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
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)
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
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)
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)
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
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
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, …
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
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
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
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)
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)
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)
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
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)
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
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)
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
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