- Email: [email protected]
Electronic properties of stable quasicrystals: towards a semiconducting quasicrystal?
J O U R N A L OF
Journal of Non-Crystalline Solids 156-158 (1993) 901-904 North-Holland
~
~lll~
Electronic properties of stable quasicrystals: towards a semiconducting quasicrystal? T. Klein, C. Berger, G. F o u r c a u d o t , J.C. Grieco, P. Lanco and F. Cyrot-Lackmann L E P E S - CNRS, BP166, 38042 Grenoble c~dex 9, France
Anomalous transport properties are presented of a series of pure AICuFe icosahedral phases of very high structural quality including a millimetre size single grain. The most salient feature is that all these metallic samples present very high resistivity values close to the metal-insulator transition (MIT) rising up to 10000 i~tq cm at 4 K in A162.5Cu25Fe12.5. The resistivity at 4 K depends strongly on the structural quality in a very peculiar way, since it increases when the structural defects are removed. It also varies strongly with the nominal composition of the sample increasing by a factor of almost 2.5 for only a 0.5% change in the composition. On the contrary, it is remarkable that the temperature dependence of the conductivity is almost independent of the composition and the structural quality. It is shown that, at low temperature, the temperature - and the magnetic field - dependence of the conductivity can be analyzed with classical weak localization theories including, however, strong electron-electron interaction similarly to that observed in systems close to a MIT. Similar peculiar behaviours are observed by preliminary measurements in the new A1PdMn stable icosahedral phase.
1. Introduction The quasicrystalline structure is a new state of condensed matter showing long range orientational order without translational periodicity. Most of these alloys are metastable phases, but a few thermodynamically stable quasicrystals (QC) have also been discovered. Among them, the AICuFe alloy allowed one for the first time to obtain very high structural quality alloys [1], including single grains [2], and is thus of peculiar interest for the study of the specific properties of this new system. The most striking feature is that this alloy seems to be close to the metal-insulator transition [3], showing resistivity values up to 10000 ~,12 cm at 4 K in AICuFe and even 30000 ~ cm in AICuRu [4]. However, despite these very high resistivities, the temperature and magnetic field dependences of the conductivity can
Corresl~ndence to: Dr C. Berger, LEPES - CNRS, 25 ave. des Martyrs, 38042 Grenoble c6dex 9, France.Tel: + 33 76 88 78 99. Telefax: + 33 76 88 79 88.
be well described [4-6] by quantum interference effects [7,8].
2. Experimental procedure Quasicrystalline samples of various compositions close t o AI63Cu25Fe12 have been prepared by melt-spinning. An annealing treatment (a few hours at 800°C) is always necessary to remove the structural defects due to the rapid quenching and traces of crystalline phases. The purity and quality of the phases are confirmed by X-ray diffraction [1,3]. For some compositions close to A162Cu25.5Fe12.5, an annealing treatment at lower temperature (600°C) allows elimination of the crystalline phases, but not the structural defects. This treatment is thus of great importance for the investigation of the influence of the structural quality on the transport properties. The resistivity was measured using the classical four-probe method down to 300 mK and in pulsed magnetic fields up to 35 T at the Toulouse National High Field Facilities (between 1.8 and 110 K). The resistivity values at room temperature are
0022-3093/93/$06.00 © 1993 - Elsevier Science Publishers B.V. All rights reserved
902
T. Klein et aL / Electronic properties of stable quasicrystals 600
12000 10000 ~ ' ~ 8000 -
6oo°c - 2h
A162.sCu25Fe12.5
~ " ~
500
800°C-3h
~
•~,
800oc - 3h
I-"..~ 400
A163Cu25Fe12
600°C - 2h
300
6000
62Cu25-sFe12-5
800°C - 3h
62.5Cu25Fe12.5
I~ 200
ca. 4000 2000 0
~3C u24.5 F e 12.5
0
50
100
150
800°C - 3h
100
600°C-3h 800°C-2h A162Cu25.5Fe12.5
0 200
250
300
0
50 100 150 200 250 300 T (K)
T (K) Fig. I. Temperature dependence of the resistivity of AICuFe samples showing the evolution of resistivity with composition and structural quality.
average values obtained on a series of about ten samples out of the same batch. A typical error margin is about 10%.
3. Results The most salient feature is that the high quality AICuFe samples show very high resistivity values up to 10000 Ixtq cm in A16zsCu25Fet2.s. Comparable values have been measured in other stable A1PdMn [9] and A1CuRu [4] QC samples. These values are two orders of magnitude higher than those observed in amorphous systems [8] or metastable QC but similar to those of heavily doped semiconductors on the metallic side of the metal-insulator transition. Further, as shown in fig. l for A162Cu25.5Fe12.5 , a non-expected feature is that the resistivity sample increases as the structural defects are removed. This behaviour is by striking contrast with that of a crystal, for which the reduction of defects reduces the resistivity. Moreover the resistivity depends strongly on the nominal composition of the sample which ranges between 4600 ~xf~ cm in A163Cu25Fe12 and 10500 IxD cm in A16z5Cu25Felz 5 (fig. 1). This steep increase for only a 0.5% change in the nominal composition is an indication for a very peculiar electronic structure.
Fig. 2. Temperature dependence of the conductivity for AICuFe samples of various compositions and annealing treatments
The temperature dependence of the conductivity, o- = l / p , has been reported in fig. 2 for different samples of varying composition and structural quality. We can see that, contrary to the conductivity at 4 K, the temperature dependence 3o,(T) = ~r4K-- ~r(T) is almost independent of the composition and the structural quality of the sample. Moreover, this temperature dependence seems to be characteristic of this complex structure since the same dependences have been observed in AIPdMn [9] and A1CuRu [4] QC samples (see fig. 3 for a comparison between A1CuFe and AIPdMn). The small differences observed at low temperature could be attributed either to small magnetic contributions in AIPdMn samples or to
500
AI72Pd19Mn9 400
A163Cu25Fe12
30(]
AI6i.sCu26Fe~2.2 A170,5Pd22Mn7.5
'7
20~
AI62.5Cu25Fe12.5
10C
G o
100 200 300 T (K) Fig. 3. Comparison between the temperature dependences of the conductivityof AICuFe and AIPdMn samples.
T. Klein et al. / Electronic properties of stable quasicrystals I
I
~ 0
AI63Cu25FeI2
0
l ~ ' ~
3t -61 -2
] AI6t.,Cu26F¢I2.2
~ ~
0.5
.fT
] A16zC%f%s AI~.~C,,~%~ 1.5
¢9 ¢9
+/!
(weak localization and electron-electron interaction effects). Indeed, this dependence can be well described using a classical fitting procedure of the form A~(T) = 3(a + ( b T ) 2 ) 1/2 - b T + cx/T between 0.3 and 100 K. The two first terms refer to weak localization effects and a and b are related to spin-orbit (rso) and inelastic scattering (~'i) times respectively:
-4
-6
i
0
50
i
t
100
150
903
a = (ee/Z~r2h)e(1/Drso),
L
200
250
c y ~ ( g 2 c m ) -1 Fig. 4. Evolution of the coefficient c ( a ( T ) = c v ~ ) with the conductivity. In the inset: conductivity as a function of v ~ for dfferent samples.
peculiar electron-electron interaction effects in A1CuFe samples. These effects are discussed in section 4.1. and are represented in fig. 4. Figure 5 presents the magnetoconductivity as a function of v/H for m162Cu25.5Fe12.5.
4. Discussion
4.1. Temperature dependence o f the conductivity
We have shown in a previous paper [5] that this temperature dependence can be analyzed with classical quantum interference theories
bT=(e2/av2h)(1/ D~). In the case of AI63Cu25Fe12 , w e could estimate the diffusivity, D, by using the measured value of the density of states at the Fermi level (specific heat measurements [3]) to D = o ' / e 2 N ( E v ) ~ 0.3 cm2/s, and we then obtain z i ~ 2 × 10-9 T - 2 (s) and %0 ~ 4 x 10-12 (S). The value of %o is typical of amorphous systems [8], whereas ri is one order of magnitude higher than usually observed in these systems. The coefficient c is related to electron-electron interaction and we have observed that this coefficient decreases and changes sign as the conductivity of the sample decreases (fig. 4). Such a dependence has already been observed in heavily doped semiconductors close to the metal-insulator transition and was attributed to peculiar band structure effects [10] (intervalley scattering, mass anisotropy ...). 4.2. Magnetoconductiuity
5 ~--
,
q
, •
0 "v
E ~o
,
r=110K 20K
-5 -10
7K
~ -15 <1 -20
4.2K u
-2 5
0
....
iu
~u
~"~ 1 2
ov
1.8K
~v
3
4
5
6
7
8
~fH ( T 1/2) Fig. 5. High magnetic field magnetoconductivity in AI62Cuzs.sFe12.5 showing a ~ behaviour on a wide magnetic field range. Inset shows the magnetoconductivity up to 35 Tesla.
As shown in fig. 5 for A162Cu25.5Fe12.5 , the magnetoconductivity (MC) exhibits a v ~ behaviour on a wide range of magnetic fields and changes sign as the temperature increases, in agreement with quantum interference theories [4-6]. Further, we have also observed a nonclassical feature in the MC of the A163Cu 25,5 Fe 12.5 samples [5] at high temperature with a MC being positive at low field and negative at higher field (see the inset in fig. 5). This striking behaviour can be attributed to competing effects between weak localization (positive MC) and electronelectron interactions (negative MC). Such a behaviour has never been observed in amorphous systems for which electron-electron interactions
904
T. Klein et al. / Electronic properties of stable quasicrystals
can usually be neglected (except at very low temperature) but it has been pointed out that the electron-electron interactions become increasingly important when approaching the m e t a l - i n sulator transition (MIT) from the metallic side [10,11]. 4.3. Proximity o f a m e t a l - i n s u l a t o r transition
The first indication for a M I T is given by the high resistivity values, a reduced density of states at the Fermi level in both A1CuFe [3,4] and A1CuRu samples [4] (deduced from specific heat measurements) and a low n u m b e r of effective carriers deduced from Hall m e a s u r e m e n t s [3,4] (neff ~ 10 21 cm-3). As presented above, another indication is the strong electron-electron interactions effects observed in the t e m p e r a t u r e dependence of the conductivity (change of sign of the c coefficient) as well as in the magnetoconductivity (maximum of MC). Finally we can deduce from fig. 2 that there is a linear correlation between the conductivity at 4 K and the conductivity at room temperature: traK =A(~r300K -- tr M) with A ~ 1. This correlation shows that the conductivity at 4 K could vanish for the peculiar value of the conductivity at 300 K of tr M = 130 (lq cm)-1. It is remarkable that this correlation can be extended to the A1PdMn and A1CuRu Q C samples. Such a correlation has first been observed by Sanquer et al. [12] in amorphous systems close to the M I T and is in agreement with the scaling theory of the M I T developed by A b r a h a m s et al. [13].
5. Conclusion In conclusion, the A1CuFe alloys provide very high structural quality icosahedral phases. These samples show very high resistivity values rising up to 10500 ~f~ cm at 4 K in m162.sCu25Fe12.5. These values depend strongly on the nominal composition and the structural quality of the sample. On the contrary, the t e m p e r a t u r e dependence of the conductivity is roughly independent of the composition and the structural quality and
seems even to be characteristic of this complex structure (the same dependence is observed in A1PdMn and AICuRu samples). Despite these very high resistivity values, the t e m p e r a t u r e and magnetic field dependence of the conductivity can be well described by quantum interference theories. This indicates strong electron-electron interaction effects as already observed for heavily doped semiconductors on the metallic side of the m e t a l - i n s u l a t o r transition. The authors would like to thank Dr D. Mayou for fruitful discussions, Dr Y. Calvayrac for supplying some of the samples, and Dr H. Rakoto for the pulsed high field measurements. T.K. acknowledges the C E A - C E R E M for a financial fellowship.
References [1] Y. Calvayrac, A. Quivy, M. Bessiere, S. Lefebvre, M. Cornier-Quiquandon and D. Gratias, J. Phys. 51 (1990) 417. [2] S. Takeuchi, H. Akiyama, N. Naito, T. Shibuya, T. Hashimoto, K. Edagawa and K. Kimura, J. Non-Cryst. Solids 153&154 (1993) 353. [3] T. Klein, C. Berger, D, Mayou and F. Cyrot-Lackmann, Phys. Rev. Lett. 66, (1991), 2907. [4] S.J. Poon, Adv. Phys. 41 (1992) 303. [5] T. Klein, H. Rakoto, C. Berger, G. Fourcaudot and F. Cyrot-Lackmann, Phys. Rev. B45 (1991) 2046. [6] A. Sahnoune, J. Strom-Olsen, A. Zaluska, to be published in Phys. Rev. B. [7] B.L. Alt'shuler and A.G. Aronov, in: Electron-Electron Interactions in Disordered Systems, ed. ALL. Efros and M. Pollack (Elsevier, Amsterdam, 1985) ch. 1. [8] M.A. Howson and B.L. Gailagher, Phys. Rep. 170 (1988) 265. [9] P. Lanco, T. Klein, C. Berger, F. Cyrot-Lackmann, G. Fourcaudot and A. Sulpice, Europhys. Lett. 18 (192) 227. [10] G.A. Thomas, A. Kawabata, Y. Ootuka, S. Katsumoto, S. Kobayashi and W. Sasaki, Phys. Rev. B26, (1982) 2113; T.F. Rosembaum, R.F. Milligan, M.A. Paalanen, G.A. Thomas, R.N. Bhatt and W. Lin, Phys. Rev, B27 (1983) 7509. [11] C. Castellani, G. Kotliar and P.A. Lee, Phys. Rev. Lett. 59 (1987) 323. [12] M. Sanquer, R. Tourbot and B. Boucher, Europhys. Lett. 7 (1988) 635. [13] E. Abrahams, P.W. Anderson, D.C. Licciardello and T.V. Ramakrishnan, Phys. Rev. Lett. 42 (1979), 673.
Journal of Non-Crystalline Solids 156-158 (1993) 901-904 North-Holland
~
~lll~
Electronic properties of stable quasicrystals: towards a semiconducting quasicrystal? T. Klein, C. Berger, G. F o u r c a u d o t , J.C. Grieco, P. Lanco and F. Cyrot-Lackmann L E P E S - CNRS, BP166, 38042 Grenoble c~dex 9, France
Anomalous transport properties are presented of a series of pure AICuFe icosahedral phases of very high structural quality including a millimetre size single grain. The most salient feature is that all these metallic samples present very high resistivity values close to the metal-insulator transition (MIT) rising up to 10000 i~tq cm at 4 K in A162.5Cu25Fe12.5. The resistivity at 4 K depends strongly on the structural quality in a very peculiar way, since it increases when the structural defects are removed. It also varies strongly with the nominal composition of the sample increasing by a factor of almost 2.5 for only a 0.5% change in the composition. On the contrary, it is remarkable that the temperature dependence of the conductivity is almost independent of the composition and the structural quality. It is shown that, at low temperature, the temperature - and the magnetic field - dependence of the conductivity can be analyzed with classical weak localization theories including, however, strong electron-electron interaction similarly to that observed in systems close to a MIT. Similar peculiar behaviours are observed by preliminary measurements in the new A1PdMn stable icosahedral phase.
1. Introduction The quasicrystalline structure is a new state of condensed matter showing long range orientational order without translational periodicity. Most of these alloys are metastable phases, but a few thermodynamically stable quasicrystals (QC) have also been discovered. Among them, the AICuFe alloy allowed one for the first time to obtain very high structural quality alloys [1], including single grains [2], and is thus of peculiar interest for the study of the specific properties of this new system. The most striking feature is that this alloy seems to be close to the metal-insulator transition [3], showing resistivity values up to 10000 ~,12 cm at 4 K in AICuFe and even 30000 ~ cm in AICuRu [4]. However, despite these very high resistivities, the temperature and magnetic field dependences of the conductivity can
Corresl~ndence to: Dr C. Berger, LEPES - CNRS, 25 ave. des Martyrs, 38042 Grenoble c6dex 9, France.Tel: + 33 76 88 78 99. Telefax: + 33 76 88 79 88.
be well described [4-6] by quantum interference effects [7,8].
2. Experimental procedure Quasicrystalline samples of various compositions close t o AI63Cu25Fe12 have been prepared by melt-spinning. An annealing treatment (a few hours at 800°C) is always necessary to remove the structural defects due to the rapid quenching and traces of crystalline phases. The purity and quality of the phases are confirmed by X-ray diffraction [1,3]. For some compositions close to A162Cu25.5Fe12.5, an annealing treatment at lower temperature (600°C) allows elimination of the crystalline phases, but not the structural defects. This treatment is thus of great importance for the investigation of the influence of the structural quality on the transport properties. The resistivity was measured using the classical four-probe method down to 300 mK and in pulsed magnetic fields up to 35 T at the Toulouse National High Field Facilities (between 1.8 and 110 K). The resistivity values at room temperature are
0022-3093/93/$06.00 © 1993 - Elsevier Science Publishers B.V. All rights reserved
902
T. Klein et aL / Electronic properties of stable quasicrystals 600
12000 10000 ~ ' ~ 8000 -
6oo°c - 2h
A162.sCu25Fe12.5
~ " ~
500
800°C-3h
~
•~,
800oc - 3h
I-"..~ 400
A163Cu25Fe12
600°C - 2h
300
6000
62Cu25-sFe12-5
800°C - 3h
62.5Cu25Fe12.5
I~ 200
ca. 4000 2000 0
~3C u24.5 F e 12.5
0
50
100
150
800°C - 3h
100
600°C-3h 800°C-2h A162Cu25.5Fe12.5
0 200
250
300
0
50 100 150 200 250 300 T (K)
T (K) Fig. I. Temperature dependence of the resistivity of AICuFe samples showing the evolution of resistivity with composition and structural quality.
average values obtained on a series of about ten samples out of the same batch. A typical error margin is about 10%.
3. Results The most salient feature is that the high quality AICuFe samples show very high resistivity values up to 10000 Ixtq cm in A16zsCu25Fet2.s. Comparable values have been measured in other stable A1PdMn [9] and A1CuRu [4] QC samples. These values are two orders of magnitude higher than those observed in amorphous systems [8] or metastable QC but similar to those of heavily doped semiconductors on the metallic side of the metal-insulator transition. Further, as shown in fig. l for A162Cu25.5Fe12.5 , a non-expected feature is that the resistivity sample increases as the structural defects are removed. This behaviour is by striking contrast with that of a crystal, for which the reduction of defects reduces the resistivity. Moreover the resistivity depends strongly on the nominal composition of the sample which ranges between 4600 ~xf~ cm in A163Cu25Fe12 and 10500 IxD cm in A16z5Cu25Felz 5 (fig. 1). This steep increase for only a 0.5% change in the nominal composition is an indication for a very peculiar electronic structure.
Fig. 2. Temperature dependence of the conductivity for AICuFe samples of various compositions and annealing treatments
The temperature dependence of the conductivity, o- = l / p , has been reported in fig. 2 for different samples of varying composition and structural quality. We can see that, contrary to the conductivity at 4 K, the temperature dependence 3o,(T) = ~r4K-- ~r(T) is almost independent of the composition and the structural quality of the sample. Moreover, this temperature dependence seems to be characteristic of this complex structure since the same dependences have been observed in AIPdMn [9] and A1CuRu [4] QC samples (see fig. 3 for a comparison between A1CuFe and AIPdMn). The small differences observed at low temperature could be attributed either to small magnetic contributions in AIPdMn samples or to
500
AI72Pd19Mn9 400
A163Cu25Fe12
30(]
AI6i.sCu26Fe~2.2 A170,5Pd22Mn7.5
'7
20~
AI62.5Cu25Fe12.5
10C
G o
100 200 300 T (K) Fig. 3. Comparison between the temperature dependences of the conductivityof AICuFe and AIPdMn samples.
T. Klein et al. / Electronic properties of stable quasicrystals I
I
~ 0
AI63Cu25FeI2
0
l ~ ' ~
3t -61 -2
] AI6t.,Cu26F¢I2.2
~ ~
0.5
.fT
] A16zC%f%s AI~.~C,,~%~ 1.5
¢9 ¢9
+/!
(weak localization and electron-electron interaction effects). Indeed, this dependence can be well described using a classical fitting procedure of the form A~(T) = 3(a + ( b T ) 2 ) 1/2 - b T + cx/T between 0.3 and 100 K. The two first terms refer to weak localization effects and a and b are related to spin-orbit (rso) and inelastic scattering (~'i) times respectively:
-4
-6
i
0
50
i
t
100
150
903
a = (ee/Z~r2h)e(1/Drso),
L
200
250
c y ~ ( g 2 c m ) -1 Fig. 4. Evolution of the coefficient c ( a ( T ) = c v ~ ) with the conductivity. In the inset: conductivity as a function of v ~ for dfferent samples.
peculiar electron-electron interaction effects in A1CuFe samples. These effects are discussed in section 4.1. and are represented in fig. 4. Figure 5 presents the magnetoconductivity as a function of v/H for m162Cu25.5Fe12.5.
4. Discussion
4.1. Temperature dependence o f the conductivity
We have shown in a previous paper [5] that this temperature dependence can be analyzed with classical quantum interference theories
bT=(e2/av2h)(1/ D~). In the case of AI63Cu25Fe12 , w e could estimate the diffusivity, D, by using the measured value of the density of states at the Fermi level (specific heat measurements [3]) to D = o ' / e 2 N ( E v ) ~ 0.3 cm2/s, and we then obtain z i ~ 2 × 10-9 T - 2 (s) and %0 ~ 4 x 10-12 (S). The value of %o is typical of amorphous systems [8], whereas ri is one order of magnitude higher than usually observed in these systems. The coefficient c is related to electron-electron interaction and we have observed that this coefficient decreases and changes sign as the conductivity of the sample decreases (fig. 4). Such a dependence has already been observed in heavily doped semiconductors close to the metal-insulator transition and was attributed to peculiar band structure effects [10] (intervalley scattering, mass anisotropy ...). 4.2. Magnetoconductiuity
5 ~--
,
q
, •
0 "v
E ~o
,
r=110K 20K
-5 -10
7K
~ -15 <1 -20
4.2K u
-2 5
0
....
iu
~u
~"~ 1 2
ov
1.8K
~v
3
4
5
6
7
8
~fH ( T 1/2) Fig. 5. High magnetic field magnetoconductivity in AI62Cuzs.sFe12.5 showing a ~ behaviour on a wide magnetic field range. Inset shows the magnetoconductivity up to 35 Tesla.
As shown in fig. 5 for A162Cu25.5Fe12.5 , the magnetoconductivity (MC) exhibits a v ~ behaviour on a wide range of magnetic fields and changes sign as the temperature increases, in agreement with quantum interference theories [4-6]. Further, we have also observed a nonclassical feature in the MC of the A163Cu 25,5 Fe 12.5 samples [5] at high temperature with a MC being positive at low field and negative at higher field (see the inset in fig. 5). This striking behaviour can be attributed to competing effects between weak localization (positive MC) and electronelectron interactions (negative MC). Such a behaviour has never been observed in amorphous systems for which electron-electron interactions
904
T. Klein et al. / Electronic properties of stable quasicrystals
can usually be neglected (except at very low temperature) but it has been pointed out that the electron-electron interactions become increasingly important when approaching the m e t a l - i n sulator transition (MIT) from the metallic side [10,11]. 4.3. Proximity o f a m e t a l - i n s u l a t o r transition
The first indication for a M I T is given by the high resistivity values, a reduced density of states at the Fermi level in both A1CuFe [3,4] and A1CuRu samples [4] (deduced from specific heat measurements) and a low n u m b e r of effective carriers deduced from Hall m e a s u r e m e n t s [3,4] (neff ~ 10 21 cm-3). As presented above, another indication is the strong electron-electron interactions effects observed in the t e m p e r a t u r e dependence of the conductivity (change of sign of the c coefficient) as well as in the magnetoconductivity (maximum of MC). Finally we can deduce from fig. 2 that there is a linear correlation between the conductivity at 4 K and the conductivity at room temperature: traK =A(~r300K -- tr M) with A ~ 1. This correlation shows that the conductivity at 4 K could vanish for the peculiar value of the conductivity at 300 K of tr M = 130 (lq cm)-1. It is remarkable that this correlation can be extended to the A1PdMn and A1CuRu Q C samples. Such a correlation has first been observed by Sanquer et al. [12] in amorphous systems close to the M I T and is in agreement with the scaling theory of the M I T developed by A b r a h a m s et al. [13].
5. Conclusion In conclusion, the A1CuFe alloys provide very high structural quality icosahedral phases. These samples show very high resistivity values rising up to 10500 ~f~ cm at 4 K in m162.sCu25Fe12.5. These values depend strongly on the nominal composition and the structural quality of the sample. On the contrary, the t e m p e r a t u r e dependence of the conductivity is roughly independent of the composition and the structural quality and
seems even to be characteristic of this complex structure (the same dependence is observed in A1PdMn and AICuRu samples). Despite these very high resistivity values, the t e m p e r a t u r e and magnetic field dependence of the conductivity can be well described by quantum interference theories. This indicates strong electron-electron interaction effects as already observed for heavily doped semiconductors on the metallic side of the m e t a l - i n s u l a t o r transition. The authors would like to thank Dr D. Mayou for fruitful discussions, Dr Y. Calvayrac for supplying some of the samples, and Dr H. Rakoto for the pulsed high field measurements. T.K. acknowledges the C E A - C E R E M for a financial fellowship.
References [1] Y. Calvayrac, A. Quivy, M. Bessiere, S. Lefebvre, M. Cornier-Quiquandon and D. Gratias, J. Phys. 51 (1990) 417. [2] S. Takeuchi, H. Akiyama, N. Naito, T. Shibuya, T. Hashimoto, K. Edagawa and K. Kimura, J. Non-Cryst. Solids 153&154 (1993) 353. [3] T. Klein, C. Berger, D, Mayou and F. Cyrot-Lackmann, Phys. Rev. Lett. 66, (1991), 2907. [4] S.J. Poon, Adv. Phys. 41 (1992) 303. [5] T. Klein, H. Rakoto, C. Berger, G. Fourcaudot and F. Cyrot-Lackmann, Phys. Rev. B45 (1991) 2046. [6] A. Sahnoune, J. Strom-Olsen, A. Zaluska, to be published in Phys. Rev. B. [7] B.L. Alt'shuler and A.G. Aronov, in: Electron-Electron Interactions in Disordered Systems, ed. ALL. Efros and M. Pollack (Elsevier, Amsterdam, 1985) ch. 1. [8] M.A. Howson and B.L. Gailagher, Phys. Rep. 170 (1988) 265. [9] P. Lanco, T. Klein, C. Berger, F. Cyrot-Lackmann, G. Fourcaudot and A. Sulpice, Europhys. Lett. 18 (192) 227. [10] G.A. Thomas, A. Kawabata, Y. Ootuka, S. Katsumoto, S. Kobayashi and W. Sasaki, Phys. Rev. B26, (1982) 2113; T.F. Rosembaum, R.F. Milligan, M.A. Paalanen, G.A. Thomas, R.N. Bhatt and W. Lin, Phys. Rev, B27 (1983) 7509. [11] C. Castellani, G. Kotliar and P.A. Lee, Phys. Rev. Lett. 59 (1987) 323. [12] M. Sanquer, R. Tourbot and B. Boucher, Europhys. Lett. 7 (1988) 635. [13] E. Abrahams, P.W. Anderson, D.C. Licciardello and T.V. Ramakrishnan, Phys. Rev. Lett. 42 (1979), 673.