vortex matter in superconductors with ferromagnetic dot arrays margriet j. van bael martin lange,...
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VORTEX MATTER IN SUPERCONDUCTORS WITH FERROMAGNETIC DOT ARRAYS
Margriet J. Van Bael
Martin Lange, Victor V. Moshchalkov
Laboratorium voor Vaste-Stoffysica en Magnetisme, K.U.Leuven,
Belgium
A.N. Grigorenko, Simon J. Bending
Department of Physics, University of Bath, United Kingdom
1
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Artificial pinning arrays: matching effects
0
1
2
34
5
12
34
5 µm
50 00 A
0
Pb(500Å) film with a square antidot lattice
Strong enhancement of critical current
‘matching’ effects
H1
M. Baert et al. PRL 74 (1995), V.V. Moshchalkov et al. PRB 54 (1996), PRB 57 (1998)
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MAGNETIC PINNING CENTRES
Influence of magnetic moment on pinning efficiency
Field-induced superconductivity
Influence of magnetic stray fieldon pinning efficiency
Co dots with in-plane magnetization
Co/Pt dots with out-of-plane magnetization
Hybrid ferromagnetic/superconducting systemArray of magnetic dots covered with superconducting film
m
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Square array of Co dipoles
d
0.36 µm
0.54 µm
1.5 µm
thickness: 380 Å
SiO2
Co (polycrystalline)AuPreparation:
e-beam lithography +molecular beam deposition +Lift-off
AFM & MFM @ H=0, RT
Enhance stray field
Not magnetizedMulti domain
MagnetizedSingle domain
M.J. Van Bael et al. PRB 59, 14674 (1999)
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j c (
10
7A
/m2)
-2 -1 0 1 2
multi - domain
single - domain multi - domain
single - domain multi - domain
single - domain
H/H1
5
10
15
dot flux line
Triangular array of Co dots
Electrical transport measurements
H1 = = 10.6
Oe3 (1.5 m)2
0 2
H/H1 = 2
honeycomb lattice only stable for strong pinning(Reichhardt et al. PRB 57, 1998)
L. Van Look et al. Physica C 332 (2000)
T/Tc = 0.985
Magnetic dots create strong pinning
potential
Clear matching effects close to Tc
Better pinning for single domain dots
structural + magnetic contributions
M.J. Van Bael et al. PRB 59, 14674 (1999)
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Array of Co dipoles
Pb C o C o
Flux lines pinned at Co dotsSingle domain -> better pinning
‘Tunable pinning’-6 -4 -2 0 2 4 6
0
2
4
6
323/2
1T/T
c= 0.97
M (
10-4
em
u)
H/H1
multi domain
no dots
single domain
M.J. Van Bael et al. PRB 59 (1999)
BUT … WHAT HAPPENS LOCALLY ??
Position of vortex on dipole ??
Superconductor
and dipole are not
independent
Fluxoid quantizatio
n
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Scanning Hall probe microscopy (SHPM)@ University of Bath
AuSTM tip
10 m
• 2DEG material for better
sensitivity (2 µV/G)
• Active area: 2 µm × 2 µm
0.25 µm × 0.25 µm
• Spatial resolution < 1 µm
• Typical sensor-surface distance: ~ 200-300 nm
probe and picture in collaboration with imec
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Pb-film on square array of single domain Co dots T = 6K << Tc
Subtract dipole contribution:
Visualization of vortex lattice in magnetic dot array
- =
[dipoles + flux lines] - dipoles (T > Tc) = flux lines square vortex lattice
T = 6K, H = H1 T = 7.5 K, H = H1
Ordered vortex patterns at integer and fractional matching
fields: H/H1 = 1/2, 1, 3/2, 2, …
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Fluxoid quantization effects: field contrast in zero field
SHPM image at H = 0
SHPM image at H = 0
5.5 6.0 6.5 7.0 7.5 8.02.4
2.6
2.8
3.0
3.2
pe
ak-
to-p
ea
k m
od
ula
tion
(G
)
T(K)
Tc = 7.16 K
S Nfield
con
trast
(G
)
field profile
contrast
M.J. Van Bael et al. PRL 86, 155 (2001)
Pb
SiO 2
0
‘Vortex–antivortex’ pair induced
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T > Tc vorticesT < Tc
Pb
SiO 2
Attraction and annihilation
of negative vortex and positive fluxoidPb
SiO 2
T > Tc
+ ½H1
In applied field: position of vortex on dipole ?
- ½H1
Field polarity dependent pinning
Confirmed by theoretical model (Milosevic et al. PRB 69 (2004)) M.J. Van Bael et al. PRL 86, 155 (2001)
vorticesT < Tc
+ ½H1
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0.4 m
1 m
MFM magnetized H> 0
single-domain all up
MFM magnetized H< 0
single-domain all down
MFM demagnetized
single-domainrandom up - down
Array of Co/Pt dots with out-of-plane magnetization
x [ m ]
0
0.51.
01 .5
y [
m]
00.5
1.01 .5
AFM
Preparatione-beam lithography + molecular beam deposition + lift-off
SiO2
Co/Pt (111) 270 Å
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m > 0m < 0
Co/Pt dots as artificial pinning centers
strong pinning
strong pinning
parallel parallel
weak pinning
weak pinning
antiparallel antiparallel
-3 -2 -1 0 1 2 3
-4
-2
0
2
4
M (
10-4
em
u)
H/H1
T = 7.00 K T = 7.10 K
-3 -2 -1 0 1 2 3
-4
-2
0
2
4
M (
10-4
em
u)
H/H1
T = 7.00 K T = 7.10 K
M.J. Van Bael et al. PRB 68, 014509 (2003)
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total current:screening current js
vortex current jv
Line energy vortex (~2)stray field outside SC
(dot + vortex)
magnetic moment in vortex field
-m.bz
Interaction between vortex and magnetic dot
Einteraction = Ekinetic + Efield + Emoment
Stray field of dot is screened below Tc js
js
m
jv
bz
Attractive interaction when field and moment are parallel
Strong on-site pinning
vortexdot
Repulsive interaction when field and moment are antiparallel
Weak interstitial pinning
jv
bz
Attractive interaction when field and moment are parallel
Strong on-site pinning
M.J. Van Bael et al. PRB 68, 014509 (2003)
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S C
T = 6.8 K H = 1.6 Oe >0T = 6.8 K H = -1.6 Oe <0
Asymmetric pinning in magnetized Co/Pt dot array
Dots magnetized in negative direction
Vortex-dot interaction: attractive for parallel alignment
repulsive for anti-parallel alignment
S C
Vortices pinned by dots
Vortices between dots
M.J. Van Bael et al. PRB 68, 014509 (2003)
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Schematic sample cross-section
Case of larger dots
What if the dots induce flux quanta ?
larger dots Co/PdDiameter 0.8 µmPeriod 1.5 µm
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Magnetized state: Critical current
Dots magnetized down
Pb
m < 0T = 7.10KT = 7.15KT = 7.18K
Dots magnetized up
Pb
m > 0T = 7.10KT = 7.15KT = 7.18K
Pinning is strongly field-polarity dependent
Maximum critical current shifted to non-zero field cfr. M.V. Milosevic and F.M. Peeters, PRL 93, 267006 (2004)
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7.18 7.20 7.22 7.24
4
2
0
-2
-4
HH
/
1
T (K )
N
S
Nm =
0
7.18 7.20 7.22 7.24
T (K )
4
2
0
-2
-4
HH
/ 1
mz < 0N
S
7.18 7.20 7.22 7.24
T (K )
4
2
0
-2
-4H
H /
1
mz > 0
N
S
H-T phase diagram
For magnetized dots
• Phase diagram asymmetric
• Shift of maximum Tc
• Superconductivity induced by magnetic field (~ 2 mT)
-4 -2 0µ H0 (mT)
2 4
n
1.0
0.8
0.6
0.4
0.2
0
mz > 0
-4 -2 0µ H0 (mT)
2 4
n
1.0
0.8
0.6
0.4
0.2
0
mz < 0
-4 -2 0µ H0 (mT)
2 4
n
1.0
0.8
0.6
0.4
0.2
0
m = 0
Magnetoresistivity
-4 -2 0µ H0 (mT)
2 4
n
1.0
0.8
0.6
0.4
0.2
0
m = 0
M. Lange et al. PRL 90, 197006 (2003)
-4 -2 0µ H0 (mT)
2 4
n
1.0
0.8
0.6
0.4
0.2
0
mz < 0
-4 -2 0µ H0 (mT)
2 4
n
1.0
0.8
0.6
0.4
0.2
0
m = 0
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Field compensation effectsApplied field H = 0
Stray field of dots destroys superconductivitybetween and below dots ~20 per unit cell
Applied field H = 2H1
Between the dots, the stray field compensates the applied field (2H1= 1.84
mT) and superconductivity emerges
Cond-mat/0209101M. Lange et al. PRL 90, 197006 (2003)
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CONCLUSION
Artificial pinning arrays
Very efficient pinning
Induce particular geometry of vortex lattice
Magnetic pinning centers
Magnetism provides extra parameter
Fundamental interaction between pinning center and flux line ?
Domain state and stray field important
Field polarity dependent pinning
Magnetic dots can create vortex-antivortex pairs
Field compensation effects and field-induced superconductivity