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Magnetoconductivity of Nd2−xCexCuO4 thin film above Tc
PhysicaC 235-240(1994) 1405-1406 North-Holland
PHYSlCA
Magnetoconductivity of Nd2.xCexCuO4 thin film above Tc Y. Yamasakia, T. Nishizakia T. Fukamia, T. Aominea, S. Kubob and M. Suzukib a Department of Physics, Kyushu University, Fukuoka 812, Japan b~ Interdisciplinary Research Laboratories, Nippon Telegraph Telephone Corporation, 162 Tokai, Ibaraki 319-11, Japan The electrical resistivity p(T,H) vs. magnetic fields H up to 12 T parallel to the c-axis has been measured as a function of temperature T above the superconducting critical temperature Tc to study the effect of thermodynamic fluctuations on the dectrieal conductivity o(T,H)of Nd2.xCexCuO4 (x~ 0.15).
I. INTRODUCTION The magnetoconductivity due to thermodynamic fluctuations above the superconducting transition temperature Tc has been investigated since it gives us important infon~aation on the coherence lengths and the phase relaxation time of electrons through Aslamazov-Larkin term and Maki-Thompson term of the magnetocoaductivity [1,2]. In order to investigate the magnetoconductivity due to thermodyneanic fluctuations in Nd2.j~CexCuO4 (x~ 0.15) (NCC), in this work the normal magnetoconductivity in high temperature region is examined.
from the e-axis toward the basal plane keeping H 2. I, the field dependence decreases rapidly. The curves of p(T,H)/p(T,0) vs. H near Tc are convex upward but they change the shape gradually to be quadratic with increasing T. This magnetoresistivity mu~t b~ considered not to be ascribed to the fluctuations, because the measurement temperatures are far from To. Therefore, when the thermodynamic fluctuations in magnetic fields just above Tc is estimated, the normal magnetoconduetivity must be removed from the total conductivity.
2. EXPERIMENTAL RF~ULTS
70 w , - ,
NCC thin films were prepared by the reactive coevaporation technique. The c-axis of NCC film is oriented perpendicularly to the surface of the substrate. The current I is flowed along the film surface. The magnetic field H is applied parallel to the c-axis. The temperature is detected using a carbon glass thermometer. The electrical resistivity p(T,H) vs. H has been measured as a function of temperature T above the superconducting transition temperature Tc (~ 16.5 K). Figure 1 shows the results of p(T,H) vs. H as a function of T from I0 K to 90 K. Fig~e 2 shows plots of p(T,H)/p(T,0) vs. H as a function of T from 20 K to 90 K. Even in high T region above 40 K, which would not include the thermodynamic fluctuations effect on p(T,H), p(T,H) increases with increasing H, and the maximum increment of p(T,H) in/4--12 T at 40 K reaches about 1.6 % of that in 0 T. This magnetoresistivity decreases with the increase of temperature and is negligibly small above 90 K. Furthermore, when H is rotated
60 ~ DU
,-,,401
90K ~ .
17:=_~-SSL.
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.............. rill I ~
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."
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O ~L_'':
0
~'"ltO L12
t = ! t -i ~ I = = ~ | L - L ~~
2
4
6 8 H (T)
10
12
Figure 1. p(T,H)vs.Hbetween 10Kand90K. Inset shows the enlargement at p=41,-46~tff~era. 3. DISCUSSION
0921-4534/94/$07.00© 1994- ElsevierScienceB.V. All rights reserved,
SSD10921-4534(94)01266-0
: , , , . , ,,.,, '..L'; '___.2.' '-i.'-- ' q
In order to simplify the discussion, the resistivity
1406
Y Yamasakiet al./Physica C 235-240 (1994) 1405-1406
1.05 ~
0.03 ~m,~.,J,,.,..,,,,. ,.,, .,..., ,.,.~.-.., ;!;.:.~.;ii"S'
t
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~
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7 ; ; , , , . ,. , ,
0
2
4
. ,.
, .
, : . , , . . . . , ..... , . . . . , . . . . ,
6 8 10 12 14 H (T)
0 .... -20
40
i
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..
I.l
I
l . i..
l__lll
.
60 T (K)
80
100
Figure 2. p(H)/p(0) vs. H as a function of 7".
Figure 3. B vs. T. inset shows A vs. T.
is used for a while for conductivity. We estimate the normal resistivity pn(T,/'/), which does not include the effect of thermodynamic fluctuations, using the data in the 7" region above 40 K under the following assumptions: (1) the effect of fluctuations on p(T,H) can be neglected at temperatures above 2To, (2) pn(T,H) can be represented as
estimated in the region of the thermodynamic fluctuations between 40 K and Tc because this extended region is rather narrow as compared with that used to determine A(7) and B(T). If B(T) and n are considered as a set of parameters, pn(T,H) can be estimated without determining n in the extended region between 40 K and Tc. Thus, by using the resistivity not including the normal magnetoresistivity in the region of fluctuations, pf(T,H) = p(T,H) -B(T)H n, the magnetoconductivity due to the fluctuations Ao (T,/-/) would be estimated as Ao (T,H) = 1/pf(T,l'O - 1/pf(T,0). Generally, the origin of the quadratic H dependence of pn(T,H) will be ascribed to the anisotropic scattering mechanism of carriers and/or to the coexistence of two kinds of carriers which means the coexistence of electrons and holes or s-electrons and d-electrons or open orbits and dosed orbits. Further study of the x'wrmal magnetoresistance with a quadratic H dependence and the magnetoconductivity due to fluctuations are in progress at present.
Pn( T,H) = A(T) +B(T) H n
(1)
where A(T), B(T) and n are fitting parameters. Under the assumption of (1), p(T,H) = pn(T,H). By fitting eq. (1) to the experimental results in the high T region beyond 40 K, we obtain these parameters as a function of T, which are shown by marks in Fig. 3. Since the values of B(T) change with n, B(T)'s are shown as a function of n. By fitting functional forms of A ( T ) a n d B ( T ) t o the experimental results, six coefficients are estimated. Here A(T)=ao+ al T+a2T2and B(~---bo+b1 T+b2 T2 respectively. Three coefficients for A ( T ) a r e determined regardless ot" n to be ao= 42.8, a1=1.88× 10-2 and a2=2.67× 10"3. The coefficients for B(T) are b0=2.26× 10 -2, bl =- 1.76x 10 .`4 and b2=-5.55 x ! 0 -T for n=l.6. Since A(T) is determined almost independently of n in the region from 40 K to 90 K, it would be reasonable for A(T) to be
REFERENCES 1. S. Hikami and A. I. Larkin, Mod. Phys. Lett. B 2 (1988) 693. 2. A. G. Aronov, S. Hi -'kami and A. I. Larkin, Phys. Rev. Lett. 62 (1989) 965.
PHYSlCA
Magnetoconductivity of Nd2.xCexCuO4 thin film above Tc Y. Yamasakia, T. Nishizakia T. Fukamia, T. Aominea, S. Kubob and M. Suzukib a Department of Physics, Kyushu University, Fukuoka 812, Japan b~ Interdisciplinary Research Laboratories, Nippon Telegraph Telephone Corporation, 162 Tokai, Ibaraki 319-11, Japan The electrical resistivity p(T,H) vs. magnetic fields H up to 12 T parallel to the c-axis has been measured as a function of temperature T above the superconducting critical temperature Tc to study the effect of thermodynamic fluctuations on the dectrieal conductivity o(T,H)of Nd2.xCexCuO4 (x~ 0.15).
I. INTRODUCTION The magnetoconductivity due to thermodynamic fluctuations above the superconducting transition temperature Tc has been investigated since it gives us important infon~aation on the coherence lengths and the phase relaxation time of electrons through Aslamazov-Larkin term and Maki-Thompson term of the magnetocoaductivity [1,2]. In order to investigate the magnetoconductivity due to thermodyneanic fluctuations in Nd2.j~CexCuO4 (x~ 0.15) (NCC), in this work the normal magnetoconductivity in high temperature region is examined.
from the e-axis toward the basal plane keeping H 2. I, the field dependence decreases rapidly. The curves of p(T,H)/p(T,0) vs. H near Tc are convex upward but they change the shape gradually to be quadratic with increasing T. This magnetoresistivity mu~t b~ considered not to be ascribed to the fluctuations, because the measurement temperatures are far from To. Therefore, when the thermodynamic fluctuations in magnetic fields just above Tc is estimated, the normal magnetoconduetivity must be removed from the total conductivity.
2. EXPERIMENTAL RF~ULTS
70 w , - ,
NCC thin films were prepared by the reactive coevaporation technique. The c-axis of NCC film is oriented perpendicularly to the surface of the substrate. The current I is flowed along the film surface. The magnetic field H is applied parallel to the c-axis. The temperature is detected using a carbon glass thermometer. The electrical resistivity p(T,H) vs. H has been measured as a function of temperature T above the superconducting transition temperature Tc (~ 16.5 K). Figure 1 shows the results of p(T,H) vs. H as a function of T from I0 K to 90 K. Fig~e 2 shows plots of p(T,H)/p(T,0) vs. H as a function of T from 20 K to 90 K. Even in high T region above 40 K, which would not include the thermodynamic fluctuations effect on p(T,H), p(T,H) increases with increasing H, and the maximum increment of p(T,H) in/4--12 T at 40 K reaches about 1.6 % of that in 0 T. This magnetoresistivity decreases with the increase of temperature and is negligibly small above 90 K. Furthermore, when H is rotated
60 ~ DU
,-,,401
90K ~ .
17:=_~-SSL.
'
_
~
- .......
~~
~
,--. - .....I : I T U ~ . . - - " - - - - - ~
l
.............. rill I ~
~ 302010L6"5K 4 ; ~~"~342~4~ 1 0 . i < : : "
."
41~_ 2 ' " ~ "
O ~L_'':
0
~'"ltO L12
t = ! t -i ~ I = = ~ | L - L ~~
2
4
6 8 H (T)
10
12
Figure 1. p(T,H)vs.Hbetween 10Kand90K. Inset shows the enlargement at p=41,-46~tff~era. 3. DISCUSSION
0921-4534/94/$07.00© 1994- ElsevierScienceB.V. All rights reserved,
SSD10921-4534(94)01266-0
: , , , . , ,,.,, '..L'; '___.2.' '-i.'-- ' q
In order to simplify the discussion, the resistivity
1406
Y Yamasakiet al./Physica C 235-240 (1994) 1405-1406
1.05 ~
0.03 ~m,~.,J,,.,..,,,,. ,.,, .,..., ,.,.~.-.., ;!;.:.~.;ii"S'
t
.,..¢"
~
l
7 ; ; , , , . ,. , ,
0
2
4
. ,.
, .
, : . , , . . . . , ..... , . . . . , . . . . ,
6 8 10 12 14 H (T)
0 .... -20
40
i
•
..
I.l
I
l . i..
l__lll
.
60 T (K)
80
100
Figure 2. p(H)/p(0) vs. H as a function of 7".
Figure 3. B vs. T. inset shows A vs. T.
is used for a while for conductivity. We estimate the normal resistivity pn(T,/'/), which does not include the effect of thermodynamic fluctuations, using the data in the 7" region above 40 K under the following assumptions: (1) the effect of fluctuations on p(T,H) can be neglected at temperatures above 2To, (2) pn(T,H) can be represented as
estimated in the region of the thermodynamic fluctuations between 40 K and Tc because this extended region is rather narrow as compared with that used to determine A(7) and B(T). If B(T) and n are considered as a set of parameters, pn(T,H) can be estimated without determining n in the extended region between 40 K and Tc. Thus, by using the resistivity not including the normal magnetoresistivity in the region of fluctuations, pf(T,H) = p(T,H) -B(T)H n, the magnetoconductivity due to the fluctuations Ao (T,/-/) would be estimated as Ao (T,H) = 1/pf(T,l'O - 1/pf(T,0). Generally, the origin of the quadratic H dependence of pn(T,H) will be ascribed to the anisotropic scattering mechanism of carriers and/or to the coexistence of two kinds of carriers which means the coexistence of electrons and holes or s-electrons and d-electrons or open orbits and dosed orbits. Further study of the x'wrmal magnetoresistance with a quadratic H dependence and the magnetoconductivity due to fluctuations are in progress at present.
Pn( T,H) = A(T) +B(T) H n
(1)
where A(T), B(T) and n are fitting parameters. Under the assumption of (1), p(T,H) = pn(T,H). By fitting eq. (1) to the experimental results in the high T region beyond 40 K, we obtain these parameters as a function of T, which are shown by marks in Fig. 3. Since the values of B(T) change with n, B(T)'s are shown as a function of n. By fitting functional forms of A ( T ) a n d B ( T ) t o the experimental results, six coefficients are estimated. Here A(T)=ao+ al T+a2T2and B(~---bo+b1 T+b2 T2 respectively. Three coefficients for A ( T ) a r e determined regardless ot" n to be ao= 42.8, a1=1.88× 10-2 and a2=2.67× 10"3. The coefficients for B(T) are b0=2.26× 10 -2, bl =- 1.76x 10 .`4 and b2=-5.55 x ! 0 -T for n=l.6. Since A(T) is determined almost independently of n in the region from 40 K to 90 K, it would be reasonable for A(T) to be
REFERENCES 1. S. Hikami and A. I. Larkin, Mod. Phys. Lett. B 2 (1988) 693. 2. A. G. Aronov, S. Hi -'kami and A. I. Larkin, Phys. Rev. Lett. 62 (1989) 965.