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Magnetoresistance of Pr1.85Ce0.15CuO4+δ single crystals in the nonsuperconducting state
PHYSICA
Physica B 194-]96 (1994) 1625-1626 Noah-Holland
Magnetoresistance of Pr1.85Ceo.15CuO4+Single Crystals in the Nonsuperconducting State M. Brinkmann, K. Westerholt and H. Bach Institut ffir Experimentalphysik IV, Ruhr-Universit£t, D-4630 Bochum, Germany We report
magnetoresistance
m e a s u r e m e n t s of single crystals from the
n-type superconductor
Pr2_~Ce,~Cu04+6 for concentrations of o p t i m u m superconductivity z .~ 0.15. In the as-prepared state we find a strongly anisotropic negative magnetoresistance at low t e m p e r a t u r e s . For the magnetic field direction parallel to the c-axis the magnetoresistance can perfectly be fitted by two-dimensional weak localization theory• For the inelastic scattering time we derive a power law rl "-" T - ° 4 6 .
In the as-prepared, oxygen-rich state of the ntype high-To superconductors Ln2-~Ce, Cu04+6 (Ln = Pr, Nd, Sm) there is a broad concentration range where the resistivity is metallic with a weak logarithmic increase towards low temperaturesO)-(3). This behaviour indicates weak localization in the quasi two-dimensional metals and is caused by coherent backscatterins or by electron-electron interactions in a disordered metal(4). Measurements of the magnetoresistance (MR) in the regime of' weak localization provides important insight into the scattering processes involved. In single crystals Nd2-~:Ce~Cu04+6 at low Ceconcentrations the MR was found to be large and negative for the field direction perpendicular to the CuO2-planes(1). For the parallel field direction the MR was very small. This behaviour is well consistent with the coherent backscattering MR. In single crystals of the same system at higher Ce-concentrations z ~ 0.15, however, the MR was found to be negative but nearly isotropic for the two magnetic field directions(2), a result which is difficult to reconcile with the theory of weak localization. In a c-axis oriented thin film with a similar composition (s) the anisotropy of the M R was much larger. In the present p a p e r we study the MR of a single crystal with the composition Prl.ssCe0.15CuO4+~. We have grown high quality single crystals of Pr2-~Ce~CuO4~r6 with dimensions of typically 2 × 2 × 0.02 rnm J in the concentration range 0.08 < z < 0.2 from a CuO rich flux (5). The composition of the crystals was determined by
5
•
!
i
50
100
E 5 (9 C E
3
11;
cv 1 0 0
!
I
200
250
300
7 /< Figure 1: In-plane resistivity as a function of temperature for a single crystal Prl.ssCeo.15Cu04+~ in the as-prepared state (upper curve) and the reduced state (lower curve) quantitative x-ray microprobe analysis, the crystal quality was checked by x-ray rocking curves. The resistivity was measured by a low frequency 4-point ac-technique in a cryostat with a horizontal superconducting split coil assembly allowing an in-situ orientation of the sample in the magnetic field. In Fig.1 we show the resistivity of a sample with the Ce-concentration z = 0.15 in the as-prepared, oxygen-rich state and the oxygen-poor, superconducting state. The superconducting state has been achieved by reducing the crystal in pure Aratmosphere at 1030°C for 10 h. T h e superconducting transition t e m p e r a t u r e is 22K with a resistive transition width of 1K. In the as-prepared
0921-4526/94/$07.00 © 1994 - Elsevier Science B.V. All rights reserved
SSDI 0921-4526(93)1393-Z
!
150
1626
1.02
,
O"
,
,--~.
,
(with bile = ~ ,nc
1 al
0.98
I-I II
oJ 0.96 \
i%,'--.. ~
0.92 .,
Q*
K
1.8
~ H.I.
0.94
~ - - F - ~ I-"
0.9 0.88
,
0
HZ
L _ _ ~ L
10
20 H
,
30 /
40
50
kOe
Figure 2: Magnetoresistance at 1.8K for the sin-
gle crystal of Fig.l for parallel and perpendicular field. The relative orientation of the c-axis to the current and the field is plotted in the inset. 1
- - -
!. 0.98 ~
0.96
Z
o.92
f
c~ 0"9[ 0.88
0
HJ-. "
10
,
.
20
~ 30
H /
,
-430'~
40
50
60
70
kOe
Figure 3: Perpendicular magnetoresistance at dif-
ferent temperatures for the sample from Fig. l. The drawn line is the fit using the equation from the main text. The inelastic scattering length li is given in the figure. state the sample exhibits the typical logarithmic increase at low t e m p e r a t u r e s with a resistance m i n i m u m at 120 K. In Fig.2 we show the magnetoresistance of the sample in the as-prepared state for the two field directions parallel and perpendicular to the CuO2-planes at 1.8K. The MR is negative and large reaching 10% at 3.5 T for the perpendicular field. In Fig.3 we show the perpendicular MR at different t e m p e r a t u r e s together with theoretical curves obtained from the fit of the experimental curves with the formula for coherent backscattering MR (4). ~(,2')(H)
v~e2
= -7-#('~(:).
1
b,
+ -~) -
k~(l+ b¢ ,
y)
-
ln(~))
lil~ being the (in)elastic scat-
tering length, a an empirical p a r a m e t e r of order unity and • the d i g a m m a function) For the t e m p e r a t u r e independent elastic scattering length l~ we determine 198~,. The numerical values for the inelastic scattering length li resulting from the fit are given in Fig.3. The inelastic scattering time n = (l~)/D (D being the diffusion constant) follows a power law ri --, T = with x ~ - 0 . 4 6 approximately. A similar power law with x ~ - 0 . 4 has been derived for the sample Ndl.gsCeo.o2Cu04+~ in (t). For a single crystal from the p - t y p e system B i : S r 2 C u 0 6 one finds rl "-- T - ° 3 (6). This unusual t e m p e r a t u r e dependence should be compared to v, .~ ( T l n ( T ) ) -1 expected for strong electron-electron scattering in 2D at low t e m p e r a t u r e s (r). For the parallel field direction we find a small negative MR. In this case the coherent backscattering MR should vanish and the electron interaction MR from the suppression of the singlet contribution to the particle-hole propagator should be positive (4). An intriguing possible explanation for the negative parallel MR and its sensitive dependence from preparation conditions is the assumption of a magnetic scattering on spin fluctuations. Close to the Ce-concentration x ~ 0.15 the aN long range order is expected to break down (s/, thus dependent on the preparation conditions the sample might be in an a ~ s t a t e with weak long range order or in a dynamically ordered spin-liquid state. References (1) S.J. Hagen et al., Phys. Rev.B 45 (1902) 515 (2) S.Ugi and H.Aoki, Physica C 109 (1992) 231 (3) A.Kussmaul et al., Physica C 177 (1991) 415 (4) P.A.Lee and T.V. Ramakrishnan, Rev. Mod Phys. 57 (1985) 287 (5) M.Matsuda and al., Physica C 170 (1901) 347 (6) T . W . J i n g e t al., Phys. Rev. Lett. 67 (1991) 761 (7) E. A b r a h a m s et al., Phys. Rev. B 24 (1081) 6783 (8) T. R. Thurston et al., Phys. Rev. Lett. 65 (1990) 263
Physica B 194-]96 (1994) 1625-1626 Noah-Holland
Magnetoresistance of Pr1.85Ceo.15CuO4+Single Crystals in the Nonsuperconducting State M. Brinkmann, K. Westerholt and H. Bach Institut ffir Experimentalphysik IV, Ruhr-Universit£t, D-4630 Bochum, Germany We report
magnetoresistance
m e a s u r e m e n t s of single crystals from the
n-type superconductor
Pr2_~Ce,~Cu04+6 for concentrations of o p t i m u m superconductivity z .~ 0.15. In the as-prepared state we find a strongly anisotropic negative magnetoresistance at low t e m p e r a t u r e s . For the magnetic field direction parallel to the c-axis the magnetoresistance can perfectly be fitted by two-dimensional weak localization theory• For the inelastic scattering time we derive a power law rl "-" T - ° 4 6 .
In the as-prepared, oxygen-rich state of the ntype high-To superconductors Ln2-~Ce, Cu04+6 (Ln = Pr, Nd, Sm) there is a broad concentration range where the resistivity is metallic with a weak logarithmic increase towards low temperaturesO)-(3). This behaviour indicates weak localization in the quasi two-dimensional metals and is caused by coherent backscatterins or by electron-electron interactions in a disordered metal(4). Measurements of the magnetoresistance (MR) in the regime of' weak localization provides important insight into the scattering processes involved. In single crystals Nd2-~:Ce~Cu04+6 at low Ceconcentrations the MR was found to be large and negative for the field direction perpendicular to the CuO2-planes(1). For the parallel field direction the MR was very small. This behaviour is well consistent with the coherent backscattering MR. In single crystals of the same system at higher Ce-concentrations z ~ 0.15, however, the MR was found to be negative but nearly isotropic for the two magnetic field directions(2), a result which is difficult to reconcile with the theory of weak localization. In a c-axis oriented thin film with a similar composition (s) the anisotropy of the M R was much larger. In the present p a p e r we study the MR of a single crystal with the composition Prl.ssCe0.15CuO4+~. We have grown high quality single crystals of Pr2-~Ce~CuO4~r6 with dimensions of typically 2 × 2 × 0.02 rnm J in the concentration range 0.08 < z < 0.2 from a CuO rich flux (5). The composition of the crystals was determined by
5
•
!
i
50
100
E 5 (9 C E
3
11;
cv 1 0 0
!
I
200
250
300
7 /< Figure 1: In-plane resistivity as a function of temperature for a single crystal Prl.ssCeo.15Cu04+~ in the as-prepared state (upper curve) and the reduced state (lower curve) quantitative x-ray microprobe analysis, the crystal quality was checked by x-ray rocking curves. The resistivity was measured by a low frequency 4-point ac-technique in a cryostat with a horizontal superconducting split coil assembly allowing an in-situ orientation of the sample in the magnetic field. In Fig.1 we show the resistivity of a sample with the Ce-concentration z = 0.15 in the as-prepared, oxygen-rich state and the oxygen-poor, superconducting state. The superconducting state has been achieved by reducing the crystal in pure Aratmosphere at 1030°C for 10 h. T h e superconducting transition t e m p e r a t u r e is 22K with a resistive transition width of 1K. In the as-prepared
0921-4526/94/$07.00 © 1994 - Elsevier Science B.V. All rights reserved
SSDI 0921-4526(93)1393-Z
!
150
1626
1.02
,
O"
,
,--~.
,
(with bile = ~ ,nc
1 al
0.98
I-I II
oJ 0.96 \
i%,'--.. ~
0.92 .,
Q*
K
1.8
~ H.I.
0.94
~ - - F - ~ I-"
0.9 0.88
,
0
HZ
L _ _ ~ L
10
20 H
,
30 /
40
50
kOe
Figure 2: Magnetoresistance at 1.8K for the sin-
gle crystal of Fig.l for parallel and perpendicular field. The relative orientation of the c-axis to the current and the field is plotted in the inset. 1
- - -
!. 0.98 ~
0.96
Z
o.92
f
c~ 0"9[ 0.88
0
HJ-. "
10
,
.
20
~ 30
H /
,
-430'~
40
50
60
70
kOe
Figure 3: Perpendicular magnetoresistance at dif-
ferent temperatures for the sample from Fig. l. The drawn line is the fit using the equation from the main text. The inelastic scattering length li is given in the figure. state the sample exhibits the typical logarithmic increase at low t e m p e r a t u r e s with a resistance m i n i m u m at 120 K. In Fig.2 we show the magnetoresistance of the sample in the as-prepared state for the two field directions parallel and perpendicular to the CuO2-planes at 1.8K. The MR is negative and large reaching 10% at 3.5 T for the perpendicular field. In Fig.3 we show the perpendicular MR at different t e m p e r a t u r e s together with theoretical curves obtained from the fit of the experimental curves with the formula for coherent backscattering MR (4). ~(,2')(H)
v~e2
= -7-#('~(:).
1
b,
+ -~) -
k~(l+ b¢ ,
y)
-
ln(~))
lil~ being the (in)elastic scat-
tering length, a an empirical p a r a m e t e r of order unity and • the d i g a m m a function) For the t e m p e r a t u r e independent elastic scattering length l~ we determine 198~,. The numerical values for the inelastic scattering length li resulting from the fit are given in Fig.3. The inelastic scattering time n = (l~)/D (D being the diffusion constant) follows a power law ri --, T = with x ~ - 0 . 4 6 approximately. A similar power law with x ~ - 0 . 4 has been derived for the sample Ndl.gsCeo.o2Cu04+~ in (t). For a single crystal from the p - t y p e system B i : S r 2 C u 0 6 one finds rl "-- T - ° 3 (6). This unusual t e m p e r a t u r e dependence should be compared to v, .~ ( T l n ( T ) ) -1 expected for strong electron-electron scattering in 2D at low t e m p e r a t u r e s (r). For the parallel field direction we find a small negative MR. In this case the coherent backscattering MR should vanish and the electron interaction MR from the suppression of the singlet contribution to the particle-hole propagator should be positive (4). An intriguing possible explanation for the negative parallel MR and its sensitive dependence from preparation conditions is the assumption of a magnetic scattering on spin fluctuations. Close to the Ce-concentration x ~ 0.15 the aN long range order is expected to break down (s/, thus dependent on the preparation conditions the sample might be in an a ~ s t a t e with weak long range order or in a dynamically ordered spin-liquid state. References (1) S.J. Hagen et al., Phys. Rev.B 45 (1902) 515 (2) S.Ugi and H.Aoki, Physica C 109 (1992) 231 (3) A.Kussmaul et al., Physica C 177 (1991) 415 (4) P.A.Lee and T.V. Ramakrishnan, Rev. Mod Phys. 57 (1985) 287 (5) M.Matsuda and al., Physica C 170 (1901) 347 (6) T . W . J i n g e t al., Phys. Rev. Lett. 67 (1991) 761 (7) E. A b r a h a m s et al., Phys. Rev. B 24 (1081) 6783 (8) T. R. Thurston et al., Phys. Rev. Lett. 65 (1990) 263