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Influence of periodic and random local crystal fields on magnetic properties of NdxY1−xCo5 compounds
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 300 (2006) e433–e436 www.elsevier.com/locate/jmmm
Influence of periodic and random local crystal fields on magnetic properties of NdxY1xCo5 compounds Yu.A. Kulikov, A.S. Ermolenko, N.V. Mushnikov Institute of Metal Physics, Ural Division of RAS, 620219, Ekaterinburg, Russia Available online 18 November 2005
Abstract The magnetization processes have been studied for single crystals of NdxY1xCo5 compounds in magnetic fields up to 360 kOe at temperatures 4.2–300 K. The experimental results have been used for determination of parameters of crystal field (CF) splitting of the energy levels of the ground J multiplet of Nd3+ ions. A single set of CF parameters was found for all x values and all temperatures from above-mentioned range allowing satisfactory description of all experimental magnetization curves. An alternative set of parameters was obtained assuming presence, in studied compounds, of local random CFs generated by impurities (for instance, absorbed hydrogen). r 2005 Elsevier B.V. All rights reserved. PACS: 75.30.Cr; 7530.Gw Keywords: Rare-earth compounds; Crystal fields; Magnetic properties
1. Introduction Intermetallic compounds NdxY1xCo5 with hexagonal structure of CaCu5 type have some interesting peculiarities of magnetic properties including the temperature and compositional spin-reorientation phenomena, magnetic field-induced first-order magnetization processes (FOMP) and large basal-plane magnetization anisotropy. Therefore, these compounds are very convenient objects for verifying mechanisms of the magnetocrystalline anisotropy (MCA) of rare earth (R)—3d metal intermetallics. Several works have been devoted to experimental studies of magnetocrystalline anisotropy of NdxY1xCo5 compounds [1–4]. In these early works it was concluded that NdxY1xCo5 compounds must be considered as two-sublattice magnetic systems, and their MCA is a sum of contributions from cobalt and neodymium subsystems. The cobalt contribution usually considered as independent on x and equal to MCA of YCo5 in which the high uniaxial MCA of RCo5 series was discovered for the first time [5]. The anisotropy constants K1Nd and K2Nd of Nd subsystem in the first Corresponding author. Tel.: +73433744472; fax: +73433745244.
E-mail address: [email protected] (Y.A. Kulikov). 0304-8853/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2005.10.185
approximation can be determined as a difference between corresponding constants of Nd-containing compound and those of YCo5. It was shown already in Ref. [1] that K1Nd and K2Nd are linearly dependent on x pointing to the single-ion nature of MCA of Nd-sublattice. The most detailed investigation of magnetic properties of NdxY1xCo5 compounds was given in Refs. [4,5]. Along with experimental studies, the attempt of calculation of magnetization curves of single crystals was undertaken on the basis of classical expressions for MCA energy. It was shown that it is impossible to describe the experimental results for all alloys with the assumption that anisotropy coefficients of Nd ions and Nd–Co exchange parameter do not depend on x. The authors of Refs. [6,7] provided the theoretical analysis of experimental results obtained in Refs. [4,5] using quantum-mechanical treatment of crystal field (CF), and exchange and external magnetic field effects on the energy spectrum of ground J-multiplet of Nd3+ ion in NdxY1xCo5 compounds. At first glance, they reached a good agreement of calculated and experimental results. However, they obtained fitting CF and exchange parameters which depend on x and temperature T, what is difficult to approve. Thus, there is no adequate description
ARTICLE IN PRESS Y.A. Kulikov et al. / Journal of Magnetism and Magnetic Materials 300 (2006) e433–e436
of magnetic properties of NdxY1xCo5 system up to now. To our mind, one of the reasons is the absence of systematic experimental studies of the magnetization processes in NdxY1xCo5 single crystals in high magnetic fields. In this paper we present the results of measurements of NdxY1xCo5 single crystals in pulsed magnetic fields up to 360 kOe. The analysis of experimental results was fulfilled in terms of CF theory. 2. Experimental details The compounds NdxY1xCo5 were prepared for x values varying with a step Dx ¼ 0:1 by induction melting under argon atmosphere. They were homogenized at 1100 1C during 24 h. Metallographic and X-ray analyses showed a single-phase structure of CaCu5 type. The ball single crystal specimens were cut from coarse grains of ingots for magnetic measurements along the a-, b- or c-axis of hexagonal lattice. The magnetization curves were measured by induction method in pulsed magnetic fields up to 360 kOe with a pulse duration time of 8 ms at temperatures of 4.2–300 K. 3. Calculations The basic scheme for calculation of magnetization curves of NdxY1xCo5 single crystals was similar to that used in Ref. [6]. The free energy per formula unit is given by F ðH; H ex ; TÞ ¼ xkB T ln Z þ K 1Co ðTÞsin2 yCo þ K 2Co ðTÞsin4 yCo M Co ðyCo ; TÞ H; ð1Þ where X Z¼ expðE n =kB TÞ;
(2)
n
K1Co(T), K2Co(T) and MCo(yCo, T) are the first and second MCA constants and magnetic moment of the Co sublattice, respectively, taken as those of YCo5 [8]; yCo is an angle between MCo and c-axis; E n are the eigenvalues of ground J multiplet of Nd3+ ion obtained by diagonalizing the matrix of the following Hamiltonian of the Nd ion in the compound: H R ¼ H CF þ 2mB S H ex þ mB ðL þ 2SÞ H,
(6)
with yCo determined by minimization of Eq. (1). 4. Results and discussion The magnetization curves along c-axis of NdCo5 single crystal at temperatures 4.2–270 K are shown in Fig. 1. It is seen that FOMP processes take place at high fields at temperatures below 120 K. Only the rising branch of magnetization process is shown for clarity, though a small hysteresis was observed in the FOMP region at 4.2–80 K. The FOMP in NdCo5 at 4.2 K was forecasted earlier [9], and was observed experimentally [10]. Our present result for 4.2 K is in good agreement with that of Ref. [10], though our magnetic field was not high enough to reach saturation. The calculated curve at 4.2 K (thick solid line) was obtained with the set 1 of CF and exchange shown in Table 1. The coincidence of calculated curve with experiment is reasonable. These parameters were successfully used for calculation of magnetization curves of NdCo5 at various temperatures (Fig. 1). Moreover, the set 1 of parameters provides a good description of anisotropic properties of NdCo5 single crystal along the a- and b-axis and their temperature variation. The magnetization curves of various NdxY1xCo5 single crystals along c-axis at 4.2 K are shown in Fig. 2. One can see that FOMP takes place for all crystals beginning from x ¼ 0:3. Our attempts to describe these curves using the parameters of set 1 from above Table 1 become successful only by condition that nNd–Co increases while x decreases from 1 to 0.3 as shown in Fig. 3. It is possible that nNd–Co really increases on going from NdCo5 to YCo5 due to decrease of Nd–Co distances. Similar mechanism was considered in Ref. [11].
10 8 6
T= 4.2 K 40 K 60 K 77 K 120 K 160 K 200 K 220 K 250 K 270 K
4
(4)
where Am n are CF parameters and X Cm ½4p=ð2n þ 1Þ1=2 Y m n ¼ n ðyj ; jj Þ
2 0
j
ðn ¼ 2; 4; 6; m ¼ 0; 6; jmjpnÞ,
MðTÞ ¼ xM Nd ðTÞ þ M Co ðyCo ; TÞ
(3)
consisting of CF interaction, Nd–Co exchange interaction, and Zeeman energy. The Hamiltonian of CF interaction is written as H CF ¼ A02 C 02 þ A04 C 04 þ A06 C 06 þ A66 ðC 66 þ C 6 6 Þ;
standard procedure, and the magnetic moment of the NdxY1xCo5 system was found as
M (µB/f.u.)
e434
ð5Þ
Ym n (yj,jj) are the spherical harmonics, and yj and jj are the polar angles of the position vector of the jth 4f electron. The magnetic moment of Nd ion MNd was calculated by a
0
50
100
150
200 250 H (kOe)
300
350
400
Fig. 1. Magnetization curves along c-axis of NdCo5 single crystal at various temperatures: points—experiment, solid lines—calculation with parameters of set 1 (thick lines) or set 2 (thin lines).
ARTICLE IN PRESS Y.A. Kulikov et al. / Journal of Magnetism and Magnetic Materials 300 (2006) e433–e436 Table 1 Two sets of CF and Nd–Co exchange parameters providing the satisfactory description of magnetization processes of NdxY1xCo5 single crystals
e435
90 80 70
A02 (K)
A04 (K)
A06 (K)
A66 (K)
A02 (K)
nNd–Co (K)
1 2
340 1400
190 500
1600 500
1400 250
— 250
57 46
60 (deg)
Set
50 40 x = 0.3 0.4 0.5 0.6 0.8 1.0
30 20 10
10 0
M (µB/f.u.)
8
0
80
120
160 T (K)
200
240
280
6 Fig. 4. The temperature dependence of angle y0 between easy direction and c-axis of NdxY1xCo5 compounds: points—experiment [3]; solid lines—calculations with parameters of set 1 (thick lines) and 2 (thin lines).
x = 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
4 2 0 0
50
100
150
200 250 H (kOe)
300
350
400
Fig. 2. Magnetization curves along c-axis of NdxY1xCo5 single crystals for various x values: points—experiment [3], solid lines—calculation with parameters of set 1 (thick lines) or set 2 (thin lines).
74 72 70 68 66 64 nNd-Co (K)
40
set 1
62 60 58 56 54 52 set 2
50 48 46 0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
x Fig. 3. The compositional dependence of fit Nd–Co exchange parameter found from calculations with CF parameters of sets 1 and 2 for NdxY1xCo5 compounds.
The calculated dependences of the angle y0 between the easy magnetization direction and c-axis on temperature are shown for all alloys in Fig. 4. We see again a satisfactory accordance with experiment [3]. Thus, set 1 of CF
parameters allows to describe magnetic properties of NdxY1xCo5 single crystals including: (i) magnetization curves along a-, b-, c-axis in magnetic fields up to 360 kOe at temperatures 4.2–300 K; (ii) large magnetization anisotropy in basal plane along a- and b-axis and its temperature dependence; (iii) FOMP phenomenon at high magnetic field; (iv) temperature spin reorientation processes. However, the sixth-order CF parameters of set 1 look unusually high, and they can hardly be approved. Obviously, there are some additional contributions to the magnetocrystalline anisotropy of the studied compounds. Rosenfeld [12] took into account a magnetoelastic contribution and has explained the peculiarities of magnetization curves of NdCo5-based compounds neglecting the CF terms of the fourth and sixth orders. We have considered another possible contribution from random local CFs due to impurity ions (hydrogen, for example). The electric charge of such ions generates an additional potential acting on the nearest R ions. Most probably, it has a low symmetry, and can be taken into account as an additional local randomly oriented second-order term with A02 parameter. We carried out model calculations taking into account this term and got a new set 2 (see Table 1) of parameters allowing reasonable description of all our results (thin solid lines in figures). In our opinion, the set 2 is more realistic since the lowest order CF parameter is considerably higher than those of high order. Details of calculations will be published elsewhere.
Acknowledgements This work is supported by Project No. 10 of Russian Academy of Sciences.
ARTICLE IN PRESS e436
Y.A. Kulikov et al. / Journal of Magnetism and Magnetic Materials 300 (2006) e433–e436
References [1] E. Tatsumoto, T. Okamoto, H. Fujii, C. Inoue, J. Phys. 32 (C1) (1971) 550. [2] J.P. Heinrich, A.E. Miller, IEEE Trans. Magn. Mag-13 (1977) 1336. [3] A.S. Ermolenko, IEEE Trans. Magn. Mag-15 (1979) 1765. [4] A.S. Ermolenko, Fiz. Met. Metalloved. 50 (1980) 962. [5] G. Hoffer, K. Strnat, IEEE Trans. Magn. Mag-2 (1966) 487. [6] Zhao Tie-song, Jin Han-min, Guo Guang-Hua, Han Xiu-Feng, Chen Hong, Phys. Rev. B 43 (1991) 8593.
[7] X.R. Huang, Z.S. Li, B.F. Li, C.C. Sun, H.M. Jin, J. Magn. Magn. Mater. 128 (1993) 73. [8] M. Alameda, D. Givord, R. Lemaire, Q. Lu, J. Appl. Phys. 52 (1981) 2079. [9] A.S. Ermolenko, Fiz. Met. Metalloved. 53 (1982) 520. [10] M.I. Bartashevich, T. Goto, M. Yamaguchi, I. Yamamoto, Tech. Rep. ISSP A 2699 (1993) 1. [11] E. Belorizky, M.A. Fremy, D. Givord, J. Appl. Phys. 61 (1987) 3971. [12] E.V. Rosenfeld, J. Exp. Theor. Phys. 97 (2003) 958.
Journal of Magnetism and Magnetic Materials 300 (2006) e433–e436 www.elsevier.com/locate/jmmm
Influence of periodic and random local crystal fields on magnetic properties of NdxY1xCo5 compounds Yu.A. Kulikov, A.S. Ermolenko, N.V. Mushnikov Institute of Metal Physics, Ural Division of RAS, 620219, Ekaterinburg, Russia Available online 18 November 2005
Abstract The magnetization processes have been studied for single crystals of NdxY1xCo5 compounds in magnetic fields up to 360 kOe at temperatures 4.2–300 K. The experimental results have been used for determination of parameters of crystal field (CF) splitting of the energy levels of the ground J multiplet of Nd3+ ions. A single set of CF parameters was found for all x values and all temperatures from above-mentioned range allowing satisfactory description of all experimental magnetization curves. An alternative set of parameters was obtained assuming presence, in studied compounds, of local random CFs generated by impurities (for instance, absorbed hydrogen). r 2005 Elsevier B.V. All rights reserved. PACS: 75.30.Cr; 7530.Gw Keywords: Rare-earth compounds; Crystal fields; Magnetic properties
1. Introduction Intermetallic compounds NdxY1xCo5 with hexagonal structure of CaCu5 type have some interesting peculiarities of magnetic properties including the temperature and compositional spin-reorientation phenomena, magnetic field-induced first-order magnetization processes (FOMP) and large basal-plane magnetization anisotropy. Therefore, these compounds are very convenient objects for verifying mechanisms of the magnetocrystalline anisotropy (MCA) of rare earth (R)—3d metal intermetallics. Several works have been devoted to experimental studies of magnetocrystalline anisotropy of NdxY1xCo5 compounds [1–4]. In these early works it was concluded that NdxY1xCo5 compounds must be considered as two-sublattice magnetic systems, and their MCA is a sum of contributions from cobalt and neodymium subsystems. The cobalt contribution usually considered as independent on x and equal to MCA of YCo5 in which the high uniaxial MCA of RCo5 series was discovered for the first time [5]. The anisotropy constants K1Nd and K2Nd of Nd subsystem in the first Corresponding author. Tel.: +73433744472; fax: +73433745244.
E-mail address: [email protected] (Y.A. Kulikov). 0304-8853/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2005.10.185
approximation can be determined as a difference between corresponding constants of Nd-containing compound and those of YCo5. It was shown already in Ref. [1] that K1Nd and K2Nd are linearly dependent on x pointing to the single-ion nature of MCA of Nd-sublattice. The most detailed investigation of magnetic properties of NdxY1xCo5 compounds was given in Refs. [4,5]. Along with experimental studies, the attempt of calculation of magnetization curves of single crystals was undertaken on the basis of classical expressions for MCA energy. It was shown that it is impossible to describe the experimental results for all alloys with the assumption that anisotropy coefficients of Nd ions and Nd–Co exchange parameter do not depend on x. The authors of Refs. [6,7] provided the theoretical analysis of experimental results obtained in Refs. [4,5] using quantum-mechanical treatment of crystal field (CF), and exchange and external magnetic field effects on the energy spectrum of ground J-multiplet of Nd3+ ion in NdxY1xCo5 compounds. At first glance, they reached a good agreement of calculated and experimental results. However, they obtained fitting CF and exchange parameters which depend on x and temperature T, what is difficult to approve. Thus, there is no adequate description
ARTICLE IN PRESS Y.A. Kulikov et al. / Journal of Magnetism and Magnetic Materials 300 (2006) e433–e436
of magnetic properties of NdxY1xCo5 system up to now. To our mind, one of the reasons is the absence of systematic experimental studies of the magnetization processes in NdxY1xCo5 single crystals in high magnetic fields. In this paper we present the results of measurements of NdxY1xCo5 single crystals in pulsed magnetic fields up to 360 kOe. The analysis of experimental results was fulfilled in terms of CF theory. 2. Experimental details The compounds NdxY1xCo5 were prepared for x values varying with a step Dx ¼ 0:1 by induction melting under argon atmosphere. They were homogenized at 1100 1C during 24 h. Metallographic and X-ray analyses showed a single-phase structure of CaCu5 type. The ball single crystal specimens were cut from coarse grains of ingots for magnetic measurements along the a-, b- or c-axis of hexagonal lattice. The magnetization curves were measured by induction method in pulsed magnetic fields up to 360 kOe with a pulse duration time of 8 ms at temperatures of 4.2–300 K. 3. Calculations The basic scheme for calculation of magnetization curves of NdxY1xCo5 single crystals was similar to that used in Ref. [6]. The free energy per formula unit is given by F ðH; H ex ; TÞ ¼ xkB T ln Z þ K 1Co ðTÞsin2 yCo þ K 2Co ðTÞsin4 yCo M Co ðyCo ; TÞ H; ð1Þ where X Z¼ expðE n =kB TÞ;
(2)
n
K1Co(T), K2Co(T) and MCo(yCo, T) are the first and second MCA constants and magnetic moment of the Co sublattice, respectively, taken as those of YCo5 [8]; yCo is an angle between MCo and c-axis; E n are the eigenvalues of ground J multiplet of Nd3+ ion obtained by diagonalizing the matrix of the following Hamiltonian of the Nd ion in the compound: H R ¼ H CF þ 2mB S H ex þ mB ðL þ 2SÞ H,
(6)
with yCo determined by minimization of Eq. (1). 4. Results and discussion The magnetization curves along c-axis of NdCo5 single crystal at temperatures 4.2–270 K are shown in Fig. 1. It is seen that FOMP processes take place at high fields at temperatures below 120 K. Only the rising branch of magnetization process is shown for clarity, though a small hysteresis was observed in the FOMP region at 4.2–80 K. The FOMP in NdCo5 at 4.2 K was forecasted earlier [9], and was observed experimentally [10]. Our present result for 4.2 K is in good agreement with that of Ref. [10], though our magnetic field was not high enough to reach saturation. The calculated curve at 4.2 K (thick solid line) was obtained with the set 1 of CF and exchange shown in Table 1. The coincidence of calculated curve with experiment is reasonable. These parameters were successfully used for calculation of magnetization curves of NdCo5 at various temperatures (Fig. 1). Moreover, the set 1 of parameters provides a good description of anisotropic properties of NdCo5 single crystal along the a- and b-axis and their temperature variation. The magnetization curves of various NdxY1xCo5 single crystals along c-axis at 4.2 K are shown in Fig. 2. One can see that FOMP takes place for all crystals beginning from x ¼ 0:3. Our attempts to describe these curves using the parameters of set 1 from above Table 1 become successful only by condition that nNd–Co increases while x decreases from 1 to 0.3 as shown in Fig. 3. It is possible that nNd–Co really increases on going from NdCo5 to YCo5 due to decrease of Nd–Co distances. Similar mechanism was considered in Ref. [11].
10 8 6
T= 4.2 K 40 K 60 K 77 K 120 K 160 K 200 K 220 K 250 K 270 K
4
(4)
where Am n are CF parameters and X Cm ½4p=ð2n þ 1Þ1=2 Y m n ¼ n ðyj ; jj Þ
2 0
j
ðn ¼ 2; 4; 6; m ¼ 0; 6; jmjpnÞ,
MðTÞ ¼ xM Nd ðTÞ þ M Co ðyCo ; TÞ
(3)
consisting of CF interaction, Nd–Co exchange interaction, and Zeeman energy. The Hamiltonian of CF interaction is written as H CF ¼ A02 C 02 þ A04 C 04 þ A06 C 06 þ A66 ðC 66 þ C 6 6 Þ;
standard procedure, and the magnetic moment of the NdxY1xCo5 system was found as
M (µB/f.u.)
e434
ð5Þ
Ym n (yj,jj) are the spherical harmonics, and yj and jj are the polar angles of the position vector of the jth 4f electron. The magnetic moment of Nd ion MNd was calculated by a
0
50
100
150
200 250 H (kOe)
300
350
400
Fig. 1. Magnetization curves along c-axis of NdCo5 single crystal at various temperatures: points—experiment, solid lines—calculation with parameters of set 1 (thick lines) or set 2 (thin lines).
ARTICLE IN PRESS Y.A. Kulikov et al. / Journal of Magnetism and Magnetic Materials 300 (2006) e433–e436 Table 1 Two sets of CF and Nd–Co exchange parameters providing the satisfactory description of magnetization processes of NdxY1xCo5 single crystals
e435
90 80 70
A02 (K)
A04 (K)
A06 (K)
A66 (K)
A02 (K)
nNd–Co (K)
1 2
340 1400
190 500
1600 500
1400 250
— 250
57 46
60 (deg)
Set
50 40 x = 0.3 0.4 0.5 0.6 0.8 1.0
30 20 10
10 0
M (µB/f.u.)
8
0
80
120
160 T (K)
200
240
280
6 Fig. 4. The temperature dependence of angle y0 between easy direction and c-axis of NdxY1xCo5 compounds: points—experiment [3]; solid lines—calculations with parameters of set 1 (thick lines) and 2 (thin lines).
x = 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
4 2 0 0
50
100
150
200 250 H (kOe)
300
350
400
Fig. 2. Magnetization curves along c-axis of NdxY1xCo5 single crystals for various x values: points—experiment [3], solid lines—calculation with parameters of set 1 (thick lines) or set 2 (thin lines).
74 72 70 68 66 64 nNd-Co (K)
40
set 1
62 60 58 56 54 52 set 2
50 48 46 0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
x Fig. 3. The compositional dependence of fit Nd–Co exchange parameter found from calculations with CF parameters of sets 1 and 2 for NdxY1xCo5 compounds.
The calculated dependences of the angle y0 between the easy magnetization direction and c-axis on temperature are shown for all alloys in Fig. 4. We see again a satisfactory accordance with experiment [3]. Thus, set 1 of CF
parameters allows to describe magnetic properties of NdxY1xCo5 single crystals including: (i) magnetization curves along a-, b-, c-axis in magnetic fields up to 360 kOe at temperatures 4.2–300 K; (ii) large magnetization anisotropy in basal plane along a- and b-axis and its temperature dependence; (iii) FOMP phenomenon at high magnetic field; (iv) temperature spin reorientation processes. However, the sixth-order CF parameters of set 1 look unusually high, and they can hardly be approved. Obviously, there are some additional contributions to the magnetocrystalline anisotropy of the studied compounds. Rosenfeld [12] took into account a magnetoelastic contribution and has explained the peculiarities of magnetization curves of NdCo5-based compounds neglecting the CF terms of the fourth and sixth orders. We have considered another possible contribution from random local CFs due to impurity ions (hydrogen, for example). The electric charge of such ions generates an additional potential acting on the nearest R ions. Most probably, it has a low symmetry, and can be taken into account as an additional local randomly oriented second-order term with A02 parameter. We carried out model calculations taking into account this term and got a new set 2 (see Table 1) of parameters allowing reasonable description of all our results (thin solid lines in figures). In our opinion, the set 2 is more realistic since the lowest order CF parameter is considerably higher than those of high order. Details of calculations will be published elsewhere.
Acknowledgements This work is supported by Project No. 10 of Russian Academy of Sciences.
ARTICLE IN PRESS e436
Y.A. Kulikov et al. / Journal of Magnetism and Magnetic Materials 300 (2006) e433–e436
References [1] E. Tatsumoto, T. Okamoto, H. Fujii, C. Inoue, J. Phys. 32 (C1) (1971) 550. [2] J.P. Heinrich, A.E. Miller, IEEE Trans. Magn. Mag-13 (1977) 1336. [3] A.S. Ermolenko, IEEE Trans. Magn. Mag-15 (1979) 1765. [4] A.S. Ermolenko, Fiz. Met. Metalloved. 50 (1980) 962. [5] G. Hoffer, K. Strnat, IEEE Trans. Magn. Mag-2 (1966) 487. [6] Zhao Tie-song, Jin Han-min, Guo Guang-Hua, Han Xiu-Feng, Chen Hong, Phys. Rev. B 43 (1991) 8593.
[7] X.R. Huang, Z.S. Li, B.F. Li, C.C. Sun, H.M. Jin, J. Magn. Magn. Mater. 128 (1993) 73. [8] M. Alameda, D. Givord, R. Lemaire, Q. Lu, J. Appl. Phys. 52 (1981) 2079. [9] A.S. Ermolenko, Fiz. Met. Metalloved. 53 (1982) 520. [10] M.I. Bartashevich, T. Goto, M. Yamaguchi, I. Yamamoto, Tech. Rep. ISSP A 2699 (1993) 1. [11] E. Belorizky, M.A. Fremy, D. Givord, J. Appl. Phys. 61 (1987) 3971. [12] E.V. Rosenfeld, J. Exp. Theor. Phys. 97 (2003) 958.