys. 105 (2009) 103904.

[14] S. Khazzan, N. Mliki, L. Bessais, C. Djega-Mariadassou, J. Magn. Magn. Mater.

322 (2010) 224.

[15] L. Bessais, C. Djega-Mariadassou, Phys. Rev. B 63 (2001) 054412.

[16] L. Bessais, C. Djega-Mariadassou, E. Koch, J. Phys.: Condens. Matter 14 (2002) 8111.

[17] R. Harris, M. Pilschke, M.J. Zukermann, Phys. Rev. Lett. 31 (1973) 160.

[18] E.M. Chudnovsky, W.M. Saslow, R.A. Serota, Phys. Rev. B 33 (1986) 251.

[19] E.M. Chudnovsky, J. Appl. Phys. 64 (1988) 5770.

[20] E.M. Chudnovsky, J. Magn. Magn. Mater. 79 (1989) 127.

[21] H. Lassri, R. Krishnan, J. Magn. Magn. Mater. 157 (1992) 104.

[22] Y.D. Zhang, J.I. Budnick, W.A. Hines, B.G. Shen, Z.H. Cheng, J. Appl. Phys. 85 (1999) 4663.

0 20 40 60 80 100

0 200 400 600 800 1000

Fe ₈₈ Sm ₉ Mo ₃ Fe ₈₈ Sm ₉ Mo ₃ C M(emu/cm

3

)

H (kOe)

Fig. 6.

The magnetization versus magnetic field for the Fe

88

Sm

9

Mo

3

and Fe

88

Sm

9-

Mo

3

alloys at 10 K.

Table 2

Some magnetic parameters of Fe

88

Sm

9

Mo

3

and Fe

88

Sm

9

Mo

3

C compounds at 10 K.

M

S

(emu/cm

³

) H

r

(kOe) H

u

+ H

ex

(kOe) K

L

(10

⁷

erg/cm

³

)

Fe

88

Sm

9

Mo

3

980 43 17.4 2.1

Fe

88

Sm

9

Mo

3

C 690 54 21.7 1.86

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