Ferromagnet/Superconductor hybrid systems, proximity effects Marco - PowerPoint PPT Presentation

Ferromagnet/Superconductor hybrid systems, proximity effects Marco Aprili 1 CSNSM-CNRS Bât.108 Université Paris-Sud 91405 ORSAY and “Pôle Supraconductivité” ESPCI 10, rue Vauquelin 75005 Paris

Outline 1. Inhomogeneous superconductivity : gain & price of S/F nanostructures 2. Macroscopic and microscopic measurements 3. Josephson coupling in S/F/S (better S/F/I/S) Macroscopic Quantum-Mechanics : π -SQUIDs and π -rings 4.

Superconductivity Cooper pair Order parameter = i ϕ ξ o Ψ Ψ e condensate o Coherence Length: ξ ο Phase Amplitude Below T c the system condenses in a macroscopic number of Cooper pairs

Cooper Pairs Order parameter ψ S-wave p=0 l=0 x k -k Quantum Mechanics ∆ p θ = ∆ p x ψ Π -wave p?0 l=0 + + - - x k+ ∆ p -k+ ∆ p θ D-wave p=0 l=2

The Fulde-Ferrell-Larkin-Ovchinnikov state Superconductor Superconductor + Ferromagnet Exchange interaction Singlet state +p F -p F -p F + ∆ p +p F + ∆ p ∆ p = E ex Fulde and Ferrell PR 135, A550 h v F Larkin and Ovchinnikov Sov.Phys. JETP 20, 762

Never found, why ? scattering 1. Sensitivity to disorder : + < ∆ > Fermi = 0 - 2. Phase diagram : E ex ˜ ∆ usually E ex ˜ 0.1-1 eV ∆ ˜ 1 meV

Ferromagnet/Superconductor proximity effect +p F -p F -p F + ∆ p +p F + ∆ p Ψ Superconductor Ferromagnet + + + - - d F

Question : Where’s the gain ? Why S/F hybrid structures rather than bulk superconductors ?

Andreev Reflection Superconductor Normal Metal e - e - No +p F +p F e - e - +p F -p F h + electron-hole excitation e - e - h + -p F -p F +p F Cooper pair

Superconducting Correlation Propagation S N ψ e = e − iEt h × ψ 0 ( x) S F e - e - +E +E+E ex h + h + -E -E-E ex ψ h = e iEt h × ψ 0 ( x ) No condensate ϕ (E,x) = Et/ h As E<<E ex Phase coherence is lost when = ξ F x ˜ h v F /E ex ϕ (E,x) ˜ 1 ? ˜ h v F /E Coherent superposition of ψ e and ψ h ψ = ψ e + ψ h ∝ cos( E / ) E E ˜ E ex Th E Th =x/ h v F

Answer 1. ξ F does not depend on ∆ . Superconducting correlations survive in F even if E ex >> ∆ Therefore S/F does not require comparable energy scales !!! 2. Only phase coherence is needed. No pairing equation in F. Therefore oscillations even in the dirty limit !!!

But...Spin must be a good Quantum Number e - + E + E ex -E ex ψ = ψ e + ψ h ∝ cos( E / ) E Th ex is lost if Spin-Orbit scattering h + + E ex -E-E ex SO scattering Calculations by Demler et al. PRB 55, 15174 Condition : τ so v F > ξ F Therefore 1/ τ so < E ex 1/ τ so = 0.9 E ex 1/ τ so = 0.5 E ex 1/ τ so = 0.0

The price to pay: Nanostructures ! ξ F = h v F /E ex ξ F ˜ 0.5-5 nm E ex ˜ 0.1-1 eV ξ N = h v F /K B T ξ N ˜ 1 µ m T ˜ 1 K Reduced to 0.1-1 nm in the dirty limit 1. Deposition of thin films by e-gun and magnetron sputtering (thickness control down to 0.1 nm) 2. Materials : Nb (high T c and H c2, small coherence length) Ferromagnetic materials and alloys : Gd, CuNi and PdNi E ex ˜ 0.01 eV ξ F ˜ 10 nm homogeneous thin films

= R B + PdNi ρ o R s M s Hall (Orsay-group) Hall Normal Anomalous resisitivity Ni Ni R s ˜ ρ 2 30 50Å Ni=7.0% M s 20 ˜ 15 Å T=1.5K Ni=5.5% 10 2 ρ Hall / ρ Indirect exchange 0 Ni=2.4% -10 µ ˜ 2.4 µ B per Ni µ Ni = 0.6 µ B -20 Itinerant ferromagnetism -30 -8000 -4000 0 4000 8000 H(G)

Curie’s Temperature 150 1.3 Ni =12% 100 T Curie 1.2 50 Å ρ Hall /ρ 2 (Ω -1 .cm -1 ) 50 1.1 R Hall ( Ω ) 0 1.0 H c =1000 G -50 0.9 -100 0.8 T=1.5 K -150 0.7 0 20 40 60 80 100 120 -4000 -2000 0 2000 4000 H (G) T (K)

T c oscillations : Calculations solving the Usadel eqs. S/F Multilayer d M d S Radovic et al. PRB 44, 759 see also Buzdin et al. Sov. Phys. JETP 74, 124

T c oscillations : measures BUT ξ F =1.35 nm other pair breaking mechanism ? dead layer ? Jiang et al. PRL 74, 314 see also: Strunk et al. PRB 49, 4053 Aarts et al. PRB 44, 7745

The superconducting Density of States + 0-state + - π -state - 1.4 1.2 N s (E) 1.0 0.8 E ex >> ∆ S 0.6 -3 -2 -1 0 1 2 3 Kontos, Ph.D Thesis (Orsay) ∆ s Energy/ see also: Guoya Sun et al. PRB 65, 174508 Buzdin PRB 62, 11377

Planar Tunnel Junctions Junction Area TEM I 1 A 2 B V Nb Al Si PdNi ∫ G N PdNi (E) ?f [ ] - = G n N PdNi (E F ) ?eV S FI N Substrate High energy and amplitude resolution

BCS Density of States without PdNi 3.5 Nb=500Å T=350mK 3.0 G AC Tc=8.7K 2.5 n 2.0 G G DC + AC 1.5 1.0 junction fit BCS 0.5 ∆ = 1.42 meV 0.0 -4 -2 0 2 4 V DC Energy(meV)

Tunneling Spectroscopy ξ F ˜ 50 Å Pd 1-x Ni x x ˜ 10% T c ˜ 100 K E ex ˜ 10 meV + 1.010 + 75 Å 1.005 Normalized conductance F 1.000 - 0.995 Ni=10 % T=350mK H=100 Gauss 0.990 50 Å 0.985 -3 -4 -2 0 2 4x10 Energy(eV)

Density of States at Zero Energy - 1.005 1.000 + 0.995 N(0) 0.990 Theory R interface ˜ 10 -6 Ω 0.985 0.980 Kontos et al. PRL 86, 304 (2001) 0.975 0 1 2 3 4 5 d F / ξ F

Josephson Coupling Macroscopically Microscopically +E+E ex e - F S 1 S 2 h + -E-E ex Current-phase relationship Cooper pair transfert I = I c sin θ 12 ? ? g? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Oscillations ~ Ψ

Josephson Coupling I+ S F S I- Kontos et al. PRL 89, 137007 ( 2002 ) V- 80 d F1 d F2 V+ experiment at 1.5K 20 60 x10 theory 10 IcRn(µV) SIS -6 40 I (mA) Interface = 10 R Ω 0 ξ F = 46 Å -10 SIFS 20 -20 -3 -2 -1 0 1 2 3 V (mV) 0 40 60 80 100 120 140 160 180 I-V characteristics d F (Å) I=I c sin ∆θ I= - I c sin ∆θ π -junction 0-junction

SFS Temperature dependence SFIS 12 11 I c ( µΑ) 10 9 8 7 1.5 2.0 2.5 3.0 3.5 4.0 4.5 T (K) I c R n ˜ 2nV I c R n ˜ 5 µ V V. Ryazanov et al., PRL 86 2427 (2001) Kontos et al. PRL 89, 137007 (2002)

d F1 d F2 Quantum Interference Devices Resine mask SQUID I c F F After deposition and lift-off In collaboration with W. Guichard, O. Bourgeois & P. Gandit , CRTBT-Grenoble

Diffraction Linearity :I c L<< Φ o I=2I c cos ( πΦ / Φ o + ϕ /2) 0 0 π 0 π π Guichard et al. PRL 90, 167001 (2003)

Sponteneous Supercurrents   Free energy : 2 − φ 0 ) = LI 2 2 π I c cos 2 π ϕ =0 zero ring ( U φ , φ ext  φ + ϕ  ϕ = π π ring φ 0   magnetic term Josephson term zero ring, φ ext =0 π ring , φ ext =0 Groundstate = +/- Φ 0 /2 π ring I c L/ φ 0 >>1 φ=φ ext + LI - +

Question : Can superconductivity be used to change the magnetic order ? How nano-structures can help on that ?

Heterostructure Pd Fe < 1% . . . . . . . . 6nm d Nb Tc=8.5K 60nm Idea : χ Pd is reduced by induced superconductivity 1. Why proximity effect ? We do not need similar energy scales as in bulk superconductors. ∆ =1 meV E ex =0.1-1 eV 2. Why dilute alloys ? d> ξ F = 2-20nm