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