Point-contact Andreev-reflection spectroscopy of doped manganites: Charge carrier spin-polarization and proximity effects (Review Article)
Materials with spin-polarized charge carriers are the most demanded in the spin-electronics. Particularly requested are the so-called half-metals which have the maximum attainable value of carrier spin polarization. Doped manganites are in the list of compounds with, potentially, half-metallic pro...
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irk-123456789-1182232017-05-30T03:04:42Z Point-contact Andreev-reflection spectroscopy of doped manganites: Charge carrier spin-polarization and proximity effects (Review Article) Krivoruchko, V.N. D’yachenko, A.I. Tarenkov, V.Yu. К 75-летию со дня рождения И. К. Янсона Materials with spin-polarized charge carriers are the most demanded in the spin-electronics. Particularly requested are the so-called half-metals which have the maximum attainable value of carrier spin polarization. Doped manganites are in the list of compounds with, potentially, half-metallic properties. The point-contact (PC) Andreevreflection (AR) spectroscopy is a robust and direct method to measure the degree of current spin polarization. In this report, advances in PCAR spectroscopy of ferromagnetic manganites are reviewed. The experimental results obtained on “classic” s-wave superconductor — ferromagnetic manganites PCs, as well as related theoretical models applied to deduce the actual value of charge carrier spin-polarization, are discussed. Data obtained on “proximity affected” contacts is also outlined. Systematic and repeatable nature of a number of principal experimental facts detected in the AR spectrum of proximity affected contacts suggests that some new physical phenomena have been documented here. Different models of current flow through a superconductor–half-metal ferromagnet interface, as well as possibility of unconventional superconducting proximity effect, have been discussed. 2013 Article Point-contact Andreev-reflection spectroscopy of doped manganites: Charge carrier spin-polarization and proximity effects (Review Article) / V.N. Krivoruchko, A.I. D’yachenko, V.Yu. Tarenkov // Физика низких температур. — 2013. — Т. 39, № 3. — С. 276–292. — Бібліогр.: 118 назв. — англ. 0132-6414 PACS: 72.25.Mk, 74.45.+c, 72.25.Ba http://dspace.nbuv.gov.ua/handle/123456789/118223 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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К 75-летию со дня рождения И. К. Янсона К 75-летию со дня рождения И. К. Янсона |
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К 75-летию со дня рождения И. К. Янсона К 75-летию со дня рождения И. К. Янсона Krivoruchko, V.N. D’yachenko, A.I. Tarenkov, V.Yu. Point-contact Andreev-reflection spectroscopy of doped manganites: Charge carrier spin-polarization and proximity effects (Review Article) Физика низких температур |
| description |
Materials with spin-polarized charge carriers are the most demanded in the spin-electronics. Particularly requested
are the so-called half-metals which have the maximum attainable value of carrier spin polarization. Doped
manganites are in the list of compounds with, potentially, half-metallic properties. The point-contact (PC) Andreevreflection
(AR) spectroscopy is a robust and direct method to measure the degree of current spin polarization. In this
report, advances in PCAR spectroscopy of ferromagnetic manganites are reviewed. The experimental results obtained
on “classic” s-wave superconductor — ferromagnetic manganites PCs, as well as related theoretical models
applied to deduce the actual value of charge carrier spin-polarization, are discussed. Data obtained on “proximity affected”
contacts is also outlined. Systematic and repeatable nature of a number of principal experimental facts detected
in the AR spectrum of proximity affected contacts suggests that some new physical phenomena have been
documented here. Different models of current flow through a superconductor–half-metal ferromagnet interface, as
well as possibility of unconventional superconducting proximity effect, have been discussed. |
| format |
Article |
| author |
Krivoruchko, V.N. D’yachenko, A.I. Tarenkov, V.Yu. |
| author_facet |
Krivoruchko, V.N. D’yachenko, A.I. Tarenkov, V.Yu. |
| author_sort |
Krivoruchko, V.N. |
| title |
Point-contact Andreev-reflection spectroscopy of doped manganites: Charge carrier spin-polarization and proximity effects (Review Article) |
| title_short |
Point-contact Andreev-reflection spectroscopy of doped manganites: Charge carrier spin-polarization and proximity effects (Review Article) |
| title_full |
Point-contact Andreev-reflection spectroscopy of doped manganites: Charge carrier spin-polarization and proximity effects (Review Article) |
| title_fullStr |
Point-contact Andreev-reflection spectroscopy of doped manganites: Charge carrier spin-polarization and proximity effects (Review Article) |
| title_full_unstemmed |
Point-contact Andreev-reflection spectroscopy of doped manganites: Charge carrier spin-polarization and proximity effects (Review Article) |
| title_sort |
point-contact andreev-reflection spectroscopy of doped manganites: charge carrier spin-polarization and proximity effects (review article) |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2013 |
| topic_facet |
К 75-летию со дня рождения И. К. Янсона |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/118223 |
| citation_txt |
Point-contact Andreev-reflection spectroscopy of doped
manganites: Charge carrier spin-polarization and
proximity effects
(Review Article) / V.N. Krivoruchko, A.I. D’yachenko, V.Yu. Tarenkov // Физика низких температур. — 2013. — Т. 39, № 3. — С. 276–292. — Бібліогр.: 118 назв. — англ. |
| series |
Физика низких температур |
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2025-07-08T13:35:06Z |
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2025-07-08T13:35:06Z |
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1837085972342243328 |
| fulltext |
© V.N. Krivoruchko, A.I. D’yachenko, and V.Yu. Tarenkov, 2013
Low Temperature Physics/Fizika Nizkikh Temperatur, 2013, v. 39, No. 3, pp. 276–292
Point-contact Andreev-reflection spectroscopy of doped
manganites: Charge carrier spin-polarization and
proximity effects
(Review Article)
V.N. Krivoruchko, A.I. D’yachenko, and V.Yu. Tarenkov
A.A. Galkin Donetsk Physics and Technology Institute National Academy of Sciences of the Ukraine
72 R. Luxemburg Str., Donetsk 83114, Ukraine
E-mail: krivoruc@gmail.com
Received September 18, 2012
Materials with spin-polarized charge carriers are the most demanded in the spin-electronics. Particularly re-
quested are the so-called half-metals which have the maximum attainable value of carrier spin polarization. Doped
manganites are in the list of compounds with, potentially, half-metallic properties. The point-contact (PC) Andreev-
reflection (AR) spectroscopy is a robust and direct method to measure the degree of current spin polarization. In this
report, advances in PCAR spectroscopy of ferromagnetic manganites are reviewed. The experimental results ob-
tained on “classic” s-wave superconductor — ferromagnetic manganites PCs, as well as related theoretical models
applied to deduce the actual value of charge carrier spin-polarization, are discussed. Data obtained on “proximity af-
fected” contacts is also outlined. Systematic and repeatable nature of a number of principal experimental facts de-
tected in the AR spectrum of proximity affected contacts suggests that some new physical phenomena have been
documented here. Different models of current flow through a superconductor–half-metal ferromagnet interface, as
well as possibility of unconventional superconducting proximity effect, have been discussed.
PACS: 72.25.Mk Spin transport through interfaces;
74.45.+c Proximity effects; Andreev reflection; SN and SNS junctions;
72.25.Ba Spin-polarized transport in metals.
Keywords: current spin polarization, Andreev-reflection spectroscopy, ferromagnetic manganites, unconven-
tional pairing.
Contents
1. Introduction .......................................................................................................................................... 277
2. Manganites and PCAR technique ......................................................................................................... 278
2.1. Ferromagnetic half-metallic manganites ...................................................................................... 278
2.2. Fabrication and characterization of point contacts ....................................................................... 278
3. Theoretical basis of the AR spectroscopy of current spin polarization ................................................ 279
3.1. Ballistic-type contacts .................................................................................................................. 279
3.2. Diffusive-type contacts ................................................................................................................ 280
3.3. Contacts with spin-dependent transmission.................................................................................. 280
4. Conventional half-metallic characteristics of point contacts ................................................................ 280
5. Proximity affected contacts, “anomalous” Andreev reflection ............................................................. 282
6. Triplet transport in proximity sSC-HMF point contacts ...................................................................... 284
6.1. Triplet pairing in sSC/F heterostructures ...................................................................................... 284
6.2. Triplet supercurrent in sSC-manganites PCs ................................................................................ 287
6.3. Latent superconductivity of doped manganites ........................................................................... 287
7. Conclusions .......................................................................................................................................... 289
References ................................................................................................................................................ 289
Point-contact Andreev-reflection spectroscopy of doped manganites: Charge carrier spin-polarization
Low Temperature Physics/Fizika Nizkikh Temperatur, 2013, v. 39, No. 3 277
1. Introduction
Spintronics is a research field wherein two fundamental
branches of physics — magnetism and electronics — are
combined [1–4], and is based on the opportunity of ferro-
magnetic materials to provide spin-polarized current. The
performance of many spintronics devices improves dra-
matically as the degree of charger carriers spin polariza-
tion, PC, increases, and materials with highly spin-
polarized current are of crucial importance here. Particular
attention has focused on the so-called “half-metals”. Half-
metals are ferromagnets having a Fermi surface in one spin
band, and a gap for the opposite spin direction; i.e., half-
metals have the maximum attainable value of spin polari-
zation (PC = 100%). Yet, measuring PC is not an easy task.
Almost all methods of measuring it necessitate removing
electrons from the material under investigation. The densi-
ties of quasiparticle states at the Fermi level EF must there-
fore be weighted by their probability of escape, which gen-
erally depends on the measuring method and is also
different for electrons with up (↑) and down (↓) spin.
The degree of spin polarization can be defined in sever-
al different ways. Methods available to measure spin pola-
rization include spin-polarized photoemission [5], and
transport measurements in point contacts and tunnel junc-
tions with two ferromagnetic electrodes (see, e.g., [6]), or
with ferromagnetic and superconducting electrodes. The
latter case splits into two spectroscopic methods: the
tunneling spectroscopy, originated in Tedrow–Meservey
works on probing spin polarization [7], and the point-con-
tact (PC) Andreev-reflection (AR) spectroscopy based on
the way of supercurrent conversion into quasiparticle cur-
rent at superconductor (SC)–normal metal (N) interface
invented by Andreev [8].
The conventional technique of spin-resolved photoe-
mission [5] measures the spin of the electrons emitted from
a region close to the surface of a ferromagnet of order of
5–10 Å, and thus is quite surface-sensitive. The Tedrow
and Meservey [7] method requires the material under in-
vestigation to be fabricated as part of a ferromagnet/super-
conductor tunnel junction, in which the superconducting
density of states is then Zeeman split by the application of
a magnetic field of several Tesla. The PC method offers
several apparent advantages compared to these techniques.
There are no restrictions on the sample geometry and one
can avoid complex fabrication steps. In addition, it has
excellent energy resolution, typically about 0.1 meV, and
does not necessarily require an applied magnetic field.
This spectroscopic method was invented over 35 years
ago by I.K. Yanson [9] as an experimental tool to investi-
gate the interaction mechanisms between electrons and pho-
nons in metals. The PC technique was later used to study all
kinds of scattering of electrons by elementary excitation in
metals [10–12]. If one of the sides of a PC is a SC, the PC’s
differential conductance contains fundamental information
on the excitation spectrum of quasiparticles. For this reason
PC spectroscopy has become an important, sometimes
unique, tool for investigation of superconductors (see, e.g.,
recent review [13] and references therein).
The PCAR spectroscopy is a technique in which the dif-
ferential conductance G = dI/dV is measured for an elec-
trical PC with little or no tunneling barrier established be-
tween the superconducting tip and the counter-electrode
(or vice versa). The idea that AR at the interface between a
ferromagnet (F) and a SC can be used for direct probing of
current spin polarization was apparently suggested for the
first time by de Jong and Beenakker [14]. The idea is sim-
ple: the Andreev reflection can be visualized as two cur-
rents of electrons with opposite spins flowing inside a
normal metal towards its interface with a SC. At the inter-
face (more precisely, within the coherence length from the
interface) the two currents recombine creating the current
of singlet Cooper pairs. In a nonmagnetic metal both spin
subband currents are the same, so in the superconducting
state one can observe a 100% increase in the net current
over the normal state. It was suggested [14] that in a fer-
romagnetic metal the total Andreev current is defined by
that spin channel where the normal-state current is smaller,
because the excess electrons in the other channel will not
find partners to form Cooper pairs with.
The success of the first experiments for measuring
charge carrier’s spin polarization [15,16] with a direct su-
perconductor PC to an F established AR as a useful tool for
characterizing materials for spin-electronics applications.
Since then, this technique has been used to measure spin
polarization in a broad range of ferromagnetic materials,
including the transition metal elements Fe, Ni, and Co
[15,17], metallic alloys of transition metals such as permal-
loy [15,18], Heusler alloys such as NiMnSb [15,19], half-
metals such as CrO2 [15,19–21], doped manganites [15,19,
22–29], and other ferromagnetic metals and semiconduc-
tors. The foregoing may lead to a conclusion that the
PCAR technique is indeed a robust and universal way for
measuring spin polarization applicable to all magnetic
compounds. There are, however, a few cases when this
technique can not be applied. For example, magnetite,
Fe3O4, is ferrimagnet with anomalously high Curie tem-
perature ~ 850 K. The band-structure calculations (see,
e.g., [30]) have predicted that Fe3O4 is a half-metal with
only one spin subband at the Fermi level. Experimentally,
the spin-resolved photoemission on epitaxial thin films
indeed indicated a spin polarization about 80% at room
temperature [31] However, below a Verwey transition at
about 120 K, single crystal Fe3O4 shows a nonmetallic
(polaronic) type of conductivity (see, e.g., [32]), and, in
fact, the PCAR method cannot be used.
The objective of the report is to give a short review of
experiments exploring charge carrier’s spin-polarization in
half-metallic manganites by the PCAR technique. We start,
Sec. 2, with brief review of physics of ferromagnetic man-
V.N. Krivoruchko, A.I. D’yachenko, and V.Yu. Tarenkov
278 Low Temperature Physics/Fizika Nizkikh Temperatur, 2013, v. 39, No. 3
ganites as materials with half-metallic band structure.
Then we discuss major issues concerning the fabrication
and characterization of point contacts and possible related
imperfections. Section 3 is devoted to the theoretical basis
for the PCAR spectroscopy of current spin polarization.
The models of point contacts with different character of
conduction (ballistic, diffusive, etc.) are discussed. The
following three sections are central. Firstly, we overview
the experimental results obtained for conventional PCs of
s-wave SC-manganite and estimate the degree of charge
carrier’s spin polarization for doped manganites (Sec. 4).
Then, in Sec. 5, we discuss the results obtained for the so-
called “proximity affected” contacts for which a few un-
conventional features have been detected. A possible phys-
ical scenario explaining the observations is discussed in
Sec. 6. We end with summary and conclusions.
2. Manganites and PCAR technique
2.1. Ferromagnetic half-metallic manganites
In doped manganites, the ferromagnetic ordering has
been attributed to the double-exchange interaction between
the valence electronic states of Mn3+–O2––Mn4+ bonds.
Within the double-exchange model [33–36] the itinerant
charge carriers provide both the magnetic interaction be-
tween nearest Mn3+–Mn4+ ions and the electrical conduc-
tivity. Due to the short mean free path (that is typically the
distance of a few lattice parameters), the charge carrier
probes the magnetization on a very short length scale. As a
result, for these systems a strong interplay between local
magnetic order and electric properties exists. Also, there is
a large onsite Hund’s energy, which for Mn3+ is about
1.5 eV. A direct consequence of Hund’s interaction is a
large spin splitting of the conduction band into majority
and minority subbands in the ferromagnetic phase. In op-
timally doped compounds, e.g., La0.7Ca0.3MnO3 and
La0.7Sr0.3MnO3, the ge↑ (Mn) holes are itinerant while gt
↓
(Mn) electrons are localized, i.e., the ground state electrons
are nearly perfectly spin polarized.
Note that in general, the Fermi level EF intersects both
up and down bands, so that densities of states of both the ↑
and ↓ carriers are present at EF. According to the general
classification [6], when the ↑ carriers are itinerant and the ↓
carriers are localized (or visa versa), we have transport
half-metal, classified as a type IIIA (or IIIB) half-metal.
(The suffix A or B indicates whether the conduction elec-
trons are ↑ or ↓ with respect to magnetization direction.)
Thus, doped manganites are type IIIA half-metallic ferro-
magnets (HMFs). For further discussion, it is noteworthy
that numerous experimental results, including transport
studies [33–37], indicate that doped manganites are, in
fact, “bad” metals even in at low temperature.
Theoretically, HMFs has been justified by band struc-
ture calculations [38–43]. For the first time direct experi-
mental evidence of half-metallic density of states in ferro-
magnetic La0.7Ca0.3MnO3 was obtained by scanning
tunneling spectroscopy by Wei et al. [44]. These results
were then confirmed by optical [5,45–48] and transport
measurements [15,22–29,49–55]. However, it should be
taken into account that different experiments yield quite
different value of spin polarization (see Table 1). The rea-
sons are obvious: the electron densities of state at the Fer-
mi level EF must be properly weighted and weighting fac-
tor depends on the physical process used in measurements.
In tunneling experiments, the weighting factors are the
appropriate spin-dependent tunneling matrix elements. In
PC experiments depending on the character of transport
involved, either ballistic or diffusive, the density of states
must be weighted either by the Fermi velocity of the elec-
trons or its square, respectively [56,57], and so on.
2.2. Fabrication and characterization of point contacts
A PC is simply a contact between two metals, a metal
and a semiconductor, or a metal and a superconductor,
with a nanoscale radius. PCs may be fabricated in a num-
ber of ways [12,13]. Traditionally, most often used is the
so-called “needle-anvil” configuration when the sample to
be studied is one electrode and the other is a metallic tip,
which is gently pressed against the sample surface. Typi-
cally, the tip has an ending diameter of some tens of mi-
crometers and is easily deformed during the contact. This
means that, as a rule, parallel contacts are formed between
the sample and the tip. In general, this is not harmful to
spectroscopy, unless the sample is highly inhomogeneous
on a length scale compared with tip end.
The needle-anvil technique offers several apparent ad-
vantages compared to other techniques: it is nondestruc-
tive and several measurements can be carried out on the
same sample; there are no restrictions on the sample geo-
metry and one can avoid complex fabrication steps, etc.
Yet, there are some objective drawbacks such as poor
thermal and mechanical stability of the junction. A surface
modification due to uncontrolled surface oxides or other
chemical reactions on the surface of both the sample and
the tip are also possible and should be taken into account,
however, the impact of these effects on, e.g., PC is diffi-
cult to quantify.
An important characteristic of a PC is its diameter d (it
is assumed that the shape of a contact is a circular orifice).
Depending on the value of the d, different regimes of con-
duction are possible. The diameter d of a PC with resis-
tance RN can be estimated using the Wexler interpolation
formula [58]:
2
16 ,
3N
lR
dd
ρ ρ
≈ +
π
(1)
where ρ is the resistivity of the crystal, and l stands for the
charge carriers mean free path. The mean free path in the
metals can be estimated using the well known expression
for conductivity: σ = e2N(EF)D, where D = lvF/3 is the
Point-contact Andreev-reflection spectroscopy of doped manganites: Charge carrier spin-polarization
Low Temperature Physics/Fizika Nizkikh Temperatur, 2013, v. 39, No. 3 279
electron diffusive constant, N(EF) stands for the density of
state, and vF is the electron velocity at the Fermi surface.
Using for the parameter values available from literature
[33–36], one can get the mean free path for carriers in
doped manganites l ~ 100 Å. Then, for a contact with typi-
cal resistance RN ~ 100 Ω, we find from Eq. (1) the contact
diameter d ~ 100 Å. The relation l ~ d means that the con-
tact with RN ~ 100 Ω borders between the diffusive (l << d)
and ballistic (l >> d) types of conductivity. Correspon-
dingly, contacts with lower resistance are close to the dif-
fusive type of conduction and contacts with higher resis-
tance are close to the ballistic type of conduction.
For contacts of N metal with SC there is an additional
characteristic length. The solution of the Bogoliubov-de
Gennes equations near an N/SC interface yields that the
AR does not occur abruptly at the interface but over a
length scale of the order of the superconducting coherence
lengths ξS and ξN in both directions, respectively. In gener-
al, ξS and ξN characterize the so-called “proximity” effects.
Namely, ξN is the length over which superconducting cor-
relations spread into N metal, and ξS is the length over
which superconductivity of SC can be depressed due to
contact with N metal [59]. If the contact size is considera-
bly smaller than ξS proximity effects can be neglected; if
not, proximity effects should be taken into account [13].
3. Theoretical basis of the AR spectroscopy of current
spin polarization
As was discovered in the early 1960s, at energies below
the superconducting gap, a charge transport through a
normal nonmagnetic metal being in contact with a SC is
possible only due to a specific process called Andreev ref-
lection [8]: a two-particle process in which, in the N metal,
an incident electron above the Fermi energy EF and an
electron below EF with an opposite momentum and spin
are coupled together and transferred across the interface in
the SC side forming a Cooper pair in the condensate. Si-
multaneously, an evanescent hole appears in the N metal.
The charge doubling at the interface enhances the subgap
conductance and this phenomenon has indeed been ob-
served in the case of a perfectly transparent interface. The
picture is significantly modified when spin comes into
play. For a conventional s-wave pairing, a Cooper pair is
spin-less (S = 0) and spin is not carried through the N/SC
interface. Therefore, if the N metal is an F and there is an
imbalance between spin-up and spin-down populations, the
AR is suppressed and the subgap conductance can be re-
duced below the normal-state value down to zero as the
polarization approaches 100%.
Theoretically, the behavior of normal metal–constric-
tion–superconductor (N–c–SC) systems or N–SC point
contacts was analyzed by Zaitsev [60]. This work was ex-
panded on by Blonder et al. [61] who added the possibility
of a delta-function scattering potential at the N/SC inter-
face. This provides a simple means for including the effect
of interfacial scattering, allowing the successful modeling
of N–SC point contacts where the transport ranges from the
high current density, purely ballistic or Sharvin [62] regime,
to the low current density, a tunneling regime. Subsequently
de Jong and Beenakker [14] pointed out that for an F–SC
contact the spin polarization of the conduction electrons in
the F would affect AR, because not every incident electron
from the F is able to be reflected as a hole to form a Cooper
pair that can move into the SC. They argued that (for an
ideal F–SC contact) this will reduce the AR transmission
probability to a factor (1 − PC) where PC is the polarization
of the current in the F. Given the widespread interest to un-
derstanding the spin-dependent current and related spintron-
ic effects in heterogeneous structures, this led to the devel-
opment of the PCAR method for determining the degree of
current spin polarization in ferromagnetic systems of spin-
tronics interest, and to the development of several different
models to interpret the F–SC PC data.
Below we very briefly discuss the conventional models
of conductivity for a point SC–F contact: ballistic, diffu-
sive, and a contact with possible spin discrimination of
transmission at SC/F interface. (For more details see origi-
nal reports [14,27,56,57,61,63,64], textbook [12] and re-
cent review [13].)
3.1. Ballistic-type contacts
The most simplified but theoretically most self-
consistent is the 1D (i.e., all the involved momenta are
normal to the interface) model of a PC with ballistic type
of conduction. That is, the charge carriers elastic mean free
path l is much larger than the diameter of the contact d and
there is no scattering in the contact area. The barrier is
represented by a repulsive potential located at the interface
with a dimensionless amplitude, ~ Zδ(x) (here it is sup-
posed that the interface lies in the yz-lane); the value Z = 0
describes a clean interface, and values of Z > 5 correspond
to the tunneling type of conductivity. Note that, if the Fer-
mi velocities of N and SC metals in a contact are different
(vFN ≠ vFS), then the effective parameter Z ≠ 0 even if there
is no scattering of carriers at the interface. It can be as-
sumed that almost all the voltage V is applied directly to
the contact itself and, therefore, the metals on both sides of
the contact are in equilibrium state and can be described by
the Fermi distribution functions.
For the F–SC contact with the ballistic type of conduc-
tivity, the contact conductance G can be conveniently
represented as the sum of two terms [15]:
( ) (1 – ) ( ) ( ),C NS C PSG V P G V P G V= + (2)
the nonpolarized part GNS (which corresponds to an An-
dreev contact with nonmagnetic metal) and the completely
polarized part GPS (which corresponds to a SC–ferro-
magnetic metal contact with full polarization of charge
V.N. Krivoruchko, A.I. D’yachenko, and V.Yu. Tarenkov
280 Low Temperature Physics/Fizika Nizkikh Temperatur, 2013, v. 39, No. 3
carriers). The Andreev conductance of the N/SC contact,
GNS, is given by the well-known expression (the BTK
model [61]):
( )NSG V =
[ ]( , )/ 1 ( , ) ( , ) .NN F N NG dn eV T dV A Z B Z d
∞
−∞
= ε − + ε − ε ε∫
(3)
Here GNN is the normal state conductance (or for the case
of eV >> Δ); the electron energy ε is measured from the
Fermi level of the superconductor; nF is the Fermi func-
tion; the function AN(ε,Z) gives the probability of the AR
and BN(ε,Z) corresponds to usual reflection.
The conductance of the completely polarized channel
GPS can be given in the form:
( )PSG V =
[ ]( , )/ 1 ( , ) ( , )NF F P PG dn eV T dV A Z B Z d
∞
−∞
= ε − + ε − ε ε∫
(4)
where GNF is the conductance of the contact for eV >> Δ,
the parameter AP (ε,Z) describes the AR of polarized cur-
rent, and BP (ε,Z) describes the usual reflection. If |ε| < Δ,
the AR of completely polarized electrons is impossible and
AP (ε,Z) = 0. The explicit expressions for the amplitudes
AN (ε,Z), BN (ε,Z), AP (ε,Z), and BP (ε,Z), can be found in
[14,27,56,57,61,63,64].
3.2. Diffusive-type contacts
For contacts with a normal state resistance RN < 100 Ω,
the diffusive conductivity approximation is more appropri-
ate. Accordingly, the electron momentum is no longer a
good quantum number since l << d but with only elastic
scattering in the contact region (i.e., d << lel, where lel is
the inelastic-scattering length). This limit usually relates to
N-SC contacts made by rubbing. Typically, it is assumed
also that the superconductor remains in the clean limit (i.e.,
lS >> ξS) but, in addition to the N/SC interface, there is a
wide layer of disordered ferromagnetic metal (adjacent to
the contact area) where the electron mean free path is
much shorter than the contact size.
The total conductance of the contact in the diffusive
approximation is given by Eqs. (2)–(4), where now all the
amplitudes, AN (ε,Z), BN (ε,Z), AP (ε,Z), and BP (ε,Z), must
be accordingly generalized. We will not write out here
the extended expressions referring the reader to reports
[13,18,24,27].
If not only the mean free path l is much less than the di-
ameter, but the inelastic-scattering length, as well, d >> lel,
we deal with the so-called thermal regime of conductance.
There is both elastic and inelastic scattering in the contact
region. In this case, Joule heating occurs in the contact
region and causes a local increase in temperature. The in-
terpretation of data obtained on such contacts is an ambi-
guous task (see, e.g., discussion in [12,13]).
3.3. Contacts with spin-dependent transmission
In spite of the conventional models success in fitting the
experiments, several basic questions naturally arise for the
SC-F contacts. For example, how to describe spin-
dependent properties of the SC/F interface? Indeed, if the
Fermi velocities for spin up and down electrons are differ-
ent (vF↑ ≠ vF↑), then the effective parameter Z, and thus all
other transmission coefficients, are also different for the
majority- and minority – spin bands.
The minimal model [65,66] which describes transport
in the SC-F contacts and accounts for the spin-dependent
transmission gives the following expressions for zero-
temperature conductance:
1
2 2 , ,
(1 ) 4 ( / )
SF NN
T T
G G eV
r r r r eV
− ↑ ↓
↑ ↓ ↑ ↓
= ≤ Δ
+ − Δ
(5a)
1
2
( ) ( / )
, ,
[(1 ) (1 ) ( / )]
SF NN
T T T T T T eV
G G eV
r r r r eV
− ↑ ↓ ↑ ↓ ↑ ↓
↑ ↓ ↑ ↓
+ + − β Δ
= ≥ Δ
− + + β Δ
(5b)
where Tσ (σ = ↑ or↓ ) is the effective transmission coeffi-
cient for electrons with spin up and down, respectively;
rσ = (1 – Tσ)
1/2, β(eV/Δ) = [1 – (Δ/eV)2]1/2. The normal state
conductance is read as GNN = (T↑ + T↓)/4, and the current
polarization is defied as PC = (T↑ – T↓)/(T↑ + T↓). The con-
tact conductivity at T ≠ 0 is given by Eq. (3) with GSF (5a),
(5b) replacing the factor [ ]1 ( , ) ( , ) .N NA Z B Z+ ε − ε The
main approximation of this model is the assumption that
we can describe the point contact with a single pair of
transmission coefficients, T↑ and T↓, which is finally justi-
fied by the agreement with the experiment.
Summarizing, the effects of the interface structure, spe-
cific details of the contact preparation method, etc. should
also be taken into account when finding the polarization of
the ferromagnetic materials. In fact, one needs to test all
models to obtain trustful value of spin polarization. For
example, if the contact is in the diffusive limit, then fitting
the data using the ballistic model may result in an underes-
timated current polarization. For more detailed discussion
of these questions we refer to Refs 12,13 and references
therein. The examples of such fitting will be discussed in
the next section.
4. Conventional half-metallic characteristics of point
contacts
We start with the results from samples that reveal con-
ventional properties of sSC-HMF PCs. Conventional sce-
nario predicts that in the extreme case of a completely
spin polarized metal being in contact with a singlet s-wave
SC (sSC) the AR is suppressed. Thus, a fingerprint of the
conventional half-metallic characteristics of PC is a quite
visible increase of the contact’s resistivity just after su-
Point-contact Andreev-reflection spectroscopy of doped manganites: Charge carrier spin-polarization
Low Temperature Physics/Fizika Nizkikh Temperatur, 2013, v. 39, No. 3 281
perconducting transition temperature of the electrode. In
Fig. 1, representative low-temperature characteristics of
Pb/La0.65Sr0.35MnO3 PC are shown. The I–V dependence is
shown in the main panel, the top inset exhibits the tem-
perature dependence of the contact’s resistance R(T), and
the bottom inset illustrates the contact’s AR spectra, the dif-
ferential conductance dI/dV. The quasiparticles energy gap
of Pb is pointed in the bottom inset by arrows. (Further on,
we simply denote the position of dI/dV minimum by Δ. For
a PC with not too large Γ parameter, introduced by Dynes
et al. [67], this value does not differ too much from the true
energy gap [68].) Sharp increase of the contact’s resistivity
just after TC(Pb) = 7.2 K is the main distinguishing feature
of such type PCs. Below TC(Pb) we observe excess voltage
and almost doubling of the contact’s resistivity. Reduction in
the conductivity for the PC shown is about 50%.
Similar results for Ca-doped manganite are shown
in Fig. 2. Here temperature dependence of the
Pb/La0.67Ca0.33MnO3 contact resistance is shown in the
main panel. Inset in this figure illustrates the AR spectra
for this PC.
Figure 3 illustrates normalized conductivity (dI/dV)/(I/V)
of some other contacts: MgB2/La0.65Ca0.35MnO3 (1)
Pb/La0.7Sr0.3MnO3 (2), and Pb/La0.65Ca0.35MnO3 (3) (the
graphs are shifted along the vertical axis for clarity); note
that in case (3) the contact is in the thermal regime. Fitting
the model predictions for different junction conduction to
the experimental data (in Fig. 3, theory is solid line, expe-
riment is symbols) one can restore the degree of charge
carrier spin polarization for a given compound. The degree
of spin polarization of charge carriers obtained by this
Fig. 1. The current-voltage dependence of the Pb/La0.65Sr0.35MnO3
contact without visible superconducting proximity effect; T =
= 4.2 K. Top inset: the temperature dependence of the contact’s
resistance R(T); arrow indicates TC Pb = 7.2 K. Bottom inset: the
contact’s Andreev-reflection spectra; T = 4.2 K; arrows indicate
superconducting gap of Pb. Adopted from Ref. 29.
0.9
1.8
1.5
1.2
5 10 15 20 25 30 35
R
,
�
T, K
–5–10
6.0
0 5 10
5.5
5.0
4.5
4.0
3.5
3.0
d
I/
d
V
,
ar
b
.
u
n
it
s
V, mV
2�Pb
TC
Pb
–5–10 0 5 10
V, mV
–5
–10
0
5
10
15
–15
I,
m
A
Fig. 2. Temperature dependence of a resistance of
Pb/La0.67Ca0.33MnO3 contact. Inset: Andreev-reflection spectra.
Adopted from Ref. 28.
4 6 8 10 12
30
35
40
45
50
55
–4 –2 0 2 4
0.4
0.6
0.8
1.0
T = 4.2 K
Voltage, mV
T, K
R
,
�
d
I/
d
V
,
ar
b
.
u
n
it
s
Fig. 3. Normalized conductivity (dI/dV)/(I/V) of
MgB2/La0.65Ca0.35MnO3 (1) Pb/La0.7Sr0.3MnO3 (2), and
Pb/La0.65Ca0.35MnO3 (3) PCs (the graphs are shifted along the
vertical axis for clarity). In case (3), the contact is in the thermal
regime (theory is solid line, experiment is symbols). The degree
of the spin polarization of charge carriers obtained by fitting
are PC ≈ 83, 78, and 65%, respectively. T = 4.2 K. Adopted from
Ref. 27.
–14 –7 0 7 14
0,3
0,6
0,9
1,2
V, mV
3
2
1
d
I/
d
V
/
I/
V
(
)
V.N. Krivoruchko, A.I. D’yachenko, and V.Yu. Tarenkov
282 Low Temperature Physics/Fizika Nizkikh Temperatur, 2013, v. 39, No. 3
mode for the PCs shown in Fig. 3 is PC equals 83, 78, and
65%, respectively.
The values of charge carrier spin polarization obtained
for doped manganites are summarized in Table 1. In spite
of some scattering in absolute magnitudes, in general, the
data in the Table yields that the degree of spin polarization
of the current can be unambiguously determined using the
PCAR method.
As already mentioned, the electron and the hole involved
in the AR are coherently coupled. The phase-coherent elec-
tron-hole conversion results in a nonzero pair amplitude
in the F metal. For singlet pairing in the dirty limit, super-
conducting coherence length is ξF ~ (DF/2πTCurie)1/2 and
for manganites one obtains an extremely short distance
ξF ~ 5–7 Ǻ. (Here DF is the diffusivity of the F metal; we
choose = kB = 1.) Contribution of such a small region to
the contact’s resistance is less than 1%. That is indeed
observed for the most part of the samples [15,22–29,49–
55]. However, for some of the cases, the measured con-
tact’s spectra revealed very distinct features which were
interpreted as manifestation of an unconventional prox-
imity effect.
5. Proximity affected contacts, “anomalous”
Andreev reflection
Typically, the normal state resistivity of proximity af-
fected contacts is larger than that for the contacts without
proximity effect (PE). Following the conventional physics
[see discussion below Eq. (1)], the conductivity of these
contacts should be close to the ballistic type and, accor-
dingly, the spectroscopic characteristics would be more
perfect than those shown in Figs. 1–3. Yet, the characteris-
tics observed were fundamentally different.
Figure 4 illustrates representative low-temperature cha-
racteristics of Pb/La0.7Sr0.3MnO3 proximity affected PC.
As in Fig. 1, the I–V dependence is shown in the main pan-
el, the top inset exhibits the temperature dependence of the
contact’s resistance R(T), and the bottom inset illustrates
the contact’s AR spectra. In contrast to the data in Fig. 1,
quite visible decrease of the contact’s resistivity is seen
just after superconducting transition of a SC tip. Decrease
of the PC resistivity is the main distinguishing feature of
proximity affected contacts. Also, in contrast to the data in
Fig. 1, below TC(Pb) = 7.2 K we now observe excess cur-
rent and almost doubling of the contact’s conductivity.
Figure 5 illustrates the properties of another
Pb/La0.7Sr0.3MnO3 PC. In comparison with the PC in
Fig. 4, the normal-state resistivity of this contact is about
six times larger; however, it demonstrates all specific fea-
tures of a proximity affected contact, namely: excess cur-
rent, anomalous AR spectra, proximity induced gap, Δtr,
Table 1. Degree of spin polarization deduced for doped manga-
nites. Technique: SPT — spin-polarized tunneling; SPPh — spin-
polarized photoemission; BC — band calculation; PCAR — point-
contact Andreev reflection; STS — scanning tunneling spectrosco-
py; ARPES — angle-resolved photoemission spectroscopy
Compound Spin polarization Technique, Refs.
La0.67Sr0.33MnO3 36% BC, [38]
La0.67Sr0.33MnO3 72% SPT, [53]
La0.67Sr0.33MnO3 54% SPT, [51]
La0.67Sr0.33MnO3 81% SPT, [52]
La0.7Sr0.3MnO3 100% SPPh, [5]
La0.7Sr0.3MnO3 78% PCAR, [27]
La0.7Sr0.3MnO3 58%–92% PCAR, [22]
La0.7Sr0.3MnO3 78% PCAR, [23]
La0.6Sr0.4MnO3 83% PCAR, [23]
La0.7Sr0.3MnO3 78% PCAR, [15]
La0.66Sr0.34MnO3 100% BC, [42]
La0.6Sr0.4MnO3 100% ARPES, [48]
La2/3Sr1/3MnO3 90% SPT, [55]
La2/3Sr1/3MnO3 78%-82% PCAR, [24]
La0.7Sr0.3MnO3 100% SPPh, [46]
La0.7Sr0.3MnO3 83% PCAR, [23]
La1–xCaxMnO3 100% BC, [39]
La0.65Ca0.35MnO3 65%–83% PCAR, [27]
La2/3Ca1/3MnO3 36% BC, [38]
La0.7Ca0.3MnO3 100% STS, [44]
La1–xCaxMnO3 80% BC, [43]
La0.75Ca0.25MnO3 100% BC, [40]
La0.7Ca0.3MnO3 86% SPT, [54]
La0.7Ce0.3MnO3 100% SPPh, [47]
La0.7Ce0.3MnO3 100% BC, [41]
Fig. 4. The current-voltage dependence of the proximity affected
Pb/La0.7Sr0.3MnO3 contact; T = 4.2 K. Top inset: the temperature
dependence of the contact’s resistance R(T). Bottom inset: the
contact’s Andreev-reflection spectra at T = 4.2 K. Reproduced
form Ref. 29.
–30 –20 –10 0 10 20 30
–6
–3
0
3
6
0.15
0.20
0.25
0.30
0.35
0.40
–30 –15 0 15 304 6 8 10 12 14 16 18
2.5
3.0
3.5
4.0
4.5
5.0
R
,
�
d
I/
d
V
,
ar
b
.
u
n
it
s
V, mV
V, mV
I,
m
A
T, K
Point-contact Andreev-reflection spectroscopy of doped manganites: Charge carrier spin-polarization
Low Temperature Physics/Fizika Nizkikh Temperatur, 2013, v. 39, No. 3 283
which is much larger than that for Pb. In the bottom inset,
the evolution of the AR spectra with temperature is shown.
These data directly prove that the anomalous behavior of
the junction is due to the superconducting state of Pb. In
the top inset, the temperature dependence of proximity
induced quasiparticle gap is shown.
In Figs. 6 and 7, the normalized conductance spectra for
some additional proximity affected PCs of Pb or MgB2
with films of Ca- and Sr-doped manganites are shown. For
low voltage, the fine structure of the AR spectra is directly
visible. This structure is the so-called subharmonic gap
structure (SGS) and manifests itself in a set of downward
peaks in the differential conductance that are pointed by
labeled arrows in Figs. 6 and 7.
According to contemporary models (see, for example,
Refs. 69–71 and references therein), for SC–N–SC weak
links or short constrictions SC–c–SC between two super-
conductors, the differential conductance dI/dV drops fairly
abruptly due to multiple ARs. These conductance drops
appear at voltage that correlates with the energy of quasi-
particle gaps divided by integers. The voltages at which the
conductance SGS appears (roughly, because the boundary
conditions at interface are also important [71]) are: eVn =
= Δ1/n, eVm = Δ2/m, and eVl = (Δ1 + Δ2)/(2l + 1), where
the integers (l, n, m) are restricted depending on the energy
gap ratio (Δ1/Δ2). What is important for us here is that the
resonances can be observed only if both electrodes are
superconductors. So, the observation of the SGS (Figs. 6
and 7) is a strong argument in favor of the fact that the
manganites are in a superconducting state with actual gap
independent on SC partner.
From the experimental results in Figs. 4–7, we extract
that the proximity induced single-particle gap at the
Pb/La0.7Sr0.3MnO3 and Pb/La0.65Ca0.35MnO3 interface is
as large as Δtr ≈ 18–20 meV. Note that the detected gap Δtr
is much larger than that of Pb or of MgB2; for these SCs
we have at T = 4.2 K: Δ = 1.41 meV for Pb, and for MgB2
two superconducting energy gaps (the σ and π gaps) with
Δπ = 2.3 meV and Δσ = 7.1 meV for MgB2 [72]. Knowing
energy gap for the SC tip, the subharmonic gap structure
can be classified as shown in Table 2.
To conclude on this section, we summarize the main re-
sults detected for proximity affected PCs (Figs. 4–7).
Firstly, such principal fact as spectacular drop of the con-
tact’s resistance with the onset of the SC tip superconduc-
tivity has been observed. Secondly, the subharmonic gap
resonances due to multiple AR are directly visible. Thirdly,
in proximity affected PCs, the magnitude of a proximity
induced gap is much larger than that of the SC tip and may
be as large as Δtr ≈ 18–20 meV. These facts strongly sug-
gest that both electrodes are in a superconducting state
with independent gaps. All these anomalies are observed
only in the superconducting state of the tip.
Fig. 5. The current-voltage dependence of the proximity affected
Pb/La0.7Sr0.3MnO3 contact; T = 4.2 K. Top inset: the evolution of
the proximity induced quasiparticle gap Δtr with temperature.
Bottom inset: the temperature dependence of the contact’s An-
dreev-reflection spectra. The curves are shifted for clarity. Re-
produced form Ref. 29.
–48 –36 –24 –12 0 12 24 36 48
–1.5
–1.0
–0.5
0
0.5
1.0
1.5
4.0 4.5 5.0 5.5 6.0 6.5
0
2
4
6
8
10
12
0.98
1.00
1.02
1.04
1.06
–20 –10 0 10 20
T = 4.2 K
5.4 K
6.0 K
6.3 K
6.7 K
d
I/
d
V
,
ar
b
.
u
n
it
s
V, mV
V, mV
I,
m
A
T, K
2
,
m
eV
�
tr
Fig. 6. Normalized conductance spectra for proximity affected
Pb/La0.65Ca0.35MnO3 point contacts (CP#2 and CP#4), and
MgB2/La0.65Ca0.35MnO3 contact (CMg#7). The curves are
shifted for clarity. The arrows indicate the energies of the subhar-
monic gap resonances for CP#2 contact. See Table 3 for classifica-
tion of the resonances; Δtr is the apparent proximity induced single-
particle gap of the La0.65Ca0.35MnO3. Reproduced form Ref. 28.
–60 –30 0 30 60
3
4
5
6
7
8
9
2�tr
d
d
c
b
c
b
aCPb#2
CPb#4
CMg#7
V, mV
d
I/
d
V
,
ar
b
.
u
n
it
s
V.N. Krivoruchko, A.I. D’yachenko, and V.Yu. Tarenkov
284 Low Temperature Physics/Fizika Nizkikh Temperatur, 2013, v. 39, No. 3
To proceed further, let us briefly discuss models ex-
tending the conventional concepts of interplay between
superconductivity and ferromagnetism.
6. Triplet transport in proximity affected sSC–HMF
point contacts
Conventional model of PE predicts that proximity in-
duced superconductivity decays rapidly (a few nanome-
ters) inside the F layer owing to the incompatible nature of
singlet superconductivity and ferromagnetic order, and
thus proximity induced superconductivity of the F metal
can be neglected [59]. This expectation was indeed con-
firmed in various materials and geometries. On the other
hand, an increasing number of experimental facts [73-82]
present clear evidences that a simple physical interpreta-
tion of the PE, reading that the Cooper pairs are broken by
strong exchange field in the F layer, is in reality too sim-
plistic, and an extension of the existing concepts of inter-
play between superconductivity and ferromagnetism is
needed. Long-ranged PE has been observed in a variety of
ferromagnetic materials, including wires [74,74], bi- and
multilayers [75,81], half metallic CrO2 [78] rare earth met-
als with helical magnetic structure [77], etc.
Concerning the manganites, note that much earlier
Kasai et al., investigated current-voltage characteris-
tics of YBCO/La1–xCaxMnOz/YBCO [83] and YBCO/
La1–xSrxMnOz/YBCO [84] layered junctions (here YBCO
stands for YBa2Cu3Oy). Surprisingly, supercurrent was
observed through magnetic barrier as thick as 300 nm for
junctions with La1–xCaxMnOz and 200 nm for junctions
with La1–xCaxMnOz. That is for barrier’s thicknesses
much larger than a distance one may expect based on con-
ventional proximity effect. Yet, this phenomenon occurred
only for manganese oxides with x = 0.3–0.4. The authors
suggested the results may be due to a novel proximity ef-
fect between YBCO and doped manganites. Further neu-
tron measurements on YPrBaCuO/La0.7Ca0.3MnO3 multi-
layers [85] suggest a possibility of inducing spin-triplet
superconducting phase in manganite layers, which could
be the source of long-range proximity effect observed in
La0.7Ca0.3MnO3/YBCO multilayers [76,86], trilayers [87],
and bilayers [89].
From the theoretical viewpoint, a hybrid system of an F
with a uniform exchange field in a metallic contact with a
SC is well understood and the PE may be described by
taking into account the splitting of electronic bands of op-
posite spins [59]. The situation becomes more complicated
if the magnetic structure is inhomogeneous. Theories [89–
93] predict the appearance of the long-range unconven-
tional PE if there is spatial variation of magnetization (or
exchange field) at the SC/F interface. Particularly, the
triplet components of correlations need to be taken into
consideration with a characteristic coherence length of
ξF = (DF/2πT)1/2 that can be as large as ~ 100 nm at low
temperatures.
Before giving a qualitative explanation of the results
detected on PE PCs (Figs. 4–7), we summarize the physics
of proximity effect at spin-active sSC/F interface which
looks as follows (for details see, e.g., [92,93] and refe-
rences therein).
6.1. Triplet pairing in sSC/F heterostructures
As it is well known, superconducting correlations are
quantified by the anomalous Green’s function (see, e.g.,
[94]): Gαβ(r1,τ1;r2,τ2) = <TτΨα(r1,τ1)Ψβ(r2,τ2)>. Here all
notations are conventional: the field operators Ψα(ri,τi)
hold anticommutation relations, α and β are spin indexes,
Tτ is an ordering operator for imaginary time τ, etc. The
Fig. 7. Those as in Fig. 6 for proximity affected
Pb/La0.7Sr0.3MnO3 point contact at 4.2 K. Reproduced form
Ref. 29.
–40 –20 0 20 40
0.008
0.012
0.016
0.020
0.024
0.028
0.032
f f
d dc c
bb
a a
2 �tr
V, mV
d
I/
d
V
,
ar
b
.
u
n
it
s
LSMO-Pb
Table 2. The voltage corresponding to the SGS in Figs. 6 and
7, point contacts Pb–(La,Ca)MnO3 and Pb–(La,Sr)MnO3, respec-
tively; here ΔPb ≈ 1.4 meV, Δtr ≈ ΔLCMO ≈ ΔLSMO ≈ 18–20 meV
Label (Fig. 6, CPb#2) Voltage
a ΔPb
b ΔLCMO/2
c 2ΔLCMO/3
d ΔLCMO
Label (Fig. 7) Voltage
a ΔPb
b (ΔPb + ΔLSMO)/5
c ΔLSMO/3
d ΔLSMO/2
f ΔLSMO
Point-contact Andreev-reflection spectroscopy of doped manganites: Charge carrier spin-polarization
Low Temperature Physics/Fizika Nizkikh Temperatur, 2013, v. 39, No. 3 285
Pauli principle requires that this function changes sign
when the two particles are interchanged. For Fourier trans-
formed Green’s function its reads:
Gαβ(p,ωn) = – Gβα(-p,-ωn). (6)
The symmetry restriction on Eq. (6) in spin, S, momen-
tum, p, and Matsubara frequency, ωn = (2n + 1)πT, can be
satisfied in four different ways (see, e.g., Table 1 in Ref. 92).
It is convenient to separate the Green’s function
Gαβ(p,ωn) into singlet and triplet components as
Gαβ(p,ωn) = Gs(p,ωn) (iσy)αβ + Gtr(p,ωn) (σiσy)αβ. (7)
Here σ is the vector of the three Pauli matrices. The singlet
spin matrix (iσy)αβ is odd under the interchange α ↔ β,
while the three triplet matrices (σ iσy)αβ are even.
To illustrate the physics, we consider a case of a super-
conductor-weak ferromagnet heterostructure in the ballistic
transport regime and spin-active interface scattering. For
simplicity, it was also suggested that the proximity induced
pairing amplitudes in the F are small. In this case, within
quasi-classical approximation, the anomalous Green’s
function follows the (linearized) Eilenberger equations (we
follow Ref. 92):
( ) tr
exc2 2 sgn( ) 2s
F n nf iH f
↑↓ ↑↓
∇ + ω = πΔ ω −v (8)
( ) tr
exc2 2 s
F n f iH f
↑↓ ↑↓
∇ + ω = −v (9)
( ) tr
,2 0.F n f
↑↑ ↓↓
∇ + ω =v (10)
tr ( )f
↑↓
= ↑↓> + ↓↑> (m = 0) and tr
, ( , )f
↑↑ ↓↓
= ↑↑> ↓↓>
(m = 1) are normalized triplet pairing amplitudes, and
( )sf
↑↓
= ↑↓> − ↓↑> stands for the singlet one. The super-
conducting gap Δ is nonzero in the SC, while the exchange
field Hexc exists in the F.
Note, the exchange field Hexc is presented only in the eq-
uations for the pairing correlations involving two spin bands,
sf
↑↓
and tr ,f
↑↓
and is absent for the pairing correlations
involving one spin band tr
, .f
↑↑ ↓↓
The eigenvalues of the
sf
↑↓
and trf
↑↓
amplitudes for a given vF are
exc2( i )/ .n n Fk H v± = ω ± Thus, both the singlet sf
↑↓
and
the triplet trf
↑↓
amplitudes oscillate on the clean-limit mag-
netic length scale ξF = vF/2Hexc, and decay exponentially on
the length scale ξn = vF/2|ωn|; the latter is dominated by the
lowest Matsubara frequency, ω0 = πT, and occurs on the
thermal length scale ξT = vF/2πT. The equations for the
tr
,f
↑↑ ↓↓
triplet pairing amplitudes do not contain the ex-
change field, and these components are monotonic decaying
functions on the thermal length scale ξT = vF/2πT.
Yet, the presence of the tr
, ( , )f
↑↑ ↓↓
= ↑↑> ↓↓> compo-
nents requires spin-active interface scattering, i.e., appro-
priate boundary conditions. Indeed, the conversion process
between the singlet and equal-spin triplet supercurrents is
governed by two important phenomena taking place at the
SC/F interface: (i) a spin mixing and (ii) a spin-flip scatter-
ing. Spin mixing is the result of scattering phase difference
θ that electrons with opposite spin acquire when scattered
(reflected or transmitted) from an interface [95]:
i i( ) ( e e )θ − θ↑↓> − ↓↑> => ↑↓> − ↓↑> =
( )cos( ) ( )sin( ).i= ↑↓> − ↓↑> θ + ↑↓> + ↓↑> θ
It results from difference in orientations between magneti-
zation of the F film and the spin of quasiparticle, or differ-
ences in the wave-vector mismatches for spin up and spin
down quasiparticles, etc. It is a robust and ubiquitous fea-
ture for interfaces involving spin-polarized ferromagnets.
However, triplet spin state ( )↑↓> + ↓↑> can transform
into equal-spin pair states ( , )↑↑> ↓↓> only if there are
spin-flip processes at the interfaces or if quantization direc-
tion changes, or both. Its origin depends on microscopic
magnetic state at the SC/F interface, character of local
magnetic moments coupling with itinerant electrons, etc.,
and even varies from sample to sample. But, the exact mi-
croscopic origin of spin-flip processes at the interface is
important only for the effective interface scattering matrix
[92,93,96,97] and not for superconducting phenomena,
since Cooper pairs are of the size of the coherence length
ξS which is much larger than the atomic scale.
Thus, due to spin mixing at the interfaces, a spin triplet
(S = 1, m = 0) amplitude, tr ,f
↑↓
is created and extends from
the interface about the length ξT = vF/2πT into the F layer
oscillating on very short length scale ξF = vF/2Hexc (in
typical cases exchange field Hexc is much larger than TC).
At the same time, triplet pairing correlations with equal
spin pairs (S = 1, m = +1 or m = –1) are also induced (due
to spin-flip processes) in the F layer smoothly decaying on
the length scale ξT = vF/2πT. It is worthy to emphasize that
it is only the m = 0 triplet component that is coupled via
the spin-active boundary condition to the equal-spin m = 1
pairing amplitudes in the half-metal. The singlet compo-
nent in the s-wave superconductor, ,sf
↑↓
being invariant
under rotations around any quantization axis, is not directly
involved in the creation of the triplet m = 1 pairing ampli-
tudes in the half-metal.
Considering the simplest spin-active model in which the
scattering matrix is independent on the momentum parallel
to the interface, for small constant transmission and small
spin-mixing one can obtain analytical expressions for the
amplitudes. Referring the reader for details to Ref. 92, for
the singlet and triplet amplitudes with zero spin projection
we have in the region ξF << x << ξT:
( )sf l
↑↓
=
0
sin ( / ) cos( / )
cos cos exp( / ),
/ /
F F
T
F F
x x
f x
x x
⎡ ⎤ξ ξ
= − θ + α − ξ⎢ ⎥ξ ξ⎣ ⎦
V.N. Krivoruchko, A.I. D’yachenko, and V.Yu. Tarenkov
286 Low Temperature Physics/Fizika Nizkikh Temperatur, 2013, v. 39, No. 3
tr ( )f l
↑↓
=
0
cos( / ) sin( / )
cos cos sin exp( / ).
/ /
F F
T
F F
x x
if x
x x
⎡ ⎤ξ ξ
= − θ − α θ − ξ⎢ ⎥ξ ξ⎣ ⎦
Here l is Legendre polynomials index; α is an angle be-
tween a different spin-quantization axis and θ stands for
the spin-mixing angle of spin-active interface; the ampli-
tude f0 is determined by the related matrix elements [92].
The triplet amplitudes with nonzero spin projection in this
region is approximately constant and the asymptotic beha-
vior is reached if x >> ξT, and is of the form
tr
0, ( ) ~ sin exp( / ).T
Tf l if x
x↑↑ ↓↓
ξ
θ − ξ
In Fig. 8 the first partial wave (l = 0) of the singlet ( )sf x
↑↓
and triplet, tr ( )f x
↑↓
and tr
, ( ),f x
↑↑ ↓↓
pairing amplitudes
[ ( 0),sf l = ( 0)tzf l = and ( 0),tf l⊥ = respectively] spatial
behaviors are shown in clean sSC/F structures at tempera-
ture near the superconducting critical temperature for
the lowest Matsubara frequency, ω0 = πT. The higher or-
der partial waves (l ≠ 0) look very similar and have simi-
lar amplitudes. As can be seen in Fig. 8(a), in the region
ξF << x << ξ0 = ξT the correlation functions ( )sf x
↑↓
and
tr ( )f x
↑↓
decay like 1/x and are rapidly reduced by a factor
ξF/ξT (= 0.01 for the data in Fig. 8). On the same scale the
triplet correlation function with non-zero spin projection
tr
, ( )f x
↑↑ ↓↓
varies smoothly and very slowly. In a much
larger distance, x >> ξT, Fig. 8(b), all components continue
to decay according to (1/x) exp(-x/ξT). However, the mag-
nitudes of ( )sf x
↑↓
and tr ( )f x
↑↓
are considerably reduced
compared with tr
, ( )f x
↑↑ ↓↓
before this region is reached.
(For more details see Ref. 92.)
The picture changes a little bit in the case of a fully spin
polarized ferromagnet. Now the conversion of singlet pairs
into triplet ones takes place entirely within the singlet SC.
To be definite, we concentrate on an sSC/HMF structure
suggesting the dirty limit for both metals.
Due to spin mixing at the interfaces, a spin triplet (S = 1,
m = 0) amplitude tr ( )f x
↑↓
is created. This results in a boun-
dary layer with coexisting singlet ( )sf x
↑↓
and triplet
tr ( )f x
↑↓
amplitudes near the interface which extend about a
coherence length ξS = (DS/2πT)1/2 into the SC. Triplet com-
ponents tr
, ( )f x
↑↑ ↓↓
are generated if spin-flip centers are
present in the interface region. Being created, the equal-spin
proximity-induced amplitudes decay slowly in the half-
metallic region on the thermal length scale ξT = (DF/2πT)1/2.
The magnitude of the triplet correlations at the interface is
proportional to that of the singlet amplitude at the inter-
face, and both are insensitive to impurity scattering. (More
discussion is given in Ref. 92.)
Naturally, the physical mechanisms applicable for
sSC/HMF heterostructures remain in force for the point-
contact geometry, as well. The impact of spin-mixing and
spin-flip AR processes at sSC/HMF interface on PC spectra
was theoretically studied just recently in [93,96–99]. It was
found that spin-active interface and spin-flip AR can be re-
sponsible for the long-range triplet proximity effect. Refer-
ring the reader to these reports for a detailed discussion of
the problem, we only note here that the authors of Refs.
[93,98,99] have proposed an alternative interpretation of the
PCAR experimental results that goes beyond the de Jong
and Beenakker theory [14]. This alternative interpretation is
based on a realistic suggestion that, as already mentioned in
Sec. 3.3, it is reasonable to expect that the scattering proper-
ties of quasiparticles depend on their spin. In particular, the
model utilizes the spin mixing angle θ. It was shown that
scattering phase may play an important role in AR process at
interfaces to strong ferromagnets. Indeed, the scattering
phase difference θ, that quasiparticles incident from the sSC
acquire upon being reflected at sSC/HMF interface, induces
a triplet Cooper pairs, tr ,f
↑↓
which leads to enhanced subgap
conductance. This allows for an alternative interpretation of
Fig. 8. Pair correlation functions in the ferromagnet of a ballistic
s-wave superconductor–weak spin-polarized ferromagnet junc-
tion. Adopted from Ref. 92.
0 1 0 2 0
x/�F
–0.2
–0.1
0
0.1
0.2
0.3
0.4
Re ( = 0)f ls
Im ftz( = 0)l
Im ft�( = 0)l
(a)
0 50 100
–0.2
–0.1
0
0.1
0.2
0.3
0.4
x = �0
(b)
x/�F
Point-contact Andreev-reflection spectroscopy of doped manganites: Charge carrier spin-polarization
Low Temperature Physics/Fizika Nizkikh Temperatur, 2013, v. 39, No. 3 287
the PCAR spectra, which in this picture can be turned by the
fitting parameter θ [98,99].
It is worth to notice that, when no tunneling potential is
present, an inverse magnetic proximity effect [100,101]
may affect the sSC/F interface transport properties, too.
6.2. Triplet supercurrent in sSC-manganites PCs
Let us now go back to the results in Figs. 4–7. If the con-
tact’s size is not small, d > ξS, the PE can be important. For
proximity affected contacts, it was suggested [25,26,28,29]
that the conditions for an unconventional PE are fulfilled.
Indeed, the main condition for spin triplet pairing to be
induced at sSC/F interface is the “spin active” interface,
i.e., the ability of the sSC/F interface to convert a singlet
pair into a triplet one. For manganites, several theoretical
models and numerous experimental data, including such
local probing as nuclear magnetic resonance [102,103],
point that nanoscale nonhomogeneity is an intrinsic feature
of these compounds. Another characteristic important for
our discussion is that, due to strong Hund’s interaction, spin
disorder serves as strong spin scattering center for charge
carriers. Accordingly, depending on the local magnetic non-
homogeneity at the sSC/doped manganite boundary, the
manganites surface causes coherent equal spin p-wave even
frequency pairing correlations, which spread over large dis-
tance into the manganite’s bulk [25,26,28,29].
However, the induction of pairing correlations in the
normal region is not enough for the realization of multiple
AR. As already mentioned, the observation of the sub-
harmonic structure requires the existence of actual gaps in
both superconducting electrodes. Thus, experimental find-
ing of the SGS point that the proximity induced supercon-
ducting state of manganites possesses an intrinsic super-
conducting gap [28,29].
Following the physics described, in Fig. 9, the spatial
structure of the current through the proximity affected con-
tact is shown. The figure explains mutual conversion of the
currents along the contact. In fact, due to a long-range PE,
we deal here with a charge transport through an sSC–tSC–
HMF heterostructure. Namely, there is a region at the
sSC/HMF interface where a conversion from spin singlet
pairs into spin triplet pairs takes place. The equal spin trip-
let supercurrent flows through the HMF, while the singlet
part is completely blocked. The sum of the singlet and trip-
let currents is constant, obeying the continuity equation. At
the boundary of superconducting and normal phases of the
manganite a spin polarized supercurrent is continued as a
quasiparticle current jq due to the usual AR mechanism.
In.deed, at both sides of the tSC/HMF interface the charge
current is spin polarized and there is no restriction (because
of spin) on the AR. As a result, excess current and doubl-
ing of the normal-state conductance have to be observed.
The region where transformation of spin singlet pair in-
to spin triplet pairs (and vise verse) takes place is shown in
Fig. 10. Figure 10(a) illustrates the so-called “semiconduc-
tor picture” of the proximity affected PC. Figure 10(b)
explains the mechanism of conversion between spin singlet
and spin triplet pairs due to multiple ARs. At the sSC/tSC
interface we deal, in fact, with a weak link (or short constric-
tion) between two different superconductors. The “weak
link” here is a region where both singlet and triplet pairing
amplitudes are suppressed. In the semiclassical picture, for a
given voltage V < Δ/e across a weak link a quasiparticle
accelerated from Fermi surface suffers n ~ Δ/eV ARs until it
reaches the top of the pair potential well. In the particular
case shown in Fig. 10(b), an incoming electron/hole of a
given spin subband and under the energy gap ΔsSC cannot
enter in the triplet superconducting electrode. It is spin
flipped and then Andreev reflected (spin-flip AR process)
as a hole/electron back to the sSC, simultaneously adding a
triplet Cooper pair to the condensate in the tSC. This
hole/electron is spin flipped and then is reflected by An-
dreev mechanism as an electron/hole back to the tSC, si-
multaneously adding a singlet Cooper pair to the conden-
sate in the sSC. For a given voltage across the sSC/tSC
interface a quasiparticle undergoes n ~ ΔsSC/eV, ΔtSC/eV,
or m ~ (ΔsSC + ΔtSC)/eV reflections (depending on elec-
trodes and energy it starts) until it reaches the top of the
pair potential well. As was already indicated, within this
physics the subharmonic peaks shown in Figs. 6 and 7 can
be specified as it is given in Table 2.
6.3. Latent superconductivity of doped manganites
Let us now make some suggestions concerning the ori-
gin of the quasiparticle gap Δtr the magnitude of which
cannot be explained in terms of conventional theory of
proximity effect.
In mean field BCS-Eliashberg theories with Δ(r) =
= |ΔMF(r)|exp{φ(r)}, the characteristic energy scale re-
sponsible for the global transition temperature TC is the
superconducting energy gap |ΔMF(r)|. This silently implies
that the spatial variation in |ΔMF(r)| is small, and that glob-
al phase coherence temperature Tφ is larger than (or equal
to) TC. However, for a system with small superfluid densi-
Fig. 9. Spatial structure of the current through the proximity af-
fected sSC/half-metallic manganite contact. The x axis is directed
perpendicular to the sSC/HMF interface that is at x = 0; the HMF
is placed in the region x > 0, while the sSC is located at x < 0.
Proximity affected region LPE is much longer than the supercon-
ducting coherence length ξT = (DF/2πT)1/2 and LPE >> ξT. Repro-
duced form Ref. 28.
LPE >> ξT
j
q
spin-polarizedj
S
singlet
j
S
triplet
singlet SC
normal phase
x = 0 x
j
S
triplet
Half-metal
V.N. Krivoruchko, A.I. D’yachenko, and V.Yu. Tarenkov
288 Low Temperature Physics/Fizika Nizkikh Temperatur, 2013, v. 39, No. 3
ty (bad metal) the spatial variations in the mean-field value
|ΔMF(r)| could be large. As a consequence, due to large spa-
tial variations, fluctuation effects become crucial in the re-
gions where Δ(r) is small. Of these, the most important are
the thermal fluctuations in the phase of the order parameter
φ(r). In this case, the fluctuations in the phase of the order
parameter in mesoscopic “islands” prevent the long-range
superconductivity, i.e., the global critical temperature TC is
determined by the global phase coherency, whereas the pair
condensate could exist well above TC [104,105].
The important consequence of the presence of the
Cooper pair fluctuation above TC is an appearance of the
so-called pseudogap [104,106,107] i.e., decreasing of the
one-electron density of state near the Fermi level. In par-
ticular, according to one point of view [104], in the pseu-
dogap state high-TC cuprates could be considered as an
unconventional metal, i.e., as a SC that has lost its phase
rigidity due to phase fluctuations. As already mentioned,
doped manganites are bad metals. Also, a large pseudogap
is indeed detected in numerous experiments on manganites
[33–36] and it may be suggested that at least a portion of
the observed pseudogap value is due to pairing without
global phase coherency. Precursor diamagnetism above TC
provides additional arguments for survival of the pair con-
densate well above TC in cuprates [108,109]. However, for
manganites, this kind of response may be strongly sup-
pressed by ferromagnetic order of the localized moments
and spin-triplet state of the condensate.
As a likely hypothesis, the authors [28,29] suggested
that the results obtained on proximity affected contacts are
the observation of a new type of superconducting proximi-
ty effect which follows the scenario of a proximity induced
superconducting order parameter phase stiffness. Namely,
the manganites are thermodynamically very close to a trip-
let p-wave superconducting state and, at low temperature,
the local triplet superconducting fluctuations with pairing
energy Δtr intrinsically exist (“latent” high-TC supercon-
ductivity of doped manganites). Being proximity coupled
with singlet superconductor, the phase coherency of a su-
perconducting state is restored.
To verify this phase-disordering scenario for anomalous
superconductivity of proximity affected PCs, the authors of
a communication [110] prepared and studied normal and
superconducting properties of the MgB2 — (nano)
La0.67Sr0.33MnO3 (MgB:LSMO) composite. The key idea
was to obtain such a composite, where proximity affected
HMF/SC interfaces govern superconducting properties of
the bulk sample. Fortunately, the idea was successful: the
bulk samples of MgB:LSMO (nano)composite demonstrate
direct evidences for unconventional superconductivity.
Superconductivity of MgB:LSMO samples with 3:1 and
4:1 weight ratio has been observed with large, up to 20 K,
critical temperature. A few features have been detected for
bulk samples’ characteristics which, most probably, can
hardly be explained within the framework of the conven-
tional percolation model. Using the point-contact spectros-
copy, three distinct quasiparticle energy gaps Δ1(π), Δ2(σ),
and Δtr are clearly revealed. Two of these gaps were identi-
fied as enhanced gaps in the quasiparticle spectrum of the
MgB2 in the composite; the third gap Δtr was the same as
those earlier detected in PCs of (La,Sr)MnO3 and
(La,Ca)MnO3 with Pb or MgB2. A noteworthy argument
was the temperature behavior of the Δtr gap which did not
follow the BCS dependence. The Andreev-reflection spec-
troscopy on PCs between the samples and half-metallic
La0.65Ca0.35MnO3 electrode provides an additional evi-
dence in favor of an unconventional superconducting state
in the MgB:LSMO composite.
The results obtained assert upon the new type of super-
conducting proximity effect which provides for the phase-
coherency stiffness. At low temperature in a half-metallic
ferromagnetic state of (La,Sr)MnO3, a phase incoherent
Fig. 10. Semiconductor picture of proximity affected sSC/half-
metallic manganite contact. Weak link here is a region where
both singlet and triplet pairing interactions are suppressed (a).
Trajectory of a quasiparticle that is accelerated out of the conden-
sate by the electric field suffering multiple Andreev reflections.
In the case of singlet and triplet superconducting electrodes every
Andreev reflection is foregone with a spin-flip scattering. Spin-
flip Andreev-reflection processes are illustrated by lines with
stars (a). Reproduced form Ref. 29.
HMF
x = 0 x
Weak link Triplet SC Normal phase
Weak link
ΔtS
ΔsS
HMF’s
surface
region
e
e
e
e
h
h
tSCsSC
sSC LPE T>> ξ
ΔtS
ΔsS
Point-contact Andreev-reflection spectroscopy of doped manganites: Charge carrier spin-polarization
Low Temperature Physics/Fizika Nizkikh Temperatur, 2013, v. 39, No. 3 289
superconductivity (local triplet pairing condensate) exists.
However, though the local gap amplitude is large, there is
no phase stiffness and the system is incapable to display
long-range superconducting response. Being proximity
coupled to MgB2, the long-range coherency is restored.
Inversely, the manganite in superconducting state with
large energy pairing, due to proximity effect, enhances the
MgB2 superconducting state. That is, here we deal with
some kind of “mutual” proximity effect.
Naturally, at this stage of investigation, other possible
explanations and/or mechanisms, which could be related to
the physics of proximity affected PCs of manganites
should also be discussed. It was predicted that in sSC/F
structures, the so-called odd frequency pairing could take
place [89,90,111]. In this case, the Cooper pair wave func-
tion is symmetric under exchange of spatial- and spin-
coordinates but antisymmetric under exchange of time-
coordinates. The study of such pairing in sSC/F junction
was addressed by a number of authors over the last years
[111]. However, if the superconducting correlations are
odd in frequency, a pairing interaction has to be additional-
ly frequency dependent (due to strong retardation effect) in
order to have a nonzero intrinsic gap in the ferromagnetic
metal (see details in Ref. 92).
Nonlocal or crossed AR in which an electron from one
magnetic domain is Andreev reflected as a hole into oppo-
sitely polarized domain while a pair is transmitted into a
superconductor [112–114] is, in principle, possible. How-
ever, in order for the data on proximity affected junctions
to be in agreement with the crossed AR mechanism, the
total current through the contact has to be unpolarized. In
may be if the portion of domains with opposite magnetiza-
tion is exactly equal. It seems improbable that in all the
proximity affected PCs the portion of domains with oppo-
site magnetization is exactly equal.
A conversion of spin-less Cooper pair into spin pola-
rized Cooper pair and vice versa is also possible due to
absorption (respectively, emission) of a magnon [115]. If
this mechanism is governing, the junction’s current-voltage
characteristic has to be, at low temperatures, asymmetric
with respect to the base voltage. The I(V) characteristics of
all PCs explored are symmetric, and thus it is hard to sug-
gest that the magnon assisted mechanism controls the
charge transport in PCs.
A giant proximity effect (a logarithmic dependence of
the junction critical temperature on the junction width) was
predicted for a tunnel junction of two SCs with the barrier
formed by a SC that has lost its phase rigidity due to phase
fluctuations [116]. We think that to a certain extent this
scenario of proximity effect could be relevant to our case.
Extended discussion, including more exotic explana-
tions and/or mechanisms, which could be related to the
physics of proximity affected PCs of manganites the reader
can find in Ref. [28,29].
7. Conclusions
The interplay between superconductivity and spin-
polarized materials has potential applications in the emerg-
ing field of spin-electronics. Specifically, the so-called
superconducting spintronics [3,117,118] is among the most
attractive subjects of spintronics, and requires a class of
superconducting materials with spin-polarized transport,
which would necessarily have to be triplet. The controlled
production of triplet supercurrents will open several direc-
tions for possible applications. With the availability of ful-
ly polarized triplet supercurrents, spin-dependent quantum-
coherence phenomena will make implementation of differ-
ent spintronics devices a reality. Superconducting spintron-
ics devices are appealing since they introduce in a natural
way the elements of nonlocality, entanglement, and quan-
tum coherence, all of which are crucial, e.g., for quantum
computing. Already existing data [73–82] demonstrate that
an effective source of spin-polarized supercurrent can be
designed using nanohybrids of metallic ferromagnets and a
conventional s-wave SCs. Out-of-the-mainstream is the
idea that, at low temperature, incoherent superconducting
fluctuations are essentially sustained in half-metallic man-
ganites and, in proximity affected region, the singlet super-
conductor establishes phase coherence of the spin-
polarized superconducting state of the manganites [28,29].
If it is a success, a promising source of spin-polarized su-
percurrent can be designed using nano-junctions of man-
ganites and a conventional s-wave SC.
Systematic character and repeatability of a number of
principal experimental facts suggest that some general
physical phenomena have been observed in transport prop-
erties of proximity affected singlet superconductor-half-
metallic manganite contacts. Whether the origin of these
features can be traced to a thermodynamic state of manga-
nites with local triplet superconducting fluctuations, is a
matter of further investigations. Further experiments are
definitely needed in order to prove (or disprove) this scena-
rio and understand the mechanism causing the local triplet
pairing in doped manganites. We hope that our short re-
view stimulates further experimental and theoretical works
on this subject.
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