The Paramagnetic Meissner Effect in. Josephson Junction Arrays. Aaron P. Nielsen, A. B. Cawthorne, P. Barbara,. F. C. Wellstood, C. J. Lobb. Center for ...
The Paramagnetic Meissner Effect in Josephson Junction Arrays Aaron P. Nielsen, A. B. Cawthorne, P. Barbara, F. C. Wellstood, C. J. Lobb Center for Superconductivity Research University of Maryland College Park, MD 20742
F. M. Araujo-Moreira UFSCar, Sao Paulo, Brazil
R. S. Newrock Department of Physics,University of Cincinnati
M. G. Forrester Northrop-Grumman Corporation
Support: AFOSR Grant F49620-98-1-0072, Center for Superconductivity Research, UMD
Outline • • • • • • •
Paramagnetic Meissner effect. Arrays. Bulk susceptibility. Single-loop model. Scanning SQUID measurements. Single loop revisited. Possible explanations.
Field cooled BSCCO1,2
1W.
Braunisch et al. PRL 68 1908 (1992) 2J. R. Kirtley et al. J. Phys.: Cond. Mat. 10 L97 (1998)
3A.
K. Geim et al. Nature. 396 144 (1998) J. Thompson et al PRL 75 529 (1995) 5P. Kostic et al. PRB 53 791 (1996)
4D.
π-junctions in d-wave ceramics?
PME observations Nb -
D.J. Thompson et al. PRL 75 529 (1995) P. Kostic et al. PRB 53 791 (1996)
Al -
A.K. Geim et al. Nature 396 144 (1998)
BSCCO -
W. Braunisch et al. PRL 68 1908 (1992) J.R. Kirtley et al. J. Phys: Cond Mat. 10 L97 (1998)
YBCO NCCO HgCCO -
S. Reidling et al. PRB 49 13283 ( 1994) G. S. Okram et al. J. Phys:Cond Mat. 9 L525 (1997) U. Onbasli et al. Phys. Stat. Sol. B 194 371 (1996)
Proposed causes • • • •
π-junctions Surface effects Random pinning Non-equilibrium
Bulk susceptibility 2 mm
pick-up coils
hA C
primary coil
sample
HDC
6 mm
H EXT = h AC cos(zt) Â M(t) = h AC S[x m cos(mzt) + x ÂÂm sin(mzt) ]
M 1(t) = h AC [xÂ1 cos(zt) + x ÂÂ1 sin(zt) ]
Data 2
4
6
8
0.2
10
2
4
6
8
10
0.2
0.7 0.0
0.0
0.6
(a)
-0.4
-0.6
-0.4
(b)
0.6
0.5
-0.2
χ" (S.I.)
χ' (S.I.)
-0.2
(a)
0.4
0.4
0.3
(b)
-0.6
0.2 -0.8
0.2
-0.8
0.1
(c) -1.0
(c)
-1.0
0.0 2
4
6
8
10
0.0
2
4
6
T (K)
(a) hAC=96 mOe, array. (b) hAC= 7 mOe, array. (c) hAC=10 mOe, Nb film
8
10
Data, loops only 0.3
0.4
0.2 0.3
0.0
χ''(S.I.)
χ' (S.I.)
0.1
-0.1 -0.2
0.2
0.1
-0.3 0.0
-0.4 2
4
6
8
10
2
4
6
8
T(K)
(Nb background subtracted)
10
Single-loop simulation 1
2
4
3
H EXT = h AC cos(zt)
F TOT = F EXT + LI I = IC sin c ij +
2 F O dc ij F O C d c ij 2oR dt + 2o dt2
M=
LI loa2
 M(t) = h AC S[x m cos(mzt) + x ÂÂm sin(mzt) ]
M 1(t) = h AC [xÂ1 cos(zt) + x ÂÂ1 sin(zt) ]
Single-loop simulation 0.2
(d)
1.4
0.1
(d)
0.0
1.2
-0.1 1.0
(c)
χ1'' (S.I.)
-0.2
χ1' (S.I)
-0.3
0.8
(c)
-0.4
0.6
-0.5
(b)
-0.6
(b)
(a)
-0.7
0.4 0.2
-0.8
(a)
-0.9 0.0
-1.0
4
5
6
7
8
4
9
5
T (K)
(a) (b) (c) (c)
hAC= 5 mOe, loop. hAC= 29 mOe, loop. hAC= 69 mOe, loop. hAC= 118 mOe, loop.
6
7
8
9
Single-loop simulation 10 PARA
5
DIA
0 -5
T=7.6 K
-10 -10
-8
-6
-4
-2
0
2
4
6
8
10
Φ TOT/Φ 0
10 PARA
5
DIA
0 -5
T=6.0 K
-10 -10
-8
-6
-4
-2
0
2
4
6
8
10
10 PARA
5
DIA
0 -5 T=4.0 K -10 -10
-8
-6
-4
-2
0 2 Φ ext/Φ 0
4
6
8
10
Susceptibility summary • • • •
Nb-AlOx-Nb arrays are paramagnetic No π junctions Little disorder Single-loop: paramagnetic and diamagnetic states • Is single-loop model enough? C. Auletta et al.; Physica C 235-240, 3315 (1994); Phys. Rev. B 51, 12844 (1995). F. M. Araujo-Moreira et al., Phys. Rev. Lett. 78, 4625 (1997); P. Barbara et al., Phys. Rev. B 60, 7489 (1999).
Scanning SQUID Experiment Unshunted Array Nb - AlOx -Nb 30 x 100 junctions
2πLI c = 30 βl = Φ0 50 µm
SQUID Sapphire solenoid coil
Sample is field cooled Measured with field turned on
Paramagnetic Image of JJ Array Φexternal=4.8Φ0
5 mm
-0.3
0.0
0.3
(Φtotal- Φexternal) /Φ0
M=
B - H
Histogram of Flux Values for JJ Array Φexternal=4.8Φ0
125 Count
100 75 50 25 -0.3
0.0 (Φτotal- Φexternal )/Φ0
0.3
Diamagnetic Φexternal=1.2Φ0
5 mm
-0.3
0.0
0.3
(Φtotal- Φexternal) /Φ0
Histogram of Flux Values for JJ Array Φexternal=1.2Φ0
100
Count
75 50 25
-0.3
0.0 (Φτotal- Φexternal )/Φ0
0.3
Array Exhibits Paramagnetism For Some Cooling Fields!
M vs. H 0.20 0.15
(Φtot-Φext)/Φ0
0.10 0.05 0.00 -0.05 -0.10 -0.15 -0.20 -15
-10
-5
0
Φext/Φ0 Paramagnetic Diamagnetic
5
10
15
Four Junction Loop
k
I = Ic sin γ
k-1 1
4
2π γ i = θ k − θ k −1 − Φ0
k −1
∫ A ⋅ dl k
2
L = self- inductance of loop
3
2π ∑i γi = 2πn − Φ 0Φtotal
Φ total = Φ external + LI By symmetry:
γ 1 = γ 2 = γ 3 = γ 4 = γi
π π Φ total γi = n − 2 2 Φ0 Φ tot Φ ext LIc π π Φ tot + sin( 2 n − 2 ) = Φ0 Φ0 Φ0 Φ0
Four Junction Loop
Φtot vs. Φext 5
Φtot = Φext
4
n=3
Φtotal/Φ0
3
n=2
2
n=1
1
n=0
0 -1 -6
-4
-2
0
2
4
6
8
Φexternal/Φ0
Φ tot Φ ext LIc π π Φ tot sin( 2 n − 2 ) = + Φ0 Φ0 Φ0 Φ0
10
Single Loop Magnetization 0.8 0.6
(Φtot-Φext)/Φ0
0.4 0.2 0.0 -0.2 -0.4 -0.6 -0.8 -15
-10
-5
0
5
Φext/Φ0 Paramagnetic Diamagnetic
10
15
M vs. H 0.8 0.6
(Φtot-Φext)/Φ0
0.4 0.2 0.0 -0.2 -0.4 -0.6 -0.8 -15
-10
-5
0
5
10
15
Φext/Φ0 Paramagnetic Diamagnetic
Single Loop Array Data
Conclusions Conventional Josephson junction arrays can be paramagnetic
+
π-junctions are not necessary for paramagnetism + + +
The 4-junction loop can be paramagnetic
Arrays more likely to be paramagnetic than diamagnetic; single loop nearly equally likely. What are the differences with π-junction arrays?
