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The magnetoresistance dependence on temperature in Al, Al-Ga, Al-Zn, Cu and Cu-Au
Physica 100B (1980) 99-101 © North-Holland Publishing Company
LETTER TO THE EDITOR
THE MAGNETORESlSTANCE DEPENDENCE ON TEMPERATURE IN AI, AI-Ga, AI-Zn, Cu AND Cu-Au E. ROCOFYLLOU and C. PAPATHANASSOPOULOS N. R. C Demokritos, Aghia Paraskevi A ttikis, Athens, Greece
Received 22 October 1979
Magnetoresistance dependence on temperature was measured (a) for dilute alloys of A1 with Zn and Ge, (b) for dilute alloys of Cu with Au, and (c) for pure A1 and Cu with different RRR. A maximum in this magnetoresistance dependence is observed in the case of pure samples, known as anomalous behavior, due to the anisotropie scattering, which is suppressed with the presence of foreign atoms which is caused by the isotropization of the scattering process.
The magnetoresistance dependence on temperature of pure A1, Cu and some A1, Cu based alloys is studied. Little relevant experimental work has been done until now. First, Fickett [1 ] measured the magnetoresistance and its temperature dependence in polycrystalline aluminum. Snodgrass et al. [2] have also made experiments in this field in A1-Ga and A1-Mg alloys. Some of our data concerning the temperature dependence of magnetoresistance in aluminum and aluminum alloys has been presented at the Conference on Transport Properties of 1977 [3]. At about the same time Klopkin et al. [4] have measured the magnetoresistance as function of temperature for A1, A1-Mg, A1-Zn and A1-Ga. Schwarz and Stangler [5] have measured also the temperature dependence of magnetoresistance in pure copper with different R R R (residual resistivity ratio). In all these experiments an anomalous behaviour of magnetoresistance dependence on temperature in pure A1 and Cu and an influence of the concentration of diamagnetic impurities on tiffs anomalous behaviour in the case o f aluminum has been observed. In the present we have carried out a systematic experimental investigation by measuring magneto-resistivity in the temperature range between 4.2 - 70 K in zero field and different magnetic field up to 38 kG in: a) pure AI (99.999%) and weak solutions o f Ge and Zn;
b) pure Cu (99.999%) and weak solutions of Au; and c) pure samples of A1 and Cu with different residual resistivity ratio (RRR). The main features indicated by our experimental results in pure A1 and A1-Ge, A1-Zn alloys are the following: An increase of magnetoresistivity with temperature occurs in pure A1 till 2 0 - 3 0 K. A broad maximum in this temperature range followed by a sharp decrease is observed. The existence of the maximum is the socalled anomalous behavior. These results are in very good agreement with other investigations [ 1,3]. The influence of the different parameters in this behavior are: (i) The influence of the magnetic field is evident. The maximum of the magnetoresistance increases witt increasing magnetic field (fig. 1). (ii) The increase of impurities concentration reduces the maximum of the magnetoresistance. For the very low temperature the addition of foreign atoms in pure A1 increases the magnetoresistance ratio compared with that of pure A1. As previously, however, this ratio decreases with increasing impurities concentration (fig. 2). For A1-Zn this is also observed by Klopkin et al. [4]. (iii) The influence of the impurities depends on the kind of the foreign atoms (fig. 3). After Kagan and Flerov [6] the magnetoresistance in the isotropic approximation is equal to zero and 99
1O0
Magnetoresistance in A 1 and Cu-alloys 1.4
A_£_p
1-2
l
*
O
I£
B = 3 8 kG ÷ AI p u r e e AI ÷ OO2Clt */*Z n •AI,,0.1 a t * / , ,,
P.(T)
1"2 Ap P.(T)
l
"°
÷
0.8
e
0.6
~
" ÷
÷
AI-pure ° B=37.9 kG ÷ B-- 3 0 5 kG • B = 21.3 k G
° +
•
•
• AI*(27 *AI*~0
*
, , , .
, .
o
o +
e
®
÷
0.6
•
e
O
Q4
•
÷ A
÷
O.4!
•A
Q ÷
•
02
Q A
+
÷ ÷
+e
O.2
o ma
m
m
A
m B
o
•
o
÷ Q
o x
I
0
10
2'0
4}::) ,T(K5?
36
6~0 ÷~ 7'0
Fig. 1. Magnetoresistance ratio as a function of temperature for pure A1 and for different magnetic fields.
the value of magnetoresistance ApH , is due to the anisotropy of the electron distribution function. In the case of pure metals this anisotropy is the result of the anisotropy of the Fermi surface, the anisotropy of phonon spectrum and the anisotropy in the electron-phonon interaction (Umklapp process). The temperature dependence of the magnetoresistance reflects the temperature dependence of anisotropy in this distribution function. The impurities tend to reduce this anisotropy of the electron distribution function due to the elastic scattering of electrons with the foreign atoms. The
1~,
Ap ~(T)
"
B=38kG AI - G e
.
1.2 R
1.0 •
®
•
pu re
° •
0.02 0.1 03 0.5
*
ate/° at°/o at°/o ot%
0'8 m o
e Q Q e e
0.6
o o o o
0.4
o
o %
m
~Q m •
0'2
••
• ' •
•
4
m •
AA I+
0
+÷
m •
+ ÷÷
20
30
40
50
Fig. 2. Magnetoresistance ratio as a function of temperature at a fixed magnetic field and for various A I - Z n alloys.
0
x ,
10
x
x
x ,
20
x ,
30
x
~
~
• i
4'0
50
•
60
~o÷.
70
,-T(K) Fig. 3. Magnetoresistance ratio as a function of temperature at a fixed magnetic field and for A I - G e alloys.
concentration dependence reflects this isotropisation of the electron distribution function. In other words the magnetoresistance of a metal depends both on the geometry of the Fermi surface and on the electron- phonon scattering process. Taking into account that in the case of A1 the geometry of the Fermi surface is isotropic and that the impurity atoms concentration is small, the change in the geometry of the Fermi surface is negligible. So, we can attribute the temperature dependence of the magnetoresistance to the anisotropy of electron-pho. non scattering and especially to the anisotropy of phonon spectrum. In alloys the anisotropy of electron-phonon scattering is partially suppressed by scattering of electrons in the impurities. The existence of a 6pH/p o in the low temperature range was predicted [4] for an impurity that scatters anisotropically as we have found in the case of A1-Zn. We have also studied the magnetoresistance dependence on temperature of Cu and Au-alloyed Cu with different concentrations in the same temperature range 4 . 6 - 7 0 K and for various magnetic fields. The results are quite different from those of A1 and A1alloys. A maximum in the function of the relative magnetoresistance with temperature for the above systems was not observed not even in the case of pure Cu as it was expected. This function presents a continuous decrease with increasing temperature. At low temperature (4.6 K) we obtained the highest value of magnetoresistance, then the magnetoresistance ratio
Magnetoresistance in AI and Cu-alloys
1.0 Q8
®
ee o AP e o ~(T) 0.6 [
B= 38KG Cu-Au o
0
e
pure
0.0 2 o t ° / o 0,06 ,, Q1 ,, 0.2 ,
• +
0.4 0 ® ®
0 -0'21
1(3
2b
3'0
4b
5'0
8b
7b
.T(K)
Fig. 4. Magnetoresistance ratio as a function of temperature at a fixed magnetic field and for various Cu-Au alloys.
passes through a plateau (10 K) and after that decreases monotonically with temperature (fig. 4). Another point is the negative value towards which the magnetoresistance ratio was observed to tend asymptotically at about 50 K. This negative value is possibly due to residual impurities. This is possible because the samples of Cu are not pure enough ( R R R 1000) and we may have foreign atoms in very small concentration but with strong scattering range, such as magnetic impuri-
1.4
101
ties. It is known that magnetic impurities cause negative magnetoresistance [7]. In Cu alloys we have observed the same process o f isotropisation o f the distribution function due to the scattering o f electrons with the impurities. This isotropisation is stronger than that in the case o f A1. To explain the different behavior between A1 and Cu and the influence o f the purity o f the samples, we have measured the magnetoresistance dependence with temperature of some pure A1 and Cu samples with different R R R (fig. 5). The results for A1, as we have seen, can be explained quite well by Kagan and Flerov's theory, and the influence o f existing impurities are obvious. In the case o f copper we observed the same behavior as previously. In the work of Schwarz and Stangler [5] the temperature dependence of magnetoresistance shows a maximum for the two samples which have the greater value of RRR, but they have plotted the absolute magnetoresistance ( p ( H ) - p(O) and not the relative p ( H ) - p(O)/p(O). In this plot we see also a very smooth maximum in the same temperature region 2 5 - 3 0 K. In the case o f copper the existing impurities play a predominant role in the scattering process. This, perhaps, can be explained by the fact that the most significant impurity in the copper used in the present experiments was iron and it is known that iron in copper interacts very strongly with electron spins [8].
't
Ap
B= 38kG Cu Pure
~ f
AI pure e RRR 4 0 0 0
\
i,.:.... \
Q8
-(21
"-../, \
'* ......... .... ~'
10
".~. \ '~.~
20
References
: ,...,%0
o
30 40 "T(K)
50
60
70
Fig. 5. Magnetoresistance ratio as a function of temperature at a fixed magnetic field for some pure A1 and pure Cu sampies, with different RRR.
[1] F.R. Fickett, Phys. Rev. B3 (1970) 1941. [2] M.L. Snodgrass, F.J. Blatt, J.L. Opsal and C.K. Chiagn, Phys. Rev. B13 (1976) 574. [3] K. Papathanassopoulos, E. Rocofyllou and K. Chountas, Proc. of E.P.S. Study Conf. on Transport Properties of Normal Metals and Alloys below 0p, Cavtat (1977). [4] M.N. Klopkin, G. Kh. Panova and B.N. Samoilov, Sov. Phys. JETP 45 (1977) 2. [5] R.J. Schwarz and F. Stangler, Phys. stat. sol. (b) 60 (1973 K69. [6] Yu. Kagan and V.N. Flerov, Soy. Phys. JETP 39 (1974) 673. [7] J. Kuppens, W. Boon and L. Janssens, Physica 88B (1977) 459. [8] J.O. Strom-Olsen, Proc. Roy. Soc. A302 (1967) 83.
LETTER TO THE EDITOR
THE MAGNETORESlSTANCE DEPENDENCE ON TEMPERATURE IN AI, AI-Ga, AI-Zn, Cu AND Cu-Au E. ROCOFYLLOU and C. PAPATHANASSOPOULOS N. R. C Demokritos, Aghia Paraskevi A ttikis, Athens, Greece
Received 22 October 1979
Magnetoresistance dependence on temperature was measured (a) for dilute alloys of A1 with Zn and Ge, (b) for dilute alloys of Cu with Au, and (c) for pure A1 and Cu with different RRR. A maximum in this magnetoresistance dependence is observed in the case of pure samples, known as anomalous behavior, due to the anisotropie scattering, which is suppressed with the presence of foreign atoms which is caused by the isotropization of the scattering process.
The magnetoresistance dependence on temperature of pure A1, Cu and some A1, Cu based alloys is studied. Little relevant experimental work has been done until now. First, Fickett [1 ] measured the magnetoresistance and its temperature dependence in polycrystalline aluminum. Snodgrass et al. [2] have also made experiments in this field in A1-Ga and A1-Mg alloys. Some of our data concerning the temperature dependence of magnetoresistance in aluminum and aluminum alloys has been presented at the Conference on Transport Properties of 1977 [3]. At about the same time Klopkin et al. [4] have measured the magnetoresistance as function of temperature for A1, A1-Mg, A1-Zn and A1-Ga. Schwarz and Stangler [5] have measured also the temperature dependence of magnetoresistance in pure copper with different R R R (residual resistivity ratio). In all these experiments an anomalous behaviour of magnetoresistance dependence on temperature in pure A1 and Cu and an influence of the concentration of diamagnetic impurities on tiffs anomalous behaviour in the case o f aluminum has been observed. In the present we have carried out a systematic experimental investigation by measuring magneto-resistivity in the temperature range between 4.2 - 70 K in zero field and different magnetic field up to 38 kG in: a) pure AI (99.999%) and weak solutions o f Ge and Zn;
b) pure Cu (99.999%) and weak solutions of Au; and c) pure samples of A1 and Cu with different residual resistivity ratio (RRR). The main features indicated by our experimental results in pure A1 and A1-Ge, A1-Zn alloys are the following: An increase of magnetoresistivity with temperature occurs in pure A1 till 2 0 - 3 0 K. A broad maximum in this temperature range followed by a sharp decrease is observed. The existence of the maximum is the socalled anomalous behavior. These results are in very good agreement with other investigations [ 1,3]. The influence of the different parameters in this behavior are: (i) The influence of the magnetic field is evident. The maximum of the magnetoresistance increases witt increasing magnetic field (fig. 1). (ii) The increase of impurities concentration reduces the maximum of the magnetoresistance. For the very low temperature the addition of foreign atoms in pure A1 increases the magnetoresistance ratio compared with that of pure A1. As previously, however, this ratio decreases with increasing impurities concentration (fig. 2). For A1-Zn this is also observed by Klopkin et al. [4]. (iii) The influence of the impurities depends on the kind of the foreign atoms (fig. 3). After Kagan and Flerov [6] the magnetoresistance in the isotropic approximation is equal to zero and 99
1O0
Magnetoresistance in A 1 and Cu-alloys 1.4
A_£_p
1-2
l
*
O
I£
B = 3 8 kG ÷ AI p u r e e AI ÷ OO2Clt */*Z n •AI,,0.1 a t * / , ,,
P.(T)
1"2 Ap P.(T)
l
"°
÷
0.8
e
0.6
~
" ÷
÷
AI-pure ° B=37.9 kG ÷ B-- 3 0 5 kG • B = 21.3 k G
° +
•
•
• AI*(27 *AI*~0
*
, , , .
, .
o
o +
e
®
÷
0.6
•
e
O
Q4
•
÷ A
÷
O.4!
•A
Q ÷
•
02
Q A
+
÷ ÷
+e
O.2
o ma
m
m
A
m B
o
•
o
÷ Q
o x
I
0
10
2'0
4}::) ,T(K5?
36
6~0 ÷~ 7'0
Fig. 1. Magnetoresistance ratio as a function of temperature for pure A1 and for different magnetic fields.
the value of magnetoresistance ApH , is due to the anisotropy of the electron distribution function. In the case of pure metals this anisotropy is the result of the anisotropy of the Fermi surface, the anisotropy of phonon spectrum and the anisotropy in the electron-phonon interaction (Umklapp process). The temperature dependence of the magnetoresistance reflects the temperature dependence of anisotropy in this distribution function. The impurities tend to reduce this anisotropy of the electron distribution function due to the elastic scattering of electrons with the foreign atoms. The
1~,
Ap ~(T)
"
B=38kG AI - G e
.
1.2 R
1.0 •
®
•
pu re
° •
0.02 0.1 03 0.5
*
ate/° at°/o at°/o ot%
0'8 m o
e Q Q e e
0.6
o o o o
0.4
o
o %
m
~Q m •
0'2
••
• ' •
•
4
m •
AA I+
0
+÷
m •
+ ÷÷
20
30
40
50
Fig. 2. Magnetoresistance ratio as a function of temperature at a fixed magnetic field and for various A I - Z n alloys.
0
x ,
10
x
x
x ,
20
x ,
30
x
~
~
• i
4'0
50
•
60
~o÷.
70
,-T(K) Fig. 3. Magnetoresistance ratio as a function of temperature at a fixed magnetic field and for A I - G e alloys.
concentration dependence reflects this isotropisation of the electron distribution function. In other words the magnetoresistance of a metal depends both on the geometry of the Fermi surface and on the electron- phonon scattering process. Taking into account that in the case of A1 the geometry of the Fermi surface is isotropic and that the impurity atoms concentration is small, the change in the geometry of the Fermi surface is negligible. So, we can attribute the temperature dependence of the magnetoresistance to the anisotropy of electron-pho. non scattering and especially to the anisotropy of phonon spectrum. In alloys the anisotropy of electron-phonon scattering is partially suppressed by scattering of electrons in the impurities. The existence of a 6pH/p o in the low temperature range was predicted [4] for an impurity that scatters anisotropically as we have found in the case of A1-Zn. We have also studied the magnetoresistance dependence on temperature of Cu and Au-alloyed Cu with different concentrations in the same temperature range 4 . 6 - 7 0 K and for various magnetic fields. The results are quite different from those of A1 and A1alloys. A maximum in the function of the relative magnetoresistance with temperature for the above systems was not observed not even in the case of pure Cu as it was expected. This function presents a continuous decrease with increasing temperature. At low temperature (4.6 K) we obtained the highest value of magnetoresistance, then the magnetoresistance ratio
Magnetoresistance in AI and Cu-alloys
1.0 Q8
®
ee o AP e o ~(T) 0.6 [
B= 38KG Cu-Au o
0
e
pure
0.0 2 o t ° / o 0,06 ,, Q1 ,, 0.2 ,
• +
0.4 0 ® ®
0 -0'21
1(3
2b
3'0
4b
5'0
8b
7b
.T(K)
Fig. 4. Magnetoresistance ratio as a function of temperature at a fixed magnetic field and for various Cu-Au alloys.
passes through a plateau (10 K) and after that decreases monotonically with temperature (fig. 4). Another point is the negative value towards which the magnetoresistance ratio was observed to tend asymptotically at about 50 K. This negative value is possibly due to residual impurities. This is possible because the samples of Cu are not pure enough ( R R R 1000) and we may have foreign atoms in very small concentration but with strong scattering range, such as magnetic impuri-
1.4
101
ties. It is known that magnetic impurities cause negative magnetoresistance [7]. In Cu alloys we have observed the same process o f isotropisation o f the distribution function due to the scattering o f electrons with the impurities. This isotropisation is stronger than that in the case o f A1. To explain the different behavior between A1 and Cu and the influence o f the purity o f the samples, we have measured the magnetoresistance dependence with temperature of some pure A1 and Cu samples with different R R R (fig. 5). The results for A1, as we have seen, can be explained quite well by Kagan and Flerov's theory, and the influence o f existing impurities are obvious. In the case o f copper we observed the same behavior as previously. In the work of Schwarz and Stangler [5] the temperature dependence of magnetoresistance shows a maximum for the two samples which have the greater value of RRR, but they have plotted the absolute magnetoresistance ( p ( H ) - p(O) and not the relative p ( H ) - p(O)/p(O). In this plot we see also a very smooth maximum in the same temperature region 2 5 - 3 0 K. In the case o f copper the existing impurities play a predominant role in the scattering process. This, perhaps, can be explained by the fact that the most significant impurity in the copper used in the present experiments was iron and it is known that iron in copper interacts very strongly with electron spins [8].
't
Ap
B= 38kG Cu Pure
~ f
AI pure e RRR 4 0 0 0
\
i,.:.... \
Q8
-(21
"-../, \
'* ......... .... ~'
10
".~. \ '~.~
20
References
: ,...,%0
o
30 40 "T(K)
50
60
70
Fig. 5. Magnetoresistance ratio as a function of temperature at a fixed magnetic field for some pure A1 and pure Cu sampies, with different RRR.
[1] F.R. Fickett, Phys. Rev. B3 (1970) 1941. [2] M.L. Snodgrass, F.J. Blatt, J.L. Opsal and C.K. Chiagn, Phys. Rev. B13 (1976) 574. [3] K. Papathanassopoulos, E. Rocofyllou and K. Chountas, Proc. of E.P.S. Study Conf. on Transport Properties of Normal Metals and Alloys below 0p, Cavtat (1977). [4] M.N. Klopkin, G. Kh. Panova and B.N. Samoilov, Sov. Phys. JETP 45 (1977) 2. [5] R.J. Schwarz and F. Stangler, Phys. stat. sol. (b) 60 (1973 K69. [6] Yu. Kagan and V.N. Flerov, Soy. Phys. JETP 39 (1974) 673. [7] J. Kuppens, W. Boon and L. Janssens, Physica 88B (1977) 459. [8] J.O. Strom-Olsen, Proc. Roy. Soc. A302 (1967) 83.