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Magnetic coupling in the Gd-T intermetallics (T-Fe, Co)
Journal of Magnetism and Magnetic Materials 104-107 (1992) 1344-1346 North-Holland
Magnetic coupling in the G d - T intermetallics (T = Fe, Co) N . H . D u c a, T . D . H i e n a a n d D . G i v o r d b a Cryogenic" Laboratory, UniL,ersity of Hanoi, Hanoi, Viet Nam b Laboratoire Louis Ndel, C.N.R.S. 166X, 38042, Grenoble-cedex, France
Using the strength of the Gd-Gd interactions, deduced in different G d - T intermetallics from the ordering temperature of GdNi2, the G d - T exchange coupling parameter (A~d T) of the R,,,T,, (T = Fe or Co; m / n = 1/2; 1/3; 6/23; 1/5 and 2/17) and RmTnA k (A = metalloids and other metals; m / n / k = 1/4/1; 2/14/1; 1/11/1 and 1/10/2) systems has been evaluated from analysis of the Curie temperature. Going from T-poor to T-rich compounds, a tendency to decrease is found for both AGd_Co and AGd_Fe ; these variations are compared with those observed in the exchange parameters Aco co and
AFe-FeThe magnetic properties of the rare earth ( R ) - t r a n sition metal (T) compounds are determined, among others, by the large R - T exchange interactions. These interactions are thought to be caused by a combination of the intra-atomic 4 f - 5 d and inter-atomic 5 d - 3 d interactions [1]. It is usual to express them as an effective exchange Hamiltonian in the form Hexch = - - 2 A R T S R S T,
(1)
where ART is the R - T exchange coupling parameter, S R is the spin of the rare earth ion and S T the quasi-spin of the transition metal atom. In a two-sublattice model, the molecular field approximation leads to an expression for the exchange energy:
in addition that A a c o and AAFe have a tendency to decrease when going from T-poor to T-rich compounds and these variations were discussed in relation with the 3d magnetic moment values. However, in this analysis, the R - R interactions were neglected. In the present paper, the evaluation of ART from Tc is reconsidered for a number of G d - T intermetallics with taking into account the influence of the R - R interactions. The indirect method used to evaluate the value of ART is to compare the magnetic ordering temperatures of isostructural compounds with magnetic and nonmagnetic R elements according to the mean-field expression ( A R T / k ) 2= 9 ( T c - T R ) ( Tc - T T ) / 4 Z R T Z T R G R G T ,
(5) Eexch = - - n R T M R M T.
(2)
If only nearest neighbours are considered and assuming that the R - T exchange coupling is spatially isotropic and distance independent, the molecular field coefficient nRT relates to ART through nRT = Z R T A RT( g -- l ) / g l x Z N T ,
(3)
where ZRT is the number of nearest T neighbours of a given R atom, N T the number of the T atoms per mole and the other factors have their usual meaning. Analogously, one can define a molecular field coefficient nTR, proportional to A T R ( = A R T ) and the number of nearest R-neighbours of a T atom ZXR, as nTR = Z T R A R T ( g -- 1 ) / g l x Z NR .
(4)
In a given series of compounds, a usual first approximation is to assume that the R - T exchange coupling p a r a m e t e r ART is a constant [2,3]. However, in a systematic analysis of the ordering temperatures in R - F e and R C o 2 compounds, Belorizky et al. [4] have shown that the p a r a m e t e r A R T increases in a given series from compounds with heavy R elements to compounds with light R elements. Recently, Duc [5] showed
where Tc is the Curie temperature and T R and T.r represent the contribution to Tc due to R - R and T - T interactions, respectively. G R is the Gennes factor (gR -- 1)2JR(JR + 1) for rare earth atoms. GT, the corresponding factor for the transition metal, is inserted to obtained a symmetric expression. Assuming that the orbital moment of the T atom is quenched leads to gT = 2 and G T = St(S T + 1). T R is given by (6)
TR = 2ZRRARRGR/3k.
H e r e ZRR is the number of the R nearest neighbours of a given R atom and ARR is the R - R exchange exchange coupling parameter. As a first approximation, ARR may be deduced from the ordering temperature of the G d N i 2 compound in which Ni atoms are not magnetic. From Tc = 77 K, it is deduced that ARR = 2.5 X 10 -23 J. In relation (5) the value of T T was obtained by linear interpolation between the Tc values of compounds with nonmagnetic La and Lu. Finally, the effective spin value S T can be determined from the experimental data of the 3d paramagnetic susceptibility [3,5 and references therein]: CT = 4NTST(S T + 1)/3k(T-
0312-8853/92/$05.00 © 1992 - Elsevier Science Publishers B.V. All rights reserved
TT).
(7)
1345
N.H. Duc et aL / Magnetic coupling in the Gd-Tintermetallics
Gd-C0 systems
1.8
2/+
1.6
20
1./.
76
2.0
1.2
I
II
l I
I
I
12
I
~.5
-
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,,~
1
1.6
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1 ,,
''
'
'
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~
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o
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10
-\lp
L~
10
,,
1.0
,,
i ~ , , ,
, ~I~,
L5
2.0 lifT (JaB/at)
0.8
Fig. 2. The variations of ART as a function of the 3d magnetic moment in a number of G d - T intermetallics (I: this work; 2: from ref. [5]).
6
/ 0.6 0
o
Gd-Fe systems
i
~
i
L
0.1
0.2
0.3
0.~
2 crease significantly from T-poor to T-rich compounds, in agreement with ref. [5]. The dependences of ARC o a n d A RFe on the concentration of R element are presented in fig. 1. The variation obtained is approximately linear; only R F e l l T i and RFel0V 2 deviate significantly from this law. The values of ARCo and ARFe may be discussed in relation with the value of the 3d magnetic m o m e n t (fig. 2). The systematic increase of A R X with decreasing 3d magnetic moment, already reported in ref. [5], is confirmed, with some modification at low Mco values. According to Brooks et al. [10], the 3 d - 5 d interactions depend critically on 3 d - 5 d hybridisation. These results
R - c0ncentrafion Fig. I. ARX values (e) deduced for (a) the Gd-Fe and (b) G d - C o compounds. For comparison, the values of ATT representing T - T interactions are also indicated (©).
A systematic analysis of the ordering temperature was p e r f o r m e d in order to estimate the values of ART for a n u m b e r of the rare e a r t h - t r a n s i t i o n metal compounds. The results obtained are listed in table 1 together with those deduced from high-field magnetisation measurements [6-9]. Both ARC o and ARF e de-
Table 1 Experimental Tc and deduced exchange coupling parameter ART for a number of G d - T intermetallics. The ART values in the brackets are taken from high-field magnetisation measurements [6-9]. The temperatures TR, T.r and Aa~r (see eqs. (6-8) in the text) are also listed Compounds
Tc (K)
TR (K)
TT (K)
GdFe 2 GdFe 3 Gd6Fe23 Gd2Fei7 Gd2Fe]4B GdFel iTi GdFe 10V2
780 728 655 460 664 627 626
77 125 77 77 96 154 154
495 505 475 232 510 482 482
GdCo2 GdCo3 GdCo4B GdCo5 Gd2Coi7 Gd2Col4B
395 615
200 125 154 154 77 96
300 375 925 1145 955
505
1020 1240 1050
-
a) The recalculated value of ART [8] with ZRT = 18 for Er6Fe23,
ATT (10 22 j)
AR T (10-22 j)
13.5 10.2 6.9 2.2 4.9 5.8 5.8
1.62 (2.45) 1.28 (1.95) 1.24 (1.2) a) 1.12 1.15 (1.25) 1.26 1.26 (1.17)
-
8.5 12.9 15.7 17.1 16.6
-
(1.35)
1.75 (1.96) 1.55 (1.38) 1.49 (1.4) 1.50 (1.1) 1.41 (1.42)
1346
N.H. Duc et al. / Magnetic coupfing & the G d - T intermetallics
suggest thus t h a t hybridisation effects in rare e a r t h transition m e t a l alloys increase with the p e r c e n t a g e of R alloyed elements.
References [1] I.A. Campbell, J. Phys. F 2 (1972) L47. [2] R.J. Radwanski, Phys. Stat. Sal. 137b (1987) 487. [3] N.H. Duc, T.D. Hien and N.H. Chau, Acta Phys. Pol. A 78 (1990) 471. [4] E. Belorizky, M.E. Fremy, J.P. Gavigan, D. Givord and H.S. Li, J. Appl. Phys. 61 (1987) 3971.
[5] N.H. Duc, Phys. Stat. Sol. 164 (1991) 545. [6] J.P. Liu, X.P. Zhong, F.R. de Boer and K.H.J. Buscbow, J. Appl. Phys. 69 (1991) 5536. [7] T. Kohashi, M. Ono, M. Date, A. Yamagishi, X.P. Zhong, Q. Wang, F.M. Yang, R.J. Radwanski and F.R. de Boer, J. Appl. Phys. 69 (1991) 5542. [8] F.R. de Boer, X.P. Zhong, K.H.J. Buschow and T.H. Jacobs, to be published. [9] R. Verhoerf, P.H. Quang, J.J.M. Franse and R.J. Radwanski, J. Magn. Magn. Mater. 83 (1990) 139. [10] M.S.S. Brooks, L. Nordstrom and B. Johanson, J. Phys.: Condens. Matter 3 (1991) 2357.
Magnetic coupling in the G d - T intermetallics (T = Fe, Co) N . H . D u c a, T . D . H i e n a a n d D . G i v o r d b a Cryogenic" Laboratory, UniL,ersity of Hanoi, Hanoi, Viet Nam b Laboratoire Louis Ndel, C.N.R.S. 166X, 38042, Grenoble-cedex, France
Using the strength of the Gd-Gd interactions, deduced in different G d - T intermetallics from the ordering temperature of GdNi2, the G d - T exchange coupling parameter (A~d T) of the R,,,T,, (T = Fe or Co; m / n = 1/2; 1/3; 6/23; 1/5 and 2/17) and RmTnA k (A = metalloids and other metals; m / n / k = 1/4/1; 2/14/1; 1/11/1 and 1/10/2) systems has been evaluated from analysis of the Curie temperature. Going from T-poor to T-rich compounds, a tendency to decrease is found for both AGd_Co and AGd_Fe ; these variations are compared with those observed in the exchange parameters Aco co and
AFe-FeThe magnetic properties of the rare earth ( R ) - t r a n sition metal (T) compounds are determined, among others, by the large R - T exchange interactions. These interactions are thought to be caused by a combination of the intra-atomic 4 f - 5 d and inter-atomic 5 d - 3 d interactions [1]. It is usual to express them as an effective exchange Hamiltonian in the form Hexch = - - 2 A R T S R S T,
(1)
where ART is the R - T exchange coupling parameter, S R is the spin of the rare earth ion and S T the quasi-spin of the transition metal atom. In a two-sublattice model, the molecular field approximation leads to an expression for the exchange energy:
in addition that A a c o and AAFe have a tendency to decrease when going from T-poor to T-rich compounds and these variations were discussed in relation with the 3d magnetic moment values. However, in this analysis, the R - R interactions were neglected. In the present paper, the evaluation of ART from Tc is reconsidered for a number of G d - T intermetallics with taking into account the influence of the R - R interactions. The indirect method used to evaluate the value of ART is to compare the magnetic ordering temperatures of isostructural compounds with magnetic and nonmagnetic R elements according to the mean-field expression ( A R T / k ) 2= 9 ( T c - T R ) ( Tc - T T ) / 4 Z R T Z T R G R G T ,
(5) Eexch = - - n R T M R M T.
(2)
If only nearest neighbours are considered and assuming that the R - T exchange coupling is spatially isotropic and distance independent, the molecular field coefficient nRT relates to ART through nRT = Z R T A RT( g -- l ) / g l x Z N T ,
(3)
where ZRT is the number of nearest T neighbours of a given R atom, N T the number of the T atoms per mole and the other factors have their usual meaning. Analogously, one can define a molecular field coefficient nTR, proportional to A T R ( = A R T ) and the number of nearest R-neighbours of a T atom ZXR, as nTR = Z T R A R T ( g -- 1 ) / g l x Z NR .
(4)
In a given series of compounds, a usual first approximation is to assume that the R - T exchange coupling p a r a m e t e r ART is a constant [2,3]. However, in a systematic analysis of the ordering temperatures in R - F e and R C o 2 compounds, Belorizky et al. [4] have shown that the p a r a m e t e r A R T increases in a given series from compounds with heavy R elements to compounds with light R elements. Recently, Duc [5] showed
where Tc is the Curie temperature and T R and T.r represent the contribution to Tc due to R - R and T - T interactions, respectively. G R is the Gennes factor (gR -- 1)2JR(JR + 1) for rare earth atoms. GT, the corresponding factor for the transition metal, is inserted to obtained a symmetric expression. Assuming that the orbital moment of the T atom is quenched leads to gT = 2 and G T = St(S T + 1). T R is given by (6)
TR = 2ZRRARRGR/3k.
H e r e ZRR is the number of the R nearest neighbours of a given R atom and ARR is the R - R exchange exchange coupling parameter. As a first approximation, ARR may be deduced from the ordering temperature of the G d N i 2 compound in which Ni atoms are not magnetic. From Tc = 77 K, it is deduced that ARR = 2.5 X 10 -23 J. In relation (5) the value of T T was obtained by linear interpolation between the Tc values of compounds with nonmagnetic La and Lu. Finally, the effective spin value S T can be determined from the experimental data of the 3d paramagnetic susceptibility [3,5 and references therein]: CT = 4NTST(S T + 1)/3k(T-
0312-8853/92/$05.00 © 1992 - Elsevier Science Publishers B.V. All rights reserved
TT).
(7)
1345
N.H. Duc et aL / Magnetic coupling in the Gd-Tintermetallics
Gd-C0 systems
1.8
2/+
1.6
20
1./.
76
2.0
1.2
I
II
l I
I
I
12
I
~.5
-
."
'~
,,~
1
1.6
<
1 ,,
''
'
'
22
~
i.~_ ~
r-~ er~
o
1.z~
18 <
1.2
It+
1.0
10
-\lp
L~
10
,,
1.0
,,
i ~ , , ,
, ~I~,
L5
2.0 lifT (JaB/at)
0.8
Fig. 2. The variations of ART as a function of the 3d magnetic moment in a number of G d - T intermetallics (I: this work; 2: from ref. [5]).
6
/ 0.6 0
o
Gd-Fe systems
i
~
i
L
0.1
0.2
0.3
0.~
2 crease significantly from T-poor to T-rich compounds, in agreement with ref. [5]. The dependences of ARC o a n d A RFe on the concentration of R element are presented in fig. 1. The variation obtained is approximately linear; only R F e l l T i and RFel0V 2 deviate significantly from this law. The values of ARCo and ARFe may be discussed in relation with the value of the 3d magnetic m o m e n t (fig. 2). The systematic increase of A R X with decreasing 3d magnetic moment, already reported in ref. [5], is confirmed, with some modification at low Mco values. According to Brooks et al. [10], the 3 d - 5 d interactions depend critically on 3 d - 5 d hybridisation. These results
R - c0ncentrafion Fig. I. ARX values (e) deduced for (a) the Gd-Fe and (b) G d - C o compounds. For comparison, the values of ATT representing T - T interactions are also indicated (©).
A systematic analysis of the ordering temperature was p e r f o r m e d in order to estimate the values of ART for a n u m b e r of the rare e a r t h - t r a n s i t i o n metal compounds. The results obtained are listed in table 1 together with those deduced from high-field magnetisation measurements [6-9]. Both ARC o and ARF e de-
Table 1 Experimental Tc and deduced exchange coupling parameter ART for a number of G d - T intermetallics. The ART values in the brackets are taken from high-field magnetisation measurements [6-9]. The temperatures TR, T.r and Aa~r (see eqs. (6-8) in the text) are also listed Compounds
Tc (K)
TR (K)
TT (K)
GdFe 2 GdFe 3 Gd6Fe23 Gd2Fei7 Gd2Fe]4B GdFel iTi GdFe 10V2
780 728 655 460 664 627 626
77 125 77 77 96 154 154
495 505 475 232 510 482 482
GdCo2 GdCo3 GdCo4B GdCo5 Gd2Coi7 Gd2Col4B
395 615
200 125 154 154 77 96
300 375 925 1145 955
505
1020 1240 1050
-
a) The recalculated value of ART [8] with ZRT = 18 for Er6Fe23,
ATT (10 22 j)
AR T (10-22 j)
13.5 10.2 6.9 2.2 4.9 5.8 5.8
1.62 (2.45) 1.28 (1.95) 1.24 (1.2) a) 1.12 1.15 (1.25) 1.26 1.26 (1.17)
-
8.5 12.9 15.7 17.1 16.6
-
(1.35)
1.75 (1.96) 1.55 (1.38) 1.49 (1.4) 1.50 (1.1) 1.41 (1.42)
1346
N.H. Duc et al. / Magnetic coupfing & the G d - T intermetallics
suggest thus t h a t hybridisation effects in rare e a r t h transition m e t a l alloys increase with the p e r c e n t a g e of R alloyed elements.
References [1] I.A. Campbell, J. Phys. F 2 (1972) L47. [2] R.J. Radwanski, Phys. Stat. Sal. 137b (1987) 487. [3] N.H. Duc, T.D. Hien and N.H. Chau, Acta Phys. Pol. A 78 (1990) 471. [4] E. Belorizky, M.E. Fremy, J.P. Gavigan, D. Givord and H.S. Li, J. Appl. Phys. 61 (1987) 3971.
[5] N.H. Duc, Phys. Stat. Sol. 164 (1991) 545. [6] J.P. Liu, X.P. Zhong, F.R. de Boer and K.H.J. Buscbow, J. Appl. Phys. 69 (1991) 5536. [7] T. Kohashi, M. Ono, M. Date, A. Yamagishi, X.P. Zhong, Q. Wang, F.M. Yang, R.J. Radwanski and F.R. de Boer, J. Appl. Phys. 69 (1991) 5542. [8] F.R. de Boer, X.P. Zhong, K.H.J. Buschow and T.H. Jacobs, to be published. [9] R. Verhoerf, P.H. Quang, J.J.M. Franse and R.J. Radwanski, J. Magn. Magn. Mater. 83 (1990) 139. [10] M.S.S. Brooks, L. Nordstrom and B. Johanson, J. Phys.: Condens. Matter 3 (1991) 2357.