Enhancement of the Josephson current by magnetic field in superconducting tunnel structures with a paramagnetic spacer
The dc Josephson critical current of a (S/M)IS tunnel structure in a parallel magnetic field is investigated (here S is a superconductor, S/M is a proximity-coupled S and paramagnetic metal M bilayer, and I is an insulating barrier). We consider the case when, due to Hund’s rule, in the metal...
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irk-123456789-1213902017-06-15T03:02:38Z Enhancement of the Josephson current by magnetic field in superconducting tunnel structures with a paramagnetic spacer Krivoruchko, V.N. Koshina, E.A. Свеpхпpоводимость, в том числе высокотемпеpатуpная The dc Josephson critical current of a (S/M)IS tunnel structure in a parallel magnetic field is investigated (here S is a superconductor, S/M is a proximity-coupled S and paramagnetic metal M bilayer, and I is an insulating barrier). We consider the case when, due to Hund’s rule, in the metal M the effective molecular interaction aligns the spins of the conduction electrons antiparallel to the localized spins of magnetic ions. It is predicted that for the tunnel structures under consideration there are conditions such that the destructive action of the internal and the applied magnetic fields on Cooper pairs is weakened, and increase of the applied magnetic field causes field-induced enhancement of the critical tunnel current. The experimental realization of this interesting effect of the interplay between superconductivity and magnetism is also discussed. 2005 Article Enhancement of the Josephson current by magnetic field in superconducting tunnel structures with a paramagnetic spacer / V.N. Krivoruchko, E.A. Koshina // Физика низких температур. — 2005. — Т. 31, № 2. — С. 164-168. — Бібліогр.: 24 назв. — англ. 0132-6414 PACS: 74.78.Fk, 74.50.+ r http://dspace.nbuv.gov.ua/handle/123456789/121390 ru Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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| topic |
Свеpхпpоводимость, в том числе высокотемпеpатуpная Свеpхпpоводимость, в том числе высокотемпеpатуpная |
| spellingShingle |
Свеpхпpоводимость, в том числе высокотемпеpатуpная Свеpхпpоводимость, в том числе высокотемпеpатуpная Krivoruchko, V.N. Koshina, E.A. Enhancement of the Josephson current by magnetic field in superconducting tunnel structures with a paramagnetic spacer Физика низких температур |
| description |
The dc Josephson critical current of a (S/M)IS tunnel structure in a parallel magnetic field is
investigated (here S is a superconductor, S/M is a proximity-coupled S and paramagnetic metal M
bilayer, and I is an insulating barrier). We consider the case when, due to Hund’s rule, in the
metal M the effective molecular interaction aligns the spins of the conduction electrons
antiparallel to the localized spins of magnetic ions. It is predicted that for the tunnel structures
under consideration there are conditions such that the destructive action of the internal and the
applied magnetic fields on Cooper pairs is weakened, and increase of the applied magnetic field
causes field-induced enhancement of the critical tunnel current. The experimental realization of
this interesting effect of the interplay between superconductivity and magnetism is also discussed. |
| format |
Article |
| author |
Krivoruchko, V.N. Koshina, E.A. |
| author_facet |
Krivoruchko, V.N. Koshina, E.A. |
| author_sort |
Krivoruchko, V.N. |
| title |
Enhancement of the Josephson current by magnetic field in superconducting tunnel structures with a paramagnetic spacer |
| title_short |
Enhancement of the Josephson current by magnetic field in superconducting tunnel structures with a paramagnetic spacer |
| title_full |
Enhancement of the Josephson current by magnetic field in superconducting tunnel structures with a paramagnetic spacer |
| title_fullStr |
Enhancement of the Josephson current by magnetic field in superconducting tunnel structures with a paramagnetic spacer |
| title_full_unstemmed |
Enhancement of the Josephson current by magnetic field in superconducting tunnel structures with a paramagnetic spacer |
| title_sort |
enhancement of the josephson current by magnetic field in superconducting tunnel structures with a paramagnetic spacer |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2005 |
| topic_facet |
Свеpхпpоводимость, в том числе высокотемпеpатуpная |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/121390 |
| citation_txt |
Enhancement of the Josephson current by magnetic field in superconducting tunnel structures with a paramagnetic spacer / V.N. Krivoruchko, E.A. Koshina // Физика низких температур. — 2005. — Т. 31, № 2. — С. 164-168. — Бібліогр.: 24 назв. — англ. |
| series |
Физика низких температур |
| work_keys_str_mv |
AT krivoruchkovn enhancementofthejosephsoncurrentbymagneticfieldinsuperconductingtunnelstructureswithaparamagneticspacer AT koshinaea enhancementofthejosephsoncurrentbymagneticfieldinsuperconductingtunnelstructureswithaparamagneticspacer |
| first_indexed |
2025-07-08T19:49:03Z |
| last_indexed |
2025-07-08T19:49:03Z |
| _version_ |
1837109497294749696 |
| fulltext |
Fizika Nizkikh Temperatur, 2005, v. 31, No. 2, p. 164–168
Enhancement of the Josephson current by magnetic field
in superconducting tunnel structures
with a paramagnetic spacer
V.N. Krivoruchko and E.A. Koshina
A. Galkin Donetsk Physics and Technology Institute of the National Academy of Sciences of Ukraine
72 R. Luxemburg Str., Donetsk 83114, Ukraine
E-mail: krivoruc@krivoruc.fti.ac.donetsk.ua
Received May 17, 2004, revised July 12, 2004
The dc Josephson critical current of a (S/M)IS tunnel structure in a parallel magnetic field is
investigated (here S is a superconductor, S/M is a proximity-coupled S and paramagnetic metal M
bilayer, and I is an insulating barrier). We consider the case when, due to Hund’s rule, in the
metal M the effective molecular interaction aligns the spins of the conduction electrons
antiparallel to the localized spins of magnetic ions. It is predicted that for the tunnel structures
under consideration there are conditions such that the destructive action of the internal and the
applied magnetic fields on Cooper pairs is weakened, and increase of the applied magnetic field
causes field-induced enhancement of the critical tunnel current. The experimental realization of
this interesting effect of the interplay between superconductivity and magnetism is also discussed.
PACS: 74.78.Fk, 74.50.+ r
1. Introduction
In ferromagnetic (F) metals the exchange field HE
acting on the spin of the conduction electrons via the ex-
change interaction with the magnetic moments of ions
is, in general, so large as to inhibit superconductivity.
When an external magnetic field is applied, supercon-
ductivity is suppressed due to orbital and spin pair
breaking effects, as well. However, there are magnetic
metals, such as (EuSn)Mo6S8 [1,2] or HoMo6S8 [3],
where an applied magnetic field can induce super-
conductivity. Several mechanisms that may enable
superconductivity to develop in a ferromagnet or a
paramagnet have been investigated in more or less detail
(see [4,5] and references therein). One of them is the
so-called Jaccarino–Peter effect [6]. It takes place in
those para- and ferromagnetic metals, in which, due to
the Hund coupling energy, the exchange interaction,
JsS, orients the spins s of the conduction electrons
antiparallel to the spins S of rare-earth magnetic ions.
The effective field acting on the spin of a conduction
electron is � �B BH g J S� � �, with J � 0 (�B is the
Bohr magneton, g is the g factor). In such magnetic me-
tals the exchange field g J SB� � � can be reduced by an
external magnetic field �BH, so that the destructive
action of both fields on the conduction electrons can be
weakened or even canceled. If, in addition, these metals
posses an attractive electron–electron interaction, as, for
example, in pseudoternary compounds [5], it is possible
to induce bulk superconductivity by a magnetic field.
In this report, we consider the dc Josephson effect for
a tunnel structure where one electrode is a proximity-cou-
pled bilayer of a superconducting film (S) and a para-
magnetic metal (M), while the second electrode is an S
layer. The system is under the effect of a weak external
magnetic field, which by itself is insufficient to destroy
superconductivity. The dc critical current of such a junc-
tion has been calculated using an approximate micro-
scopic treatment based on the Gor’kov equations. We
discuss the case when in the M metal the localized para-
magnetic moments of the ions, oriented by magnetic field,
exert an effective interaction JsS on the spins of the con-
duction electrons. The latter, whether it arises from the
usual exchange interaction or due to configuration
mixing, according to Hund’s rules, is of the antifer-
romagnetic type, i.e., J � 0. In particular, such an M
metal could be a layer of pseudoternary compounds like
(EuSn)Mo6S8 or HoMo6S8. (While experimentally the
Jaccarino–Peter phenomenon was observed [1–5] for
© V.N. Krivoruchko and E.A. Koshina, 2005
paramagnets, this mechanism is applicable both to ferro-
magnetic and paramagnetic metals, and both type of the
magnetic orders will be assumed here.) We demonstrate
that in the region where the destructive action of the
fields on both tunnel electrodes is decreased, an increase
of the magnetic field causes enhancement of the
Josephson critical current.
2. The model
The system we are interested in is the (S/M)IS
layered structure of a superconducting S/M bilayer
and S films separated by a very thin insulating (I) bar-
rier (see Fig. 1). The S/M bilayer consists of proxim-
ity—coupled superconducting and paramagnetic met-
als in good electrical contact. It is assumed that the
thicknesses of the S layers are smaller than the super-
conducting coherence length and that the thickness of
the magnetic layer is smaller than the condensate pen-
etration length, i.e., dS S�� � and dM M�� � . Here
�S M( ) is the superconducting coherence length of the
S(M) layer; dS M( ) is the thickness of the S(M) layer.
In this case, the superconducting order parameter may
be regarded as being independent of the coordinates,
and the influence of the magnetic layer on the super-
conductivity is not local. Other physical quantities
characterizing the S/M bilayer are modified, as well.
Such an approach was recently discussed in [7,8] for
SFIFS structures, and, as was demonstrated, under
these assumptions, a thin S/F bilayer is equivalent to
a superconducting ferromagnetic film with a homoge-
neous superconducting order parameter and an effec-
tive exchange field. Similarly, we can consider the
S/M bilayer as a thin SM film which is characterized
by the effective values of the superconducting order
parameter � eff , the coupling constant �eff , and the ex-
change field HEeff that are determined by the follow-
ing relations:
� �eff eff/ / d d dS S S S M M �
� � � � �( ) ,1 (1)
H /H d d dE E M M S S M Meff �
� � �( ) ,1 (2)
where �S and �M are the densities of quasiparticles
states in the superconductor and magnetic metals, re-
spectively; � is the coupling constant in the S metal.
We emphasize that the superconductivity of the M
metal is due to the proximity effect. The applied
magnetic field is too weak to induce superconducting
properties through the Jaccarino–Peter scenario, if
the M metal is a pseudoternary compound. While in
the latter case the M metal can posses a nonzero
electron–electron interaction, we will neglect this
interaction, assuming for the M layer a vanishing
value of the bare superconducting order parameter
� M
0 0 , so that relation (1) still remains valid.
The system is under the effect of a parallel mag-
netic field H. We will also assume that the thicknesses
of the SM and S films are smaller than the London
penetration depth �SM and �S , respectively. Then the
magnetic field is homogeneous in both electrodes. The
conditions dS S�� � , dM M�� � ensure that orbital
effects can be neglected, as well. The longitudinal di-
mension of the junction, W, is assumed to be much
less than the Josephson penetration depth, W J�� � ,
so that a flux quantum cannot be trapped by the junc-
tion: HW d d tM S( )� � ��2 0
, where
0 is the flux
quantum and t is the thickness of the insulator.
If the transparency of the insulating layer is small
enough, we can neglect the effect of a tunnel current on
the superconducting state of the electrodes and use the
relation of the standard tunnel theory [9], according to
which the distribution of the Josephson current density
j xT ( ) flowing in the z direction through the barrier
(see Fig. 1) takes the form j x I xT C( ) sin ( ) � . Here
�( )x is the phase difference of the order parameter
across the barrier, while the Josephson current density
maximum IC is determined by the properties of the
electrodes. In this report we present the results of a cal-
culation of the critical current IC for the tunnel junc-
tion under consideration.
3. Critical current
Insofar as the exchange field and the external mag-
netic field act only on the spin of electrons, we can
write the Gor’kov equations for the S and SM layers
in the magnetic field in the form
( ) � � �
( ) ( ) ( ) ( )i H G Fn S SM S SM S SM S SM� � � � ��
� � 1,
(3)
Enhancement of the Josephson current by magnetic field
Fizika Nizkikh Temperatur, 2005, v. 31, No. 2 165
Id S W
dM
dS
M
y H
z
x
Fig. 1. (S/M)IS system in a parallel magnetic field. Here S
is a superconductor; M is a magnetic metal; I is an insulat-
ing barrier; W is the longitudinal dimension of the junction.
( ) � � � ,( ) ( ) ( ) ( )
�
� i H F Gn S SM S SM S SM S SM� � � � �� 0
(4)
where � � �
( )p F , �F is the Fermi energy; �( )p is
the quasiparticle spectrum; � �1; � �n T n �( )2 1 ,
n � � �0 1 2 3, , , ,... are Matsubara frequencies; T is
the temperature of the junction (here and below we
have taken the system of units with � �B Bk 1);
H H HSM E
eff is the resultant magnetic field in
the SM bilayer (the subscript SM) and HS H is the
magnetic field in the S layer (the subscript S); G�
and F� are normal and anomalous Green functions.
The equations are also supplemented with the
well-known self-consistency equations for the order
parameters. In the case of conventional singlet super-
conducting pairing, when �� � i y� (� y is Pauli ma-
trix), one can easily find (see, e.g., [8]):
ln
( )
�
�
0
S SM
�
�
�
�
�
�
�
�
dx
x x H x
S SM S SM S SM
D
2 2
0
2 2
1
1
1
� �
�
��
� �
( ) ( ) ( )exp [ ] exp[
�
� � 2 2 1� � �
�
�
�
�
�
!
�
"
��
S SM S SMH
( ) ( )]
(5)
where � �0 0 0 ( , ) is the BCS gap at zero temperature and in the absence of both the applied and the exchange
fields; �D is the Debye frequency; � 1/T; � SM SMT H( , ) and � S ST H( , ) are the superconducting order param-
eters of the SM and S electrodes, respectively. If HS SM( ) 0, formula (5) is reduced to Eq. (16.27) of Ref. 10.
In accordance with the Green’s function formalism, the critical current of the SMIS junction can bewritten as
follows:
I T/eR f H f HC N SM
n
SM S S #( ) ( ) ( ),
,
2�
�
Sp (6)
where RN is the contact resistance in the normal state and f SM S� ( ) are anomalous Green functions averaged over
energy �. From Eqs. (3) and (4) one can easily find that:
f i HSM S n SM S
/
� � �( ) ( )[( ) ] . � �
� �2 2 1 2 (7)
Using Eqs. (6) and (7), after summation over spin index, we find for the reduced (i.e., eR T IN C{ }4 0
2 1� �
)
quantity
j T H T H T HC SM SM S( , ) ( , ) ( , ) $
� � � 0
2
$
�
� �Re [( ( )) ( ,| | )][( ){ � �n E SM E ni H H T H H iHeff eff
2 2 2� � S
/
n
T H2 1 2( , )] .}
# (8)
The Josephson critical current of the junction, as
function of the fields and temperature, can be
calculated using formula (8) and self-consistency
equation (5). In the general case, the dependence of
the superconducting order parameter on effective
field can be rather complicated due to the possibility
of transition to the inhomogeneous (Larkin–Ovchin-
nikov–Fulde–Ferrell) phase [11,12]. We will not
touch upon this scenario here, restricting the consid-
eration below to the region with the homogeneous
superconducting state. Even in this case at arbitrary
temperatures the values of � SM ET H H( ,| | )eff
and
� S T H( , ) can be determined only numerically. The
phase diagram of a homogeneous superconducting
state in the H T
plane has been obtained earlier
(see, e.g., [8]). At finite temperatures, it is found
that �( , )T H has a sudden drop from a finite value to
zero at a threshold of H, exhibiting a first-order phase
transition from a superconducting state to a normal
state. Using these results, from Eq. (5) we take only
one branch of solutions, corresponding to a stable
homogeneous superconducting state. It should be also
noted that, insofar as H SE % � �, a self-consistency
equation should be used for HEeff , as well. However,
we will suppose that HEeff , while being much smaller
than in an isolated M film, is still larger than
� SM ET H H( ,| ( )| )eff
for the full temperature
region of the homogeneous superconducting state. So,
proceeding in such a way as to tackle the new
physics, we will ignore the temperature dependence
of HEeff in Eq. (8).
166 Fizika Nizkikh Temperatur, 2005, v. 31, No. 2
V.N. Krivoruchko and E.A. Koshina
Figures 2 and 3 show the results of numerical
calculations of expression (8) for the Josephson critical
current versus external magnetic field for the case of low
T TC 01. and finite T TC 0 7. temperatures, and
different values of the exchange field. To keep the discus-
sion simple, for the SM and S layers we put� SM( , )0 0
� �S ( , )0 0 0. As is seen in the figures, for some inter-
val of the applied magnetic field enhancement of the dc
Josephson current takes place in comparison with the case
H 0. Note that the larger the effective field HEeff is,
the larger the growth of the critical current that can be
observed (compare, for example, the jC curves for HEeff
= 0 4 0. � and HEeff = 0 6 0. � at H 0 in Fig. 2). This
behavior is also predicted by expression (8). The sudden
breakoff in the j HC( ) dependences in the presence of H
is due to a first-order phase transition from a supercon-
ducting state with finite �( , )T H to a normal state with
�( , )T H 0.
4. Discussion
As is well known [13,14], due to the difference in en-
ergy between spin-up and spin-down electrons and holes
under the exchange field of a ferromagnet, a singlet
Cooper pair, adiabatically injected from a superconduc-
tor into a ferromagnet, acquires a finite momentum. As a
result, the proximity-induced superconductivity of the F
layer is spatially inhomogeneous, and the order parame-
ter contains nodes where the phase changes by �. In par-
ticular, the transport properties of tunnel SF structures
have turned out to be quite unusual. The � state is char-
acterized by a phase shift of � in the ground state of the
junction and is formally described by a negative critical
current IC in the Josephson current–phase relation:
j IC( ) sin( )� � . The �-phase state of an SFS weak link
due to Cooper pair spatial oscillation was first predicted
by Buzdin et al. [15,16]. Experiments that have by now
been performed on SFS weak links [17,18] and SIFS
tunnel junctions [19] directly prove the �-phase super-
conductivity.
There is another interesting case of a thin F layer,
dF F�� � , being in contact with an S layer. Insofar as
the thickness of the F layer dF is much less than the
corresponding superconducting coherence length �F
there is spin splitting but no order parameter oscilla-
tion in the F layer. Surprisingly, but it was recently
predicted [7,8,20–24] that for SFIFS tunnel struc-
tures with very thin F layers one can, on condition of
parallel orientation of the F layers magnetization,
turn the junction into the �-phase state with the criti-
cal current inversion; if the internal fields of the F
layers have antiparallel orientation, one can even en-
hance the tunnel current. It is obvious that the physics
behind the inversion and the enhancement of the
supercurrent in this case differs from that proposed by
Buzdin et al. Namely, in this case the �-phase state is
due to a superconducting phase jump at the SF inter-
face [21,24]. The exchange-field enhancement of the
critical current for SFIFS tunnel structure can be
qualitatively understood using the simple fact that the
Cooper pairs consist of two electrons with opposite
spin directions. Pair-breaking effects due to spin-po-
larized electrons are weaker in the antiparallel-aligned
configuration, since the spin polarizations from the ex-
Enhancement of the Josephson current by magnetic field
Fizika Nizkikh Temperatur, 2005, v. 31, No. 2 167
0 0.2 0.4 0.6
H /� 0.3 (1)
Eeff 0
0.4 ( )
0.5 ( )
0.6 ( )
2
3
4
1
2
3
4
3.4
3.3
3.2
j
C
H/�0
Fig. 2. Critical current of the SMIS tunnel junction
versus external magnetic field for T TC 01. , �SM( , )0 0
� �S( , )0 0 0, and different values of the effective ex-
change field in the SM bilayer.
H / = 0.2 ( )� 1
Eeff 0
0.25 ( )
0.3 ( )
0.35 ( )
2
3
4
H/� 0
j
C
0.100
0.099
1
2
3
4
0 0.1 0.2 0.3
Fig. 3. Critical current of the SMIS tunnel junction ver-
sus external magnetic field for T TC 07. , �SM( , )0 0
� �S( , )0 0 0 and different values of the effective ex-
change field in the SM bilayer.
change fields of the F layers are of opposite signs and
under certain conditions can cancel each other. More
formally, one can show that the maximum of the
supercurrent is achieved exactly at those values of the
exchange field for which two singularities in the
quasiparticle density of states do overlap [23].
We emphasize that the scenario of the mag-
netic-field enhancement of the critical current dis-
cussed here differs from those studied before for
SFIFS tunnel structures. In our case the pair-breaking
effect due to spin-polarized electrons is weakened in
the SM electrode, since the spin polarizations from the
exchange field of the magnetic ions and the applied
field are of opposite signs and reduce each other. On
the other hand, the paramagnetic effect induced by
the external field is increased for the Cooper pairs of
the S electrode if the applied field is increased. Com-
petition between these two opposite effects determines
the critical current behavior for the SMIS junction in
magnetic field. In our case the mechanism described
above is valid for the full temperature region of the
homogeneous superconducting state (see, e.g.,
Fig. 3), while for the SFIFS system with antiparallel
geometry—only at low temperature T TC�� [7,8].
In conclusion, we have calculated the dc critical cur-
rent of an (S/M)IS tunnel structure in which one elec-
trode is a proximity-coupled bilayer of a superconducting
film and a paramagnetic metal, while the second elec-
trode is an S layer. The structure is under the effect of a
weak parallel external magnetic field. In the magnetic
metal the localized magnetic moments of the ions, ori-
ented by the magnetic field, exert the effective interac-
tion JsS on spins of the conduction electrons. The latter,
whether it arises from the usual exchange interaction or
due to configuration mixing, according to Hund’s rules,
is of the antiferromagnetic type, i.e., J � 0 . In particular,
such a film can be a layer of pseudoternary compounds
like (EuSn)Mo6S8, HoMo6S8, etc. There are no specific
requirements on the superconductor, so that it can be any
superconducting film proximity coupled with the mag-
netic metal. Using approximate microscopic treatment of
the S/M bilayer and the S layer, we have predicted the
effect of magnetic-field-induced supercurrent enhance-
ment in the tunnel structure. This striking behavior con-
trasts with the suppression of the critical current by mag-
netic field. The idea of using a magnetic material in which
the effective magnetic interaction aligns the spins of the
conduction electrons antiparallel to the localized spin of
the magnetic ions in order to enhance superconductivity
of superconductor—magnetic metal multilayered struc-
tures has not been considered before and, to the best of
our knowledge, is new. The existing large variety of mag-
netic materials, the ternary compounds in particular,
should allow experimental realization of this interesting
new effect of the interplay between superconducting and
magnetic orders.
We thank Dr. M. Belogolovskii for helpful discussions.
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