Vortices in superconductors IV. Hybrid systems François Peeters
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
Nanostructured ferromagnets + superconducting film D.S. Golubović et al, Phys. Rev. B 68, 172503 (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
Single magnetic disk on top of a superconducting film Superconducting Wigner vortex molecule
Single magnetic dot on top of a SC film M.V. Milosevic and F.M. Peeters, Phys. Rev. B 68, 024509 (2003) I II III IV V F/F 0 0 2 4 6 8 10 12-0.96-0.97-0.98-0.99-1.00 0 I II Φ + /Φ 0 III IV VII VIII d/ξ=0.5 d d /ξ=0.5 R d /ξ=1.0 κ=1.0 0 5 10 15 20 25 30 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, 090502 (2007)
Evolution of vortex-antivortex configurations with increasing m the baby vortex-antivortex pair F/F 0 0 2 4 6 8 10 12-0.96 IV -0.97 III -0.98 II -0.99 I 0-1.00 Φ + /Φ 0 VI V IV III III VIII VII 8 10 12 14 16 18 0 5 10 15 20 25 30 m/m 0 m/m 0 time evolution IV
5 y/ξ 0-5 -5 0 5 x/ξ 5 y/ξ 0-5 -5 0 5 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).
Magnet geometry imposed vortex-antivortex configurations
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 =10.0 2 1 0-1 0-0.09000-0.1800-0.2700-0.3600-0.4500-0.5400-0.6300-0.7200-0.8100-0.9000 y/λ 2 1 0-1 -2-3 -3-2 -1 0 1 2 3 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. -2-2 -1 0 1 2 x/λ
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)
Asymmetric flux pinning Strong pinning Weak pinning
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, 014509 (2003)
Field-polarity dependent pinning by in-plane magnets y/λ 3 2 1 0-1 -2 a/λ=1.0 d/λ=0.1 m/m 0 =10.0 0.08000 0.06933 0.05867 0.04800 0.03733 0.02667 0.01600 0.005333-0.005333-0.01600-0.02667-0.03733-0.04800-0.05867-0.06933-0.08000 y/λ 2 1 0-1 -3-3 -2-1 0 1 2 3 x/λ -2-2 -1 0 1 2 x/λ Larger magnetization magnet induces a vortex-antivortex pair
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)
Field polarity & magnetization dependent flux pinning
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
Effects of the applied homogeneous magnetic field on the critical parameters H 0
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
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, 197006 (2003) Φ + /Φ 0 = 2.28 H H/H 1 =0 H/H 1 =2
Magnetic-field-induced superconductivity (theory vs. experiment) - Critical field enhancement by magnetic nanostructuring N S N M=3.32 10 5 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 0 2.78 * * Same qualitative behavior observed for Φ + /Φ 0 = 2.21-3.22 [1] M. Lange et al., Phys. Rev. Lett. 90, 197006 (2003)
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.