Transcript Diapositive 1

Coexistence of Ferromagnetism and
Superconductivity at the Nano-Scale
A. Buzdin
Institut Universitaire de France, Paris
and Condensed Matter Theory Group, University of Bordeaux
MISIS, Moscow 2009
1
• Recall on magnetism and superconductivity
coexistence
• Origin and the main peculiarities of the proximity
effect in superconductor-ferromagnet systems.
• Josephson π-junction.
• Domain wall superconductivity.
• Spin-valve effet.
• Possible applications
2
Magnetism and Superconductivity
Coexistence
dTc
  m x
dx
(Abrikosov and Gorkov, 1960)
The critical temperature variation versus the concentration n of the Gd atoms in
La1-xGdxAl2 alloys (Maple, 1968). Tc0=3.24 K and ncr=0.590 atomic percent Gd.
The earlier experiments (Matthias et al., 1958) demonstrated that the
presence of the magnetic atoms is very harmful for superconductivity.
3
4
Antagonism of magnetism (ferromagnetism) and
superconductivity
• Orbital effect (Lorentz force)
p
FL
B
-p
FL
Electromagnetic
mechanism
(breakdown of Cooper pairs
by magnetic field
induced by magnetic moment)
• Paramagnetic effect (singlet pair)
μBH~Δ~Tc
Sz=+1/2
Sz=-1/2
 
 
I S  s  Tc
Exchange interaction
5
No antagonism between antiferromagnetism and
superconductivity
Tc (K)
TN (K)
NdRh4B4
5.3
1.31
SmRh4B4
2.7
0.87
TmRh4B4
9.8
0.4
GdMo6S8
1.4
0.84
TbMo6S8
2.05
1.05
DyMo6S8
2.05
0.4
ErMo6S8
2.2
0.2
GdMo6Se8
5.6
0.75
ErMo6Se8
6.0
1.1
DyNi2B2C
6.2
11
ErNi2B2C
10.5
6.8
TmNi2B2C
11
1.5
HoNi2B2C
8
5
Usually Tc>TN
6
7
FERROMAGNETIC CONVENTIONAL (SINGLET)
SUPERCONDUCTORS
A. C. susceptibility and
resistance versus temperature
in ErRh4B4 (Fertig et al.,1977).
RE-ENTRANT
SUPERCONDUCTIVITY
in ErRh4B4 !
8
Coexistence phase
Em  
Q
 (Q) 2
hQ
2
At T=0 and Q0>>1 following (Anderson and Suhl, 1959)
 s (Q)   (Q)


 (0)
2Q 0
Intensity of the neutron Bragg
scattering and resistance as a
function of temperature in an
ErRh4B4 (Sinha et al.,1982).
The satellite position
corresponds to the wavelength
of the modulated magnetic
structure around 92 Å.
9
HoMo6S8
Tc=1.8 K
Tm=0.74 K
Tc=0.7 K
10
Auto-waves in reentrant
superconductors?
current I
T<Tc2
11
12
FERROMAGNETIC UNCONVENTIONAL (TRIPLET)
SUPERCONDUCTORS
UGe2 (Saxena et al., 2000)
and URhGe (Aoki et al., 2001)
Triplet pairing
UGe2
URhGe (a) The total magnetic moment M total and
Very recently (2007): UCoGe θ=3K; Tc=0.8K
the component Mb measured for H// to the b axis .
In (b), variation of the resistance at 40 mK and 500 mK
with the field re-entrance of SC between 8-12 T
14
(Levy et al 2005).
15
16
17
18
Superconducting order parameter
behavior in ferromagnet
Standard Ginzburg-Landau
functional:
1
b 4
2
2
F a 
  
4m
2
The minimum energy corresponds
to Ψ=const
The coefficients of GL functional are functions of internal exchange field h !
Modified Ginzburg-Landau functional ! :
2
F  a          ...
2
2
2
The non-uniform state Ψ~exp(iqr) will correspond to
minimum energy and higher transition temperature
19
F
F  (a  q  q ) q
2
q0
4
2
q
Ψ~exp(iqr) - Fulde-Ferrell-Larkin-Ovchinnikov state (1964).
Only in pure superconductors and in the very narrow region.
Proximity effect in ferromagnet ?
In the usual case (normal metal):
a 
1 2
   0, and solut ionfor T  Tc is   e qx , where q  4ma
4m
20
E
kF -dkF
k
kF +dkF
The total momentum of the Cooper pair is
-(kF -dkF)+ (kF -dkF)=2 dkF
21
In ferromagnet ( in presence of exchange field) the equation
for superconducting order parameter is different
a       0
2
4
Its solution corresponds to the order parameter which decays
with oscillations!
Ψ~exp[-(q1 + iq2 )x]
Ψ
Order parameter changes its sign!
x
22
Theory of S-F systems in dirty limit
Analysis on the basis of the Usadel equations

Df
2
 F f  x ,  , h    ihF f  x,  , h  0
2
G f  x,  , h  F f  x ,  , hF f  x,  ,h  1
2
*
.
leads to the prediction of the oscillatory - like dependence of
the critical current on the exchange field h and/or thickness of
ferromagnetic layer.
23
Remarkable effects come from the possible shift of sign of the
wave function in the ferromagnet, allowing the possibility of a
« π-coupling » between the two superconductors (π-phase
difference instead of the usual zero-phase difference)


S

S
F
F
S
S

« 0 phase »
«  phase »

S
F
S/F bilayer

 f  Df / h
h-exchange field,
Df-diffusion constant
24
The oscillations of the critical temperature as a function of the
thickness of the ferromagnetic layer in S/F multilayers has been
predicted in 1990 and later observed on experiment by Jiang et
al. PRL, 1995, in Nb/Gd multilayers
F
S
F
S
F
25
SF-bilayer Tc-oscillations
Ryazanov et al. JETP Lett. 77, 39
(2003) Nb-Cu0.43Ni0.57
V. Zdravkov, A. Sidorenko et al
cond-mat/0602448 (2006)
Nb-Cu0.41Ni0.59
dFmin =(1/4)  ex largest Tc-suppression
26
S-F-S Josephson junction in the clean limit
(Buzdin, Bulaevskii and Panjukov, JETP Lett. 81)
S
F
S
Damping oscillating dependence of the
critical current Ic as the function of the
parameter =hdF /vF has been predicted.
h- exchange field in the ferromagnet,
dF - its thickness
Ic

27
The oscillations of the critical current as a function of temperature (for
different thickness of the ferromagnet) in S/F/S trilayers have been
observed on experiment by Ryazanov et al. 2000, PRL
S
S
F
and as a function of a ferromagnetic layer
thickness by Kontos et al. 2002, PRL
28
Phase-sensitive experiments
-junction in one-contact interferometer
0-junction
minimum energy at 0
-junction
minimum energy at 
I
I=Icsin(+f)=-Icsinf
E= EJ[1-cos(+f)]=EJ[1+cosf]
I
L
f
f
I
2LIc > 0/2
f = =
(2 / 0)Adl
= 2 /0
E
E
f
f
Spontaneous circulating current
in a closed superconducting loop
when bL>1 with NO applied flux
bL = 0/(4 
Bulaevsky, Kuzii, Sobyanin, JETP Lett. 1977
LIc)
 = 0/2
29
Current-phase experiment.
Two-cell interferometer
Ic
30
Cluster Designs (Ryazanov et al.)
30m
2x2
unfrustrated
fully-frustrated
checkerboard-frustrated
6x6
fully-frustrated
checkerboard-frustrated
31
2 x 2 arrays: spontaneous vortices
Fully
frustrated
Checkerboard
frustrated
32
Scanning SQUID Microscope images
(Ryazanov et al., Nature Physics, 2008))
Ic
T
T = 1.7K
T = 2.75K
T
T = 4.2K
33
Critical current density vs. F-layer thickness (V.A.Oboznov et al., PRL, 2006)
Ic=Ic0exp(-dF/F1) |cos (dF /F2) + sin (dF /F2)|
dF>> F1
“0”-state
Spin-flip scattering decreases the
decaying length and increases the
oscillation period.
-state
F2 >F1
0
Nb-Cu0.47Ni0.53-Nb
“0”-state
I=Icsin
-state
I=Icsin(+ )= - Icsin()
34
Critical current vs. temperature
Nb-Cu0.47Ni0.53-Nb
dF=9-24 nm
h=Eex  850 K (TCurie= 70 K)
1
 F1
1
F2


1
F
1
F
 1
1  
 h s
 1
1  
 h s
“Temperature dependent”
spin-flip scattering
2

 1
  

 h s
2
  1
  
  h s
G = cos (T); F = sin (T)

,




 F 2   F1
Effective spin-flip rate
(T)= cos (T)/S;
35
Critical current vs. temperature
(0-- and -0- transitions)
Nb-Cu0.47Ni0.53-Nb
dF1=10-11 nm
dF2=22 nm
(V.A.Oboznov et al., PRL, 2006)
36
F/S/F trilayers, spin-valve effect
If ds is of the order of magnitude of s, the
critical temperature is controlled by the
proximity effect.
f
F
-f
S
F
R
df
2ds
R
df
Firstly the FI/S/FI trilayers has been studied experimentally
in 1968 by Deutscher et Meunier.
In this special case, we see that the critical temperature of the
superconducting layers is reduced when the ferromagnets are
polarized in the same direction
37
In the dirty limit, we used the quasiclassical Usadel equations to find the new critical temperature T *c.
We solved it self-consistently supposing that the order parameter can be taken as :
 x2 
   0 1  2 
 L 


with L>>dS
Buzdin, Vedyaev, Ryazhanova, Europhys Lett. 2000,
Tagirov, Phys. Rev. Let. 2000.
1.0
In the case of a perfect
transparency of both
interfaces
*
Tc / Tc
h Ds
d* 
D n 4Tc
0.8
0.6
Phase 
0.4
0.2
Phase 
0.0
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
d * / ds
 Tc* 
 1 d *Tc

1






ln
    Re  
1  i 
*
 Tc 
2 d T

2


s
c




 Tc* 
 1 d *Tc 
1


      

ln
*
 Tc 
 2 d T 38 
2
s c 



Recent experimental verifications
AF
F1
F layer with
fixed magnetization
S
« free » F layer
F2
CuNi/Nb/CuNi
Gu, You, Jiang, Pearson,
Bazaliy, Bader, 2002
Ni/Nb/Ni
Moraru, Pratt Jr, Birge, 2006
39
Evolution of the difference between the critical
temperatures as a function of interfaces’ transparency
B 0
Infinite transparency
B 5
Finite transparency
Tc
Tc
Tc
~
1

 Tc * 
d
Tc
1






ln
    Re  
1  i 
*
 T 
2 d T

2
s c
 c 


~


 Tc * 
d
Tc  
1
1
 




ln
     
*
 T 



2
2
d
T


s
 c 
c





Tc
~
d / ds
Ds
~
d 
4Tc

h
Dn
1  1  i  B 
h
Dn
40
Ni0.80Fe0.20/Nb (20nm)
Similar physics in F/S bilayers
Thin films : Néel domains
Rusanov et al., PRL, 2004
In practice, magnetic domains appear
quite easily in ferromagnets
w: width of the domain wall
H=0 mT
H=4.2 mT
Localized (domain wall) superconducting phase.
Theory - Houzet and Buzdin, PRB (2006).
41
z
F
Inverse effect: appearence of
the dense domain structure
under the influence of
superconductivity.
S
Not observed yet.
d
ds
s
D<<ξ
D
x
-ds
df
42
Domain wall superconductivity in purely
electromagnetic model
2

2i   
1
   
A(r )    2

0
 (T )


Ferromagnetic
layer
M
w
D
Superconducting
film
w>>D
E.B.Sonin (1988)
w<<D
Hc3
?
Pb-Co/Pt
43
Superconductivity nucleation at a single domain wall
Thin domains
Step-like magnetic field profile
M
η-
H
w<<D
x
η+
D
U
x
wavefunction
η+
x
44
S/F bilayer with
domain structure
S
Domain
Wall S
N
Nb/F
dH c 2
B0  4M ~ 1 10kOe dT ~ 0.5kOe / K
Tc ~ 9K
dTc ~ 1  3K
45
w>>D
Thick domains
B0-maximum field induced by the domain wall
Local approximation:
Particle in a linear B profile
46
Superconducting nucleus in a periodic domain
structure in an external field
H 0
B0 w2
0
B0 w2
0
5
1
Domain wall
superconductivity
47
48
Nb/BaFe12O19
Z. YANG et al, Nature Materials, 2004
49
50
51
Atomic layered S-F systems
(Andreev et al, PRB 1991, Houzet et al, PRB 2001, Europhys. Lett. 2002)
Magnetic layered superconductors like RuSr2GdCu2O8
F
exchange field h
S « 0 » BCS coupling
F
t
S «π»
F
S
«0»
Also even for the quite small exchange field (h>Tc)
the π-phase must appear.
52
Crystal structure of layered HTS
1.5 nm
!
• Bi2Sr2CaCu2O8+x
(Bi2212)
• Bi2Sr2CuO6+x
(Bi2201)
Also Tl2212, Tl2201
etc.
53
Hamiltonian of the system
BCS coupling
Exchange field
It is possible to obtain the exact solution of this
model and to find all Green functions.
54
T/Tco
1
0-phase
-phase
h/Tco
2
The limit t <<Tco
Ic
-phase
0-phase
h/Tco
55
Mechanism for the φ0 - Josephson junction
realization.
Recently the broken inversion symmetry (BIS) superconductors (like
CePt3Si) have attracted a lot of interest.
Very special situation is possible when the weak link in
Josephson junction is a non-centrosymmetric magnetic
metal with broken inversion symmetry !
Suitable candidates : MnSi, FeGe.
Josephson junctions with time reversal symmetry:
j(-φ)= - j(φ);
i.e. higher harmonics can be observed ~jnsin(nφ) –the case of the π junctions.
Without this restriction a more general dependence is possible
j(φ)= j0sin(φ+ φ0).
Rashba-type spin-orbit coupling

n

 
   p   n
is the unit vector along the asymmetric potential gradient.
56
Geometry of the junction with BIS magnetic metal

M
57
 
 
  ,
 2 b 4 
 *

*
F  a    D    n h   D   D
2
Di  i i  2eAi
2
2

a   2  2ih
 0,
x
x
a  ac
~
  exp(i x) exp( x
),

h
~
where  

φ0 - Josephson junction (A. Buzdin, PRL, 2008).
58
a  ac
~
  exp(i x) exp( x
),

h
~
where  

In contrast with a π junction
it is not possible to choose a
real ψ function !
59
φ0
Josephson junction
j   jc sin  o 
where
o 
2hL

The phase shift φ0 is proportional to the length and the strength of the BIS
magnetic interaction.
The φ0 Junction is a natural phase shifter.
Energy EJ(φ)~-jccos(φ +φ0)
60
EJ(φ)~-jccos(φ
+φ0)

E

φ
E(φ =φ0)≠ E(φ =φ0)
61
Spontaneous flux (current) in the superconducting ring with φ0 - junction.
jc 
k 2 

E( )   - cos(   0 ) 
2e 
2 
L
o
k
c 0
2Ljc
In the k<<1 limit the junction generates the flux Φ=Φ0(φ0/2π)
o 
2hL

Very important : The φ0 junction provides a mechanism of a direct coupling
between supercurrent (superconducting phase) and magnetic moment (z
component).
62
Let us consider the following geometry :
θ
voltage-biased Josephson junction
63
Magnetic anisotropy (easy z-axis) energy :
Coupling parameter :
Weak coupling regime : Γ<1.
Srong coupling regime : Γ>1.
Let us consider first the φ0 - junction when a constant current I<Ic is applied :
I
Minimum energy condition:
64
M
θ
I
The current provokes rotation of the magnetic moment :
For the case Γ>1 when I>Ic / Γ the moment will be oriented along the y-axis.
Applying to the φ0 - junction a current (phase difference) we can generate the
magnetic moment rotation.
a.c. current -> moment’s precession!
65
What happens if the SO gradient is along y-axis?
I
The total energy has two minima θ=(0, π).
θ
0
π
I>Ic / Γ
The current pulses would provoke the switches of M between θ=0 and θ= π orientations.
This corresponds to the transition of the junction from +φ0 to -φ0 state.
66
Magnetic moment precession – voltage-biased φ0- junction
Mz
My(t)
67
Landau-Lifshitz equation :
M
Magnetic moment precession :
68
Weak coupling regime : Γ<<1.
Without damping
With damping
The current acquires a
d..c. component !
69
Srong coupling regime : Γ>>1.
if r <<1
then
and without damping we have :
Comparison between analytic results (dashed line) and numerical computation.
70
Complicated regime of the magnetic dynamics :
For more details – see ( F. KonschelIe and A. Buzdin, PRL, 2009 ).
71
A very rich physics emerges if the φ0 – junction is exposed to the microwave radiatio
In addition to the Shapiro steps at ωJ=n ω1 it will appear the half-interger-steps.
The microwave field may also generate the additional precession with ω1 frequency.
Dramatic increase of the amplitude of the Shapiro steps near the ferromagnetic reson
would be expected.
72
Complementary Josephson logic
RSFQ-logic using -shifters
A.V.Ustinov, V.K.Kaplunenko. Journ. Appl. Phys. 94, 5405 (2003)
RSFQ- logic: Rapid Single Quantum logic
Conventional RSFQ-cell
LIc >0
LJ= 0 /(2 Ic)
 ~ 1/(Ic R)
RSFQ - cell
Fluxon memorizing cell
To operate at 20 GHz clock rate
Ic R~50 V has to be
We have Ic R > 0.1 V for the present
L 0
-RSFQ –Toggle
Flip-Flop
73
Superconducting phase qubit
74
Conclusions
•
Superconductor-ferromagnet heterostructures permit to study
superconductivity under huge exchange field (h>>Tc).
•
The -junction realization in S/F/S structures is quite a general
phenomenon, and it exists even for thin F-layers (d<ξf), in the
case of low interface transparency.
•
Transition to φ- junction state can be observed by decreasing
the temperature from Tc. New types of solitons, unusual current
- phase relations.
•
Domain wall superconductivity. Spin - valve effects.
•
Superconductor-ferromagnet heterostructures are very
promising for superconducting spintronics.
Some Refs.: Magnetic superconductors- M. Kulic and A. Buzdin in
Superconductivity, Springer, 2008 (eds. Benneman and Ketterson).
S/F proximity effect - A. Buzdin, Rev. Mod. Phys. (2005).
75