spin dependent tunneling in junctions involving normal and superconducting cdw metals a.m. gabovich...
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Spin dependent tunneling in junctions involving normal and superconducting CDW metals
A.M. Gabovich and A.I. Voitenko (Institute of Physics, Kyiv, Ukraine)
T. Ekino (Hiroshima University, Japan)
Mai Suan Li and H. Szymczak (Institute of Physics, Warsaw, Poland)
M. Pękała (Warsaw University, Poland)
Electronics vs. Spintronics:
Ferromagnets:
Magnetization is linked to the difference between spin sub-band populations in the conduction band
Objective: To estimate the polarization of the tunnel current
Introduction
SpinCharge
sSpintronicsElectronic
FMFM
FMFM
NNNN
P
N( )
EF
Tunnel conductances G(V) for metal/gapped material junction at temperature T0: the Fermi distribution of metal electrons serves as a probe of the electron density of states (DOS) of the gapped material electrode
Factors
in the integrand of G(V) are caused by metal electrons
Starting points of Tedrow and Meservey (1973):
)( eVKNM
deVKNN
dVdJ
VG
deVffeVNNVJ
MSSM )()(~)(
)]()()[()(~)( 21
0
M
dNM
/ d
NM()K()
BCS
N
BC
S (
)
V V
eVGMB
CS =
dJ
/ dV
TM’s original idea for FM—BCS junction:
If the gapped material = BCS superconductor, its peak-possessing DOS may also serve as a probe of the metal DOS in the vicinity of the Fermi surface (FS) !
Warning: absence of an electron spin-flipping while tunneling
Problem:
To segregate the spin-polarized components of the tunnel current
)()(~
)()()(~)(
VGVG
deVKNNNVG MMS
0
M
dNM
/ d
N
M()K()
N +
M()K()
NM()K()
BCS
N
BC
S (
)
V V
eVGMB
CS =
dJ
/ dV
*
BH *
BH *
BH*
BH 0
M
dNM
/ d
N
M()K()
N +
M()K()
NM()K()
BCS
N
BC
S (
)
V V
eVGMB
CS =
dJ
/ dV
Splitting of spin sub-bands in the BCS superconductor
Solution:
Spin sub-bands in a BCS s-wave superconductor can be split in an external magnetic filed, *
B is the effective Bohr magnetonTo apply H
Requirement:
Availability of a gapped FS section on one side and a non-gapped FS section on the other side of the junction
)()(
~)(** HeVGHeVG
eVG
BB
Meissner effect: Thin films.
Temperature smearing: Use as low T as
possible. In any case, T < Tc.
Spin-orbit interaction ~Z4: Use constituting
elements as light as possible.
The effect was measured for Al:
Z = 13, Δ=0.4 meV, Tc = 1.19 K
Counter-electrodes: Fe, Ni, Co.
New problems and their solutions
CDW metal:
FS comprises both gapped (d) and non-gapped (nd) sections.
The DOS structure: at the d-sections is similar to
that of BCS superconductor (the dielectric order parameter Σ),
at the nd-section to that of ordinary metal (no gap).
Advantages: No Meissner effect
Less stringent requirements to sample geometry
Bigger range of the dielectric gaps |Σ|: critical temperatures Td is in the range 1 K 1000 K
Spin-splitting is observable in the “symmetrical" (CDWM/CDWM') setup Possibility to use the effect in
studying CDWMs themselves.
For example: 2H-NbSe2:
ZNb = 41 (ZSe = 34), Σ = 34 meV,
Td = 33.5 K
Our idea: To use CDW metals
)0()0()0(
ndd
d
NNN
~~~~
Green’s function method of the tunnel current calculation
FM—CDWM junction
22*
*
0
*0
*0
,,,
)(
)(),,(
,2
tanh2
tanh),,(
),,,()(),,(4
~)1(
),,,(),,(4
)1(
,2
)1)(1(
),()(
H
HHf
T
eV
TTVK
HfHsignTVKdeR
PJ
HfHTVKdeR
PJ
eR
VPJ
VJVJ
B
B
Bc
Bd
n
scdnf
sf
FM—CDWM junction
Drastic distinctions from the FM—BCS case:
peaks on one CVC branch and cusps on the other one, h = *
BH/0, 0= (T=0)
Strong dependence on the parameter μ
-2 -1 0 1 20.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
= 0.1 0.3 0.5 0.8
R d
J / d
V
eV / 0
t = 0.05, P = 0.5, h = 0.2,
0 > 0
-2 -1 0 1 20.0
0.5
1.0
1.5
2.0
2.5
3.0
h = 0.1 0.2 0.3 0.4
R d
J / d
V
eV / 0
= 0.5, P = 0.5, t = 0.05,
0 > 0
Sensitivity to the parameter P and to the sign of Σ
-2 -1 0 1 20.00.5
1.0
1.5
2.0
2.5
3.0
3.5
P = 0 0.2 0.5 0.8 1
R d
J / d
V
eV / 0
= 0.5, t = 0.05, h = 0.2
(a) 0 > 0
-2 -1 0 1 20.00.5
1.0
1.5
2.0
2.5
3.0
3.5
R d
J / d
V
eV / 0
(b) 0 < 0
CVCs for the FM —I—superconducting CDWM junction
000 /
-2 -1 0 1 20.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
= 0 /4 /2 3/4
R d
J / d
V
eV / 0
= 0.5, P = 0.2, t = 0.02, h = 0.1,
0 = 0.50 - superconducting gap for T = 0
in the absence of CDWs
CDWM′—CDWM setup
-
- -
++
++
-+ -+
d d nnCDWM´ CDWM
HB*
HB*
HB*
HB*
HB*
HB*
HB*
HB*
Fermi level Fermi level
( Symmetrical CDWM—CDWM junctionDistinction from FM—BCS case:Different disposition (+ - - +) of spin-
polarized peaksBCS = (- + - +)
no effect in BCS′—BCS setup)Energy scheme, processes——— with spin splitting - - - - - without spin splitting
-3 -2 -1 0 1 2 30
1
2
3 = 0.5, t = 0.01h = 0
0.2
+ +
g =
R d
J/dV
eV / 0
(a)
Sensitivity to
gapping level μ temperature
-3 -2 -1 0 1 2 30.0
0.5
1.0
1.5h = 0.2, t = 0.05, = 0.1, 0.5, 0.7
g =
R d
J / d
V
eV / 0
-3 -2 -1 0 1 2 3
0.0
0.5
1.0
1.5
h = 0.2, = 0.5, t = 0.03, 0.1, 0.2
g =
R d
J / d
V
eV / 0
CVCs for the CDWM —I—CDWM junction
CDWMs are normal The phase of the left
electrode equals to zero
-3 -2 -1 0 1 2 30
1
2
3 r = 0
/2
R d
J/dV
eV / 0
Conclusions
CDW metals (CDW superconductors) Can be used in tunnel experiments to detect spin
splitting Possess advantages over BCS superconductors:
no Meissner effect bigger range of gap amplitudes Can be observed in symmetrical junctions, since
there are both degenerate and non-degenerate FS sections
are perspective objects for investigation in spintronics