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Pseudo-spin-gap of La2−xSrxCuO4
Physica C 412–414 (2004) 338–341 www.elsevier.com/locate/physc
Pseudo-spin-gap of La2xSrxCuO4 Y. Itoh a
a,b,*
, T. Machi a, N. Koshizuka
a
Superconductivity Research Laboratory, ISTEC, 1-10-13 Shinonome, Koto-ku, Tokyo 135-0062, Japan b Japan Society for the Promotion of Science, Tokyo 102-8471, Japan Received 29 October 2003; accepted 17 November 2003 Available online 6 May 2004
Abstract We revisited the Cu nuclear spin–lattice relaxation of 63 Cu-enriched high-Tc superconductors La2x Srx CuO4 with x ¼ 0:13 (an underdoped sample) and 0.18 (an overdoped sample). From application of the impurity-induced NMR relaxation theory, we observed a remnant of the pseudo-spin-gap effect on the host Cu nuclear spin–lattice relaxation rate 63 ð1=T1 T Þhost and the inhomogeneous slow fluctuation effect via the impurity-induced relaxation rate 63 ð1=s1 Þ. The magnetic phase diagram with the pseudo-spin-gap temperatures Ts is presented. Ó 2004 Elsevier B.V. All rights reserved. PACS: 74.72.Dn; 74.25.Nf; 74.25.)q Keywords: Nuclear quadrupole resonance; Nuclear spin–lattice relaxation; Pseudo-spin-gap; La2x Srx CuO4
1. Introduction It has been long asked whether all the high-Tc superconductors have a normal state gap in the magnetic excitation spectrum. A counterexample is a single-CuO2 -layer system La2x Srx CuO4 , which does not show any apparent, normal state gap [1]. However, the discovery of charge–spin stripe correlation by neutron scattering technique [2] and the intensive studies by nuclear quadrupole resonance (NQR)/NMR technique [3–8] renewed our understanding this material. In this paper, we
revisited the Cu nuclear spin–lattice relaxation and tested the impurity-induced NMR relaxation theory [9] to 63 Cu-enriched high-Tc superconductors La2x Srx CuO4 with x ¼ 0:13 (an underdoped sample) and 0.18 (an overdoped sample), on the analogy of the in-plane impurity substitution effect on YBa2 Cu3 O7d or YBa2 Cu4 O8 [10]. We found a remnant of the pseudo-spin-gap and the effect of inhomogeneous slow fluctuations around the optimally doped region.
2. Experimental *
Corresponding author. Address: Superconductivity Research Laboratory, ISTEC, 1-10-13 Shinonome, Koto-ku, Tokyo 135-0062, Japan. Tel.: +81-3-3536-5707; fax: +81-33536-5705. E-mail address: [email protected] (Y. Itoh).
The superconducting transition temperatures Tc of our samples, which were studied in Ref. [11] were re-estimated by magnetization measurements using a superconducting quantum interference device (SQUID) magnetometer, Tc 36 K for
0921-4534/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2003.11.076
Y. Itoh et al. / Physica C 412–414 (2004) 338–341 1
63p(t)
x ¼ 0:13 and Tc 34 K for x ¼ 0:18. A coherenttype pulsed spectrometer was utilized for zero-field 63 Cu NQR measurements. 63 Cu nuclear spin–lattice relaxation was measured by an inversion recovery spin-echo technique. The spin-echo amplitude MðtÞ was recorded as a function of a time interval t after an inversion pulse, at the peak frequency of the broad Cu NQR spectrum [11].
339 1
40 K
4.2 K
77 K
10 K
120 K
20 K
0.1
30 K
0.1
0.01
0.001
0
500
1000
0.01
1500
0
10
t (ms)
Cu nuclear spin–lattice relaxation curves
Fig. 1 shows 63 Cu nuclear spin–lattice relaxation (recovery) curves 63 pðtÞ 1 MðtÞ=Mð1Þ as a function of temperature for x ¼ 0:13. The solid curves are pfits by a function of pð0Þ exp½3t= 63 63 ðT1 Þhost 3t= s1 ] where pð0Þ, 63 ðT1 Þhost and 63 s1 are the parameters [9]. 63 ðT1 Þhost is the nuclear spin– lattice relaxation time due to host, homogeneous electron spin fluctuations, whereas 63 s1 is that due to the impurity-induced, inhomogeneous fluctuations [9,10,12]. The nonexponential recovery curves result from the stretched exponential function with 63 s1 . The impurity-induced relaxation indicates randomly distributed relaxation centers on the CuO2 planes. Since no Curie term was observed in the uniform spin susceptibility, randomly distributed staggered moments are the promising candidate for the relaxation centers.
4.
63
(T1 )host and
63
(s1 ) 63
Fig. 2 shows 1= ðT1 T Þhost (a) and 63 ð1=s1 Þ (b) as functions of temperature for x ¼ 0:13 and 0.18. 63 The pseudo-spin-gap behavior of 1= ðT1 T Þhost is seen in both materials. For comparison with the other single-CuO2 -layer superconductors, 1= 63 ðT1 T Þ of HgBa2 CuO4þd with the optimal Tc 92 K is also shown [13]. HgBa2 CuO4þd has the maximum Tc among ever reported single-CuO2 -layer superconductors. The pseudo-spin-gap temperature Ts which is defined as the peak temperature of 63 1= ðT1 T Þhost , is 130 K for x ¼ 0:13 and 90 K for x ¼ 0:18. Both 63 ð1=s1 Þ’s show maximum values around Tpeak ¼ 40–60 K. Below T ¼ 300 K, 1=63 ðT1 T Þhost increases due to the growth of antiferromagnetic spin fluctuations.
Fig. 1. Temperature dependence of recovery curve 63 pðtÞ for x ¼ 0:13.
63(1/T T)host (s-1K-1) 1
63
63
30x103
Cu nuclear spin-echo
Ts T ↓ ⇐ ↓s
20
x=0.13 0.18
(a)
⇓ ↑
↑ Tmin
10
HgBa2CuO4+δ 0 10
63(1/τ ) (ms-1) 1
3.
20
t (ms)
↔
Tpeak
(b)
1 0.1 0.01
0.001 0
100
200
300
T (K) Fig. 2. 63 Cu nuclear spin–lattice relaxation rates 1=63 ðT1 T Þhost (a) and 63 ð1=s1 ) (b) against temperature for x ¼ 0:13 and 0.18. The dashed lines indicate Tc ’s for x ¼ 0:13 and 0.18. Various characteristic temperatures of Tc , Ts , Tmin and Tpeak are defined here. For comparison, 1=63 ðT1 T ) of HgBa2 CuO4þd with the optimal Tc 96 K is reproduced from Ref. [13].
63
Below Ts , 1= ðT1 T Þhost decreases due to opening of the pseudo-spin-gap. The upturn of 1=63 ðT1 T Þhost below Tmin , which is defined in Fig. 2(a), indicates the existence of unknown gapless fluctuations. 63 Since the upturn of 1= ðT1 T Þhost is suppressed by hole doping from x ¼ 0:13 to 0.18, then the gapless fluctuations may be a remnant of the charge–spin stripe fluctuations. The stretched exponential relaxation with highly enhanced 1=s1 was observed in 139 La nuclear spin–lattice relaxation for less doped materials [14–16]. The low temperature increase of
340
Y. Itoh et al. / Physica C 412–414 (2004) 338–341
63
ð1=s1 Þ of the semiconducting La2x Srx CuO4 is explained by spin freezing effect, which is associated with the electronic characteristic of the Mott insulating state. Thus, our observation of a finite 63 ð1=s1 Þ around the optimally doped region may result from a remnant of such spin freezing effect.
5. Magnetic phase diagram Fig. 3 shows a magnetic phase diagram with the superconducting transition temperatures Tc , the pseudo-spin-gap temperatures Ts , the Cu NQR wipeout temperatures TNQR [5,8], the crossover temperatures Tf probed by muon spin relaxation [17], and the in-plane resistance minimum temperatures Tu [18] against hole concentration. Although the remnant of the pseudo-spin-gap is successfully observed below Ts , the low temperature states are still covered by the remnant of the spin freezing effect or the unknown fluctuations. The low temperature anomaly is characteristic of the La2x Srx CuO4 system. Thus, one reason why the optimal Tc (38 K) of La2x Srx CuO4 is lower than the optimal Tc (96 K) of
HgBa2 CuO4þd can be attributed to the pair breaking effect of the anomaly.
6. Conclusion We observed a remnant of the pseudo-spin-gap and the finite contribution from inhomogeneous slow fluctuations for La2x Srx CuO4 around the optimally doped region via the analysis of nonexponential Cu nuclear spin–lattice relaxation. The pseudo-spin-gap of magnetic excitation spectrum is just masked by the inhomogeneous slow fluctuations but not collapsed.
Acknowledgements This work was supported by the New Energy and Industrial Technology Development Organization (NEDO) as Collaborative Research and Development of Fundamental Technologies for Superconductivity Applications.
References La2-xSrxCuO4
Temperature (K)
300
200
TNQR Tu
(wipeout)
Ts Tmi n Tpeak Tc
100 Tf 0 0.00
(µSR)
0.05
0.10
0.15
0.20
Hole concentration x Fig. 3. Magnetic phase diagram against the hole concentration d defined as Cu2þd . The triangle symbols of Tc , Ts , Tmin and Tpeak are defined in Fig. 2. Tc (squares) and the Cu NQR wipeout temperatures TNQR (circles) are reproduced from Refs. [5,8]. The crossover temperatures Tf (crosses), which are defined as the first deviation of muon spin relaxation from Gaussian behavior, are reproduced from Ref. [17]. The in-plane resistance minimum temperatures Tu (open diamonds), at which the resistivity shows an upturn, are reproduced from Ref. [18].
[1] S. Ohsugi, Y. Kitaoka, K. Ishida, G.-q. Zheng, K. Asayama, J. Phys. Soc. Jpn. 63 (1994) 700. [2] J.M. Tranquada, B.J. Sternlieb, J.D. Axe, Y. Nakamura, S. Uchida, Nature 375 (1995) 561. [3] K. Yoshimura, T. Imai, T. Shimizu, Y. Ueda, K. Kosuge, H. Yasuoka, J. Phys. Soc. Jpn. 58 (1989) 3057. [4] K. Yoshimura, T. Uemura, M. Kato, K. Kosuge, T. Imai, H. Yasuoka, Hyperfine Interact. 79 (1993) 867. [5] A.W. Hunt, P.M. Singer, K.R. Thurber, T. Imai, Phys. Rev. Lett. 82 (1999) 4300. [6] A.W. Hunt, P.M. Singer, A.F. Cederstr€ om, T. Imai, Phys. Rev. B 64 (2001) 134525. [7] P.M. Singer, A.W. Hunt, T. Imai, Phys. Rev. Lett. 88 (2002) 047602. [8] P.M. Singer, A.W. Hunt, A.F. Cederstr€ om, T. Imai, Physica C 388–389 (2003) 209. [9] M.R. McHenry, B.G. Silbernagel, J.H. Wernick, Phys. Rev. Lett. 27 (1971) 426. [10] Y. Itoh, T. Machi, C. Kasai, S. Adachi, N. Koshizuka, M. Murakami, Phys. Rev. B 67 (2003) 064516. [11] Y. Itoh, M. Matsumura, H. Yamagata, J. Phys. Soc. Jpn. 65 (1996) 3747. [12] Y. Itoh, T. Machi, N. Watanabe, N. Koshizuka, J. Phys. Soc. Jpn. 70 (2001) 644.
Y. Itoh et al. / Physica C 412–414 (2004) 338–341 [13] Y. Itoh, T. Machi, S. Adachi, A. Fukuoka, K. Tanabe, H. Yasuoka, J. Phys. Soc. Jpn. 67 (1998) 312. [14] J.H. Cho, F. Borsa, D.C. Johnston, D.R. Torgeson, Phys. Rev. B 46 (1992) 3179. [15] F.C. Chou, F. Borsa, J.H. Cho, D.C. Johnston, A. Lascialfari, D.R. Torgeson, J. Ziolo, Phys. Rev. Lett. 71 (1993) 2323.
341
[16] M.-H. Julien, F. Borsa, P. Carretta, M. Horvatic’, C. Berthier, C.T. Lin, Phys. Rev. Lett. 83 (1999) 604. [17] C. Panagopoulos, J.L. Tallon, B.D. Rainford, T. Xiang, J.R. Cooper, C.A. Scott, Phys. Rev. B 66 (2002) 64501. [18] Y. Ando, A.N. Lavrov, S. Komiyama, K. Segawa, X.F. Sun, Phys. Rev. Lett. 87 (2001) 17001.
Pseudo-spin-gap of La2xSrxCuO4 Y. Itoh a
a,b,*
, T. Machi a, N. Koshizuka
a
Superconductivity Research Laboratory, ISTEC, 1-10-13 Shinonome, Koto-ku, Tokyo 135-0062, Japan b Japan Society for the Promotion of Science, Tokyo 102-8471, Japan Received 29 October 2003; accepted 17 November 2003 Available online 6 May 2004
Abstract We revisited the Cu nuclear spin–lattice relaxation of 63 Cu-enriched high-Tc superconductors La2x Srx CuO4 with x ¼ 0:13 (an underdoped sample) and 0.18 (an overdoped sample). From application of the impurity-induced NMR relaxation theory, we observed a remnant of the pseudo-spin-gap effect on the host Cu nuclear spin–lattice relaxation rate 63 ð1=T1 T Þhost and the inhomogeneous slow fluctuation effect via the impurity-induced relaxation rate 63 ð1=s1 Þ. The magnetic phase diagram with the pseudo-spin-gap temperatures Ts is presented. Ó 2004 Elsevier B.V. All rights reserved. PACS: 74.72.Dn; 74.25.Nf; 74.25.)q Keywords: Nuclear quadrupole resonance; Nuclear spin–lattice relaxation; Pseudo-spin-gap; La2x Srx CuO4
1. Introduction It has been long asked whether all the high-Tc superconductors have a normal state gap in the magnetic excitation spectrum. A counterexample is a single-CuO2 -layer system La2x Srx CuO4 , which does not show any apparent, normal state gap [1]. However, the discovery of charge–spin stripe correlation by neutron scattering technique [2] and the intensive studies by nuclear quadrupole resonance (NQR)/NMR technique [3–8] renewed our understanding this material. In this paper, we
revisited the Cu nuclear spin–lattice relaxation and tested the impurity-induced NMR relaxation theory [9] to 63 Cu-enriched high-Tc superconductors La2x Srx CuO4 with x ¼ 0:13 (an underdoped sample) and 0.18 (an overdoped sample), on the analogy of the in-plane impurity substitution effect on YBa2 Cu3 O7d or YBa2 Cu4 O8 [10]. We found a remnant of the pseudo-spin-gap and the effect of inhomogeneous slow fluctuations around the optimally doped region.
2. Experimental *
Corresponding author. Address: Superconductivity Research Laboratory, ISTEC, 1-10-13 Shinonome, Koto-ku, Tokyo 135-0062, Japan. Tel.: +81-3-3536-5707; fax: +81-33536-5705. E-mail address: [email protected] (Y. Itoh).
The superconducting transition temperatures Tc of our samples, which were studied in Ref. [11] were re-estimated by magnetization measurements using a superconducting quantum interference device (SQUID) magnetometer, Tc 36 K for
0921-4534/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2003.11.076
Y. Itoh et al. / Physica C 412–414 (2004) 338–341 1
63p(t)
x ¼ 0:13 and Tc 34 K for x ¼ 0:18. A coherenttype pulsed spectrometer was utilized for zero-field 63 Cu NQR measurements. 63 Cu nuclear spin–lattice relaxation was measured by an inversion recovery spin-echo technique. The spin-echo amplitude MðtÞ was recorded as a function of a time interval t after an inversion pulse, at the peak frequency of the broad Cu NQR spectrum [11].
339 1
40 K
4.2 K
77 K
10 K
120 K
20 K
0.1
30 K
0.1
0.01
0.001
0
500
1000
0.01
1500
0
10
t (ms)
Cu nuclear spin–lattice relaxation curves
Fig. 1 shows 63 Cu nuclear spin–lattice relaxation (recovery) curves 63 pðtÞ 1 MðtÞ=Mð1Þ as a function of temperature for x ¼ 0:13. The solid curves are pfits by a function of pð0Þ exp½3t= 63 63 ðT1 Þhost 3t= s1 ] where pð0Þ, 63 ðT1 Þhost and 63 s1 are the parameters [9]. 63 ðT1 Þhost is the nuclear spin– lattice relaxation time due to host, homogeneous electron spin fluctuations, whereas 63 s1 is that due to the impurity-induced, inhomogeneous fluctuations [9,10,12]. The nonexponential recovery curves result from the stretched exponential function with 63 s1 . The impurity-induced relaxation indicates randomly distributed relaxation centers on the CuO2 planes. Since no Curie term was observed in the uniform spin susceptibility, randomly distributed staggered moments are the promising candidate for the relaxation centers.
4.
63
(T1 )host and
63
(s1 ) 63
Fig. 2 shows 1= ðT1 T Þhost (a) and 63 ð1=s1 Þ (b) as functions of temperature for x ¼ 0:13 and 0.18. 63 The pseudo-spin-gap behavior of 1= ðT1 T Þhost is seen in both materials. For comparison with the other single-CuO2 -layer superconductors, 1= 63 ðT1 T Þ of HgBa2 CuO4þd with the optimal Tc 92 K is also shown [13]. HgBa2 CuO4þd has the maximum Tc among ever reported single-CuO2 -layer superconductors. The pseudo-spin-gap temperature Ts which is defined as the peak temperature of 63 1= ðT1 T Þhost , is 130 K for x ¼ 0:13 and 90 K for x ¼ 0:18. Both 63 ð1=s1 Þ’s show maximum values around Tpeak ¼ 40–60 K. Below T ¼ 300 K, 1=63 ðT1 T Þhost increases due to the growth of antiferromagnetic spin fluctuations.
Fig. 1. Temperature dependence of recovery curve 63 pðtÞ for x ¼ 0:13.
63(1/T T)host (s-1K-1) 1
63
63
30x103
Cu nuclear spin-echo
Ts T ↓ ⇐ ↓s
20
x=0.13 0.18
(a)
⇓ ↑
↑ Tmin
10
HgBa2CuO4+δ 0 10
63(1/τ ) (ms-1) 1
3.
20
t (ms)
↔
Tpeak
(b)
1 0.1 0.01
0.001 0
100
200
300
T (K) Fig. 2. 63 Cu nuclear spin–lattice relaxation rates 1=63 ðT1 T Þhost (a) and 63 ð1=s1 ) (b) against temperature for x ¼ 0:13 and 0.18. The dashed lines indicate Tc ’s for x ¼ 0:13 and 0.18. Various characteristic temperatures of Tc , Ts , Tmin and Tpeak are defined here. For comparison, 1=63 ðT1 T ) of HgBa2 CuO4þd with the optimal Tc 96 K is reproduced from Ref. [13].
63
Below Ts , 1= ðT1 T Þhost decreases due to opening of the pseudo-spin-gap. The upturn of 1=63 ðT1 T Þhost below Tmin , which is defined in Fig. 2(a), indicates the existence of unknown gapless fluctuations. 63 Since the upturn of 1= ðT1 T Þhost is suppressed by hole doping from x ¼ 0:13 to 0.18, then the gapless fluctuations may be a remnant of the charge–spin stripe fluctuations. The stretched exponential relaxation with highly enhanced 1=s1 was observed in 139 La nuclear spin–lattice relaxation for less doped materials [14–16]. The low temperature increase of
340
Y. Itoh et al. / Physica C 412–414 (2004) 338–341
63
ð1=s1 Þ of the semiconducting La2x Srx CuO4 is explained by spin freezing effect, which is associated with the electronic characteristic of the Mott insulating state. Thus, our observation of a finite 63 ð1=s1 Þ around the optimally doped region may result from a remnant of such spin freezing effect.
5. Magnetic phase diagram Fig. 3 shows a magnetic phase diagram with the superconducting transition temperatures Tc , the pseudo-spin-gap temperatures Ts , the Cu NQR wipeout temperatures TNQR [5,8], the crossover temperatures Tf probed by muon spin relaxation [17], and the in-plane resistance minimum temperatures Tu [18] against hole concentration. Although the remnant of the pseudo-spin-gap is successfully observed below Ts , the low temperature states are still covered by the remnant of the spin freezing effect or the unknown fluctuations. The low temperature anomaly is characteristic of the La2x Srx CuO4 system. Thus, one reason why the optimal Tc (38 K) of La2x Srx CuO4 is lower than the optimal Tc (96 K) of
HgBa2 CuO4þd can be attributed to the pair breaking effect of the anomaly.
6. Conclusion We observed a remnant of the pseudo-spin-gap and the finite contribution from inhomogeneous slow fluctuations for La2x Srx CuO4 around the optimally doped region via the analysis of nonexponential Cu nuclear spin–lattice relaxation. The pseudo-spin-gap of magnetic excitation spectrum is just masked by the inhomogeneous slow fluctuations but not collapsed.
Acknowledgements This work was supported by the New Energy and Industrial Technology Development Organization (NEDO) as Collaborative Research and Development of Fundamental Technologies for Superconductivity Applications.
References La2-xSrxCuO4
Temperature (K)
300
200
TNQR Tu
(wipeout)
Ts Tmi n Tpeak Tc
100 Tf 0 0.00
(µSR)
0.05
0.10
0.15
0.20
Hole concentration x Fig. 3. Magnetic phase diagram against the hole concentration d defined as Cu2þd . The triangle symbols of Tc , Ts , Tmin and Tpeak are defined in Fig. 2. Tc (squares) and the Cu NQR wipeout temperatures TNQR (circles) are reproduced from Refs. [5,8]. The crossover temperatures Tf (crosses), which are defined as the first deviation of muon spin relaxation from Gaussian behavior, are reproduced from Ref. [17]. The in-plane resistance minimum temperatures Tu (open diamonds), at which the resistivity shows an upturn, are reproduced from Ref. [18].
[1] S. Ohsugi, Y. Kitaoka, K. Ishida, G.-q. Zheng, K. Asayama, J. Phys. Soc. Jpn. 63 (1994) 700. [2] J.M. Tranquada, B.J. Sternlieb, J.D. Axe, Y. Nakamura, S. Uchida, Nature 375 (1995) 561. [3] K. Yoshimura, T. Imai, T. Shimizu, Y. Ueda, K. Kosuge, H. Yasuoka, J. Phys. Soc. Jpn. 58 (1989) 3057. [4] K. Yoshimura, T. Uemura, M. Kato, K. Kosuge, T. Imai, H. Yasuoka, Hyperfine Interact. 79 (1993) 867. [5] A.W. Hunt, P.M. Singer, K.R. Thurber, T. Imai, Phys. Rev. Lett. 82 (1999) 4300. [6] A.W. Hunt, P.M. Singer, A.F. Cederstr€ om, T. Imai, Phys. Rev. B 64 (2001) 134525. [7] P.M. Singer, A.W. Hunt, T. Imai, Phys. Rev. Lett. 88 (2002) 047602. [8] P.M. Singer, A.W. Hunt, A.F. Cederstr€ om, T. Imai, Physica C 388–389 (2003) 209. [9] M.R. McHenry, B.G. Silbernagel, J.H. Wernick, Phys. Rev. Lett. 27 (1971) 426. [10] Y. Itoh, T. Machi, C. Kasai, S. Adachi, N. Koshizuka, M. Murakami, Phys. Rev. B 67 (2003) 064516. [11] Y. Itoh, M. Matsumura, H. Yamagata, J. Phys. Soc. Jpn. 65 (1996) 3747. [12] Y. Itoh, T. Machi, N. Watanabe, N. Koshizuka, J. Phys. Soc. Jpn. 70 (2001) 644.
Y. Itoh et al. / Physica C 412–414 (2004) 338–341 [13] Y. Itoh, T. Machi, S. Adachi, A. Fukuoka, K. Tanabe, H. Yasuoka, J. Phys. Soc. Jpn. 67 (1998) 312. [14] J.H. Cho, F. Borsa, D.C. Johnston, D.R. Torgeson, Phys. Rev. B 46 (1992) 3179. [15] F.C. Chou, F. Borsa, J.H. Cho, D.C. Johnston, A. Lascialfari, D.R. Torgeson, J. Ziolo, Phys. Rev. Lett. 71 (1993) 2323.
341
[16] M.-H. Julien, F. Borsa, P. Carretta, M. Horvatic’, C. Berthier, C.T. Lin, Phys. Rev. Lett. 83 (1999) 604. [17] C. Panagopoulos, J.L. Tallon, B.D. Rainford, T. Xiang, J.R. Cooper, C.A. Scott, Phys. Rev. B 66 (2002) 64501. [18] Y. Ando, A.N. Lavrov, S. Komiyama, K. Segawa, X.F. Sun, Phys. Rev. Lett. 87 (2001) 17001.