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Resistivity anomalies due to charge fluctuations of Ce in LaCu6
Journal of Magnetism and Magnetic Materials 86 (1990) 293-295 North-Holland
293
R E S I S T I V r I ~ A N O M A L I E S DUE T O CHARGE F L U C T U A T I O N S O F Ce IN LaCu 6 A. SLEBARSKI Instytut Fizyki, UniwersytetSlaski, 40-007 Katowice, Poland Received 4 October 1989 Measurements of the electricalresistivityof polycrystallinesamples of Lal_xRExCu6 (RE= Ce, Pr, Gd) are presented. This paper presents a qualitative analysis of the resistivity anomalies correlate with the temperature-dependent fluctuation temperature Tf. 1. Introduction The main goal of this work was to enlarge the empirical basis of the resistivity anomaly A 0 ( T ) -P a l l o y - - Pmatrix of dilute rare earth (RE) impurities with unstable 4f shells in metals and in alloys. This anomaly is usually interpreted for Ce impurities in terms of the Kondo effect, namely the effective impurity cross section increases over the normal cross section due to potential scattering by an instability of the 4f shell (positive resistivity anomaly). However, it was recently found [1,2] that the resistivity anomalies of dilute Ce in ZrIr 2 are negative, i.e. that the Ap resistivity increment becomes much smaller than that of the stable impurities. It was suggested in refs. [1,2] that, at T = 0, the resistivity increment A0 comes from the potential scattering due to the charge density contrast of the impurity against the matrix, which follows from the fractional valence of both impurity and matrix. In this paper the resistivity anomalies of La l_xCexCu 6 are analysed by using the dynamic alloy model [3]. A qualitative description of such resistivity anomalies is proposed here by calculating the scattering of conduction electrons (ce) on valence fluctuations (charge fluctuations) of Ce impurities in the LaCu 6 lattice. The LaCu 6 matrix was chosen for the following reasons. Ce in C e C u 6 is in a mixed valence state according to the resistivity (v ffi 3.05 [4]) and L m X-ray absorption data (v ffi
3.11 [5]). On the other hand the susceptibility and resistivity analogy of LaCu 6 to LaAl 2 suggests that the possibility of a 4f instability of La in LaCu 6 should be considered.
2. Experiment and discussion
Polycrystalline samples of 2% and 3% of Ce, Pr and G d in LaCu 6 were prepared by melting the RECu 6 compounds in a levitation furnace under an argon atmosphere. For LaCu 6 and for t h e Ce, Pr and G d alloys the monoclinic structure were found [6]. The X-ray examination performed by the powder method, using F e K a radiation, has shown that the lattice parameter b of the Ce alloy is much smaller than that of the remaining alloys, while the a and c parameters of these alloys are comparable. The resistivity of the Lal_xRExCu 6 alloys was measured by the Van der Panw (dc) method. Fig. 1 shows the resistivity and the susceptibility of LaCu 6 matrix. Even though the residual resistivity of LaCu 6 is small (p(4 K ) = 2 t~fl cm), its susceptibility strongly depends on the temperature, which seems to be characteristic for the known La alloys. At room temperature the susceptibility equals 1.3 × 10 -4 e m u / m o l and is comparable with the literature data of single crystals [7]. Fig. 2 shows the resistivity increment A p / x of 2% and 3% of Gd, Pr and Ce alloys. The A p / x vs. T depends on the kind~ of impurity and is nearly temperature independent for G d because of the
0304-8853/90/$03.50 © 1990 - ElsevierSciencePublishers B.V. (North-Holland)
294
A. Slebarski / Resistivity anomalies in LaCu 6
same curvature of p ( T ) in LaCu 6 and GdCu 6. This is in contrast to Pr and Ce. A p / x of Pr increases for T larger than 20 K and saturates above 200 K; Ce impurities show a minimum at T = 32 K, characteristic for the diluted Kondo systems. The residual resistivities A p / x of 2% and 3% Ce alloys are comparable with the literature data for La]_xCexCu 6 single crystals [7]. However, the big discrepancy for these experiments is observed in A p / x ( T ) curvature at 4 K
21
La---REC~6
• 2 % Gd
I ~ s .*,.,,~,." .,o, o,,,,,, , , o , , ,, ,, o, , ,,~ o3%Gd OI
.....SY
3" 2,
, o,o,ooooo, o' °, °
"2%o3OloPr Pr
o
~o.op
o4 "~ 0
o 2
°,~,oo,.f I.
,2 % Ce o 3 % Ce
0 o
Temperature (g ) Fig. 2. Resistivity increment & p / x for 2% and 3% of Gd, Pr and Ce impurities in LaCu 6. T h e sofid line represents the A p ( T ) as calculated by the use of eqs. (1)-(3).
J =-~ multiplet 3000 K above without CF-splittings. For comparision with a neutron measurement, the quasi-elastic linewidth for CeCu 6 is a strongly nonlinear function of temperature with approximately FQE/k a = 5 K at T - - 0 and with FQv_/kB
LoCu 6
I\,.
E
30.
........If:IS"
a_~Gdoo2CU L 6
k
o
........:'...... ......%.SI ......
...."'S" "" .:...... :.....
~20.
~.La Cu 6
10.
II 0
0 0
1~)o
2oo
temperature { K )
3oo
o
loo
200
Temperature {K)
Fig. 1. (a) Susceptibifity of LaCu 6 versus temperature; (b) resistivity of LaCu 6.
3OO
A. Slebarski / Resistivityanomaliesin LaCu6
295
= 60 K at 300 K. C o m p a r i n g the dilute impurity state in Lal_xCexCu 6 and the C e C u r , the drastic change of Tf is not observed. T h e main idea of the d y n a m i c alloy model [3] is that the periodic intermetallic c o m p o u n d with unstable ions can be regarded as the d y n a m i c alloy. At high temperatures, the minority configuration of the two configurations 4f n and 4f n+l involved in the valence mixture can be looked at as an " i m p u r i t y " which produces a scattering potential for the c o n d u c t i o n electrons. This potential fluctuates with some fluctuation time rf = h/k~Tf. T h e second time scale in the model is an inelastic life time r e of the ce, % = h/kBT. A t high T when % << rf, ce see the full scattering potential coming f r o m the minority configuration, but at low T r e >> ~f, the ce average over the fluctuating potential and it is " s e e n " as a mean-field potential coherent scattering). T h e formula for the resistivity AO per impurity a t o m was derived in refs. [9,10]:
AO2 is the resistivity a n o m a l y of the real alloy of Ce 3+ and La ions and the scattering is entirely incoherent. I n fig. 2 the experimental d a t a o f the 3% Ce alloy are c o m p a r e d with the A o ( T ) behaviour obtained using eqs. (1)-(3). T h e values of Tf's have been extracted f r o m susceptibility, the value of J, at T = 300 K has been taken f r o m L m X - r a y absorption measurement [5]. It seems that the qualitative behaviour of the observed anomalies can be u n d e r s t o o d in terms of the d y n a m i c alloy model.
AO = AO1 + AO2
References
ne2kB------~ 1 + 4 q r 2 v 2 ( T f / T ) 2 Tt + W
I W1 12 = I WRE,÷-- WRE3+I2, I W2 ]2 = i I~,RE,+" _ WM 12.
'
(1) (2) (3)
W a is the one-site scattering potential, W M is the scattering potential of the host ions. At high T the system looks like a three-component alloy of Ce 3+, C e 4+ and L a ions, when the temperature is decreased the ce start to average o v e r C e 3 + - C e 4+ valence fluctuations and at very low T the system looks like a t w o - c o m p o n e n t alloy of La and Ce 3 +" ions. A01 is the resistivity a n o m a l y of d y n a m i c alloy of Ce ions and represents incoherent scattering at high T, but at low T it "'looks" different.
Acknowledgements I would like to thank E. Z i p p e r for helpful discussions. This work was supported b y the Polish A c a d e m y of Sciences f r o m the p r o b l e m C P B P 01.04.
[1] A. Slebarski and D. Wohl|eben, Z. Phys. B 60 (1985) 449. [2] A. ~lebarski, D. Wohlleben and P. Weidner, Z. Phys. B 61 (1985) 177. [3] D. Wohlleben and B. Wittershagen, Advan. Phys. 24 (1985) 403. [4] E. BHck, A. Nowack, N. Holm, E. Paulus and A. Freimuth, Z. Phys. B 63 (1986) 155. [5] J. Rtlhler, Handbook on the Physics and Chemistry of Rare-Earth, vol. 10, eds. K.A. Gsehneidner, Jr., L. Eyring and S. Htifner (North-Holland, Amsterdam, 1987) p. 453. [6] H. Asano, M. Umino, Y. Hataoke, Y. Shlmizu, Y. Orluki, T. Komatsubara and F. ,lzumi, J. Phys. Soe. Japan 54 (1985) 3358. [7] Y. Onuki, Y. Shimizu, 1~v~.Misbihara, Y. Machii and T. Komatsubara, J. Phys. So¢. Japan 54 (1985) 1964. [8] U. Walter, D. Wohllebea and Z. Fisk, Z. phys. B 60 (1986) 325. [9] E. Zipper, M. Drzazga and A. Freimuth, J. Magn. Magn. Mat. 71 (1987) 119. [10] A. ~lebarski, E. Zipper and M. Drzazga, J. Magn. Magn. Mat. 76&77 (1988) 249.
293
R E S I S T I V r I ~ A N O M A L I E S DUE T O CHARGE F L U C T U A T I O N S O F Ce IN LaCu 6 A. SLEBARSKI Instytut Fizyki, UniwersytetSlaski, 40-007 Katowice, Poland Received 4 October 1989 Measurements of the electricalresistivityof polycrystallinesamples of Lal_xRExCu6 (RE= Ce, Pr, Gd) are presented. This paper presents a qualitative analysis of the resistivity anomalies correlate with the temperature-dependent fluctuation temperature Tf. 1. Introduction The main goal of this work was to enlarge the empirical basis of the resistivity anomaly A 0 ( T ) -P a l l o y - - Pmatrix of dilute rare earth (RE) impurities with unstable 4f shells in metals and in alloys. This anomaly is usually interpreted for Ce impurities in terms of the Kondo effect, namely the effective impurity cross section increases over the normal cross section due to potential scattering by an instability of the 4f shell (positive resistivity anomaly). However, it was recently found [1,2] that the resistivity anomalies of dilute Ce in ZrIr 2 are negative, i.e. that the Ap resistivity increment becomes much smaller than that of the stable impurities. It was suggested in refs. [1,2] that, at T = 0, the resistivity increment A0 comes from the potential scattering due to the charge density contrast of the impurity against the matrix, which follows from the fractional valence of both impurity and matrix. In this paper the resistivity anomalies of La l_xCexCu 6 are analysed by using the dynamic alloy model [3]. A qualitative description of such resistivity anomalies is proposed here by calculating the scattering of conduction electrons (ce) on valence fluctuations (charge fluctuations) of Ce impurities in the LaCu 6 lattice. The LaCu 6 matrix was chosen for the following reasons. Ce in C e C u 6 is in a mixed valence state according to the resistivity (v ffi 3.05 [4]) and L m X-ray absorption data (v ffi
3.11 [5]). On the other hand the susceptibility and resistivity analogy of LaCu 6 to LaAl 2 suggests that the possibility of a 4f instability of La in LaCu 6 should be considered.
2. Experiment and discussion
Polycrystalline samples of 2% and 3% of Ce, Pr and G d in LaCu 6 were prepared by melting the RECu 6 compounds in a levitation furnace under an argon atmosphere. For LaCu 6 and for t h e Ce, Pr and G d alloys the monoclinic structure were found [6]. The X-ray examination performed by the powder method, using F e K a radiation, has shown that the lattice parameter b of the Ce alloy is much smaller than that of the remaining alloys, while the a and c parameters of these alloys are comparable. The resistivity of the Lal_xRExCu 6 alloys was measured by the Van der Panw (dc) method. Fig. 1 shows the resistivity and the susceptibility of LaCu 6 matrix. Even though the residual resistivity of LaCu 6 is small (p(4 K ) = 2 t~fl cm), its susceptibility strongly depends on the temperature, which seems to be characteristic for the known La alloys. At room temperature the susceptibility equals 1.3 × 10 -4 e m u / m o l and is comparable with the literature data of single crystals [7]. Fig. 2 shows the resistivity increment A p / x of 2% and 3% of Gd, Pr and Ce alloys. The A p / x vs. T depends on the kind~ of impurity and is nearly temperature independent for G d because of the
0304-8853/90/$03.50 © 1990 - ElsevierSciencePublishers B.V. (North-Holland)
294
A. Slebarski / Resistivity anomalies in LaCu 6
same curvature of p ( T ) in LaCu 6 and GdCu 6. This is in contrast to Pr and Ce. A p / x of Pr increases for T larger than 20 K and saturates above 200 K; Ce impurities show a minimum at T = 32 K, characteristic for the diluted Kondo systems. The residual resistivities A p / x of 2% and 3% Ce alloys are comparable with the literature data for La]_xCexCu 6 single crystals [7]. However, the big discrepancy for these experiments is observed in A p / x ( T ) curvature at 4 K
21
La---REC~6
• 2 % Gd
I ~ s .*,.,,~,." .,o, o,,,,,, , , o , , ,, ,, o, , ,,~ o3%Gd OI
.....SY
3" 2,
, o,o,ooooo, o' °, °
"2%o3OloPr Pr
o
~o.op
o4 "~ 0
o 2
°,~,oo,.f I.
,2 % Ce o 3 % Ce
0 o
Temperature (g ) Fig. 2. Resistivity increment & p / x for 2% and 3% of Gd, Pr and Ce impurities in LaCu 6. T h e sofid line represents the A p ( T ) as calculated by the use of eqs. (1)-(3).
J =-~ multiplet 3000 K above without CF-splittings. For comparision with a neutron measurement, the quasi-elastic linewidth for CeCu 6 is a strongly nonlinear function of temperature with approximately FQE/k a = 5 K at T - - 0 and with FQv_/kB
LoCu 6
I\,.
E
30.
........If:IS"
a_~Gdoo2CU L 6
k
o
........:'...... ......%.SI ......
...."'S" "" .:...... :.....
~20.
~.La Cu 6
10.
II 0
0 0
1~)o
2oo
temperature { K )
3oo
o
loo
200
Temperature {K)
Fig. 1. (a) Susceptibifity of LaCu 6 versus temperature; (b) resistivity of LaCu 6.
3OO
A. Slebarski / Resistivityanomaliesin LaCu6
295
= 60 K at 300 K. C o m p a r i n g the dilute impurity state in Lal_xCexCu 6 and the C e C u r , the drastic change of Tf is not observed. T h e main idea of the d y n a m i c alloy model [3] is that the periodic intermetallic c o m p o u n d with unstable ions can be regarded as the d y n a m i c alloy. At high temperatures, the minority configuration of the two configurations 4f n and 4f n+l involved in the valence mixture can be looked at as an " i m p u r i t y " which produces a scattering potential for the c o n d u c t i o n electrons. This potential fluctuates with some fluctuation time rf = h/k~Tf. T h e second time scale in the model is an inelastic life time r e of the ce, % = h/kBT. A t high T when % << rf, ce see the full scattering potential coming f r o m the minority configuration, but at low T r e >> ~f, the ce average over the fluctuating potential and it is " s e e n " as a mean-field potential coherent scattering). T h e formula for the resistivity AO per impurity a t o m was derived in refs. [9,10]:
AO2 is the resistivity a n o m a l y of the real alloy of Ce 3+ and La ions and the scattering is entirely incoherent. I n fig. 2 the experimental d a t a o f the 3% Ce alloy are c o m p a r e d with the A o ( T ) behaviour obtained using eqs. (1)-(3). T h e values of Tf's have been extracted f r o m susceptibility, the value of J, at T = 300 K has been taken f r o m L m X - r a y absorption measurement [5]. It seems that the qualitative behaviour of the observed anomalies can be u n d e r s t o o d in terms of the d y n a m i c alloy model.
AO = AO1 + AO2
References
ne2kB------~ 1 + 4 q r 2 v 2 ( T f / T ) 2 Tt + W
I W1 12 = I WRE,÷-- WRE3+I2, I W2 ]2 = i I~,RE,+" _ WM 12.
'
(1) (2) (3)
W a is the one-site scattering potential, W M is the scattering potential of the host ions. At high T the system looks like a three-component alloy of Ce 3+, C e 4+ and L a ions, when the temperature is decreased the ce start to average o v e r C e 3 + - C e 4+ valence fluctuations and at very low T the system looks like a t w o - c o m p o n e n t alloy of La and Ce 3 +" ions. A01 is the resistivity a n o m a l y of d y n a m i c alloy of Ce ions and represents incoherent scattering at high T, but at low T it "'looks" different.
Acknowledgements I would like to thank E. Z i p p e r for helpful discussions. This work was supported b y the Polish A c a d e m y of Sciences f r o m the p r o b l e m C P B P 01.04.
[1] A. Slebarski and D. Wohl|eben, Z. Phys. B 60 (1985) 449. [2] A. ~lebarski, D. Wohlleben and P. Weidner, Z. Phys. B 61 (1985) 177. [3] D. Wohlleben and B. Wittershagen, Advan. Phys. 24 (1985) 403. [4] E. BHck, A. Nowack, N. Holm, E. Paulus and A. Freimuth, Z. Phys. B 63 (1986) 155. [5] J. Rtlhler, Handbook on the Physics and Chemistry of Rare-Earth, vol. 10, eds. K.A. Gsehneidner, Jr., L. Eyring and S. Htifner (North-Holland, Amsterdam, 1987) p. 453. [6] H. Asano, M. Umino, Y. Hataoke, Y. Shlmizu, Y. Orluki, T. Komatsubara and F. ,lzumi, J. Phys. Soe. Japan 54 (1985) 3358. [7] Y. Onuki, Y. Shimizu, 1~v~.Misbihara, Y. Machii and T. Komatsubara, J. Phys. So¢. Japan 54 (1985) 1964. [8] U. Walter, D. Wohllebea and Z. Fisk, Z. phys. B 60 (1986) 325. [9] E. Zipper, M. Drzazga and A. Freimuth, J. Magn. Magn. Mat. 71 (1987) 119. [10] A. ~lebarski, E. Zipper and M. Drzazga, J. Magn. Magn. Mat. 76&77 (1988) 249.