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