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Magnetization jump due to the first-order vortex lattice melting transition in YBa2Cu3Oy single crystals
PHYSICA ELSEVIER
PhysicaC 263 (1996)409-411
Magnetization jump due to the first-order vortex lattice melting transition in YBa2Cu3Oysingle crystals Yasuaki Onodera a, Terukazu Nishizaki a, Norio Kobayashi a, Hidehito Asaoka b, Huimihiko Takei c a Institute for Materials Research, Tohoku University, Sendai 980-77, Japan b Japan Atomic Energy Research Institute, Tokai-mura, Ibaraki 319-11, Japan c Department of Earth and Space Science, Faculty of Science, Osaka University, Toyonaka 560, Japan
Abstract We have studied the temperature dependence of the magnetization for YBa2Cu3Oy single crystals with different oxygen contents. As for the oxygenated samples, an anomalous magnetization jump is observed at a certain temperature Tj just below the irreversibility line. The temperature and angular dependences of the jump are consistent with the first-order vortex lattice melting transition theory. The magnetization jump is suppressed by strong disorder due to the oxygen deficiency. 1. Introduction In the high-Te superconductors, the upper critical field Hc2 can no longer be defined because of the strong superconducting fluctuation. Therefore, irreversibility field Hir r has been focused on as a characteristic magnetic field instead of He2. Recent theoretical considerations have proposed that the vortex state changes from liquid to solid near the irreversibility field as temperature goes down. If the system has strong disorder, the vortex-liquid state is predicted to undergo a second-order phase transition into a vortex-glass state or Bose-glass state, depending on the type of disorder. In the clean limit, on the other hand, the transition is proposed to be a firstorder melting transition into the Abrikosov vortex lattice. Experimentally, Safar et al. [1] reported that clear resistive hysteresis, which suggested the firstorder melting transition, was observed using untwinned YBa2Cu3Oy single crystals. Recently, however, Jiang et al. [2] claimed that the resistive hysteresis is not direct evidence of the first-order melting transition, because of the absence of resistive
subloops upon partial heating and partial cooling, and the lack of time dependence. They proposed that a current-induced nonequilibrium effect be considered as the possible origin for the hysteresis. A true first-order phase transition should present clear thermodynamic evidence: latent heat and a discontinuous step in vortex density, but the resistivity is not a thermodynamic property. As for Bi2Sr2CaCu20 8, a discontinuous change of the magnetization was observed and has been attributed to the vortex lattice melting transition [3]. Furthermore, we reported a magnetization jump regarded as a first-order melting transition in high-quality twinned YBa2CusOy single crystals [4]. In this paper, we report the influence of oxygen deficiency on the anomalous magnetization jump.
2. Experimental The samples used in this study are high-quality twinned YBa2Cu3Oy ( y = 6.6-6.9) single crystals with dimensions of typically 1.2 X 1.2 X 1.0 mm 3
0921-4534/95/$09.50 © 1995 ElsevierScienceB.V. All fights reserved (95)00733-4
410
Y. Onodera et al. / Physica C 263 (1996)409-411
grown by a self-flux method under the peritectic condition [5]. The as-grown crystals were annealed at an appropriate temperature for I or 2 weeks in flowing oxygen. All samples showed a sharp superconducting transition T~ at 60-90 K. The oxygen content y was estimated from the annealing conditions and Tc to be 6.6-6.9. The magnetization measurements were performed using a commercial SQUID magnetometer (Quantum Design). The sample was rotated around the axis perpendicular to the magnetic field and parallel to the a- or b-axis. The rotated angle 0 was defined as the angle between the c-acxis and the direction of the magnetic field,
3. Results and discussion Fig. 1 shows the magnetization M as a function of temperature in zero-field-cooled (ZFC) and fieldcooled (FCC) modes at a constant field of H = 30 kOe parallel to the c-axis for YBa2Cu306.s5 (T~ = 87.5 K, sample # 1). A discontinuous jump in magnetization is observed at Tj = 80.9 K just below the irreversibility line. The magnitude of the jump is larger for the zero-field-cooled magnetization than for the field-cooled one. This difference seems to be understood by the pinning effect in the zero-field cooling. In the ZFC mode, the flux line distribution is inhomogeneous below T~r, due to the pinning effect. When the temperature reaches Titr, the pinning effect disappears and the flux line is rearranged. Then, the magnetization is expected to decrease at Titr. But, on the contrary, the flux lines are easy to
-2
i
i
i
i
YBa2Cu306a 5 # 1 -4
H=30t.Oe
J a° I oo
o.ooo* 8°°° o
~)-6
FCC
b 40
~
* *
78
""
0 78
I
80
I 8=2
84
T(K)
Fig. 1. Temperature dependence of the magnetization for YBa2Cu306.85 ( # 1 ) in ZFC and FCC modes at H = 30 kOe parallel to the c-axis.
; ~c /
1-1 _
~is x
.~s.ssl i
I
J 81
e (dog.)
",,,.',,~,, i
i
J 84
i
i 87
T(K) Fig. 2. Field dependence of Tj for YBa2Cu306.ss(#1) and YBa2Cu306.9(#2). The solid curves are fits to a power law H = A(Tc - Tj)2. The inset shows the angular dependence of Tj for YBa2Cu306.9(#2) at H = 5 kOe. The solid curve is calculated from Eq. (2).
move above Tirr and its distribution is homogeneous. Therefore, it would be difficult to attribute the jump in the FCC mode to the pinning phenomena. Thus, the magnetization jump in the FCC mode is considered to be caused by a discontinuous drop of the vortex density and is related to a thermodynamic first-order melting transition of the vortex lattice. The vortex density in the liquid state above Tj is denser than that in the vortex solid due to the strong thermal fluctuations in the liquid phase. A similar magnetization jump was also observed for YBa2Cu 3 06. 9 (Tc = 89 K, sample # 2 ) [4]. The magnitude of the jump for sample # 2 is as large as that for sample #1, suggesting a dependence on the oxygen deficiency. Fig. 2 shows Tj versus H for both samples #1 and #2. The behavior of Ti at constant field H is approximately expressed by H c( (T~ - Tj)" with n = 2 for both samples, though the n value tends to decrease with increasing oxygen deficiency. According to the recent theory of the first-order melting transition of the vortex lattice [6], the temperature dependence of the transition field is given by H(Tj) = A(1 - Tj/Tc) 2, where
..'"
C I
~2o[
30
lo
A= -10
.xgx, x ~
\
%;7**. . . . . .*°
~-8'
.........
42
5 4 (lr)o c L 24
= kB3' %~(0)rc
2"
(1)
where c L is the Lindemann criterion number, ~0 the flux quantum, T the anisotropy parameter, and Aab the in-plane penetration depth. For samples #1 and #2, we obtain values of A = 5 × 10 3 kOe and
Y. Onodera et al. / Physica C 263 (1996) 409-411
6 × 103 kOe, respectively. Using these A values, hab(O) = 1400 .~ and 3/= 6.3 for #1 and 7 = 6 for #2 [7], we obtain a physically reasonable value of c L = 0.13 for both samples. This sample independence of Lindemann number may imply that the origin of the magnetization jump is intrinsic in nature in our samples. The Lindemann melting criterion can also be obtained from the angular dependence of Tj. According to the scaling rules for anisotropic superconductors [8], Tj(0) shows the following angular dependence: t~5/2~2 0
kBT j =
L'L
4~r2h2(Tj)H'/2(sin 2 0 + 7 : c o s 2 0) ' / 4 ,
(2) where A(T) is the temperature-dependent penetration depth and is assumed to be expressed by the two-fluid model. The inset of Fig. 2 shows the angular dependence of Tj(0) for sample #2 at H = 5 kOe. Using values of 7 = 6 [7] and Tc = 88.5 K, the best fit is obtained for a Lindemann number of CL=0.13, which is in agreement with the value estimated from the temperature dependence. This value is also consistent with the value of 0.15 determined from transport resistive measurements [9]. The temperature dependence of the magnetization M for YBa2Cu306. 7 (To = 68 K, sample #3) at H = 20 kOe parallel to the c-axis is shown in Fig. 3. Unlike #1 and #2, the magnetization anomaly is not observed in this sample. Similar results are i
-2
E -3 ~0~--4 -5 45
YBa2Ou3067 #3 H=20kOe
I
oo~l~g00Oo0oooOO
[~(_Co,,''''"" °.%0. °~ZFC i
,
47
i
T(K)
419
I
51
Fig. 3. Temperature dependence of the magnetization for YBa2Cu3Oe. 7 (#3) in ZFC and FCC modes at H = 20 kOe parallel to the c-axis
411
also obtained for the oxygen-deficient samples with y = 6.6 and 6.8. These results indicate that the melting transition may be suppressed by disorder due to the oxygen deficiency.
4. Conclusion
We have shown a discontinuous magnetization jump in the temperature dependence of high-quality twinned YBa2Cu3Oy (y = 6.85 and 6.9) single crystals. The field and angular dependences of Tj are well interpreted by the recent theoretical model based on the first-order melting transition of the flux lines. These results strongly suggest that the origin of the magnetization jump is a first-order melting transition. The magnitude of the magnetization jump decreases with increasing oxygen deficiency and the jump is completely suppressed by strong disorder due to the oxygen deficiency for the samples with 6.6_< y < 6.8.
References [1] H. Safar, P.L. Gammel, D.A. Huse, D.J. Bishop, J.P. Rice and D.M. Ginsberg, Phys. Rev. Lett. 69 (1992) 824. [2] W. Jiang N.-C. Yeh, D.S. Reed, U. Kriplani and F. Holtzberg, Phys. Rev. Lett. 74 (1995) 1438. [3] H. Pastoriza, M.F. Goffman, A. Arribere and F. de la Cruz, Phys. Rev. Lett. 72 (1994) 2951; E. Zeldov, D. Majer, M. Konczykowski, V.B. Geshkenbein, V.M. Vinokur and H. Shtrikman, Nature 375 (1995) 373. [4] N. Kobayashi, T. Nishizaki, Y. Onodera, H. Asaoka and H. Takei, Chinese J. Phys., to be published; T. Nishizaki, Y. Onodera, N. Kobayashi, H. Asaoka and H. Takei, Phys. Rev. B, to be published. [5] H. Asaoka, H. Takei, Y. Iye, M. Tamura, M. Kinoshita and H. Takeya, Jpn. J. Appl. Phys. 32 (1993) 1091. [6] A. Houghton, R.A. Pelcovits and A. Sudbe, Phys, Rev. B 40 (1989) 6763; E.H. Brandt, Phys. Rev. Left. 63 0989) 1106. [7] N. Kobayashi, K. Hirano, T. Nishizaki, H. Iwasaki, T. Sasaki, S. Awaji, K. Watanabe, H. Asaoka and H. Takei, Physica C 251 (1995) 255. [8] G. Blatter, V.B. Geshkenbein and A. I. Larkin, Phys. Rev. Lett. 68 (1992) 875; R.G. Beck, D.E. Farrell, J.P. Rice, D.M. Ginsberg and V.G. Kogan, Phys. Rev. LeU. 68 (1992) 1594. [9] W.K. Kwok, S. Fleshier, U. Welp, V.M. Vinokur, J. Downey, G.W. Crabtree and M.M. Miller, Phys. Rev. Lett. 69 (1992) 3370.
PhysicaC 263 (1996)409-411
Magnetization jump due to the first-order vortex lattice melting transition in YBa2Cu3Oysingle crystals Yasuaki Onodera a, Terukazu Nishizaki a, Norio Kobayashi a, Hidehito Asaoka b, Huimihiko Takei c a Institute for Materials Research, Tohoku University, Sendai 980-77, Japan b Japan Atomic Energy Research Institute, Tokai-mura, Ibaraki 319-11, Japan c Department of Earth and Space Science, Faculty of Science, Osaka University, Toyonaka 560, Japan
Abstract We have studied the temperature dependence of the magnetization for YBa2Cu3Oy single crystals with different oxygen contents. As for the oxygenated samples, an anomalous magnetization jump is observed at a certain temperature Tj just below the irreversibility line. The temperature and angular dependences of the jump are consistent with the first-order vortex lattice melting transition theory. The magnetization jump is suppressed by strong disorder due to the oxygen deficiency. 1. Introduction In the high-Te superconductors, the upper critical field Hc2 can no longer be defined because of the strong superconducting fluctuation. Therefore, irreversibility field Hir r has been focused on as a characteristic magnetic field instead of He2. Recent theoretical considerations have proposed that the vortex state changes from liquid to solid near the irreversibility field as temperature goes down. If the system has strong disorder, the vortex-liquid state is predicted to undergo a second-order phase transition into a vortex-glass state or Bose-glass state, depending on the type of disorder. In the clean limit, on the other hand, the transition is proposed to be a firstorder melting transition into the Abrikosov vortex lattice. Experimentally, Safar et al. [1] reported that clear resistive hysteresis, which suggested the firstorder melting transition, was observed using untwinned YBa2Cu3Oy single crystals. Recently, however, Jiang et al. [2] claimed that the resistive hysteresis is not direct evidence of the first-order melting transition, because of the absence of resistive
subloops upon partial heating and partial cooling, and the lack of time dependence. They proposed that a current-induced nonequilibrium effect be considered as the possible origin for the hysteresis. A true first-order phase transition should present clear thermodynamic evidence: latent heat and a discontinuous step in vortex density, but the resistivity is not a thermodynamic property. As for Bi2Sr2CaCu20 8, a discontinuous change of the magnetization was observed and has been attributed to the vortex lattice melting transition [3]. Furthermore, we reported a magnetization jump regarded as a first-order melting transition in high-quality twinned YBa2CusOy single crystals [4]. In this paper, we report the influence of oxygen deficiency on the anomalous magnetization jump.
2. Experimental The samples used in this study are high-quality twinned YBa2Cu3Oy ( y = 6.6-6.9) single crystals with dimensions of typically 1.2 X 1.2 X 1.0 mm 3
0921-4534/95/$09.50 © 1995 ElsevierScienceB.V. All fights reserved (95)00733-4
410
Y. Onodera et al. / Physica C 263 (1996)409-411
grown by a self-flux method under the peritectic condition [5]. The as-grown crystals were annealed at an appropriate temperature for I or 2 weeks in flowing oxygen. All samples showed a sharp superconducting transition T~ at 60-90 K. The oxygen content y was estimated from the annealing conditions and Tc to be 6.6-6.9. The magnetization measurements were performed using a commercial SQUID magnetometer (Quantum Design). The sample was rotated around the axis perpendicular to the magnetic field and parallel to the a- or b-axis. The rotated angle 0 was defined as the angle between the c-acxis and the direction of the magnetic field,
3. Results and discussion Fig. 1 shows the magnetization M as a function of temperature in zero-field-cooled (ZFC) and fieldcooled (FCC) modes at a constant field of H = 30 kOe parallel to the c-axis for YBa2Cu306.s5 (T~ = 87.5 K, sample # 1). A discontinuous jump in magnetization is observed at Tj = 80.9 K just below the irreversibility line. The magnitude of the jump is larger for the zero-field-cooled magnetization than for the field-cooled one. This difference seems to be understood by the pinning effect in the zero-field cooling. In the ZFC mode, the flux line distribution is inhomogeneous below T~r, due to the pinning effect. When the temperature reaches Titr, the pinning effect disappears and the flux line is rearranged. Then, the magnetization is expected to decrease at Titr. But, on the contrary, the flux lines are easy to
-2
i
i
i
i
YBa2Cu306a 5 # 1 -4
H=30t.Oe
J a° I oo
o.ooo* 8°°° o
~)-6
FCC
b 40
~
* *
78
""
0 78
I
80
I 8=2
84
T(K)
Fig. 1. Temperature dependence of the magnetization for YBa2Cu306.85 ( # 1 ) in ZFC and FCC modes at H = 30 kOe parallel to the c-axis.
; ~c /
1-1 _
~is x
.~s.ssl i
I
J 81
e (dog.)
",,,.',,~,, i
i
J 84
i
i 87
T(K) Fig. 2. Field dependence of Tj for YBa2Cu306.ss(#1) and YBa2Cu306.9(#2). The solid curves are fits to a power law H = A(Tc - Tj)2. The inset shows the angular dependence of Tj for YBa2Cu306.9(#2) at H = 5 kOe. The solid curve is calculated from Eq. (2).
move above Tirr and its distribution is homogeneous. Therefore, it would be difficult to attribute the jump in the FCC mode to the pinning phenomena. Thus, the magnetization jump in the FCC mode is considered to be caused by a discontinuous drop of the vortex density and is related to a thermodynamic first-order melting transition of the vortex lattice. The vortex density in the liquid state above Tj is denser than that in the vortex solid due to the strong thermal fluctuations in the liquid phase. A similar magnetization jump was also observed for YBa2Cu 3 06. 9 (Tc = 89 K, sample # 2 ) [4]. The magnitude of the jump for sample # 2 is as large as that for sample #1, suggesting a dependence on the oxygen deficiency. Fig. 2 shows Tj versus H for both samples #1 and #2. The behavior of Ti at constant field H is approximately expressed by H c( (T~ - Tj)" with n = 2 for both samples, though the n value tends to decrease with increasing oxygen deficiency. According to the recent theory of the first-order melting transition of the vortex lattice [6], the temperature dependence of the transition field is given by H(Tj) = A(1 - Tj/Tc) 2, where
..'"
C I
~2o[
30
lo
A= -10
.xgx, x ~
\
%;7**. . . . . .*°
~-8'
.........
42
5 4 (lr)o c L 24
= kB3' %~(0)rc
2"
(1)
where c L is the Lindemann criterion number, ~0 the flux quantum, T the anisotropy parameter, and Aab the in-plane penetration depth. For samples #1 and #2, we obtain values of A = 5 × 10 3 kOe and
Y. Onodera et al. / Physica C 263 (1996) 409-411
6 × 103 kOe, respectively. Using these A values, hab(O) = 1400 .~ and 3/= 6.3 for #1 and 7 = 6 for #2 [7], we obtain a physically reasonable value of c L = 0.13 for both samples. This sample independence of Lindemann number may imply that the origin of the magnetization jump is intrinsic in nature in our samples. The Lindemann melting criterion can also be obtained from the angular dependence of Tj. According to the scaling rules for anisotropic superconductors [8], Tj(0) shows the following angular dependence: t~5/2~2 0
kBT j =
L'L
4~r2h2(Tj)H'/2(sin 2 0 + 7 : c o s 2 0) ' / 4 ,
(2) where A(T) is the temperature-dependent penetration depth and is assumed to be expressed by the two-fluid model. The inset of Fig. 2 shows the angular dependence of Tj(0) for sample #2 at H = 5 kOe. Using values of 7 = 6 [7] and Tc = 88.5 K, the best fit is obtained for a Lindemann number of CL=0.13, which is in agreement with the value estimated from the temperature dependence. This value is also consistent with the value of 0.15 determined from transport resistive measurements [9]. The temperature dependence of the magnetization M for YBa2Cu306. 7 (To = 68 K, sample #3) at H = 20 kOe parallel to the c-axis is shown in Fig. 3. Unlike #1 and #2, the magnetization anomaly is not observed in this sample. Similar results are i
-2
E -3 ~0~--4 -5 45
YBa2Ou3067 #3 H=20kOe
I
oo~l~g00Oo0oooOO
[~(_Co,,''''"" °.%0. °~ZFC i
,
47
i
T(K)
419
I
51
Fig. 3. Temperature dependence of the magnetization for YBa2Cu3Oe. 7 (#3) in ZFC and FCC modes at H = 20 kOe parallel to the c-axis
411
also obtained for the oxygen-deficient samples with y = 6.6 and 6.8. These results indicate that the melting transition may be suppressed by disorder due to the oxygen deficiency.
4. Conclusion
We have shown a discontinuous magnetization jump in the temperature dependence of high-quality twinned YBa2Cu3Oy (y = 6.85 and 6.9) single crystals. The field and angular dependences of Tj are well interpreted by the recent theoretical model based on the first-order melting transition of the flux lines. These results strongly suggest that the origin of the magnetization jump is a first-order melting transition. The magnitude of the magnetization jump decreases with increasing oxygen deficiency and the jump is completely suppressed by strong disorder due to the oxygen deficiency for the samples with 6.6_< y < 6.8.
References [1] H. Safar, P.L. Gammel, D.A. Huse, D.J. Bishop, J.P. Rice and D.M. Ginsberg, Phys. Rev. Lett. 69 (1992) 824. [2] W. Jiang N.-C. Yeh, D.S. Reed, U. Kriplani and F. Holtzberg, Phys. Rev. Lett. 74 (1995) 1438. [3] H. Pastoriza, M.F. Goffman, A. Arribere and F. de la Cruz, Phys. Rev. Lett. 72 (1994) 2951; E. Zeldov, D. Majer, M. Konczykowski, V.B. Geshkenbein, V.M. Vinokur and H. Shtrikman, Nature 375 (1995) 373. [4] N. Kobayashi, T. Nishizaki, Y. Onodera, H. Asaoka and H. Takei, Chinese J. Phys., to be published; T. Nishizaki, Y. Onodera, N. Kobayashi, H. Asaoka and H. Takei, Phys. Rev. B, to be published. [5] H. Asaoka, H. Takei, Y. Iye, M. Tamura, M. Kinoshita and H. Takeya, Jpn. J. Appl. Phys. 32 (1993) 1091. [6] A. Houghton, R.A. Pelcovits and A. Sudbe, Phys, Rev. B 40 (1989) 6763; E.H. Brandt, Phys. Rev. Left. 63 0989) 1106. [7] N. Kobayashi, K. Hirano, T. Nishizaki, H. Iwasaki, T. Sasaki, S. Awaji, K. Watanabe, H. Asaoka and H. Takei, Physica C 251 (1995) 255. [8] G. Blatter, V.B. Geshkenbein and A. I. Larkin, Phys. Rev. Lett. 68 (1992) 875; R.G. Beck, D.E. Farrell, J.P. Rice, D.M. Ginsberg and V.G. Kogan, Phys. Rev. LeU. 68 (1992) 1594. [9] W.K. Kwok, S. Fleshier, U. Welp, V.M. Vinokur, J. Downey, G.W. Crabtree and M.M. Miller, Phys. Rev. Lett. 69 (1992) 3370.