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The temperature dependence of the magnetization in the basal plane of R—T single crystals
Journal ot N1agnetism and, Magnetic Materials 177-181 (1998) 1099-1100
~ , ~ le.rnal el magnetism , ~ and magneUc materials
ELSEVIER
The temperature dependence of the magnetization in the basal plane of R-T single crystals P.D. Thang a, N.P. Thuy a'*, L.V.D. Khuong a, C.V. Thang a, J.J.M. Franse b, S. Sinnema b International Training Institute for Materials Science (ITIMS), Dai hoc bach khoa, l Dai Co Vier, Hanoi, Ih'et Nam b Van der Waals-Zeeman Institute, University of Amsterdam, The Netherlands
Abstract
The temperature dependences of the magnetizations along the a- and b-axes of R2Co1-7 compounds (R = Nd, Pr, He and Dy) have been analyzed. By fitting the experimental curves of magnetizations measured on single crystals, precise values of the high order crystalline electric field (CEF) parameter B66 and of the coupling parameter JRT have been derived. ~, I998 Elsevier Science B.V. All rights reserved. Ke)'words: Crystal field effect; Exchange coupling - intersublattice; Rare earth-transition metal compounds
Recently, magnetism of the rare earth-transition metal (R-T) intermetallic compounds have been investigated in much more detail due to the success in growing single crystals of high quality. The isothermal magnetization measured along different crystallographic directions in high magnetic fields has been well explained for several series of binary and ternary compounds based on microscopic models. The temperature dependence of the magnetization along principal axes of the crystals has been satisfactorily explained using these models. However, the differences in the temperature dependences of the magnetizations along the principal axes in the basal plane of single crystalline R-T compounds were given less attention. This work focuses on an analysis of such experimental results, namely, the temperature dependence of the magnetization along the a- and b-axes in the RzCoz7 compounds (R = Nd, Pr, He and Dy). By fitting the experimental curves, the high order CEF parameter B~ and a precise value of the coupling parameter JRT have been derived. In the R - T compounds, the Hamiltonian acting on the R-ion in the ground multiplet d is expressed as 6
^m 4- gJ¢~BJB~ + gJ~B J B , B,~m0,~
HR = E n=O
(1)
m = -n
*Corresponding author. Tel.: + 84 4 8692518; fax: + 84 4 8692963; e-mail: [email protected].
where the first term is the CEF effect on the R-ion, the last two terms are contributions of the molecular field B,,, and the external field B, respectively. The total free energy of the R - T compound is expressed in the conventional form [3]. By minimizing the free energy at a given temperature and external field, the magnetization process as well as the temperature dependence of magnetization can be deduced. The computed results for thermomagnetic curves along the principal axes of the R2Co17 single crystals (R = Nd, Pr, He and Dy) are shown in Fig. 1. The experimental results are taken from Sinnema [1]. The same calculations have also been carried out on other single crystals such as Dy2Fe17, DyCos, and HoCo4AI and have been compared with the experimental results of Refs. [1-3]. In our calculations, all the CEF parameters obtained in the literature [2-8], except for B~, have been used, whereas, B 6 and Bm are adjustable parameters to get the best fits to the experimental data. Our main results are as follows. 1. Precise values of the high order CEF parameter B66 that was neglected or roughly evaluated in previous works have been obtained (see Table 1). For the R-ion, the anisotropy constant K4R, which determines the MCA term in the basal plane K4 sin60 cos 6q), can be expressed via the CEF parameters as K§ = B 6 ( ( 0 °) + (06)/2)/16, here (0~') represents the thermal average of 0',',~.Therefore, B 6 plays a decisive role in the determination of the sixfold anisotropy of the given R-T compounds.
0304-8853/98/$19.00 ,(? 1998 Elsevier Science B.V. All rights reserved PII S 0 3 0 4 - 8 8 5 3 ( 9 7 ) 0 0 8 8 3-4
P.D. Thang et aL /Journal of Magnetism and Magnetie Materials 177-18t (t998) 1099-1t00
1100 160
Table 1 Values of Bin, JRT and B~ obtained in the fitting procedure and AM measured at 4.2 K in RzCo:-~ compounds (applied field is indicated in brackets) 1-1t
b axis
140 120
ioo
a a.xis
a iLxis
< 8D g 6o
Nd2Col7 B = IT
40 20
i
< c axis
R
Pr2Coi 7 B=IT
c axis
Jwr (10 .23 J)
Pr 280 33.80 Nd 320 25.86 Dy 9 1 . 3 11.04 Ho 63.5 9.40
0 80 70
60 S0 .< 40 30
/
B~ (10- 3 K)
AM (A m2/kg)
- 1.466 - 8.0 - 0.284 0.137
10 18.7 - 3.6 1.9
(1 T) (1 T) (1 T) (4T)
.o2co. b axis
20 10
B~ (T)
B = 1T
c axis
0 I00
200
T (IO
300
200
I00
~,
200
T{K)
Fig. 1. The calculated results (solid lines) of NdzCol 7, Pr2Col v, Ho2Co~7 and Dy2Coav single crystals with the fitting parameters B m and B~ as listed in Table 1. Other CEF parameters used in the fitting procedure were taken from Refs. [4-@ The experimental results (points) are taken from Ref. [1"1.
2. Precise values of the molecular field Bm and the exchange parameter JRT have been derived (see Table 1). Up to now, several methods have been applied for determining Jr~x such as fitting the high field magnetization curves, analyzing the Curie or compensation temperatures. Our calculation can be considered as a new method for obtaining precise values of the R - T exchange interaction. To consider the different roles of B{ and Bm in the determination of the behaviour of thermomagnetic curves, we have studied the dependence on B{ and B,, of the difference in magnetization along the a- and b-axes at 4.2 K, AM = Mb -- Ma, and of the value of critical temperature, Ter, above which the sixfold anisotropy in the basal plane disappears. It turned out from this analysis that the strength of Bm has a crucial effect on the Tc~ value, whereas B{ plays a decisive role in the determination of the AM value. In Table 1 AM values measured by Sinnema 1-1] are listed along with our fitting values of B~ of the R2Co,7 compounds. It can be clearly seen that the bigger the absolute value of B~, the larger the magnitude of AM at 4.2 K. Our analysis on Dy2Felv, DyCos and HoCo4AI single crystals (not presented here) also give similar results. Nevertheless, the simple relation between the easy magnetization direction and the sign of B~ cannot be obtained and still needs more investigation. The obtained values of JRT of R2Co17 compounds are plotted in Fig. 2 together with result of Ref. [9]. It
% 30 -7, 20
this~ork C* Outer al. [9]
•
~~ ,
:
,
i
i
,
i
Ce Pr Nd Pin Sm Eu Gd T b Rare earth elements
i Dy
Ho Er
Fig. 2. The variation of the exchange coupling parameter ,/aTin the series of RzCol-~ compounds.
is clear that in the considered R - T series, the parameter JRT has the tendency to decrease from Pr to Tm. This phenomenon has been explained on the basis of the lanthanide contraction [10].
References [t1 S. Sinnema, Thesis, University of Amsterdam, 1988. [2t M. Ohkoshi, H. Kobayashi, T. Katayama, M. Hirano, T. Tsushima, Physica B 86-88 (1977) i95. [3] C.V. Thang, Thesis, University of Amsterdam, 1996. I-4] J.H.P. Colpa, P.H. Frings, R.J. Radwanski, J.J.M. Franse, M. Alba, J. Magn. Magn, Mater. 13i (1994) 167. [51 R.J. Radwanski, J.J.M. granse, S. Sinnema, H.J.M. Heerooms, J.H.P. Colpa, J. Magn. Magn. Mater. 76-77 (1988) 1982. [6] J.H.P. CoIpa, S. Sinnema, J.J.M. Franse, R.J. Radwanski, P.H. Frings, Physica B 156 (1989) 731. 1-71 A.V. Andreev, M.L Bartashevieh, A.V. Deryagin, E.N. Tarasov, Zh. Eksp. Theor. Fiz. 89 (3) (1985) 959. [8-1 A.S. Ermolenko, in: J. Fidler (Ed.), Proc. 6th Int. Workshop on Rare Earth-Cobalt Permanent Magnets, Vienna, 1982, p. 771. [91 N.H. Duc, T.D. Hien, D. Givord, J.J.M. Franse, F.R. de Boer, J. Magn. Magn. Mater. 124 (1993) 305. [10.1 E. Belorizky, M.A. Fremy, J.P. Gavigan, D. Givord, H.S. Li, J. Appl. Phys. 61 (1987) 3791.
~ , ~ le.rnal el magnetism , ~ and magneUc materials
ELSEVIER
The temperature dependence of the magnetization in the basal plane of R-T single crystals P.D. Thang a, N.P. Thuy a'*, L.V.D. Khuong a, C.V. Thang a, J.J.M. Franse b, S. Sinnema b International Training Institute for Materials Science (ITIMS), Dai hoc bach khoa, l Dai Co Vier, Hanoi, Ih'et Nam b Van der Waals-Zeeman Institute, University of Amsterdam, The Netherlands
Abstract
The temperature dependences of the magnetizations along the a- and b-axes of R2Co1-7 compounds (R = Nd, Pr, He and Dy) have been analyzed. By fitting the experimental curves of magnetizations measured on single crystals, precise values of the high order crystalline electric field (CEF) parameter B66 and of the coupling parameter JRT have been derived. ~, I998 Elsevier Science B.V. All rights reserved. Ke)'words: Crystal field effect; Exchange coupling - intersublattice; Rare earth-transition metal compounds
Recently, magnetism of the rare earth-transition metal (R-T) intermetallic compounds have been investigated in much more detail due to the success in growing single crystals of high quality. The isothermal magnetization measured along different crystallographic directions in high magnetic fields has been well explained for several series of binary and ternary compounds based on microscopic models. The temperature dependence of the magnetization along principal axes of the crystals has been satisfactorily explained using these models. However, the differences in the temperature dependences of the magnetizations along the principal axes in the basal plane of single crystalline R-T compounds were given less attention. This work focuses on an analysis of such experimental results, namely, the temperature dependence of the magnetization along the a- and b-axes in the RzCoz7 compounds (R = Nd, Pr, He and Dy). By fitting the experimental curves, the high order CEF parameter B~ and a precise value of the coupling parameter JRT have been derived. In the R - T compounds, the Hamiltonian acting on the R-ion in the ground multiplet d is expressed as 6
^m 4- gJ¢~BJB~ + gJ~B J B , B,~m0,~
HR = E n=O
(1)
m = -n
*Corresponding author. Tel.: + 84 4 8692518; fax: + 84 4 8692963; e-mail: [email protected].
where the first term is the CEF effect on the R-ion, the last two terms are contributions of the molecular field B,,, and the external field B, respectively. The total free energy of the R - T compound is expressed in the conventional form [3]. By minimizing the free energy at a given temperature and external field, the magnetization process as well as the temperature dependence of magnetization can be deduced. The computed results for thermomagnetic curves along the principal axes of the R2Co17 single crystals (R = Nd, Pr, He and Dy) are shown in Fig. 1. The experimental results are taken from Sinnema [1]. The same calculations have also been carried out on other single crystals such as Dy2Fe17, DyCos, and HoCo4AI and have been compared with the experimental results of Refs. [1-3]. In our calculations, all the CEF parameters obtained in the literature [2-8], except for B~, have been used, whereas, B 6 and Bm are adjustable parameters to get the best fits to the experimental data. Our main results are as follows. 1. Precise values of the high order CEF parameter B66 that was neglected or roughly evaluated in previous works have been obtained (see Table 1). For the R-ion, the anisotropy constant K4R, which determines the MCA term in the basal plane K4 sin60 cos 6q), can be expressed via the CEF parameters as K§ = B 6 ( ( 0 °) + (06)/2)/16, here (0~') represents the thermal average of 0',',~.Therefore, B 6 plays a decisive role in the determination of the sixfold anisotropy of the given R-T compounds.
0304-8853/98/$19.00 ,(? 1998 Elsevier Science B.V. All rights reserved PII S 0 3 0 4 - 8 8 5 3 ( 9 7 ) 0 0 8 8 3-4
P.D. Thang et aL /Journal of Magnetism and Magnetie Materials 177-18t (t998) 1099-1t00
1100 160
Table 1 Values of Bin, JRT and B~ obtained in the fitting procedure and AM measured at 4.2 K in RzCo:-~ compounds (applied field is indicated in brackets) 1-1t
b axis
140 120
ioo
a a.xis
a iLxis
< 8D g 6o
Nd2Col7 B = IT
40 20
i
< c axis
R
Pr2Coi 7 B=IT
c axis
Jwr (10 .23 J)
Pr 280 33.80 Nd 320 25.86 Dy 9 1 . 3 11.04 Ho 63.5 9.40
0 80 70
60 S0 .< 40 30
/
B~ (10- 3 K)
AM (A m2/kg)
- 1.466 - 8.0 - 0.284 0.137
10 18.7 - 3.6 1.9
(1 T) (1 T) (1 T) (4T)
.o2co. b axis
20 10
B~ (T)
B = 1T
c axis
0 I00
200
T (IO
300
200
I00
~,
200
T{K)
Fig. 1. The calculated results (solid lines) of NdzCol 7, Pr2Col v, Ho2Co~7 and Dy2Coav single crystals with the fitting parameters B m and B~ as listed in Table 1. Other CEF parameters used in the fitting procedure were taken from Refs. [4-@ The experimental results (points) are taken from Ref. [1"1.
2. Precise values of the molecular field Bm and the exchange parameter JRT have been derived (see Table 1). Up to now, several methods have been applied for determining Jr~x such as fitting the high field magnetization curves, analyzing the Curie or compensation temperatures. Our calculation can be considered as a new method for obtaining precise values of the R - T exchange interaction. To consider the different roles of B{ and Bm in the determination of the behaviour of thermomagnetic curves, we have studied the dependence on B{ and B,, of the difference in magnetization along the a- and b-axes at 4.2 K, AM = Mb -- Ma, and of the value of critical temperature, Ter, above which the sixfold anisotropy in the basal plane disappears. It turned out from this analysis that the strength of Bm has a crucial effect on the Tc~ value, whereas B{ plays a decisive role in the determination of the AM value. In Table 1 AM values measured by Sinnema 1-1] are listed along with our fitting values of B~ of the R2Co,7 compounds. It can be clearly seen that the bigger the absolute value of B~, the larger the magnitude of AM at 4.2 K. Our analysis on Dy2Felv, DyCos and HoCo4AI single crystals (not presented here) also give similar results. Nevertheless, the simple relation between the easy magnetization direction and the sign of B~ cannot be obtained and still needs more investigation. The obtained values of JRT of R2Co17 compounds are plotted in Fig. 2 together with result of Ref. [9]. It
% 30 -7, 20
this~ork C* Outer al. [9]
•
~~ ,
:
,
i
i
,
i
Ce Pr Nd Pin Sm Eu Gd T b Rare earth elements
i Dy
Ho Er
Fig. 2. The variation of the exchange coupling parameter ,/aTin the series of RzCol-~ compounds.
is clear that in the considered R - T series, the parameter JRT has the tendency to decrease from Pr to Tm. This phenomenon has been explained on the basis of the lanthanide contraction [10].
References [t1 S. Sinnema, Thesis, University of Amsterdam, 1988. [2t M. Ohkoshi, H. Kobayashi, T. Katayama, M. Hirano, T. Tsushima, Physica B 86-88 (1977) i95. [3] C.V. Thang, Thesis, University of Amsterdam, 1996. I-4] J.H.P. Colpa, P.H. Frings, R.J. Radwanski, J.J.M. Franse, M. Alba, J. Magn. Magn, Mater. 13i (1994) 167. [51 R.J. Radwanski, J.J.M. granse, S. Sinnema, H.J.M. Heerooms, J.H.P. Colpa, J. Magn. Magn. Mater. 76-77 (1988) 1982. [6] J.H.P. CoIpa, S. Sinnema, J.J.M. Franse, R.J. Radwanski, P.H. Frings, Physica B 156 (1989) 731. 1-71 A.V. Andreev, M.L Bartashevieh, A.V. Deryagin, E.N. Tarasov, Zh. Eksp. Theor. Fiz. 89 (3) (1985) 959. [8-1 A.S. Ermolenko, in: J. Fidler (Ed.), Proc. 6th Int. Workshop on Rare Earth-Cobalt Permanent Magnets, Vienna, 1982, p. 771. [91 N.H. Duc, T.D. Hien, D. Givord, J.J.M. Franse, F.R. de Boer, J. Magn. Magn. Mater. 124 (1993) 305. [10.1 E. Belorizky, M.A. Fremy, J.P. Gavigan, D. Givord, H.S. Li, J. Appl. Phys. 61 (1987) 3791.