High-field magnetic properties in Nd–Fe intermetallic compound

Journal of Magnetism and Magnetic Materials 331 (2013) 225–231

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High-field magnetic properties in Nd–Fe intermetallic compound Wei Wang a,n, Haijun Xu a, Xiaomiao Xu a, Yajun Zhang b, Feng Li a a b

State Key Laboratory of Chemical Resource Engineering and School of Science, Beijing University of Chemical Technology, Beijing 100029, China College of Mechanical and Electrical Engineering, Beijing university of Chemical Technology, Beijing 100029, China

a r t i c l e i n f o

abstract

Article history: Received 28 August 2012 Available online 27 November 2012

On the basis of the molecular field theory, an improved two-sublattice model is applied to analyze the magnetic properties in Nd2Fe17Hx (x ¼ 0, 3 and 4.9) under high magnetic fields. As is known, two types of magnetic ions exist in Nd–Fe intermetallic compound. Here, the exchange interactions of Nd–Nd, Nd–Fe and Fe–Fe are taken into account. And, as to the ferromagnetic compounds, we define the effective exchange field Hex ¼ nweffHe, where n the molecular field coefficient, weff the effective magnetic susceptibility, and He the external magnetic field. Meanwhile, the field-dependence characteristics of magnetization at different temperatures are discussed. Also, the parameters aA and aB, associated with v and weff, are defined, and the field-dependence, temperature-dependence characteristics are analyzed. Additionally, it is confirmed that the hydrogen content shows great influence on the magnetic properties in Nd2Fe17Hx compound. & 2012 Elsevier B.V. All rights reserved.

Keywords: Two-sublattice model Exchange interaction field High magnetic field Intermetallic compound

1. Introduction In the past decades, much attention has been paid to the development and search for new permanent magnetic materials. As a kind of high performance permanent magnets, a lot of theoretical and experimental studies have been carried out on rare-earth (R) transition metal intermetallic compounds [1–4]. Particularly, great interests are shown on R2Fe17Zx (Z¼H, C, or N) compounds from both fundamental and an applied point of view, for the insertion of light elements Z will greatly affect the magnetic behaviors of R2Fe17 compound. Additionally, due to the occurrence of some novel magnetic properties under high magnetic fields, it is found that more and more researchers begin to focus on the highfield magnetic behaviors in intermetallic compounds and other ferromagnetic or ferrimangnetic materials, where some novel magnetic behaviors are experimentally revealed [5–7]. Of course, with the development of experimental technology, the associated theories on magnetic properties in intermetallic compounds are gradually brought out. It is known that, currently, two kinds of theoretical models are used to analyze the magnetic properties in intermetallic compounds. One is the classical twosublattice model based on molecular field theory, and, another is the single-ion model on the basis of quantum theory. As is known, the molecular field model was introduced to analyze the experimental data of RFe3 and R6Fe23 intermetallic compounds in 1982 by Herbst and Croat [8]. After that, it has been successfully applied to explain

n

Corresponding author. E-mail addresses: [email protected], [email protected] (W. Wang).

0304-8853/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jmmm.2012.11.032

the magnetic properties of many rare-earth transition metal intermetallic compounds. In 2002, Zhang et al. analyzed the temperature dependence of magnetization in R2Fe17C, R3Co11B4, R2Fe14B, ReFe10V2, RFe10V2Nx and other intermetallic compounds using molecular field theory [9,10]. Then, Prasongkit presented a modified two-sublattice model to excellently fit the experimental results in the intermetallic compounds GdCo4 xNixAl [11]. As to the single-ion model, Xu gave a success explanation of the magnetocrystalline anisotropy of R2Fe17Nx compounds [12]. Also, on the basis of the single-ion model, Han reported a series of studies on the magnetic properties of R2Co17 and R2Fe17 compounds [13]. However, it is found that, due to the complex of physical mechanism under high magnetic field condition, some experimental results cannot be successfully explained by available theoretical model [14,15]. Thus, obviously, new theoretical models should be suggested to study the magnetizing mechanism of these novel or abnormal magnetic behaviors in high magnetic field. In our previous paper, to illuminate the magnetic behavior in rare-earth iron garnets under high magnetic fields, based on molecular field theory, a new three-sublattice model is presented, where the theoretical calculations exactly fit the experimental data [16]. As to the paramagnetic rare-earth gallium garnet, we extended the molecular field theory, where the magnetic properties of two magnetic sublattices are discussed [17]. Then, according to the theoretical ideas in Refs. [16,17], an improved two-sublattice model will be put forward to interpret the high-field magnetic characteristics in rare-earth intermetallic compounds. It is noticed that, recently, Isnard and Guillot experimentally investigate the high-field magnetic properties of Nd2Fe17Hx (x¼0, 3 and 4.9) where the magnetization curves, the magnetic anisotropies

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and the effect of the hydrogen insertion on the magnetic characteristics were discussed [18]. Meanwhile, a expression on the field dependence of magnetization is presented, M(H)¼Ms þa/H2, but, a detailed explanation on the origin of the expression has not been given. Then, the main aim of this work is to establish a theoretical model for interpreting the experimental phenomena reported by Isnard. Also, it is known that the researchers of Refs. [9,10] mainly focused on the temperature dependence of magnetization in intermetallic compounds. Now, in this paper, much attention will be paid to the field-dependence of magnetization in intermetallic compounds. Additionally, the magnetic characteristics of two sublattices in Nd2Fe17Hx compounds will be discussed.

2. Theoretical method Nd2Fe17 has Th2Zn17-type rhombohedral structure with space group R3m with Fe atoms occupying four different sites (6c, 9d, 18f and 18h) while a unique 6c site is occupied by Nd atoms [19]. Then, according to molecular field theory, two magnetically nonequivalent sublattices, labeled as A and B, can be assumed, which corresponds to Nd and Fe sublattices. So, the total magnetization M in Nd2Fe17 can be defined as the sum of the magnetization of A and B magnetic sublattices. That is, in this two-sublattice system, the following expression can be obtained, M ¼ MA þ MB

ð1Þ

where MA and MB denote the magnetization of Nd and Fe magnetic sublattices, respectively. In terms of the Brillouin function, MA and MB can be expressed as

ð2Þ M A ¼ M SA  B yA ¼ NA J A g JA mB  B yA

M B ¼ MSB  B yA ¼ NB JB g JB mB  B yB

which can be written as


B yA ¼ ½ 2JA þ1 =2J A  coth½ 2J A þ 1 =2J A Þ  yA 

 1=2JA coth½ 1=2J A  yA 

ð4Þ



¼ ½ 2J B þ 1 =2JB  coth½ 2J B þ1 =2J B Þ  yB 

 1=2JB coth½ 1=2JB  yB 

ð5Þ

B yB

Meanwhile, the expressions of the parameters yA and yB are shown as yA ¼

J A g JA mB HA kB T

ð6Þ

yB ¼

J B g JB mB HB kB T

ð7Þ

where HA and HB are the total effective fields in A and B sublattices. According to the molecular field theory, the total effective fields acting on the Nd and Fe magnetic sublattices in Nd2Fe17Hx compounds can be expressed, respectively, as follows. HA ¼ He þ HiA ¼ He þ lAA M A þ lAB MB

ð8Þ

HB ¼ He þ HiB ¼ He þ lBB MB þ lBA M A

ð9Þ

Here, HiA and HiB are the exchange fields of A and B sublattices. And, lAA, lAB, lBB and lBA are the molecular field coefficients, which describe the Nd–Nd, Nd–Fe and Fe–Fe magnetic interactions, respectively. Meanwhile, based on the molecular field theory, lAB ¼ lBA. Then, as to the expressions of MA and MB under high magnetic fields, referring to our previous paper [20], an effective magnetic susceptibility can be introduced. So, MA ¼ wAHe, and, MB ¼ wBHe. Thus, Eqs. (6) and (7) can be rewritten as yA ¼

J A g JA mB ð1þ aA ÞHe kB T

ð10Þ

yB ¼

J B g JB mB ð1 þ aB ÞHe kB T

ð11Þ

ð3Þ

where NA and NB represent the numbers of ions contribution to magnetization per unit volume of A and B magnetic sublattices, JA and JB are the individual angular moments, gJA and gJA are the Lander factors. Here, B(yA) and B(yB) are the Brillouin functions,




Here, aA ¼ lAAwA þ lABwB, and aB ¼ lBBwB þ lBAwA. In this case, the coefficients aA and aB are associated with the molecular field coefficients and the effective magnetic susceptibilities, which

40

Magnetization (

B/mole)

35 30 25 20 15 10 5 0

0

50

100 Magnetic Field (kOe)

150

200

Fig. 1. The field-dependence of magnetization in Nd2Fe17Hx (x¼ 0, 3, 4.9) at 4.2 K when the external magnetic field is perpendicular to the alignment direction (the insets are the field-dependence magnetization of Nd and Fe sublattices).

W. Wang et al. / Journal of Magnetism and Magnetic Materials 331 (2013) 225–231

implies that aA and aB are the functions of the temperature T and the external magnetic field He. Therefore, substituting Eqs. (10) and (11) into Eqs. (2)–(5), the magnetizations of A and B sublattices can be calculated. Finally, from Eq. (1), inserting the corresponding values of MA and MB, the total magnetization of Nd2Fe17Hx can be presented.

3. Results and discussion As mentioned above, Nd and Fe ions are the magnetic ions contribution to the magnetic properties of Nd2Fe17Hx compounds. Then, as for the ground configuration (4f13) of the free Nd ion, the ground term is 4I term. In our calculations, only the lowest

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multiplet 4I9/2 of the ground term is considered. That is, the orbit angular momenta LA ¼6, SA ¼ 3/2, JA ¼9/2 and gJA ¼8/11. And, as to Fe ion, JB ¼ 5/2, gJB ¼2. Here, substituting these parameters into the above equations, the magnetic characteristics of Nd2Fe17Hx can be studied. It is known that the insertion of hydride in Nd2Fe17 will induce important modification of the exchange interaction, for, with the variation of the contents of hydride, two different sites (octahedral or tetrahedral site) can be occupied. So, it is obvious that the exchange fields in Nd2Fe17Hx will change with the variation of the contents x. Accordingly, it will lead to the variety of the values of aA and aB in Eqs. (10) and (11). Then, on the basis of the above theory, by searching the appropriate aA and aB, the fielddependence and temperature-dependence characteristics of

Fig. 2. The field-dependence of magnetization in Nd2Fe17Hx (x¼ 0, 3, 4.9) at 4.2 K when the external magnetic field is parallel to the alignment direction (the insets are the field-dependence magnetization of Nd and Fe sublattices).

Fig. 3. The magnetization of Nd2Fe17H4.9 at 300 K when the external magnetic field is perpendicular and parallel to the alignment direction (the insets are the fielddependence magnetization of Nd and Fe sublattices).

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Fig. 4. The field-dependence of aA and aB at 4.2 K under different magnetic fields for the external fields perpendicular to the alignment direction.

Fig. 5. The field-dependence of aA and aB at 4.2 K under different magnetic fields for the external fields parallel to the alignment direction.

Fig. 6. The variations of the values of aA and aB with the magnetic fields at 300 K in Nd2Fe17H4.9 for the fields perpendicular and parallel to the alignment directions.

W. Wang et al. / Journal of Magnetism and Magnetic Materials 331 (2013) 225–231

magnetization in Nd2Fe17Hx can be obtained for the external magnetic field perpendicular or parallel to the alignment direction at different temperatures under high magnetic fields. Figs. 1 and 2 give the field-dependence magnetization in Nd2Fe17Hx (x¼ 0, 3, 4.9) at 4.2 K when the external magnetic field is perpendicular and parallel to the alignment direction, respectively. It can be seen that the theory show good agreements with the experiments. Moreover, from the inserted figures in Figs. 1 and 2, the magnetic moments of Nd and Fe sublattices are also calculated at 4.2 K. Seen from Fig. 1, in lower magnetic fields, the magnetization in Nd2Fe17 is larger than those in Nd2Fe17H3 and Nd2Fe17H4.9, while, with the increase of the magnetic fields, the magnetic moments of Nd2Fe17H4.9 increase rapidly, and quickly tend to saturation. Also, it is worthy to note that, as to Nd2Fe17 and Nd2Fe17H3, a transition point appears at about 75 kOe. The following analyses will point out that these phenomena occur because of the change of the exchange field with the insertion of H. On the other hand, from the calculations of the magnetic moments in Nd and Fe magnetic sublattices in Fig. 1, the following conclusions can be drawn. (1) As to Nd sublattice, when He o50 kOe, an apparent difference of the magnetic moments in these three compounds can be seen. While, at He 450 kOe, the magnetizations become saturated. (2) Different with the properties of Nd sublattice, with the increase of the magnetic fields, the magnetization of Fe sublattice is obviously larger in Nd2Fe17H4.9 than those in Nd2Fe17 and Nd2Fe17H3, which implies that the insertion of hydride has greater effects on the magnetization in Fe sublattice than that in Nd sublattice at 4.2 K when the external magnetic field is perpendicular to the alignment direction. Compared with Fig. 2, when He is parallel to the alignment direction, the insertions of hydride show little effects on the magnetic moments in the three compounds. Meanwhile, at 4.2 K, the saturated magnetization can be seen under very low magnetic fields. Similarly, very little difference of the magnetization between Nd and Fe sublattices can be shown. The above results also indicate the discrepancy of the magnetization when He is perpendicular and parallel to the alignment directions. Then, to further illuminate the discrepancy, Fig. 3 gives the magnetization of Nd2Fe17H4.9 at 300 K under the above two conditions. It is found that, when He is lower about 30 kOe, the magnetizations present markedly anisotropic properties. However, with the increase of the magnetic fields, the magnetization tends to saturation, and an isotropy of the magnetization is shown. Also, from the inserted figures, at high temperature 300 K, the Nd sublattice shows obvious paramagnetic characteristic, whereas, the Fe sublattice is ferromagnetic, and inclined to saturation when He 430 kOe. In addition, the magnetization of Nd sublattice presents isotropy, while, at to Fe sublattice, the isotropy can be seen when the external magnetic field is higher than 30 kOe. As mentioned above, these noticeable phenomena result from the variation of exchange interaction in Nd2Fe17Hx. In our theory,

229

the parameters aA and aB can reflect the properties of exchange interaction. So, in our calculations, it is very important to search appropriate values of aA and aB. Figs. 4 and 5 give the values of aA and aB at 4.2 K under different magnetic fields for the external fields perpendicular and parallel to the alignment directions, respectively. Here, it is worthy to note that the values of aA and aB decrease with the increase of external magnetic fields, moreover, aA and aB rapidly decrease in lower magnetic fields, which is obviously different from the conclusions in YbIG obtained from Ref. [20]. Additionally, the inequality of magnetization in A and B sublattice directly leads to the difference of the values of aA and aB, then, it can be seen that, at 4.2 K, aA o0 for the external field perpendicular and parallel to the alignment directions. However, only when He is perpendicular, aB o0, and aB changes from positive to negative with the increase of the magnetic fields when He is parallel. The variation of aB also implies that the directions of magnetization apparently affect on the exchange interaction of B Table 2 The values of the parameters P1, P2, P3 and P4 of aA and aB in Nd2Fe17H4.9 at 300 K for the external fields perpendicular and parallel to the alignment directions. Perpendicular

P1 P2 P3 P4

Parallel

aA

aB

aA

aB

 0.82327  0.17678 0.00132  3.25E-06

 2.08648 935.242  4064.78 5738.342

 0.6557  0.13589 7.75E-04  1.55E-06

 0.30346 716.9388  34.98441  1237.559

Fig. 7. The magnetizations of Nd2Fe17H3 at different temperatures for He perpendicular to the alignment direction.

Table 1 The values of the parameters P1, P2, P3 and P4 of aA and aB in Nd2Fe17, Nd2Fe17H3 and Nd2Fe17H4.9 at 4.2 K for the external fields perpendicular and parallel to the alignment directions. Perpendicular Nd2Fe17

P1 P2 P3 P4

Parallel Nd2Fe17H3

Nd2Fe17H4.9

Nd2Fe17

Nd2Fe17H3

Nd2Fe17H4.9

aA

aB

aA

aB

aA

aB

aA

aB

aA

aB

aA

aB

 0.88112  0.15656 0.00106  2.42E-06

 0.9663 10.56527  45.41007 55.56343

 1.0562  0.17776 0.00133  3.18E-06

 0.98461 12.11432  33.94436 2.10541

0.61026  0.17642 0.00111  2.34E-06

 1.02458 19.72679  203.07893 717.65995

 0.26236  0.16673 0.00111  2.45E-06

 1.01125 17.12195  85.93202 294.64895

 0.731  0.1685 0.00122  2.91E-06

 0.99864 15.40906  38.44318 69.72849

 0.33753  0.14955 8.93E-04  1.77E-06

 1.00616 16.6231  80.20551 217.74475

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Fig. 8. The field-dependence of aA and aB in Nd2Fe17H3 at different temperatures for He perpendicular to the alignment direction.

sublattice. Actually, they are worthy to further experimentally and theoretically study. Fig. 6 presents the variations of the values of aA and aB with the magnetic fields at 300 K in Nd2Fe17H4.9 for the fields perpendicular and parallel to the alignment directions, where an obvious anisotropy of aA and aB can be seen under low magnetic fields. And, with the increase of magnetic fields, the magnetization tends to saturation, which results in the isotropic behavior of the exchange interaction as shown in Fig. 6. Meanwhile, in our calculations, it is worthy to note that the relationships between aA, aB and He meet with different expressions as follows.

aA ¼ P1 þ P2  He þ P3  H2e þP4  H3e

ð12Þ

2 3 aB ¼ P1 þP2  H1 e þ P 3  H e þP 4  H e

ð13Þ

Here, P1, P2, P3 and P4 are the fitting parameters, as shown in Tables 1 and 2. From Eqs. (12) and (13), an obvious difference between the two expressions can be seen. And, aA is the positive exponential function of He, while aB is the negative exponential function. This further reveal the discrepancy of magnetic mechanism in A and B sublattices. Additionally, the magnetizations of Nd2Fe17H3 at different temperatures for He perpendicular to the alignment direction are calculated as shown in Fig. 7 where the theoretical results show good agreements with the experimental data. Meanwhile, the fitting parameters aA and aB, associated with exchange interaction and effective magnetic susceptibility, are analyzed in Fig. 8. It is obviously found that aA and aB are the functions of T and He, for exchange interaction and effective magnetic susceptibility are related with the temperatures and magnetic fields. Owing to the lack of experimental data, we cannot give the specific expressions of exchange interaction and effective magnetic susceptibility on T and He in this paper. Then, it is will be further studied in the future.

4. Conclusions In this paper, the magnetic properties of Nd2Fe17Hx (x¼ 0, 3, 4.9) are theoretically analyzed by an improved two-sublattice model under high magnetic fields where the theoretical calculations are in excellent agreements with the experiments. Meanwhile, the difference of the magnetization in A and B sublattice are

discussed under different conditions. Here, the effects of the insertion of hydride on the magnetization in Nd and Fe sublattices are revealed. Additionally, the appropriate values of the fitting parameters aA and aB are given. Detailed analyses indicate that aA and aB are the functions of T and He, and the corresponding expressions are presented. Finally, it can be concluded that the change of exchange interaction and effective magnetic susceptibility, induced by the insertion of hydrogen and the different magnetization directions, leads to the difference of aA and aB. Acknowledgements This work is supported by the National Natural Science Foundation of China (Grant no. 11004005), the Program of Excellent Talents in Beijing of China (Grant no. 2011D009016000001), the Transformation and Industrialization of Scientific and Technological Achievements of the Beijing Municipal Education Commission Project (Grant no. 506152) and the Fundamental Research Funds for the Central Universities (Grant no. ZZ1228). References [1] P. Hill, I. Dubenko, T. Samanta, A. Quetz, N. Ali, Journal of Applied Physics 111 (2012) 07E333. [2] W. Bodnar, M. Szklarska-Lukasik, P. Stoch, P. Zachriasz, J. Pszczola, J. Suwakski, Journal of Alloys and Compounds 496 (2010) 37. [3] N. Sheloudko, C. Sarafidis, M. Gjoka, K.G. Efthimiadis, O. Kalogirou, Journal of Alloys and Compounds 482 (2009) 19. [4] R. Fersi, N. Mliki, L. Bessais, R. Guetari, V. Russier, M. Cabie, Journal of Alloys and Compounds 522 (2012) 14. [5] T.I. Ivanova, W. Suski, S.A. Nikitin, A.E. Bogdanov, M.V. Gavrilko, A. Gilewski, I.K. Warchulska, G.S. Burkhanov, O.D. Chistiakov, Journal of Alloys and Compounds 453 (2008) 36. [6] J. Ostorero, M. Guillot, Journal of Applied Physics 101 (2007) 09B101. [7] O. Isnard, Y. Skourski, L.V.B. Diop, Z. Arnold, A.V. Andreev, J. Wosnitza, A. Iwasa, A. Kondo, A. Matsuo, K. Kindo, Journal of Applied Physics 111 (2012) 093916. [8] J.F. Herbst, J.J. Croat, Journal of Applied Physics 53 (1982) 4304; J.F. Herbst, J.J. Croat, Journal of Applied Physics 55 (1984) 3023. [9] Z.W. Zhang, X.M. Zhang, S.W. Ren, L.P. Han, Z.C. Ni, Z.Y. Liu, Journal of Magnetism and Magnetic Materials 248 (2002) 158; X.M. Zhang, R.W. Huang, Z.W. Zhang, Journal of Magnetism and Magnetic Materials 241 (2002) 131. [10] Z.W. Zhang, R.W. Huang, Journal of Alloys and Compounds 185 (1992) 363; S.W. Ren, Z.W. Zhang, Y. Liu, Journal of Magnetism and Magnetic Materials 139 (1995) 175. [11] J. Prasongkit, I.M. Tang, Journal of Magnetism and Magnetic Materials 284 (2004) 376.

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