Percolation transitions in d-wave superconductor–half-metallic ferromagnet nanocomposites
Electrical transport properties of random binary networks composed of high-Tc superconductor Bi₂Sr₂Ca₂Cu₃O₆+x microparticles and half-metallic ferromagnet La₀.₆₇Sr0.₃₃MnO₃ (LSMO) nanoparticles have been investigated. Two resistive percolation transitions (superconductor–metal–semiconductor) have b...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
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irk-123456789-1760732021-02-04T01:28:37Z Percolation transitions in d-wave superconductor–half-metallic ferromagnet nanocomposites Krivoruchko, V.N. Tarenkov, V.Y. Надпровідність, зокрема високотемпературна Electrical transport properties of random binary networks composed of high-Tc superconductor Bi₂Sr₂Ca₂Cu₃O₆+x microparticles and half-metallic ferromagnet La₀.₆₇Sr0.₃₃MnO₃ (LSMO) nanoparticles have been investigated. Two resistive percolation transitions (superconductor–metal–semiconductor) have been observed for the nanocomposites with a volume fraction of the LSMO no more than 30%. The nanocomposites basic attributes (transition critical temperatures, current–voltage characteristics, percolation threshold, etc.), most probably, cannot be quantitatively interpreted within the framework of a conventional percolation model. We have explained the observed behavior by a two-level scale interaction in the system caused by (i) a significant geometric disparity between the constituent components and (ii) proximity-induced superconducting state of the half-metallic manganite. Досліджено електричні транспортні властивості хаотичних двокомпонентних структур, складених з мікрочастинок високотемпературного надпровідника Bi₂Sr₂Ca₂Cu₃O₆+x та наночастинок напівметалевого феромагнетика La₀.₆₇Sr0.₃₃MnO₃ (LSMO). Для нанокомпозитів з об’ємним складом LSMO не більше ніж 30% спостерігалися два резистивних перколяційних переходи (надпровідник–метал–напівпровідник). Основні характеристики нанокомпозитів (критичні температури переходів, вольт-амперні характеристики, поріг перколяційних переходів і т.п.), найбільш ймовірно, не можуть бути кількісно описані у рамках стандартної перколяційної моделі. Пояснено поведінку, що спостерігається, двома різними характерними масштабами взаємодії в системі, що обумовлено (i) істотною геометричною різницею її компонент та (іі) наведеним ефектом близькості надпровідним станом напівметалевого манганіту. Исследованы электрические транспортные свойства хаотических двухкомпонентных структур, составленных из микрочастиц высокотемпературного сверхпроводника Bi₂Sr₂Ca₂Cu₃O₆+x и наночастиц полуметаллического ферромагнетика La₀.₆₇Sr0.₃₃MnO₃ (LSMO). Для нанокомпозитов с объемным составом LSMO не более 30% наблюдались два резистивных перколяционные перехода (сверхпроводник–металл–полупроводник). Основные характеристики нанокомпозитов (критические температуры переходов, вольтамперные характеристики, порог перколяционных переходов и т.п.), наиболее вероятно, не могут быть количественно описаны в рамках стандартной перколяционной модели. Наблюдаемое поведение объяснено двумя различными характерными масштабами взаимодействия в системе, что обусловлено (i) существенной геометрической разницей ее компонент и (ii) индуцированным эффектом близости сверхпроводящим состоянием полуметаллического манганита 2019 Article Percolation transitions in d-wave superconductor–half-metallic ferromagnet nanocomposites / V.N. Krivoruchko, V.Y. Tarenkov // Физика низких температур. — 2019. — Т. 45, № 5. — С. 555-56. — Бібліогр.: 37 назв. — англ. 0132-6414 http://dspace.nbuv.gov.ua/handle/123456789/176073 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| topic |
Надпровідність, зокрема високотемпературна Надпровідність, зокрема високотемпературна |
| spellingShingle |
Надпровідність, зокрема високотемпературна Надпровідність, зокрема високотемпературна Krivoruchko, V.N. Tarenkov, V.Y. Percolation transitions in d-wave superconductor–half-metallic ferromagnet nanocomposites Физика низких температур |
| description |
Electrical transport properties of random binary networks composed of high-Tc superconductor Bi₂Sr₂Ca₂Cu₃O₆+x
microparticles and half-metallic ferromagnet La₀.₆₇Sr0.₃₃MnO₃ (LSMO) nanoparticles have been investigated. Two
resistive percolation transitions (superconductor–metal–semiconductor) have been observed for the nanocomposites
with a volume fraction of the LSMO no more than 30%. The nanocomposites basic attributes (transition critical temperatures, current–voltage characteristics, percolation threshold, etc.), most probably, cannot be quantitatively interpreted within the framework of a conventional percolation model. We have explained the observed behavior by a two-level
scale interaction in the system caused by (i) a significant geometric disparity between the constituent components and
(ii) proximity-induced superconducting state of the half-metallic manganite. |
| format |
Article |
| author |
Krivoruchko, V.N. Tarenkov, V.Y. |
| author_facet |
Krivoruchko, V.N. Tarenkov, V.Y. |
| author_sort |
Krivoruchko, V.N. |
| title |
Percolation transitions in d-wave superconductor–half-metallic ferromagnet nanocomposites |
| title_short |
Percolation transitions in d-wave superconductor–half-metallic ferromagnet nanocomposites |
| title_full |
Percolation transitions in d-wave superconductor–half-metallic ferromagnet nanocomposites |
| title_fullStr |
Percolation transitions in d-wave superconductor–half-metallic ferromagnet nanocomposites |
| title_full_unstemmed |
Percolation transitions in d-wave superconductor–half-metallic ferromagnet nanocomposites |
| title_sort |
percolation transitions in d-wave superconductor–half-metallic ferromagnet nanocomposites |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2019 |
| topic_facet |
Надпровідність, зокрема високотемпературна |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/176073 |
| citation_txt |
Percolation transitions in d-wave superconductor–half-metallic ferromagnet nanocomposites / V.N. Krivoruchko, V.Y. Tarenkov // Физика низких температур. — 2019. — Т. 45, № 5. — С. 555-56. — Бібліогр.: 37 назв. — англ. |
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Физика низких температур |
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2025-07-15T13:41:29Z |
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2025-07-15T13:41:29Z |
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| fulltext |
Low Temperature Physics/Fizika Nizkikh Temperatur, 2019, v. 45, No. 5, pp. 555–561
Percolation transitions in d-wave superconductor–half-metallic
ferromagnet nanocomposites
V.N. Krivoruchko and V.Yu. Tarenkov
Donetsk Institute for Physics and Engineering of the NAS of Ukraine, 46 Prospect Nauki, Kyev 03028, Ukraine
E-mail: krivoruc@gmail.com
Received October 30, 2018, revised December 13, 2018, published online March 26, 2019
Electrical transport properties of random binary networks composed of high-Tc superconductor Bi2Sr2Ca2Cu3O6+x
microparticles and half-metallic ferromagnet La0.67Sr0.33MnO3 (LSMO) nanoparticles have been investigated. Two
resistive percolation transitions (superconductor–metal–semiconductor) have been observed for the nanocomposites
with a volume fraction of the LSMO no more than 30%. The nanocomposites basic attributes (transition critical tem-
peratures, current–voltage characteristics, percolation threshold, etc.), most probably, cannot be quantitatively interpret-
ed within the framework of a conventional percolation model. We have explained the observed behavior by a two-level
scale interaction in the system caused by (i) a significant geometric disparity between the constituent components and
(ii) proximity-induced superconducting state of the half-metallic manganite.
Keywords: nanocomposite, d-wave superconductor, half-metallic ferromagnet, resistive percolation transition.
1. Introduction
A common feature of a random insulator–conductor
mixture is a sharp increase in an overall conductivity once
a critical volume of the conductive phase is reached. This
transition is generally interpreted as formation of a cluster
of electrically connected conductor particles which spans
the entire sample. This picture implies a power-low behav-
ior of the conductivity in the vicinity of the percolation
transition [1–3]. However, in the more general cases with a
variable coupling strength or few-level scales characteriz-
ing different geometrical lengths, the conductivity behavior
may be non-universal [4–6]. When indirect interaction
between the constituents exists or additional degrees of
freedom become available, this leads to a new or non-
universal behavior of the composite system. An example is
electrical percolation transitions in a system where a super-
conductor and a ferromagnetic metal are counterpartners. In
this case, percolation effects can be more complicated as
far as the electrical coupling between constituent compo-
nents can be both direct, geometric contact, and indirect
one, via spin-dependent proximity effects. Hybrid half-
metallic ferromagnet (hmF)–superconductor (SC) random
composite structures can enable new intelligently tailored
functionality and have gained attention over the past few
years as new functional materials [4,7–10].
A special case is hmF–SC nanocomposites. Here, due
to proximity effects, there are many important issues be-
yond the conventional percolation theory [1–3]. The point
is that for nanoparticles the geometric contacts and electri-
cal connectivity of individual particles are often not the
same [11,12]. So far, a few works have been reported on
investigations of transport properties of a SC with half-
metallic magnetic nanoparticles composites. Unconven-
tional double percolation transition is identified in Ref. 4
for a binary network composed of nanoparticles of MgB2
and CrO2. Here the double percolation transition (super-
conductor–insulator–metal) was especially pronounced at
liquid helium temperatures. It is controlled by the compo-
nents volume fractions and originates from the suppressed
interface conduction and tunneling as well as a large geo-
metric disparity between particles [4]. Acharya et al. [9]
prepared and studied electrical transport characteristics of
Bi2Sr2CaCu2O8/BiFeO3 nanocomposite with various
weight percentage of BiFeO3 nanoparticles (BiFeO3 in
nanoform is insulating and exhibits superparamagnetism).
Measurement of the critical current density reveals that the
superconducting transition temperature splits into two, Tc1
and Tc2, along with a broadening of overall superconduct-
ing transition. Authors accounted such behavior to the
weak-link nature of a granular SC as the latter is composed
of superconducting grains embedded in a nonsuper-
conducting host. Of the two superconducting transitions
temperatures, the higher one, Tc1, marks the superconduc-
tivity in grains whereas the grain boundary still remains
normal, and the lower one, Tc2, emerges when the grain
boundary also becomes superconducting. The appearance
of additional transition temperature and its broadening
© V.N. Krivoruchko and V.Yu. Tarenkov, 2019
V.N. Krivoruchko and V.Yu. Tarenkov
clearly reflects that BiFeO3 goes to the grain boundary
region and becomes superconducting only due to the prox-
imity effect at lower temperatures [9].
In this paper, we report on the results of experimental
investigations of electrical percolation transitions in ran-
dom binary nanocomposites, which have been composed
of cuprate SC Bi2Sr2Ca2Cu3O6+x (Bi2223) microparticles
and hmF La0.67Sr0.33MnO3 (LSMO) nanoparticles. Name-
ly, we designed and fabricated a number of random
nanocrystalline samples by combining with different vol-
ume ratios the hmF and d-wave SC components. This al-
lowed us to investigate the percolation effects in electrical
transport characteristics of the nanocomposites. An unusu-
ally large value of the concentration threshold for Bi2223
is detected for the realization a double percolation transi-
tion superconductor–metal–semiconductor. We argue that
the observed behavior is due to two different length scales
of effective interaction in the system and is specified by:
(i) a significant geometric disparity between the constituent
particles and (ii) an unconventional (most probably, triplet)
superconducting state induced in the nanocomposite by
spin-dependent superconducting proximity effect [13].
The structure of the paper is as follows. Section 2 is de-
voted to the experimental details. Section 3 is a central one.
To obtain a reference data, we start with measurements of the
resistance temperature dependences for compacted samples
of pure Bi2223 microparticles and LSMO nanoparticles (Sec.
3.1). In Secs. 3.2 and 3.3, the electrical transport characteris-
tics of the nanocomposites are presented at above and below
the metal–semiconductor transition temperature, respectively.
We discuss the experimental results in the context of a two-
level percolation process in the hmF:SC random nano-
composite, along with a splitting of overall superconducting
transition. We finalize with the Conclusion (Sec. 4).
2. Methods of preparation and samples
A series of nanocomposite samples have been fabri-
cated. The composites are prepared by mixing the cuprate
d-wave SC Bi2223 (Bi2Sr2Ca2Cu3O6+x, the superconduct-
ing transition temperature in the interval Tc = 100–110 K)
and the manganite LSMO (La0.67Sr0.33MnO3, the Curie
temperature TC ≈ 360 K of monocrystalline samples) with
a different volume content of the components. A specific
feature of the composites is that the high-Tc SC is used a
powder with a grain size of 5–15 μm, while the manganite
LSMO is a nanopowder with a particle size of 20–30 nm.
Note that the coherence length of Bi2223 is anisotropic
with ξab(0) ≈ 2 nm in the ab plane, which is a typical val-
ue for cuprate oxides, and along the c-axis direction ξc(0)
is less than 0.02 nm. Hence, the size of the Bi2223 grains
was much larger than the superconducting coherence
length.
Details of the LSMO nanoparticle preparation can be
found in Refs. 14, 15. Magnetization measurements, in
particular, the nuclear magnetic resonance and the nuclear
spin-spin relaxation of 55Mn nuclei of nanopowders and
polycrystalline samples of the same composition con-
firmed that manganite nanoparticles of such sizes retain
their magnetic properties and the double exchange mecha-
nism of magnetic interaction (and thus, half-metallic prop-
erties) [16,17].
The samples were prepared by using a traditional cold-
pressed technique. The raw materials were mixed accord-
ing to their volume ratios. A homogeneous composition
was achieved by mixing the components in alcohol, fol-
lowed by drying and an additional mechanical mixing at
temperature above the Curie to avoid magnetic coupling of
the manganite nanoparticles. Plates with dimensions
1×0.2×10 mm were then compacted at pressures up to P =
= 40–60 kbar from the resulting mixture. Such pressure
provides a good electrical connection between the grains
and high mechanical strength of the plate. The samples
were not subjected to sintering in order to avoid
interdiffusion and chemical reaction between the compo-
nents. Four contacts for current and potential measure-
ments were formed by introducing fine silver paste to the
designated contact region on the plate. Samples of different
compositions were prepared according to the volume frac-
tion, percentagewise, of the components LSMO:Bi2223 =
= 0:100, 10:90, 20:80, 25:75, 30:70, 40:60, 50:50, 100:0.
Inset in Fig. 1 sketches out the nanocomposite obtained
structure.
The current–voltage (I–V) characteristics were meas-
ured by using a conventional four-terminal technique. Re-
sistivity as a function of temperature was measured direct-
ly by using an ac voltage bias source with a small output
resistance and ~ 400 μV amplitude of the signal on the
sample. We measured electrical transport characteristics of
the samples and studied the percolation transition depen-
dence on the sample’s composition.
Fig. 1. Resistivity-vs-temperature dependences for pure compact-
ed samples of Bi2223 microparticles and LSMO nanoparticles.
Inset: sketch of the nanocomposite structure.
556 Low Temperature Physics/Fizika Nizkikh Temperatur, 2019, v. 45, No. 5
Percolation transitions in d-wave superconductor–half-metallic ferromagnet nanocomposites
3. Results and discussions
3.1. Pure compacted samples
The Bi–Sr–Ca–Cu–O system is known to have three
types of structures, namely Bi2Sr2Cu2O6+x (Bi2223),
Bi2Sr2CaCu2O6+x (Bi2212) and Bi2Sr2Cu2O6+x (Bi2201),
which have the critical temperature Tc of about 100, 85 and
20 K, respectively. No more than 15% of residual second-
ary phase Bi2212 has been detected in our compacted
Bi2223 samples by x-ray diffraction studies. Note, that the
residual Bi2212 phase localizes, mainly, at grain bounda-
ries of the Bi2223 phase [18].
The temperature behavior of the pure compacted Bi-2223
sample resistivity, R(T), is shown in Fig. 1. As seen in the
figure, the superconducting transition of the compacted
Bi2223 is in the interval 65–100 K and R(T) dependence
contains two decreasing segments which correspond to
Bi2223 and Bi2212 transitions to a superconducting state.
This points that a granular structure of the sample does not
affect a global sample superconductivity. The supercon-
ducting state is consolidated at ~ 65 K. Accordingly, the
compacted Bi2223 samples contain transparent interfaces
and strong links among grains. Above Tc, the sample is a
good conductor with low resistivity.
The LSMO sample’s zero-field R(T) characteristic is
shown in Fig. 1, as well. It demonstrates a metal–semi-
conductor transition at Tp ≈ 280 K (for bulk LSMO Tp ≈
≈ 360 K [19]) and a metallic behavior at low temperature.
Figure 2 illustrates the LSMO sample magnetoresistive
characteristics. The low-field (H ≈ 1 kOe) magneto-
resistive effect [ρ(T,0) – ρ(T,H)]/ρ(T,0) at T = 77 K was
about 10%. This suggests that the contribution of inter
granular junctions to the total sample resistance is relative-
ly small and confirms high quality of the nanoceramic
LSMO sample. We find it convenient to describe the
LSMO R(T) behavior in terms of the magnetic polaron
picture [20]. The main assumption of the theory [20] is that
it does not demand the existence of an abrupt metal–insu-
lator transition in doped manganites. Instead, the theory
predicts the coexistence of two electronic processes:
(i) energy-conserving tunneling process and (ii) thermally
assisted hopping process. Both processes are temperature
dependent and, with increasing temperature, the probability
of tunneling process decreases, while the probability of hop-
ping process increases. At intermediate temperature, near the
R(T) peak, the hopping process overgrows the tunneling one
and the sample behaves as an insulator (semiconductor) at
higher temperatures. The peak temperature Tp should not
coincide with the Curie temperature TC, nevertheless, it
correlates with the TC since they both are dependent on the
number of thermal magnons.
3.2. Composites’ transport characteristics at T > Tp
Let us start the discussion of the composite transport
characteristics at temperatures when LSMO behaves as an
insulator and we deal with random insulator–conductor mix-
tures. Figure 3 shows the dependence of the LSMO:Bi2223
nanocomposite resistivity R(T) on the volume content of
LSMO at T = 300 K. A rapid change in the sample’s resis-
tivity occurs in the vicinity of about 20 vol.% of LSMO.
As we see (left, logarithmic, axis in Fig. 3), as Bi2223 grains
are sufficiently decoupled, at fixed temperature the re-
sistance is controlled by a tunneling process and is given by
R = R0 exp (rij/ζ). (1)
Here R0 = R(VLSMO = 0) is a constant (or a weak function of
the LSMO volume content), ζ is the characteristic tunnel-
ing length, and is rij is the minimal distance between the
two Bi2223 particles.
As is known (see, e.g., [3]), the electrical conductivity
of a composite generated on a mechanical mixture of the
components is determined by the structure of the conduc-
Fig. 2. Compacted LSMO sample low-field magnetoresistive
effect; T = 77 K.
Fig. 3. Dependence of the LSMO:Bi2223 nanocomposite resis-
tivity R(T) on the volume content of LSMO; R0 = R(VLSMO = 0),
T = 300 K.
Low Temperature Physics/Fizika Nizkikh Temperatur, 2019, v. 45, No. 5 557
V.N. Krivoruchko and V.Yu. Tarenkov
tive percolation cluster arising in the system. If an infinite
percolation cluster for a highly conductive phase is broken,
transport properties of the composite are determined by a
high-resistive ingredient. In our case, the choice of Bi2223
as a matrix is justified by a high conductivity of the com-
pacted Bi2223 powder, as well as its well pronounced me-
tallic behavior indicating clean grain boundaries of
Bi2223. Since electron mean free path in manganite oxides
is quite small [19], we can assume that the electron
transport is of the diffusive type. Thus, in our case, the
high-resistive component is LSMO manganite. We find
that the nanocomposites resistance behavior on the LSMO
concentration, R(VLSMO) Eq. (1), is compatible with the
tunneling-percolation model [5]. According to the ap-
proach [5], in the intermediate regime between the percola-
tion-like and the hopping-like electronic processes the tun-
neling between particles is a continuous function of the
interparticle distances. Correspondingly, the resulting tun-
neling conductance of a nanocomposite decays exponen-
tially with these distances and does not imply any sharp
cutoff or threshold.
Significant deviation of R(VLSMO) from the conventional
percolation theory, which predicts a power-law behavior of
the conductance [3], we ascribe to a large geometric dis-
parity between the components and a polaron-type con-
ductivity of half-metallic manganites. As it follows from
Fig. 3, already 30 vol.% of the LSMO nanoparticles coat
the Bi2223 grains surface, preventing direct contact be-
tween them (see inset in Fig. 1). As a result, the resistance
of the composite is determined by the current flowing
through the –Bi2223–LSMO–Bi2223-channels. Above Tp
this leads to a hopping-like regime in the nanocomposite’s
electrical conductivity. Therefore, the metal–semiconductor
transition is a continuous function of the nanoparticles con-
centration and does not demonstrate a sharp cutoff or a
percolation threshold.
3.3. Composites’ transport characteristics at T < Tp
The temperature dependences of the nanocomposites
resistivity R(T) below Tp are shown in Fig. 4 for 20, 25, 30,
40, and 50 vol.% of LSMO. As seen in the figure, the addi-
tion of already 20 vol.% of LSMO significantly broadens
the resistive superconducting transition R(T) of the
nanocomposite. The resistance of the sample with 40 vol.%
of LSMO nanoparticles remains finite in all investigated
temperature range, although the onset of the R(T) reduction
matches the Tc of Bi2223.
Figure 5 illustrates the I–V characteristic of the samples
with 20, 25, and 30 vol.% of LSMO taken at 4.2 K. We ob-
serve a clear zero-resistance supercurrent branch, with an ex-
cess current Iexc of 0.32, 0.27, and 0.12 mA, respectively. The
presence of ferromagnetic LSMO nanoparticles causes the
formation of weak links at the grain’s boundaries, as well as a
local magnetic field of the hmF particles certainly limits the
critical current density in the nanocomposite [21].
As it follows from R(T) characteristics, Fig. 4, the su-
perconducting transition temperature splits into two, Tc1
and Tc2, along with a broadening of overall superconduct-
ing transition. The higher temperature, Tc1, marks the su-
perconductivity of Bi2223 grains whereas the grain bound-
ary still remains normal. The lower one, Tc2, appears when
the grain boundary becomes superconducting as well. One
of the possible origins of the second superconducting tran-
sition is the presence of the additional phases Bi2212
which has the critical temperature of about 80 K. Another
possibility is the unconventional superconducting state (a
mixture of singlet and triplet correlations) induced in the
nanocomposite.
Superconductivity in bulk composite systems was exten-
sively studied within the percolation scenario [4,8,9,11,12].
It has been established that when grains of the supercon-
ducting material, d, are large enough, d >> ξS, their basic
intra-granular characteristics (critical temperature, gap
value, etc.) are not affected by the proximity of the non-
Fig. 4. (Color online) Temperature dependences of the nanocom-
posite’s resistivity with the volume fraction, percentagewise, 20,
25, 30, 40, and 50 vol.% of the LSMO.
Fig. 5. (Color online) Current–voltage characteristics for the
nanocomposites with 20, 25, and 30 vol.% of LSMO at 4.2 K.
558 Low Temperature Physics/Fizika Nizkikh Temperatur, 2019, v. 45, No. 5
Percolation transitions in d-wave superconductor–half-metallic ferromagnet nanocomposites
superconducting component and remain close to the bulk
value both above and below the percolation threshold. For
a three-dimensional composite with roughly the same geo-
metrical size of components, the three-dimensional lattice
percolation model predicts fC = 0.16 ± 0.02 for the percola-
tion threshold of the volume fraction, f, of a superconduct-
ing component (i.e., fC being a percolation threshold of
grains with linear dimension ≳ ξS). Thus, for the composite
systems under consideration with the large enough grains
of the superconducting material, below the percolation
threshold the macroscopic transition temperature Tc should
not be strongly dependent on the contents variation. How-
ever, as it is seen in Fig. 4, even for the sample with vol-
ume fraction about f = 0.5, i.e., about three times larger
than the conventional percolation model predicts, there is
no transition into a superconducting state. Moreover, the
transition temperature Tc is strongly reduced even at con-
centrations when an infinite percolating cluster of Bi2223
constitutes: see R(T) data in Fig. 4 for the samples with 20,
25, and 30 vol.% of LSMO (80, 75, and 70 vol.% of the
superconducting component). Thus, the predictions based
on the conventional percolation model do not work for the
Bi2223:LSMO nanocomposites, most probably, due to two
factors: (i) unconventional proximity effect and (ii) essen-
tial difference in geometrical size of the components.
As is known, below a superconducting transition an indi-
rect (via proximity effect) coupling between constituent
components, SC and hmF, enters into a force. From a theo-
retical viewpoint [13,22–24], the appearance of a long-range
proximity effect can be realized if there is a spatial variation
of the magnetization at the ferromagnet surface. In this case,
the spin conservation low is not fulfilled and a triplet com-
ponent of anomalous correlations should be taken into con-
sideration. A characteristic coherence length of triplet corre-
lations ξF = (DF/2πT)1/2 can be as large as ~ 100 nm at low
temperatures (here DF is the diffusivity of the ferromagnet
metal and T is the temperature; we choose h = kB = 1). In
previous papers, anomalous superconductivity has been de-
tected in nanocomposites MgB2:La0.67Sr0.33MnO3 [25] and
MgB2:La0.7Ca0.3MnO3 [10], as well as in half-metallic
manganite, (La,Sr)MnO3 and (La,Ca)MnO3, being in con-
tact with an s-wave SC, Pb or MgB2 [26–28]. It was argued
that at low-temperatures manganites are thermodynamically
very close to a superconducting state with a triplet p-wave
even frequency pairing. Being proximity coupled to the
singlet SC, the m = 0 triplet component in the manganite is
coupled via the boundary condition to the singlet pairing
amplitude in the SC partner. At the same time, the spin-
active boundary leads to coupling of the m = 0 triplet com-
ponent with an equal-spin, m = 1, pairing amplitude in
manganite. These couplings yield phase coherency of both
the m = 0 and equal-spin m = 1 triplet Cooper pairs in the
hmF with a large quasiparticle gap [29].
Thus, in the case of the nanocomposite under consid-
eration, proximity effect possesses a several specific pe-
culiarities. Firstly, because the contacts between Bi2223
grains are through the half-metallic LSMO nanograins,
this causes a significant broadening of the nanocompo-
sites transition to a superconducting state. The depend-
ence of the superconducting properties on the exchange
field inhomogeneity is expected to be a general feature
of the proximity effect in mesoscopic F–SC structures
[13,24]. Secondly, high-Tc superconductors are widely
believed to have a dominant d-wave pairing symmetry
[30]. As theory predicts and experiment provides eviden-
ces (see, e.g., [13,24,31–36]), in proximity coupled d-wave
SC/ferromagnet structures an unconventional (spin-triplet)
superconducting state can be generated. This also means
the appearance of a new geometrical length which charac-
terizes unconventional superconducting state (a mixture of
d-wave singlet and p-wave triplet Cooper pairs) induced in
the nanocomposite. To date, we know of no reports ad-
dressing the scenario for anomalous superconductivity of
high-Tc d-wave SC–hmF nanocomposites and proximity
effects in such type of nanocomposites.
4. Conclusion
Unconventional superconducting state induced in a hmF
by d-wave SC bears a great fundamental interest and can be
useful for future applications in superconducting spintronics
(see, e.g., [37] and references therein). Traditional search of
materials for superconducting spintronics have mainly fo-
cused on multilayers and engineering of interfaces between
SC and ferromagnetic materials. The aim is to find the ways
to enhance the triplet state critical temperature and to gener-
ate a long-ranged spin-triplet state. Yet, in our opinion, there
are other ways to produce materials demonstrating long-
ranged spin-triplet correlations. A direct coupling of high-
temperature superconducting and magnetic orders can be
possible through a creation of the spin-triplet Cooper pairs in
nanocomposite materials.
In summary, we have studied random nanocomposites
of a half-metallic ferromagnet and a high-temperature su-
perconductor with different volume fractions and a large
geometrical disparity: nanoparticles of La0.67Sr0.33MnO3
and microparticles of Bi2Sr2Ca2Cu3O6+x. We have investi-
gated transport characteristics of the nanocomposites and,
in particular, a superconducting percolation transition aris-
ing through contacts between the components. It was found
that the classical percolation theory is strongly affected by
both a large geometrical disparity between components and
by the proximity effect. Double resistive percolation transi-
tion (superconductor–metal–semiconductor) has been ob-
served for nanocomposites with the volume fraction of
LSMO below 30%. The observed behavior is due to two
different effective length scales which reflect a two-level
scale interaction in the system. One is determined by a geo-
metric difference between constituent components, whereas
the another arises due to proximity effect. We have argued
Low Temperature Physics/Fizika Nizkikh Temperatur, 2019, v. 45, No. 5 559
V.N. Krivoruchko and V.Yu. Tarenkov
that the constituent particle geometrical size and indirect
interaction via proximity effect play a crucial role in
achieving conditions enabling the percolation transitions in
the nanocomposites under consideration. The unusual
transport properties of this type nanocomposites bear great
fundamental interest and make their promise for applica-
tions, e.g., as novel functional materials.
Acknowledgments
The authors are grateful to I. Danilenko and O. Gorban’
for the preparation of manganite nanoparticles, and
A.D. Rud’ for x-ray diffraction measurements. We also
thank M.A. Belogolovskii for fruitful discussions. The
work was supported by the supported by the Science and
Technology Center in Ukraine and the National Academy
of Sciences of Ukraine (project No: 6250).
_______
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___________________________
Перколяційні переходи у нанокомпозитах
d-хвильовий надпровідник–феромагнітний
напівметал
Досліджено електричні транспортні властивості хаотич-
них двокомпонентних структур, складених з мікрочастинок
високотемпературного надпровідника Bi2Sr2Ca2Cu3O6+x та
наночастинок напівметалевого феромагнетика La0,67Sr0,33MnO3
(LSMO). Для нанокомпозитів з об’ємним складом LSMO не
більше ніж 30% спостерігалися два резистивних перколяцій-
них переходи (надпровідник–метал–напівпровідник). Основ-
ні характеристики нанокомпозитів (критичні температури
переходів, вольт-амперні характеристики, поріг перколяцій-
них переходів і т.п.), найбільш ймовірно, не можуть бути
кількісно описані у рамках стандартної перколяційної моде-
560 Low Temperature Physics/Fizika Nizkikh Temperatur, 2019, v. 45, No. 5
https://doi.org/10.1103/RevModPhys.45.574
https://doi.org/10.1023/A:1009997800513
https://doi.org/10.1088/0022-3727/42/6/064003
https://doi.org/10.1103/PhysRevLett.104.035701
https://doi.org/10.1103/PhysRevLett.104.035701
https://doi.org/10.1103/PhysRevB.81.155434
https://doi.org/10.1103/PhysRevE.85.021109
https://doi.org/10.1103/PhysRevB.59.12196
https://doi.org/10.1103/PhysRevB.76.224528
https://doi.org/10.1063/1.4751277
https://doi.org/10.1063/1.4915909
https://doi.org/10.1063/1.4915909
https://doi.org/10.1103/PhysRevB.71.064515
https://doi.org/10.1088/1367-2630/15/10/103025
https://doi.org/10.1103/PhysRevB.69.024413
https://doi.org/10.1016/j.jmmm.2005.10.163
https://doi.org/10.1063/1.2747068
https://doi.org/10.1063/1.3603003
https://doi.org/10.1016/S0921-4534(00)00326-9
https://doi.org/10.1016/S0370-1573(00)00121-6
https://doi.org/10.1063/1.361717
https://doi.org/10.1007/s10948-012-1455-y
https://doi.org/10.1007/s10948-012-1455-y
https://doi.org/10.1103/PhysRevLett.86.4096
https://doi.org/10.1103/PhysRevLett.86.4096
https://doi.org/10.1209/epl/i2001-00107-2
https://doi.org/10.1209/epl/i2001-00107-2
https://doi.org/10.1103/PhysRevLett.90.137003
https://doi.org/10.1103/PhysRevLett.90.137003
https://doi.org/10.1103/PhysRevB.86.104502
https://doi.org/10.1209/epl/i2006-10115-8
https://doi.org/10.1103/PhysRevB.75.214508
https://doi.org/10.1103/PhysRevB.78.054522
https://doi.org/10.1063/1.4897410
https://doi.org/10.1103/RevModPhys.72.969
https://doi.org/10.1103/PhysRevLett.98.057005
https://doi.org/10.1007/s10948-016-3482-6
https://doi.org/10.1103/PhysRevB.80.144504
https://doi.org/10.1103/PhysRevB.83.064510
https://doi.org/10.1103/PhysRevB.83.064510
https://doi.org/10.1103/PhysRevLett.108.197201
Percolation transitions in d-wave superconductor–half-metallic ferromagnet nanocomposites
лі. Пояснено поведінку, що спостерігається, двома різними
характерними масштабами взаємодії в системі, що обумов-
лено (i) істотною геометричною різницею її компонент та (іі)
наведеним ефектом близькості надпровідним станом напів-
металевого манганіту.
Ключові слова: нанокомпозит, d-хвильовий надпровідник, напі-
вметалевий феромагнетик, резистивні перколяційні переходи.
Перколяционные переходы в нанокомпозитах
d-волновой сверхпроводник–ферромагнитный
полуметалл
В.Н. Криворучко, В.Ю. Таренков
Исследованы электрические транспортные свойства
хаотических двухкомпонентных структур, составленных
из микрочастиц высокотемпературного сверхпроводника
Bi2Sr2Ca2Cu3O6+x и наночастиц полуметаллического фер-
ромагнетика La0,67Sr0,33MnO3 (LSMO). Для нанокомпози-
тов с объемным составом LSMO не более 30% наблюдались
два резистивных перколяционные перехода (сверхпровод-
ник–металл–полупроводник). Основные характеристики нано-
композитов (критические температуры переходов, вольт-
амперные характеристики, порог перколяционных перехо-
дов и т.п.), наиболее вероятно, не могут быть количествен-
но описаны в рамках стандартной перколяционной модели.
Наблюдаемое поведение объяснено двумя различными ха-
рактерными масштабами взаимодействия в системе, что обу-
словлено (i) существенной геометрической разницей ее ком-
понент и (ii) индуцированным эффектом близости сверх-
проводящим состоянием полуметаллического манганита.
Ключевые слова: нанокомпозит, d-волновой сверхпровод-
ник, полуметаллический ферромагнетик, резистивные пер-
коляционные переходы.
Low Temperature Physics/Fizika Nizkikh Temperatur, 2019, v. 45, No. 5 561
1. Introduction
2. Methods of preparation and samples
3. Results and discussions
3.1. Pure compacted samples
3.2. Composites’ transport characteristics at T > Tp
3.3. Composites’ transport characteristics at T < Tp
4. Conclusion
Acknowledgments
|