1. 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

2. Artificial pinning arrays: matching effects Pb(500Å) film with a square antidot lattice Strong enhancement of critical current ‘matching’ effects H1H1  M. Baert et al. PRL 74 (1995), V.V. Moshchalkov et al. PRB 54 (1996), PRB 57 (1998)

3. MAGNETIC PINNING CENTRES Influence of magnetic moment on pinning efficiency Field-induced superconductivity Influence of magnetic stray field on pinning efficiency Co dots with in-plane magnetization Co/Pt dots with out-of-plane magnetization Hybrid ferromagnetic/superconducting system Array of magnetic dots covered with superconducting film m

4. Square array of Co dipoles d 0.36 µ m 0.54 µ m 1.5 µ m thickness: 380 Å SiO 2 Co (polycrystalline) Au Preparation: e-beam lithography + molecular beam deposition + Lift-off AFM & MFM @ H=0, RT Enhance stray field Not magnetized Multi domain Magnetized Single domain M.J. Van Bael et al. PRB 59, 14674 (1999)

5. Triangular array of Co dots Electrical transport measurements H 1 = = 10.6 Oe  3 (1.5  m) 2 0 0 2 H/H 1 = 2 honeycomb lattice only stable for strong pinning (Reichhardt et al. PRB 57, 1998) L. Van Look et al. Physica C 332 (2000) T/T c = 0.985 Magnetic dots create strong pinning potential Clear matching effects close to T c Better pinning for single domain dots structural + magnetic contributions M.J. Van Bael et al. PRB 59, 14674 (1999)

6. Array of Co dipoles Flux lines pinned at Co dots Single domain -> better pinning ‘Tunable pinning’ 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 quantization

7. Scanning Hall probe microscopy (SHPM) @ University of Bath Au STM 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

8. Pb-film on square array of single domain Co dots T = 6K << T c Subtract dipole contribution: Visualization of vortex lattice in magnetic dot array -= [dipoles + flux lines] - dipoles (T > T c ) = flux lines square vortex lattice T = 6K, H = H 1 T = 7.5 K, H = H 1 Ordered vortex patterns at integer and fractional matching fields: H/H 1 = 1/2, 1, 3/2, 2, …

9. Fluxoid quantization effects: field contrast in zero field SHPM image at H = 0 T c = 7.16 K SN field contrast (G) field profile contrast M.J. Van Bael et al. PRL 86, 155 (2001)  ‘Vortex–antivortex’ pair induced

10. T > T c vortices T < T c  Attraction and annihilation of negative vortex and positive fluxoid    T > T c + ½H 1 In applied field: position of vortex on dipole ? - ½H 1 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 < T c + ½H 1

11. 0.4  m 1 m1 m MFM magnetized H> 0 single-domain all up MFM magnetized H< 0 single-domain all down MFM demagnetized single-domain random up - down Array of Co/Pt dots with out-of-plane magnetization AFM Preparation e-beam lithography + molecular beam deposition + lift-off SiO 2 Co/Pt (111) 270 Å

12. m > 0m < 0 Co/Pt dots as artificial pinning centers strong pinning parallel weak pinning antiparallel M.J. Van Bael et al. PRB 68, 014509 (2003)

13. total current: screening current j s vortex current j v Line energy vortex (~  2 ) stray field outside SC (dot + vortex) magnetic moment in vortex field -m.b z Interaction between vortex and magnetic dot E interaction = E kinetic + E field + E moment Stray field of dot is screened below T c  j s jsjs m jvjv bzbz Attractive interaction when field and moment are parallel Strong on-site pinning vortexdot Repulsive interaction when field and moment are antiparallel Weak interstitial pinning jvjv bzbz Attractive interaction when field and moment are parallel Strong on-site pinning M.J. Van Bael et al. PRB 68, 014509 (2003)

14. T = 6.8 K H = 1.6 Oe >0 T = 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 Vortices pinned by dots Vortices between dots M.J. Van Bael et al. PRB 68, 014509 (2003)

15. Schematic sample cross-section Case of larger dots What if the dots induce flux quanta ? larger dots Co/Pd Diameter 0.8 µm Period 1.5 µm

16. Magnetized state: Critical current Dots magnetized down Pb m < 0 T = 7.10K T = 7.15K T = 7.18K Dots magnetized up Pb m > 0 T = 7.10K T = 7.15K T = 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)

17. N S N m = 0 m z < 0 N S m z > 0 N S H-T phase diagram For magnetized dots Phase diagram asymmetric Shift of maximum T c Superconductivity induced by magnetic field (~ 2 mT) m z > 0 m z < 0 m = 0 Magnetoresistivity m = 0 M. Lange et al. PRL 90, 197006 (2003) m z < 0 m = 0

18. Field compensation effects Applied field H = 0 Stray field of dots destroys superconductivity between and below dots ~2  0 per unit cell Applied field H = 2H 1 Between the dots, the stray field compensates the applied field ( 2H 1 = 1.84 mT ) and superconductivity emerges Cond-mat/0209101 M. Lange et al. PRL 90, 197006 (2003)

19. 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