VORTEX MATTER IN SUPERCONDUCTORS WITH FERROMAGNETIC DOT ARRAYS

Margriet J. Van Bael

Martin Lange, Victor V. MoshchalkovLaboratorium voor Vaste-Stoffysica en Magnetisme, K.U.Leuven, Belgium

A.N. Grigorenko, Simon J. BendingDepartment of Physics, University of Bath, United Kingdom

1

Artificial pinning arrays: matching effects

0

12

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 (1

07 A/m

2 )

-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 Oe

3 (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 Co 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/Tc= 0.97

M (1

0-4 e

mu)

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 ?? Superconducto

r 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

peak

-to-p

eak

mod

ulat

ion

(G)

T(K)

Tc = 7.16 K

S Nfie

ld c

ontra

st

(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 pinningConfirmed 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 < 0Co/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 (1

0-4 e

mu)

H/H1

T = 7.00 K T = 7.10 K

-3 -2 -1 0 1 2 3

-4

-2

0

2

4

M (1

0-4 e

mu)

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 parallelStrong on-site pinning

vortexdot

Repulsive interaction when field and moment are antiparallelWeak interstitial pinning

jv

bz

Attractive interaction when field and moment are parallelStrong on-site pinning

M.J. Van Bael et al. PRB 68, 014509 (2003)

SC

T = 6.8 K H = 1.6 Oe >0T = 6.8 K H = -1.6 Oe <0

Asymmetric pinning in magnetized Co/Pt dot arrayDots 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 dotsWhat if the dots induce flux quanta ?

larger dots Co/PdDiameter 0.8 µmPeriod 1.5 µm

Magnetized state: Critical currentDots 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

N m = 0

7.18 7.20 7.22 7.24T (K )

4

2

0

-2

-4

HH

/ 1

mz < 0N

S

7.18 7.20 7.22 7.24T (K )

4

2

0

-2

-4H

H /

1

mz > 0

N

S

H-T phase diagramFor 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 0

µ H0 (m T)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 = 0Magnetoresistivity

-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 centersMagnetism provides extra parameterFundamental 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