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Composition dependence of the magnetic properties of Ge-doped CeCu2Si2
Physica B 320 (2002) 380–383
Composition dependence of the magnetic properties of Ge-doped CeCu2Si2 ! M. Gomez Berissoa,*, P. Pedrazzinia, M. Deppeb, O. Trovarellib, C. Geibelb, J.G. Serenia a
! Lab. de Bajas Temperaturas, Centro Atomico Bariloche (CNEA) & CONICET, 8400, S.C. de Bariloche, Argentina b Max-Planck Institute for Chemical Physics of Solids, D-01187 Dresden, Germany
Abstract Due to the proximity of CeCu2 Si2 to a quantum critical point, the ground state of this compound is extremely sensitive to sample preparation conditions. Small excess of one component can lead to magnetic or superconducting behaviors. We found that in the alloy CeCu2 ðSi1x Gex Þ2 a small excess of Ge enhances the homogeneity range allowing a precise investigation of stoichiometric effects on the physical properties. In this system, Ge doping produces an increment of the antiferromagnetic transition temperature TN ; while the superconducting one decreases. Particularly, it was found that at x ¼ 0:1 both phases coexist at low temperature. In order to investigate the stability of these phases against changes of the Ce-ligands composition, we prepared a series of CeCu2þy ðSi0:9 Ge0:1 Þ2y samples ð0pyp0:10Þ and investigated their specific heat and electrical resistivity. We observed that the substitution of Si/Ge by Cu increases the characteristic temperature and weakens the magnetic contribution without modifying TN : A further transition, of the first order character, is observed at lower temperature. r 2002 Elsevier Science B.V. All rights reserved. Keywords: Non-Fermi liquid; Cerium systems
Since the discovery of superconductivity, the heavy fermion CeCu2 Si2 [1] has been the subject of continuous study due to an interesting interplay between magnetism and superconductivity. Due to the fact that this compound is almost exactly at the quantum critical point where magnetic order disappears, very small differences in composition lead to different physical ground state phases showing either superconductivity (S-Phase), unconventional magnetic order (A-Phase) or disordered magnetic state (X-Phase). The *Corresponding author. Tel.: +54-2944-445171; fax: +542944-445299. E-mail address: [email protected] ! (M. Gomez Berisso).
composition ground state phase diagram could be determined from a systematic study of the physical properties of slightly off-stochiometric samples [2]. This study showed that the main parameter determining the ground state is the Cu/ Si ratio. However, due to the very small homogeneity region (of the order of 1 at %), the relation between composition and physical parameters could only be established in a qualitative way, not in a quantitative one. Substituting Si by the larger, isoelectronic Ge leads to an increase of the unit cell and therefore, to a reduction of the 4f-conduction-electron hybridization and to a stabilization of the magnetic state in the alloy CeCu2 ðSi1x Gex Þ2 : However, superconductivity is still observed at x ¼ 0:1;
0921-4526/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 0 2 ) 0 0 7 5 3 - 6
! M. Gomez Berisso et al. / Physica B 320 (2002) 380–383
where it seems to coexist with magnetism in contrast to the situation at x ¼ 0: We found that in Ge-doped samples, a much larger amount of Ge/Si can be replaced by Cu, as evidenced e.g. by large changes in the lattice parameters [3]. This indicates an enlarged homogeneity range which, e.g. at x ¼ 0:1 ðCeCu2þy ðSi0:9 Ge0:1 Þ2y Þ; extends from yE0 to 0.15. This should allow a more precise determination of the effect of Cu/Siexchange on the physical properties than in pure CeCu2 Si2 : We have therefore investigated the physical properties of CeCu2þy ðSi0:9 Ge0:1 Þ2y by means of specific heat and resistivity measurements. Polycrystalline CeCu2þy ðSi0:9 Ge0:1 Þ2y samples of composition y ¼ 0; 0.03, 0.06 and 0.10 were prepared as described in Refs. [4,5]. Powder X-ray diffractometry shows that the samples are single phase with the ThCr2 Si2 -structure. Specific heat was measured by the conventional heat-pulse technique between 0.4 and 30 K and resistivity by the standard four-probe AC method in the 0.4–300 K range. The electronic specific heat Cel ðTÞ=T; after phonon subtraction, is shown in Fig. 1. The AF transition is observed for y ¼ 0 at TN ¼ 1:4 K (TN is determined at the steepest slope of Cel =T). As Cu-doping increases, the anomaly at TN ; DCel ðTN Þ=TN ; weakens and vanishes for y ¼ 0:1 1.5
while the transition temperature remains nearly constant. Below TN ; a peak is observed on the y ¼ 0ð0:6Þ sample at TII ¼ 0:9ð1:2Þ K; with the characteristics of a first order transition. This transition seems strongly dependent on the sample preparation procedure [6]. In Fig. 1 the Cel ðTÞ=T dependence of two CeCu2 ðSi0:9 Ge0:1 Þ2 samples (A and B) prepared with different annealing procedure are compared. While sample A shows a clear peak at 0:9 K; sample B shows only a weak kink. By comparing the specific heat results on both samples, an enthalpy of E0:02 J=mol is extracted for this transition. The sample with y ¼ 0:03 displays a similar behavior as sample B, while y ¼ 0:06-sample resembles to A. Finally, in the y ¼ 0:1 sample neither TN nor TII are observed. For T-0; Cel =T extrapolates to similar values ðE0:7 J=mol K2 Þ with the exception of the y ¼ 0:1 sample which extrapolates to approximately 1:25 J=mol K2 : Such a high value is expected from entropy considerations because this alloy has a lower Cel =T between 0.6 and 4 K: Although the Cel =T dependence of y ¼ 0:1 sample looks to be logarithmic between 0.7 and 1:7 K; it is found that the dependence above 2 K is better fitted by a power law. This power law also fits the dependence of all other y concentration samples up to 6 K: Although no peak is detected in the y ¼ 0:03 alloy, a closer inspection of the data shows a clear
TII
CeCu2+y(Si0.9Ge0.1)2-y
TN 2
Cel /T [J/mol K ]
381
y = 0 (A) y = 0 (B) y = 0.03 y = 0.06 y = 0.10
1.0
0.5
0.0
0
1
2
3
4
T [K] Fig. 1. Evolution of the specific heat and the two magnetic transitions of CeCu2þy ðSi0:9 Ge0:1 Þ2y samples with increasing Cu excess.
! M. Gomez Berisso et al. / Physica B 320 (2002) 380–383
382
kink observed in Cel =T: This hysteresis, observed in a particular polycrystalline sample, was not detected in a single crystal of the same composition. The high temperature rðTÞ evolution, shown in the inset of Fig. 2, exhibit the typical two maxima observed in these compounds. The first, at lower T; is usually related to the characteristic of the GS and the second to the excited crystal field (CF) levels. No significant changes in rðTÞ were detected between this sample and that of y ¼ 0: The decrease of Cel ðTÞ=T above TN as a function of y indicates that the entropy related to the Ce-doublet GS is reached in a wider range of temperature. This indicates that the characteristic energy of the Ce-4f-states ðkB T0 Þ increases with Cu-doping. Thus the disappearance of the magnetic ordered phases can be related to an increase of the 4f-characteristic energy. However, in contrast to the situation in Ge-doped and in pure CeCu2 Si2 (where TN continuously decreases with increasing T0 leading to a quantum critical point as expected in current models [7]), in CeCu2þy ðSi0:9 Ge0:1 Þ2y TN remains constant while the size of the anomaly decreases, leading to the disappearance of the magnetic order at a classical critical point but at a finite temperature. The origin of this differences is probably related to the effect of the disorder in the latter system.
change in the slope of Cel =T at TE1:1 K: In order to determine whether this feature corresponds to TII or to the onset of TN ; we have performed an accurate measurement of the resistivity on this sample in this range of temperature. A preliminary measurement of rð0:6 KoTo1:5 KÞ indicated the presence of hysteresis in that range of temperature, with a strong dependence on the previous thermal evolution. To perform a more precise determination of the hysteresis, two runs were performed along the following procedure, starting at high temperature T > 10 K; with each rðTÞ point measured at stable temperature. For the first run (see the upper curve in Fig. 2), the sample was cooled down to 1:1 K and then heated up to 1:4 K; showing a larger rðTÞ values during heating than during cooling. In a further cooling, from 1.4 to 0:6 K; rðTÞ values coincide indicating that the system underwent a first order transition. In the second run (lower curve in Fig. 2) the sample was cooled down to 0:7 K directly, showing a clear step at 1:2 K: By warming again, this time to much higher temperature, a complete hysteresis in rðTÞ is observed between 1.2 and 2:1 K: To check that the step at 1:2 K is not due to experimental instabilities, the run was repeated with the same result. It is clearly seen that the low temperature step of rðTÞ coincide with the temperature of the
1.0
ρ/ρ250K
1.4
TCF 0.8
Tρ
1.2
max
0.6
CeCu2.03(Si0.9Ge0.1)1.97 0.5
1.0
1.5
2.5 2.0
10 2.5
50 100 3.0
1.0
3.5
T [K] Fig. 2. Hysteretical behaviors of the electrical resistivity rðTÞ of a CeCu2:03 ðSi0:9 Ge0:1 Þ1:97 sample along a thermal cycle (upper data are shifted for clarity). Inset: high temperature resistivity.
! M. Gomez Berisso et al. / Physica B 320 (2002) 380–383
Remarkably, the unit cell volume does not change with y: Thus, the increase of T0 with y is not due to a reduction of the volume as in many other Kondo-lattice systems, but to the replacement of the weaker hybridization between Ce-4f-states and Si by the stronger one between Ce-4f-states and Cu when it is located in the Si crystallographic site.
References [1] F. Steglich, J. Aarts, C.D. Bredl, W. Lieke, D. Meschede, W. Franz, H. Schafer, Phys. Rev. Lett. 43 (1979) 1892.
383
[2] R. Muller-Reisener, . Diplomarbeit, Techniche Hochschule Darmstadt, December 1995; R. Modler, M. Lang, C. Geibel, C. Shank, R. Muller. Reisener, P. Hellmann, A. Link, G. Sparn, W. Assmus, F. Steglich, Physica B 206 & 207 (1995) 585. [3] M. Deppe, Diplomarbeit, Techniche Hochschule Darmstadt, March 1997. [4] K. Heuser, Diplomarbeit, Techniche Hochschule Darmstadt, July 1996. ! [5] O. Trovarelli, M. Weiden, R. Muller-Reisener, . M. Gomez Berisso, P. Gegenward, M. Deppe, C. Geibel, J.G. Sereni, F. Steglich, Phys. Rev. B 56 (1997) 678. [6] D. Bosse, Diplomarbeit, Techniche Hochschule Darmstadt, October 1998. [7] See for example J. Phys.: Condens. Mater. 8 (1996).
Composition dependence of the magnetic properties of Ge-doped CeCu2Si2 ! M. Gomez Berissoa,*, P. Pedrazzinia, M. Deppeb, O. Trovarellib, C. Geibelb, J.G. Serenia a
! Lab. de Bajas Temperaturas, Centro Atomico Bariloche (CNEA) & CONICET, 8400, S.C. de Bariloche, Argentina b Max-Planck Institute for Chemical Physics of Solids, D-01187 Dresden, Germany
Abstract Due to the proximity of CeCu2 Si2 to a quantum critical point, the ground state of this compound is extremely sensitive to sample preparation conditions. Small excess of one component can lead to magnetic or superconducting behaviors. We found that in the alloy CeCu2 ðSi1x Gex Þ2 a small excess of Ge enhances the homogeneity range allowing a precise investigation of stoichiometric effects on the physical properties. In this system, Ge doping produces an increment of the antiferromagnetic transition temperature TN ; while the superconducting one decreases. Particularly, it was found that at x ¼ 0:1 both phases coexist at low temperature. In order to investigate the stability of these phases against changes of the Ce-ligands composition, we prepared a series of CeCu2þy ðSi0:9 Ge0:1 Þ2y samples ð0pyp0:10Þ and investigated their specific heat and electrical resistivity. We observed that the substitution of Si/Ge by Cu increases the characteristic temperature and weakens the magnetic contribution without modifying TN : A further transition, of the first order character, is observed at lower temperature. r 2002 Elsevier Science B.V. All rights reserved. Keywords: Non-Fermi liquid; Cerium systems
Since the discovery of superconductivity, the heavy fermion CeCu2 Si2 [1] has been the subject of continuous study due to an interesting interplay between magnetism and superconductivity. Due to the fact that this compound is almost exactly at the quantum critical point where magnetic order disappears, very small differences in composition lead to different physical ground state phases showing either superconductivity (S-Phase), unconventional magnetic order (A-Phase) or disordered magnetic state (X-Phase). The *Corresponding author. Tel.: +54-2944-445171; fax: +542944-445299. E-mail address: [email protected] ! (M. Gomez Berisso).
composition ground state phase diagram could be determined from a systematic study of the physical properties of slightly off-stochiometric samples [2]. This study showed that the main parameter determining the ground state is the Cu/ Si ratio. However, due to the very small homogeneity region (of the order of 1 at %), the relation between composition and physical parameters could only be established in a qualitative way, not in a quantitative one. Substituting Si by the larger, isoelectronic Ge leads to an increase of the unit cell and therefore, to a reduction of the 4f-conduction-electron hybridization and to a stabilization of the magnetic state in the alloy CeCu2 ðSi1x Gex Þ2 : However, superconductivity is still observed at x ¼ 0:1;
0921-4526/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 0 2 ) 0 0 7 5 3 - 6
! M. Gomez Berisso et al. / Physica B 320 (2002) 380–383
where it seems to coexist with magnetism in contrast to the situation at x ¼ 0: We found that in Ge-doped samples, a much larger amount of Ge/Si can be replaced by Cu, as evidenced e.g. by large changes in the lattice parameters [3]. This indicates an enlarged homogeneity range which, e.g. at x ¼ 0:1 ðCeCu2þy ðSi0:9 Ge0:1 Þ2y Þ; extends from yE0 to 0.15. This should allow a more precise determination of the effect of Cu/Siexchange on the physical properties than in pure CeCu2 Si2 : We have therefore investigated the physical properties of CeCu2þy ðSi0:9 Ge0:1 Þ2y by means of specific heat and resistivity measurements. Polycrystalline CeCu2þy ðSi0:9 Ge0:1 Þ2y samples of composition y ¼ 0; 0.03, 0.06 and 0.10 were prepared as described in Refs. [4,5]. Powder X-ray diffractometry shows that the samples are single phase with the ThCr2 Si2 -structure. Specific heat was measured by the conventional heat-pulse technique between 0.4 and 30 K and resistivity by the standard four-probe AC method in the 0.4–300 K range. The electronic specific heat Cel ðTÞ=T; after phonon subtraction, is shown in Fig. 1. The AF transition is observed for y ¼ 0 at TN ¼ 1:4 K (TN is determined at the steepest slope of Cel =T). As Cu-doping increases, the anomaly at TN ; DCel ðTN Þ=TN ; weakens and vanishes for y ¼ 0:1 1.5
while the transition temperature remains nearly constant. Below TN ; a peak is observed on the y ¼ 0ð0:6Þ sample at TII ¼ 0:9ð1:2Þ K; with the characteristics of a first order transition. This transition seems strongly dependent on the sample preparation procedure [6]. In Fig. 1 the Cel ðTÞ=T dependence of two CeCu2 ðSi0:9 Ge0:1 Þ2 samples (A and B) prepared with different annealing procedure are compared. While sample A shows a clear peak at 0:9 K; sample B shows only a weak kink. By comparing the specific heat results on both samples, an enthalpy of E0:02 J=mol is extracted for this transition. The sample with y ¼ 0:03 displays a similar behavior as sample B, while y ¼ 0:06-sample resembles to A. Finally, in the y ¼ 0:1 sample neither TN nor TII are observed. For T-0; Cel =T extrapolates to similar values ðE0:7 J=mol K2 Þ with the exception of the y ¼ 0:1 sample which extrapolates to approximately 1:25 J=mol K2 : Such a high value is expected from entropy considerations because this alloy has a lower Cel =T between 0.6 and 4 K: Although the Cel =T dependence of y ¼ 0:1 sample looks to be logarithmic between 0.7 and 1:7 K; it is found that the dependence above 2 K is better fitted by a power law. This power law also fits the dependence of all other y concentration samples up to 6 K: Although no peak is detected in the y ¼ 0:03 alloy, a closer inspection of the data shows a clear
TII
CeCu2+y(Si0.9Ge0.1)2-y
TN 2
Cel /T [J/mol K ]
381
y = 0 (A) y = 0 (B) y = 0.03 y = 0.06 y = 0.10
1.0
0.5
0.0
0
1
2
3
4
T [K] Fig. 1. Evolution of the specific heat and the two magnetic transitions of CeCu2þy ðSi0:9 Ge0:1 Þ2y samples with increasing Cu excess.
! M. Gomez Berisso et al. / Physica B 320 (2002) 380–383
382
kink observed in Cel =T: This hysteresis, observed in a particular polycrystalline sample, was not detected in a single crystal of the same composition. The high temperature rðTÞ evolution, shown in the inset of Fig. 2, exhibit the typical two maxima observed in these compounds. The first, at lower T; is usually related to the characteristic of the GS and the second to the excited crystal field (CF) levels. No significant changes in rðTÞ were detected between this sample and that of y ¼ 0: The decrease of Cel ðTÞ=T above TN as a function of y indicates that the entropy related to the Ce-doublet GS is reached in a wider range of temperature. This indicates that the characteristic energy of the Ce-4f-states ðkB T0 Þ increases with Cu-doping. Thus the disappearance of the magnetic ordered phases can be related to an increase of the 4f-characteristic energy. However, in contrast to the situation in Ge-doped and in pure CeCu2 Si2 (where TN continuously decreases with increasing T0 leading to a quantum critical point as expected in current models [7]), in CeCu2þy ðSi0:9 Ge0:1 Þ2y TN remains constant while the size of the anomaly decreases, leading to the disappearance of the magnetic order at a classical critical point but at a finite temperature. The origin of this differences is probably related to the effect of the disorder in the latter system.
change in the slope of Cel =T at TE1:1 K: In order to determine whether this feature corresponds to TII or to the onset of TN ; we have performed an accurate measurement of the resistivity on this sample in this range of temperature. A preliminary measurement of rð0:6 KoTo1:5 KÞ indicated the presence of hysteresis in that range of temperature, with a strong dependence on the previous thermal evolution. To perform a more precise determination of the hysteresis, two runs were performed along the following procedure, starting at high temperature T > 10 K; with each rðTÞ point measured at stable temperature. For the first run (see the upper curve in Fig. 2), the sample was cooled down to 1:1 K and then heated up to 1:4 K; showing a larger rðTÞ values during heating than during cooling. In a further cooling, from 1.4 to 0:6 K; rðTÞ values coincide indicating that the system underwent a first order transition. In the second run (lower curve in Fig. 2) the sample was cooled down to 0:7 K directly, showing a clear step at 1:2 K: By warming again, this time to much higher temperature, a complete hysteresis in rðTÞ is observed between 1.2 and 2:1 K: To check that the step at 1:2 K is not due to experimental instabilities, the run was repeated with the same result. It is clearly seen that the low temperature step of rðTÞ coincide with the temperature of the
1.0
ρ/ρ250K
1.4
TCF 0.8
Tρ
1.2
max
0.6
CeCu2.03(Si0.9Ge0.1)1.97 0.5
1.0
1.5
2.5 2.0
10 2.5
50 100 3.0
1.0
3.5
T [K] Fig. 2. Hysteretical behaviors of the electrical resistivity rðTÞ of a CeCu2:03 ðSi0:9 Ge0:1 Þ1:97 sample along a thermal cycle (upper data are shifted for clarity). Inset: high temperature resistivity.
! M. Gomez Berisso et al. / Physica B 320 (2002) 380–383
Remarkably, the unit cell volume does not change with y: Thus, the increase of T0 with y is not due to a reduction of the volume as in many other Kondo-lattice systems, but to the replacement of the weaker hybridization between Ce-4f-states and Si by the stronger one between Ce-4f-states and Cu when it is located in the Si crystallographic site.
References [1] F. Steglich, J. Aarts, C.D. Bredl, W. Lieke, D. Meschede, W. Franz, H. Schafer, Phys. Rev. Lett. 43 (1979) 1892.
383
[2] R. Muller-Reisener, . Diplomarbeit, Techniche Hochschule Darmstadt, December 1995; R. Modler, M. Lang, C. Geibel, C. Shank, R. Muller. Reisener, P. Hellmann, A. Link, G. Sparn, W. Assmus, F. Steglich, Physica B 206 & 207 (1995) 585. [3] M. Deppe, Diplomarbeit, Techniche Hochschule Darmstadt, March 1997. [4] K. Heuser, Diplomarbeit, Techniche Hochschule Darmstadt, July 1996. ! [5] O. Trovarelli, M. Weiden, R. Muller-Reisener, . M. Gomez Berisso, P. Gegenward, M. Deppe, C. Geibel, J.G. Sereni, F. Steglich, Phys. Rev. B 56 (1997) 678. [6] D. Bosse, Diplomarbeit, Techniche Hochschule Darmstadt, October 1998. [7] See for example J. Phys.: Condens. Mater. 8 (1996).