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Vortex phase above the melting line in heavy-ion irradiated Bi 2 Sr 2 CaCu 2 O 8. Kees van der Beek Laboratoire des Solides Irradiés, Ecole Polytechnique, Palaiseau. • Sylvain Colson, Panayotis Spathis, Mikhail Indenbom, Irina Abalosheva, Marcin Konczykowski - PowerPoint PPT Presentation
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Vortex phase above the melting line in heavy-ion irradiated Bi2Sr2CaCu2O8
Kees van der BeekLaboratoire des Solides Irradiés, Ecole Polytechnique, Palaiseau
• Sylvain Colson, Panayotis Spathis, Mikhail Indenbom, Irina Abalosheva, Marcin KonczykowskiLaboratoire des Solides Irradiés, Ecole Polytechnique, Palaiseau, France
• Ming Li, Peter KesKamerlingh Onnes Laboratorium, Leiden, The Netherlands
• Marat Gaifullin, Yuji MatsudaInstitute of Solid State Physics, The University of Tokyo, Japan
• Satyajit Banerjee, Yuri Myasoedov, Eli ZeldovWeizmann Institut e of Science, Rehovot, Israel
• Mariela Menghini, Yanina Fasano, Paco de la CruzLaboratorio de Bajas Temperaturas, Centro Atomico Bariloche, Argentina
1
10
100
1000
10000
30 40 50 60 70 80 90
H ( Oe )
T ( K )
A: nh = 0.11 { FOT
IRL
Bφ = 0
1
10
100
1000
10000
30 40 50 60 70 80 90
H ( Oe )
T ( K )
A: nh = 0.11 { FOT
IRL
Bφ = 0
• 1st Order Transition
rw = (un+1-un)2 1/2 = c a0 L.I. Glazman & A.E. Koshelev, Phys. Rev. B 43 , 2835 (1991)
Vortex liquid
Vortex solid
Vortex matter phase diagram in BSCCO
BFOT = 0.5 (0/2s2) (0s / kBT )
nn+1u n,n+1cD
First Order Transition
If compressional, shear, or "collective" tilt modes dominate, then un 2
1/2 , rw decrease as function of B the vortex line tension limits fluctuations
200
400
600
800
1000
1200
1400
0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1
0.55 ≤ ≤ 0.95
FOT
r w (
nm)
T / Tc
Josephson Plasma Resonance
pl2 (B,T) = pl
2(0,T)cos(n-n+1)
0
Brw
2 = [1 - cos (n-n+1) ]
nn+1u n,n+1cD
Brandt and Sonin, PRB 66, 064505 (2002).Koshelev, Maley, Bulaevskii, Physica C 341-348, 1503 (2000).
• rw(T,B) always behaves as in the "single vortex limit", i.e. as if the line tension (Josephson) term determines everything A.E. Koshelev, L.N. Bulaevskii, Physica C 341-348 (2000)
• The temperature dependence of rw(T,B) in agreement with thermal softening of the line tension ( kmax = /rw not / ) R. Goldin, B. Horowitz, PRB 58, 9524 (1999) A.E. Koshelev, V.M. Vinokur, PRB 57, 8026 (1998)
• Up to the 1st order transition - at the FOT displacements of order a0 cannot be screened by Josephson coupling • "Melting" does not involve c66 vortex lattice positional order not required
• Robust with respect to pinning (See Satyajit Banerjee session III T7)
1
10
100
1000
10000
nh = 0.11, T
c = 69.4 K
nh = 0.12, T
c = 78 K
nh = 0.18, T
c = 86 K
30 40 50 60 70 80 90
H ( Oe )
T ( K )
A: nh = 0.11 { FOT
IRL
Bφ = 0
Bφ = T
1
10
100
1000
10000
30 40 50 60 70 80 90
H ( Oe )
T ( K )
A: nh = 0.11 { FOT
IRL
Bφ = 0
1
10
100
1000
10000
30 40 50 60 70 80 90
H ( Oe )
T ( K )
A: nh = 0.11 { FOT
IRL
Bφ = 0
1
10
100
1000
10000
A: nh = 0.11, T
c = 69.4 K
30 40 50 60 70 80 90
H ( Oe )
T ( K )
A: nh = 0.11 { FOT
IRL
Bφ = 0
Bφ = T
• 1st order transition • BFOT = 0.5 (0/2s2) (0s / kBT )
65
70
75
80
85
90
350
400
450
500
550
600
650
0.1 0.125 0.15 0.175 0.2
Tc
Tc ( )K
( Tc / )
nh
( .)B pr
,B C( .)irr
[]
( .)B pr
60
65
70
75
80
85
90
0
200
400
600
800
1000
1200
1400
0.1 0.12 0.14 0.16 0.18 0.2 0.22
Tc ( K ) 0 / s kB ( )K
Tc ( )K
0/ s k
B
( )K
nh
(un+1-un)2 1/2 = c a0 L.I. Glazman and A.E. Koshelev, Phys. Rev. B 43 , 2835 (1991)
Vortex liquid
Vortex solid
2nd order transition
Vortex matter phase diagram in heavy-ion irradiated BSCCO
0
200
400
600
800
1000
0.5 0.6 0.7 0.8 0.9 1
rw
(nm)
Tc = 75.6 K, tracks || c
IRL 30 Oe
IRL 20 Oe
IRL 10 Oe
Quantitavely the same behaviour as in unirradiated crystals
T / Tc
10-1
100
101
102
103
104
0.5 0.6 0.7 0.8 0.9 1
Bφ= 1 || T c
Bφ= || T c
Birr
( )G
/ T Tc
Vortex fluctuations in heavy-ion irr. BSCCO - low B
columnardefect
pancakeflux line
S. Colson et al,. Phys. Rev. B 69, R180510 (2004)
• Low T : cos > value before irradiation but < 1 columnar defects cannot align vortex lines as well as in the vortex solid
0
0.2
0.4
0.6
0.8
1
10 Oe20 Oe30 Oe100 Oe300 Oe500 Oe700 Oe
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
<cos(
, +1n n
)>
( ) a crystal C Tc = 75.6 K || ion tracks c Bφ= 1 T
IRL
IRL
IRL
IRL
IRL
T / Tc
10-1
100
101
102
103
104
0.5 0.6 0.7 0.8 0.9 1
Bφ= 1 || T c
Bφ= || T c
Birr
( G )
T / Tc
Vortex fluctuations in heavy-ion irr. BSCCO - high B
• High T : IRL corresponds to loss of phase coherence cf. Doyle et al. PRL 77, 1155 (1996).
Irreversibility ("Bose-glass") line1. Loss of phase coherence cf. Doyle et al. PRL 77, 1155 (1996).2. Does not depend on defect density 3. Does not depend on pinning potential
- as shown by C60 irradiation, tracks of 20 nm diameter
4. Vortices still pinned in liquid (Monte Verita 1997) Delocalization line 5. Exponential line, Power-law IV’s topological transition Feigel’man Geshkenbein Larkin 1990
1
10
100
1000
20 30 40 50 60 70 80 90
H ( Oe )
T ( K )
region of field sweep and relaxation experiments
0
0,1
0,2
0,3
72 76 80 84 88
⟨∆B
( )G
( )T K
Conclusions• Josephson Plasma Resonance probes c-axis vortex pancake alignment • Columnar defects enhance IRL only at "low enough" T• High T : vortex fluctuations / FOT as in unirradiated BSCCO
T-scale determined by 0s
B-scale determined by (Koshelev PRB 1997)
• High B : pancakes never aligned as well as in "vortex solid"
Ghost of FOT
• IRL : drop in phase correlations
Position determined mainly by 0s (in plane properties)
• High density of columns redistributed pancake vortices
• Recap on 1st order transition of the vortex ensemble in Bi2Sr2CaCu2O8+
• Columnar defects created by heavy-ion irradiation• Phase diagram as function of doping• Conclusion