University of Antwerp Condensed Matter Theory Group Vortices in superconductors IV. Hybrid systems

Transcription

1 Vortices in superconductors IV. Hybrid systems François Peeters

2 Magnetic impurities T c decreases with increasing impurity density Origin: exchange interaction between electron and impurity: Γ(r i -r e )S i s e the two electrons of a Cooper pair have opposite spins Γ-coupling acts with opposite sign Magnetic field Transition temperature decreases with increasing magnetic field Origin: orbital effect: (p A+A p)/2m the two electrons of a Cooper pair have opposite momentum orbital effect acts with opposite sign

3 Nanostructured ferromagnets + superconducting film D.S. Golubović et al, Phys. Rev. B 68, (2003) J.I. Martín et al, Phys. Rev. B 62, 9110 (2000) J.E. Villegas et al, Science 302, 1188 (2003) Ferromagnets create inhomogeneous magnetic fields with <H>=0 will locally destroy superconductivity pinning centra <H> vortex/antivortex pairs can be created

4 Single magnetic disk on top of a superconducting film Superconducting Wigner vortex molecule

5 Single magnetic dot on top of a SC film M.V. Milosevic and F.M. Peeters, Phys. Rev. B 68, (2003) I II III IV V F/F I II Φ + /Φ 0 III IV VII VIII d/ξ=0.5 d d /ξ=0.5 R d /ξ=1.0 κ= V m/(h C2 ξ 3 ) VI Experiment VI VII VIII N=2 N=3 J.S. Neal, M.V. Milosevic, S.J. Bending, A. Potenza, and C.H. Marrows, PRL 99, (2007)

6 Evolution of vortex-antivortex configurations with increasing m the baby vortex-antivortex pair F/F IV III II I Φ + /Φ 0 VI V IV III III VIII VII m/m 0 m/m 0 time evolution IV

7 5 y/ξ x/ξ 5 y/ξ x/ξ The equilibrium vortex phase diagram: solid lines illustrate transitions between different vortex configurations for different size (R d ) and magnetic moment (m) of the dot. Dashed lines denote the formation of a new ring of anti-vortices. N is the number of the anti-vortices involved. Note that the total vorticity is always equal zero. In shaded area, the multivortex state under the dot is energetically favorable (giant vortex splits into individual vortices).

8 Magnet geometry imposed vortex-antivortex configurations

9 The ferromagnet-vortex interaction 1 1 U = j Φ dv h M dv 2c 2 (1) ( fm) mv m v v Out-of-plane magnetized FM vortex interaction y/λ 3 a/λ=1.0 d/λ=0.5 m/m 0 = y/λ x/λ Vortex attracted by the disk for the parallel magnetization-vortex orientation and vice-versa, independently on the parameters * * Found for magnetic disks, all regular polygons, triangles, squares, etc x/λ

10 A regular lattice of Ni magnetic dots, with R d =60nm, d d =110nm, under a 95nm thick Nb film?? D. J. Morgan and J. B. Ketterson, PRL 80, 3614 (1998)

11 Asymmetric flux pinning Strong pinning Weak pinning

12 Asymmetric flux pinning A square lattice of 400nm x 400nm Co/Pt magnetic dots, under a 50nm thick Pb film M. J. Van Bael et al., Phys. Rev. B 68, (2003)

13 Field-polarity dependent pinning by in-plane magnets y/λ a/λ=1.0 d/λ=0.1 m/m 0 = y/λ x/λ x/λ Larger magnetization magnet induces a vortex-antivortex pair

14 Field polarity dependent flux pinning by in-plane magnetic dipoles H ext = 0 A regular lattice of 540nm x 360nm Co magnetic dipoles, under a 50nm thick Pb film H ext =H 1/2 M. J. Van Bael et al., Phys. Rev. Lett. 86, 155 (2001)

15 Field polarity & magnetization dependent flux pinning

16 Vortex-Antivortex Ionic Crystals in Superconducting Films with Magnetic Pinning Arrays a/ξ=2.0 D/ξ=2.0 l/ξ=0.1 d/ξ=0.2 κ=1.2

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18 Effects of the applied homogeneous magnetic field on the critical parameters H 0

19 Magnetic-field-enhanced critical current L/x= 6.25 a/x= 2.0 D/x= 2.0 l/x= 0.1 d/x= 0.2 k= 1.2

20 Magnetic-field-induced superconductivity A square lattice of 800nm x 800nm Co/Pd magnetic dots, on top of the 85nm thick Pb film M. Lange et al., Phys. Rev. Lett. 90, (2003) Φ + /Φ 0 = 2.28 H H/H 1 =0 H/H 1 =2

21 Magnetic-field-induced superconductivity (theory vs. experiment) - Critical field enhancement by magnetic nanostructuring N S N M= A/m ξ(0)=28 nm L = 1.5 μm [1] a = 0.8 μm [1] D = 21.5 nm [1] l = 10 nm [1] d = 85 nm [1] κ = 3.75 Φ + /Φ * * Same qualitative behavior observed for Φ + /Φ 0 = [1] M. Lange et al., Phys. Rev. Lett. 90, (2003)

22 Summary Magnets with out-of-plane magnetization attract parallel aligned vortices, and vice versa. The origin of the magnetic pinning of vortices lies in the interactions with the Meissner currents. In the case of a regular array of weakly magnetized dots we found matching configurations (both integer and rational). Asymmetric flux pinning is explained, depending on the polarity of the external field. For a superconducting film with a single magnetic disk on top, the total vorticity always equals zero - a central core of vortices (under the disk) is surrounded by antivortex shells Wigner vortex molecule, with size-magnetization-controlled magic numbers. For stronger magnetized dots, their stray field perturbs the order parameter in the vicinity of the dots. Regular vortex-antivortex lattices are formed, with vortices under the dots and antivortices at interstitial sites First and second order configurational transitions, fractional vortex-antivortex states, lattice effects on the vortex nucleation, External flux lines compensate the existing antivortices in the sample external-fieldenhanced critical current and critical field. Therefore, magnetic nano-engineering, and local defining of the magnetic field in the sample is a powerful tool for controlling the critical parameters of the superconductor.