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Oxygen chain disorder as a weak-limit scatterer in YBa2Cu3O6.50
Physica C 460–462 (2007) 914–915 www.elsevier.com/locate/physc
Oxygen chain disorder as a weak-limit scatterer in YBa2Cu3O6.50 J.S. Bobowski a
a,*
, P.J. Turner
a,b
, R. Harris
a,c
, Ruixing Liang a, D.A. Bonn a, W.N. Hardy
a
Department of Physics and Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, British Columbia, Canada V6T 1Z1 b Department of Physics, Simon Fraser University, 8888 University Drive, Burnaby, British Columbia, Canada V5A 1S6 c D-Wave Systems Inc., 4401 Still Creek Drive, Burnaby, British Columbia, Canada V5C 6G9 Available online 28 March 2007
Abstract The real part of the microwave conductivity of an ultra-pure sample of YBa2Cu3O6.50 deep in the superconducting state has been measured as a continuous function of frequency. Conductivity spectra were first measured with the Cu–O chain oxygens atoms highly ordered in the ortho-II phase (alternating full and empty chains). The measurements were then repeated after heating and quenching the sample to reduce the degree of oxygen order in the Cu–O chains which lowered Tc from 55 K to 49 K. Disordering the Cu–O chains produced conductivity spectra that were more than twice as broad as those of the ortho-II ordered phase. In both cases the width of the conductivity spectra increases approximately linearly with temperature. Moreover, within our experimental resolution we find that the low-temperature quasiparticle spectral weight does not depend on the degree of oxygen orderer in the Cu–O chains. Each of these features indicates that oxygen disorder in the Cu–O chains acts as a source of weak-limit scattering for quasiparticles propagating in the CuO2 planes. Crown Copyright Ó 2007 Published by Elsevier B.V. All rights reserved. PACS: 73.25.+i; 74.25.Fy; 74.72.Bk Keywords: Oxygen disorder; Ortho-II; Microwave spectroscopy; YBa2Cu3O6+y; Weak-limit scattering
A non-resonant bolometric apparatus has recently been developed to measure the microwave surface resistance Rs of single crystals, continuously from 0.5 to 20 GHz [1]. When combined with a separate measurement of the magnetic penetration depth k(T) the surface resistance data allow us to extract the real part of the quasiparticle conductivity spectra r1(x, T). Of the cuprates, single crystals of YBa2Cu3O6+y are the most chemically pure and crystalline samples available. In 2003 measurements of the conductivity spectra of an orthoII ordered single crystal of YBa2Cu3O6.50 were the first to show features expected for a d-wave superconductor in the weak-scattering limit [2]. Gaining access to these ultra-pure samples has, for the first time, allowed us to quantitatively study the role that oxygen order in the Cu–O chains plays in quasiparticle scattering. *
Corresponding author. E-mail address: [email protected] (J.S. Bobowski).
Fig. 1 shows the measured surface resistance and quasiparticle conductivities of an ortho-II ordered (Tc = 55 K) single crystal of YBa2Cu3O6.50 at four temperatures below 10 K. As previously seen, these conductivity spectra exhibit features expected for a d-wave superconductor in the weakscattering limit: cusp-like line shapes whose widths K 1 and integrated spectral weights nne2/mw both increase linearly with temperature [2]. The same sample was then heated and quenched to disorder the oxygens in the Cu–O chains (Tc = 49 K), without altering the oxygen content. After disordering, the microwave measurements were repeated and the results are shown in Fig. 2. The disordered spectra are more than twice as broad as the ordered spectra indicating a significant increase in quasiparticle scattering. These data, nevertheless, retain features expected for a d-wave superconductor in the weak-scattering limit. The width of the conductivity spectrum provides a measure of the quasiparticle scattering rate and is extracted by fitting the data to a phenomenological model [2]. The
0921-4534/$ - see front matter Crown Copyright Ó 2007 Published by Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2007.03.272
J.S. Bobowski et al. / Physica C 460–462 (2007) 914–915
1000
1000
YBa 2Cu3O6.50 a-axis ortho-II ordered chain oxygens TC = 55 K 1.3 K 3.1 K 5.6 K 8.6 K
RS (μΩ)
600
YBa2Cu3O6.50 a-axis disordered chain oxygens TC = 49 K 1.2 K 3.0 K 5.7 K 8.9 K
800
600
RS (μΩ)
800
915
400
400
200
200
0
0
Integrated Conductivity 2 2 1/λ (0)-1/λ (T)
16
-1 -1
20
30
ordered disordered 2 2 1/λ (0)-1/λ (T )
10
10 0 0
2
8
4 6 8 Temperature (K)
10
1
4 6 8 Temperature (K)
6
2
6
0
20
* 2
-1
-1
10
σ (x10 Ω m )
2
*
12
0
-1
-1
σ1 (x10 Ω m )
20
40
17
-1
30
17
-1
30
nne /m (x10 Ω m s )
-1 -1
nne /m (x10 Ω m s )
40
10 4
0
0
0
5
10
15
20
0
5
20
ordered disordered
2.0
1.5 11 -1
−1
temperature dependence of K 1 for ordered and disordered chain oxygens is shown in Fig. 3. In a d-wave superconductor the energy dependence of K 1 is determined by the strength of the scattering. Hirschfeld et al. have shown that at low T, in the strong-scattering limit K 1() 1, whereas in the weak-scattering limit K 1() [3]. Both linearly temperature dependent scattering rates and quasiparticle spectral weights that are independent of chain oxygen order indicate that disorder in the Cu–O chains acts as a weak scattering source for in-plane quasiparticles. We speculate that, even in the ortho-II ordered phase, for these ultra-pure samples residual chain oxygen disorder may still play a significant role in determining the observed scattering rates.
15
Fig. 2. Top panel: Measured surface resistance of YBa2Cu3O6.50 with disordered chain oxygens. Bottom panel: Extracted conductivity spectra. Inset: Within our experimental resolution the quasiparticle spectral weights before and after disordering are not noticeably changed.
Λ (x10 s )
Fig. 1. Top panel: Measured surface resistance of ortho-II ordered YBa2Cu3O6.50. Bottom panel: Conductivity spectra obtained from fits to Rs. The solid lines are generated using parameters extracted from the fits. Inset: Comparison of the normal fluid density obtained from integrating the conductivity spectra to that extracted from measurements of k(T).
10
Frequency (GHz)
Frequency (GHz)
1.0
0.5
0.0 0
2
4
6
8
10
Temperature (K)
References
Fig. 3. Scattering rates of YBa2Cu3O6.50 with ordered (solid points) and disordered (open points) chain oxygens.
[1] P.J. Turner et al., Rev. Sci. Instrum. 75 (2004) 124. [2] P.J. Turner et al., Phys. Rev. Lett. 90 (2003) 237005.
[3] P.J. Hirschfeld et al., Phys. Rev. B 50 (1994) 10250.
Oxygen chain disorder as a weak-limit scatterer in YBa2Cu3O6.50 J.S. Bobowski a
a,*
, P.J. Turner
a,b
, R. Harris
a,c
, Ruixing Liang a, D.A. Bonn a, W.N. Hardy
a
Department of Physics and Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, British Columbia, Canada V6T 1Z1 b Department of Physics, Simon Fraser University, 8888 University Drive, Burnaby, British Columbia, Canada V5A 1S6 c D-Wave Systems Inc., 4401 Still Creek Drive, Burnaby, British Columbia, Canada V5C 6G9 Available online 28 March 2007
Abstract The real part of the microwave conductivity of an ultra-pure sample of YBa2Cu3O6.50 deep in the superconducting state has been measured as a continuous function of frequency. Conductivity spectra were first measured with the Cu–O chain oxygens atoms highly ordered in the ortho-II phase (alternating full and empty chains). The measurements were then repeated after heating and quenching the sample to reduce the degree of oxygen order in the Cu–O chains which lowered Tc from 55 K to 49 K. Disordering the Cu–O chains produced conductivity spectra that were more than twice as broad as those of the ortho-II ordered phase. In both cases the width of the conductivity spectra increases approximately linearly with temperature. Moreover, within our experimental resolution we find that the low-temperature quasiparticle spectral weight does not depend on the degree of oxygen orderer in the Cu–O chains. Each of these features indicates that oxygen disorder in the Cu–O chains acts as a source of weak-limit scattering for quasiparticles propagating in the CuO2 planes. Crown Copyright Ó 2007 Published by Elsevier B.V. All rights reserved. PACS: 73.25.+i; 74.25.Fy; 74.72.Bk Keywords: Oxygen disorder; Ortho-II; Microwave spectroscopy; YBa2Cu3O6+y; Weak-limit scattering
A non-resonant bolometric apparatus has recently been developed to measure the microwave surface resistance Rs of single crystals, continuously from 0.5 to 20 GHz [1]. When combined with a separate measurement of the magnetic penetration depth k(T) the surface resistance data allow us to extract the real part of the quasiparticle conductivity spectra r1(x, T). Of the cuprates, single crystals of YBa2Cu3O6+y are the most chemically pure and crystalline samples available. In 2003 measurements of the conductivity spectra of an orthoII ordered single crystal of YBa2Cu3O6.50 were the first to show features expected for a d-wave superconductor in the weak-scattering limit [2]. Gaining access to these ultra-pure samples has, for the first time, allowed us to quantitatively study the role that oxygen order in the Cu–O chains plays in quasiparticle scattering. *
Corresponding author. E-mail address: [email protected] (J.S. Bobowski).
Fig. 1 shows the measured surface resistance and quasiparticle conductivities of an ortho-II ordered (Tc = 55 K) single crystal of YBa2Cu3O6.50 at four temperatures below 10 K. As previously seen, these conductivity spectra exhibit features expected for a d-wave superconductor in the weakscattering limit: cusp-like line shapes whose widths K 1 and integrated spectral weights nne2/mw both increase linearly with temperature [2]. The same sample was then heated and quenched to disorder the oxygens in the Cu–O chains (Tc = 49 K), without altering the oxygen content. After disordering, the microwave measurements were repeated and the results are shown in Fig. 2. The disordered spectra are more than twice as broad as the ordered spectra indicating a significant increase in quasiparticle scattering. These data, nevertheless, retain features expected for a d-wave superconductor in the weak-scattering limit. The width of the conductivity spectrum provides a measure of the quasiparticle scattering rate and is extracted by fitting the data to a phenomenological model [2]. The
0921-4534/$ - see front matter Crown Copyright Ó 2007 Published by Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2007.03.272
J.S. Bobowski et al. / Physica C 460–462 (2007) 914–915
1000
1000
YBa 2Cu3O6.50 a-axis ortho-II ordered chain oxygens TC = 55 K 1.3 K 3.1 K 5.6 K 8.6 K
RS (μΩ)
600
YBa2Cu3O6.50 a-axis disordered chain oxygens TC = 49 K 1.2 K 3.0 K 5.7 K 8.9 K
800
600
RS (μΩ)
800
915
400
400
200
200
0
0
Integrated Conductivity 2 2 1/λ (0)-1/λ (T)
16
-1 -1
20
30
ordered disordered 2 2 1/λ (0)-1/λ (T )
10
10 0 0
2
8
4 6 8 Temperature (K)
10
1
4 6 8 Temperature (K)
6
2
6
0
20
* 2
-1
-1
10
σ (x10 Ω m )
2
*
12
0
-1
-1
σ1 (x10 Ω m )
20
40
17
-1
30
17
-1
30
nne /m (x10 Ω m s )
-1 -1
nne /m (x10 Ω m s )
40
10 4
0
0
0
5
10
15
20
0
5
20
ordered disordered
2.0
1.5 11 -1
−1
temperature dependence of K 1 for ordered and disordered chain oxygens is shown in Fig. 3. In a d-wave superconductor the energy dependence of K 1 is determined by the strength of the scattering. Hirschfeld et al. have shown that at low T, in the strong-scattering limit K 1() 1, whereas in the weak-scattering limit K 1() [3]. Both linearly temperature dependent scattering rates and quasiparticle spectral weights that are independent of chain oxygen order indicate that disorder in the Cu–O chains acts as a weak scattering source for in-plane quasiparticles. We speculate that, even in the ortho-II ordered phase, for these ultra-pure samples residual chain oxygen disorder may still play a significant role in determining the observed scattering rates.
15
Fig. 2. Top panel: Measured surface resistance of YBa2Cu3O6.50 with disordered chain oxygens. Bottom panel: Extracted conductivity spectra. Inset: Within our experimental resolution the quasiparticle spectral weights before and after disordering are not noticeably changed.
Λ (x10 s )
Fig. 1. Top panel: Measured surface resistance of ortho-II ordered YBa2Cu3O6.50. Bottom panel: Conductivity spectra obtained from fits to Rs. The solid lines are generated using parameters extracted from the fits. Inset: Comparison of the normal fluid density obtained from integrating the conductivity spectra to that extracted from measurements of k(T).
10
Frequency (GHz)
Frequency (GHz)
1.0
0.5
0.0 0
2
4
6
8
10
Temperature (K)
References
Fig. 3. Scattering rates of YBa2Cu3O6.50 with ordered (solid points) and disordered (open points) chain oxygens.
[1] P.J. Turner et al., Rev. Sci. Instrum. 75 (2004) 124. [2] P.J. Turner et al., Phys. Rev. Lett. 90 (2003) 237005.
[3] P.J. Hirschfeld et al., Phys. Rev. B 50 (1994) 10250.