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Quantum criticality in the electron doped cuprates
Physica C 460–462 (2007) 1109–1110 www.elsevier.com/locate/physc
Quantum criticality in the electron doped cuprates Y. Dagan b
a,b,*
, R.L. Greene
a
a Center for Superconductivity Research, Department of Physics, University of Maryland, College Park, MD 20743, USA School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel
Available online 28 March 2007
Abstract We report transport measurements at low temperatures on the electron doped superconductor Pr2 xCexCuO4 d. Above a certain doping level we observe an abrupt change in the doping dependence of the Hall coefficient along with a significant change in the temperature dependence of the resistivity. At this doping the spin scattering channel in the magnetoresistance vanishes and the temperature dependence of the Hall angle changes. This suggests a quantum phase transition as a function of doping. This transition is most probably due to vanishing of an antiferromagnetic order persisting into the superconducting dome. Ó 2007 Elsevier B.V. All rights reserved. Keywords: Quantum criticality; Normal state properties; Transport measurements
1. Introduction The electron doped (n-doped) cuprates, (RE2 xCexCuO4 d (RCCO) with RE = Nd, Pr, La and Sm), superconductors offer a unique system for studying the low temperatures normal state properties of a high Tc cuprate. In most of the high Tc cuprates a very high field, usually inaccessible, is needed to quench superconductivity. The normal state is thus obscured by the occurrence of superconductivity. Moreover, there is now compelling evidence that a quantum phase transition occurs as a function of doping slightly above optimum doping: the normal state Hall coefficient of Pr2 xCexCuO4 at 350 mK exhibits an abrupt change at x = 0.165 ± 0.005 [1]. This possibly singular behavior is accompanied by significant changes in the temperature dependence of the resistivity below 20 K. These changes in the resistivity and Hall coefficient were suggested as strong evidence for a quantum critical point (QCP) at xc = 0.165 ± 0.005. We also found that the spin related magnetoresistance (MR) suddenly vanishes above * Corresponding author. Address: Center for Superconductivity Research, Department of Physics, University of Maryland, College Park, MD 20743, USA. E-mail address: [email protected] (Y. Dagan).
0921-4534/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2007.03.230
x = 0.16 at T = 1.5 K. This MR appears in the region of the doping-temperature phase diagram where dq/dT < 0, or an upturn in the resistivity appears, thus suggesting that the upturn originates from spin scattering processes that vanish at the QCP [2]. The broad antiferromagnetic (AFM) region from x = 0 to just above x = 0.15 found in the phase diagram of the n-doped cuprates [3,4] suggests that the QCP found in Ref. [1] can be associated with the disappearance of the AFM phase as the doping is increased at T = 0. 2. Sample preparation and experiment PCCO c-axis oriented films of various cerium doping concentrations were deposited from stoichiometric targets on (1 0 0) oriented SrTiO3 substrates using the pulsed laser deposition (PLD) technique [5]. The annealing procedure and the films’ quality analysis are discussed elsewhere [1]. The films were patterned using a mechanical mask and ion milling technique to form Hall bars 6.5 mm long and 0.5 mm wide. Measurements at high magnetic fields are discussed in Ref. [2]. Resistivity measurements show a sharp transition with DTc 0.2 K. The Hall resistivity is measured as a function of magnetic field and RH is taken to be the slope of qxy vs. H.
1110
Y. Dagan, R.L. Greene / Physica C 460–462 (2007) 1109–1110
4.2
0
100K
-20
4.0
1.9
-40
Exponent
-10
RH 10 Ω m/T
2.0
-60 -80
T=0.35K T=10K
-100
3.8
1.8
3.6
1.7
3.4
-120 -140
3.2 0.06
0.09
0.12
0.15
0.18
Ce concentration Fig. 1. Circles: The Hall coefficient as a function of doping at 0.35 K. Squares: Data taken from Ref. [6]. For comparison dashed line and the dotted line are curves calculated using naı¨ve electrons counting using x and 1/(1 x), respectively.
Cot(θH)=A+BT ρ=A+BT
1.6
0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 Cerium Doping
Fig. 3. The exponents obtained from fits of cot(hH) (circles) and q (squares) to a power law temperature dependence.
Above optimum doping the data cannot be fitted to a power law for this temperature range. Δρ spin(16.2T)/ρ(32.4T) (%)
6
4. Discussion
5 4 3 2 1 0
0.12
0.14 0.16 Ce doping
0.18
Fig. 2. The spin component of the magnetoresistance at 1.5 K and 16.2 T found using the procedure described in Ref. [2].
3. Results In Fig. 1 we show RH at 0.35 K as a function of cerium doping for x = 0.11–0.19 (circles). The abrupt change in RH at 0.35 K and x = 0.16 is an indication of a significant reorganization of the Fermi surface (FS), which we believe may result from a quantum phase transition [1]. We were able to separate out the orbital magnetoresistance (MR) and the spin MR. In Fig. 2 we show the spin MR as a function of Ce doping at 1.5 K. We note a sharp increase at optimum doping and then at x = 0.16 the spin MR vanishes, consistent with the QCP scenario. We fit the temperature dependence of both the resistivity and cot(h) for the temperature range 100 > T > 300 K to a power law. In Fig. 3 we show the obtained powers as a function of Ce doping. While the resistivity shows no doping dependence cot(hH) increases with increasing doping.
The abrupt change in the doping dependence of RH suggests that the FS rearranges around x = 0.16. This is consistent with recent calculations using a spin density waves model [7]. However, the deviations from the dashed(dotted) lines in Fig. 1 for high(low) dopings still need an explanation. The abrupt disappearance of the spin channel in the MR with the sharp rise at optimum doping deserves theoretical attention. It seems to be consistent with the vanishing of a magnetic scattering channel possibly resulting from the disappearance of the AFM order. The different temperature dependences for cot(hH) and q suggest that these two transport quantities are sensitive to different regions on the FS. The largest deviation between the two scattering times is observed at x = 0.15 suggesting well defined ‘‘hot’’ regions on the FS at optimum doping. Acknowledgements Support from NSF and NHMFL is acknowledged. References [1] [2] [3] [4] [5] [6] [7]
Y. Dagan et al., Phys. Rev. Lett. 92 (2004) 167001. Y. Dagan et al., Phys. Rev. Lett. 94 (2005) 057005. M. Fujita et al., Phys. Rev. Lett. 93 (2004) 147003. Y. Onose et al., Phys. Rev. Lett. 87 (2001) 217001. E. Maiser et al., Physica C 297 (1998) 15. Y. Onose et al., Phys. Rev. Lett. 87 (2001) 217001. J. Lin, A.J. Millis, Phys. Rev. B 72 (2005) 214506.
Quantum criticality in the electron doped cuprates Y. Dagan b
a,b,*
, R.L. Greene
a
a Center for Superconductivity Research, Department of Physics, University of Maryland, College Park, MD 20743, USA School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel
Available online 28 March 2007
Abstract We report transport measurements at low temperatures on the electron doped superconductor Pr2 xCexCuO4 d. Above a certain doping level we observe an abrupt change in the doping dependence of the Hall coefficient along with a significant change in the temperature dependence of the resistivity. At this doping the spin scattering channel in the magnetoresistance vanishes and the temperature dependence of the Hall angle changes. This suggests a quantum phase transition as a function of doping. This transition is most probably due to vanishing of an antiferromagnetic order persisting into the superconducting dome. Ó 2007 Elsevier B.V. All rights reserved. Keywords: Quantum criticality; Normal state properties; Transport measurements
1. Introduction The electron doped (n-doped) cuprates, (RE2 xCexCuO4 d (RCCO) with RE = Nd, Pr, La and Sm), superconductors offer a unique system for studying the low temperatures normal state properties of a high Tc cuprate. In most of the high Tc cuprates a very high field, usually inaccessible, is needed to quench superconductivity. The normal state is thus obscured by the occurrence of superconductivity. Moreover, there is now compelling evidence that a quantum phase transition occurs as a function of doping slightly above optimum doping: the normal state Hall coefficient of Pr2 xCexCuO4 at 350 mK exhibits an abrupt change at x = 0.165 ± 0.005 [1]. This possibly singular behavior is accompanied by significant changes in the temperature dependence of the resistivity below 20 K. These changes in the resistivity and Hall coefficient were suggested as strong evidence for a quantum critical point (QCP) at xc = 0.165 ± 0.005. We also found that the spin related magnetoresistance (MR) suddenly vanishes above * Corresponding author. Address: Center for Superconductivity Research, Department of Physics, University of Maryland, College Park, MD 20743, USA. E-mail address: [email protected] (Y. Dagan).
0921-4534/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2007.03.230
x = 0.16 at T = 1.5 K. This MR appears in the region of the doping-temperature phase diagram where dq/dT < 0, or an upturn in the resistivity appears, thus suggesting that the upturn originates from spin scattering processes that vanish at the QCP [2]. The broad antiferromagnetic (AFM) region from x = 0 to just above x = 0.15 found in the phase diagram of the n-doped cuprates [3,4] suggests that the QCP found in Ref. [1] can be associated with the disappearance of the AFM phase as the doping is increased at T = 0. 2. Sample preparation and experiment PCCO c-axis oriented films of various cerium doping concentrations were deposited from stoichiometric targets on (1 0 0) oriented SrTiO3 substrates using the pulsed laser deposition (PLD) technique [5]. The annealing procedure and the films’ quality analysis are discussed elsewhere [1]. The films were patterned using a mechanical mask and ion milling technique to form Hall bars 6.5 mm long and 0.5 mm wide. Measurements at high magnetic fields are discussed in Ref. [2]. Resistivity measurements show a sharp transition with DTc 0.2 K. The Hall resistivity is measured as a function of magnetic field and RH is taken to be the slope of qxy vs. H.
1110
Y. Dagan, R.L. Greene / Physica C 460–462 (2007) 1109–1110
4.2
0
100K
-20
4.0
1.9
-40
Exponent
-10
RH 10 Ω m/T
2.0
-60 -80
T=0.35K T=10K
-100
3.8
1.8
3.6
1.7
3.4
-120 -140
3.2 0.06
0.09
0.12
0.15
0.18
Ce concentration Fig. 1. Circles: The Hall coefficient as a function of doping at 0.35 K. Squares: Data taken from Ref. [6]. For comparison dashed line and the dotted line are curves calculated using naı¨ve electrons counting using x and 1/(1 x), respectively.
Cot(θH)=A+BT ρ=A+BT
1.6
0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 Cerium Doping
Fig. 3. The exponents obtained from fits of cot(hH) (circles) and q (squares) to a power law temperature dependence.
Above optimum doping the data cannot be fitted to a power law for this temperature range. Δρ spin(16.2T)/ρ(32.4T) (%)
6
4. Discussion
5 4 3 2 1 0
0.12
0.14 0.16 Ce doping
0.18
Fig. 2. The spin component of the magnetoresistance at 1.5 K and 16.2 T found using the procedure described in Ref. [2].
3. Results In Fig. 1 we show RH at 0.35 K as a function of cerium doping for x = 0.11–0.19 (circles). The abrupt change in RH at 0.35 K and x = 0.16 is an indication of a significant reorganization of the Fermi surface (FS), which we believe may result from a quantum phase transition [1]. We were able to separate out the orbital magnetoresistance (MR) and the spin MR. In Fig. 2 we show the spin MR as a function of Ce doping at 1.5 K. We note a sharp increase at optimum doping and then at x = 0.16 the spin MR vanishes, consistent with the QCP scenario. We fit the temperature dependence of both the resistivity and cot(h) for the temperature range 100 > T > 300 K to a power law. In Fig. 3 we show the obtained powers as a function of Ce doping. While the resistivity shows no doping dependence cot(hH) increases with increasing doping.
The abrupt change in the doping dependence of RH suggests that the FS rearranges around x = 0.16. This is consistent with recent calculations using a spin density waves model [7]. However, the deviations from the dashed(dotted) lines in Fig. 1 for high(low) dopings still need an explanation. The abrupt disappearance of the spin channel in the MR with the sharp rise at optimum doping deserves theoretical attention. It seems to be consistent with the vanishing of a magnetic scattering channel possibly resulting from the disappearance of the AFM order. The different temperature dependences for cot(hH) and q suggest that these two transport quantities are sensitive to different regions on the FS. The largest deviation between the two scattering times is observed at x = 0.15 suggesting well defined ‘‘hot’’ regions on the FS at optimum doping. Acknowledgements Support from NSF and NHMFL is acknowledged. References [1] [2] [3] [4] [5] [6] [7]
Y. Dagan et al., Phys. Rev. Lett. 92 (2004) 167001. Y. Dagan et al., Phys. Rev. Lett. 94 (2005) 057005. M. Fujita et al., Phys. Rev. Lett. 93 (2004) 147003. Y. Onose et al., Phys. Rev. Lett. 87 (2001) 217001. E. Maiser et al., Physica C 297 (1998) 15. Y. Onose et al., Phys. Rev. Lett. 87 (2001) 217001. J. Lin, A.J. Millis, Phys. Rev. B 72 (2005) 214506.