Andreev reflection study of a new magnetic superconductor Mo3Sb7 in magnetic field
Andreev reflection in contacts based on a magnetic superconductorMo3Sb7in magnetic field has been investigated by the point-contact method. It is found that the behavior of the order parameter in the magnetic field Δ(H) is essentially dependent on the value of Δ, which varies widely (Δ(0,0) ≈ 0.01-0...
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nasplib_isofts_kiev_ua-123456789-77642025-02-23T19:30:31Z Andreev reflection study of a new magnetic superconductor Mo3Sb7 in magnetic field Dmitriev, V.M. Rybaltchenko, L.F. Ishchenko, L.A. Khristenko, E.V. Bukowski, Z. Troć, R. Сверхпроводимость, в том числе высокотемпературная Andreev reflection in contacts based on a magnetic superconductorMo3Sb7in magnetic field has been investigated by the point-contact method. It is found that the behavior of the order parameter in the magnetic field Δ(H) is essentially dependent on the value of Δ, which varies widely (Δ(0,0) ≈ 0.01-0.31meV) for different contacts at practically invariant Tc. At high the dependence max(H)deviates slightly from the theoretical prediction applicable under the point-contact conditions. As the order parameter decreases, the deviation starts to increase and becomes very large when Δ approaches its minimum. Proceeding from the results obtained in this study and from the temperature measurements on Mo3Sb7performed formerly, we are inclined as before to assign the compound to the class of superconductors with anisotropic gap function. So, in no way can it be considered as conventional BCS-type superconductor. The upper critical field Hc2 ≈16.5 kOe found here is close to that obtained from magnetization measurements in another study. According to the estimation performed, the pair-breaking effect of the Pauli paramagnetism is rather weak in Mo3Sb7. 2007 Article Andreev reflection study of a new magnetic superconductor Mo3Sb7 in magnetic field / V.M. Dmitriev, L.F. Rybaltchenko, L.A. Ishchenko, E.V. Khristenko, Z. Bukowski, R. Troć // Физика низких температур. — 2007. — Т. 33, № 12. — С. 1331-1337. — Бібліогр.: 24 назв. — англ. 0132-6414 https://nasplib.isofts.kiev.ua/handle/123456789/7764 en application/pdf Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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Сверхпроводимость, в том числе высокотемпературная Сверхпроводимость, в том числе высокотемпературная |
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Сверхпроводимость, в том числе высокотемпературная Сверхпроводимость, в том числе высокотемпературная Dmitriev, V.M. Rybaltchenko, L.F. Ishchenko, L.A. Khristenko, E.V. Bukowski, Z. Troć, R. Andreev reflection study of a new magnetic superconductor Mo3Sb7 in magnetic field |
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Andreev reflection in contacts based on a magnetic superconductorMo3Sb7in magnetic field has been investigated by the point-contact method. It is found that the behavior of the order parameter in the magnetic field Δ(H) is essentially dependent on the value of Δ, which varies widely (Δ(0,0) ≈ 0.01-0.31meV) for different contacts at practically invariant Tc. At high the dependence max(H)deviates slightly from the theoretical prediction applicable under the point-contact conditions. As the order parameter decreases, the deviation starts to increase and becomes very large when Δ approaches its minimum. Proceeding from the results obtained in this study and from the temperature measurements on Mo3Sb7performed formerly, we are inclined as before to assign the compound to the class of superconductors with anisotropic gap function. So, in no way can it be considered as conventional BCS-type superconductor. The upper critical field Hc2 ≈16.5 kOe found here is close to that obtained from magnetization measurements in another study. According to the estimation performed, the pair-breaking effect of the Pauli paramagnetism is rather weak in Mo3Sb7. |
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Dmitriev, V.M. Rybaltchenko, L.F. Ishchenko, L.A. Khristenko, E.V. Bukowski, Z. Troć, R. |
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Dmitriev, V.M. Rybaltchenko, L.F. Ishchenko, L.A. Khristenko, E.V. Bukowski, Z. Troć, R. |
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Dmitriev, V.M. |
| title |
Andreev reflection study of a new magnetic superconductor Mo3Sb7 in magnetic field |
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Andreev reflection study of a new magnetic superconductor Mo3Sb7 in magnetic field |
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Andreev reflection study of a new magnetic superconductor Mo3Sb7 in magnetic field |
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Andreev reflection study of a new magnetic superconductor Mo3Sb7 in magnetic field |
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Andreev reflection study of a new magnetic superconductor Mo3Sb7 in magnetic field |
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andreev reflection study of a new magnetic superconductor mo3sb7 in magnetic field |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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Сверхпроводимость, в том числе высокотемпературная |
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Andreev reflection study of a new magnetic superconductor Mo3Sb7 in magnetic field / V.M. Dmitriev, L.F. Rybaltchenko, L.A. Ishchenko, E.V. Khristenko, Z. Bukowski, R. Troć // Физика низких температур. — 2007. — Т. 33, № 12. — С. 1331-1337. — Бібліогр.: 24 назв. — англ. |
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Fizika Nizkikh Temperatur, 2007, v. 33, No. 12, p. 1331–1337
Andreev reflection study of a new magnetic
superconductor Mo3Sb7 in magnetic field
V.M. Dmitriev1,2, L.F. Rybaltchenko1, L.A. Ishchenko1, E.V. Khristenko1,
Z. Bukowski3, and R. Troæ3
1
B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine
47 Lenin Ave., Kharkov 61103, Ukraine
E-mail: dmitriev@ilt.kharkov.ua
2
International Laboratory of High Magnetic Fields and Low Temperatures, P.O. Box 4714, 50-985 Wroclaw 47, Poland
3
W. Trzebiatowski Institute of Low Temperature and Structure Research, Polish Academy of Sciences
P.O. Box 1410, 50-950 Wroclaw 2, Poland
Received July 10, 2007
Andreev reflection in contacts based on a magnetic superconductor Mo Sb3 7 in magnetic field has been in-
vestigated by the point-contact method. It is found that the behavior of the order parameter in the magnetic
field �( )H is essentially dependent on the value of �, which varies widely (�( , ) . .00 0 01 0 31� � meV) for differ-
ent contacts at practically invariant Tc. At high � the dependence �max( )H deviates slightly from the theoret-
ical prediction applicable under the point-contact conditions. As the order parameter decreases, the devia-
tion starts to increase and becomes very large when � approaches its minimum. Proceeding from the results
obtained in this study and from the temperature measurements on Mo Sb3 7 performed formerly, we are in-
clined as before to assign the compound to the class of superconductors with anisotropic gap function. So, in
no way can it be considered as conventional BCS-type superconductor. The upper critical field Hc2 16 5� .
kOe found here is close to that obtained from magnetization measurements in another study. According to
the estimation performed, the pair-breaking effect of the Pauli paramagnetism is rather weak in Mo Sb3 7.
PACS: 74.70.Ad Metals; alloys and binary compounds (including A15, MgB2, etc.).
Keywords: magnetic superconductor, point-contact method, Andreev reflection.
Introduction
Recently the family of superconducting Mo-based
compounds has been enlarge by a new member, Mo 3Sb 7.
This compound was synthezied by Bukowski et al. who
also measured its resistive and magnetic properties [1].
According to their results, the superconducting transition
in Mo Sb3 7 starts at T � 2 2. K. Mo Sb3 7 has a cubic D f8
(Ir 3Ge 7)-type crystal lattice (space group Im m3 ) in which
Sb can hold two nonequivalent positions in the cubic cell:
Sb 1 at the site 12(d) and Sb 11 at the site 16(f) [2]. Mo Sb3 7
is the only intermetallic compound in the Mo–Sb system.
This largely determines the single-phase character of the
samples despite their somewhat exotic preparation by the
peritetic reaction of the structural components. Before
the advent of Mo Sb3 7, the superconducting Mo-based
compounds were widely represented by the Chevrel pha-
ses M xMo 6X 8 (M — metal, X = S or Se, 1 4� �x )
having a complicated magnetic structure. In these com-
pounds superconductivity coexists tolerantly with anti-
ferromagnetism in a wide temperature range or even with
ferromagnetic order, though in a very narrow temperature
interval [3]. The new superconductor Mo Sb3 7 is free of
any magnetic transitions and remains paramagnetic in the
investigated interval from room temperature to the tem-
perature of the superconducting transition [1].
We thoroughly investigated the basic superconducting
characteristics (order parameter � and upper critical field
H c2) of a new magnetic superconductor Mo Sb3 7 using
the point-contact method. This is the most efficient tech-
nique for superconductors with complicated crystal struc-
ture enables one to obtain spectroscopic information from
© V.M. Dmitriev, L.F. Rybaltchenko, L.A. Ishchenko, E.V. Khristenko, Z. Bukowski, and R. Troæ, 2007
small-volume areas of different crystallographic orienta-
tion. These results were partly published in Refs. 4, 5.
The point-contact spectra of the Andreev reflection in
metallic (no dielectric barriers) Ag–Mo Sb3 7 contacts,
measured at different temperatures, are presented in Ref. 4.
They are seen to vary considerably from contact to con-
tact. The matching of the experimental data and the mo-
dified Blonder–Tinkham–Klapwijk (BTK) theory, which
most adequately accounts for the Andreev reflection
in N–S contacts, shows that the order parameter � is
strongly anisotropic and varies widely depending on the
contact orientation: � max can be up to 40 times in excess
of � min , in spite of practically unchanged Tc . The de-
pendence � max( )T agrees closely with the BCS theory,
while � min ( )T diverges from it drastically. These results
suggest that Mo Sb3 7 is not a conventional BCS supercon-
ductor with the s symmetry of the Cooper pairing. Most
likely, it has an anisotropic gap function.
Here we present the experimental dependences of the
order parameter on the magnetic field �( )H and of the up-
per critical field on temperature H Tc2( ) that were mea-
sured on the magnetic superconductor Mo Sb3 7. The pre-
liminary data on H Tc2( ) are partly available in Ref. 5.
The data analysis shows that the dependence �( )H for
contacts with rather large � is comparable with that fol-
lowing from the Ginzburg–Landau theory within some
reasonable assumptions. However, there is a considerable
discrepancy between theory and experiment for contacts
with low �. In both cases the behavior of �( )H suggests
the existence of a narrow gap-free region near H c2. H c2
was obtained from the dependences dV/dI H V( ) �0 measu-
red at different temperatures. It varies within 7.8–9.2 kOe
at 1.6 K for different contacts and does not correlate with
�. This means that H c2 is independent of the crys-
tallographic orientation. The order parameter has such
dependence, which was demonstrated convincingly in
Ref. 5. The dependence H Tc2( ) matched to the empiri-
cal law H T T Tc c2
21( ) ( / )� � leads us to conclude that
Mo Sb3 7 is a weak Pauli paramagnet.
Experiment
The Mo Sb3 7 crystals were prepared in the process of
the peritectical reaction between liquid Sb and solid Mo
in an inert Ar atmosphere at T � �1000 C. The crystalline
structure and the chemical composition were examined
using x-ray and electron-diffraction methods, which
showed a perfect quality of the samples and no evidence
of impurities and foreign phases. The point contacts were
made in liquid He by touching gently a fresh cleaved facet
of the Mo Sb3 7 polycrystalline sample (prepared immedi-
atelly before placing it into the cryostat) with a chemi-
cally etched sharpened Ag wire. Note that the spectro-
scopic characteristics of the cleaved surface remained
practically unchanged even after a prolonged exposure to
air. Moreover, in many cases the results measured on
contacts formed on a natural surface of the sample and
on a freshly cleaved facet were closely similar. In both
cases the experiments were made on irregular, rather
rough pieces 2–3 mm in section. Owing to the large
(� 20–50 m) crystallites in the Mo Sb3 7 polycrystals,
there was a high probability that the Ag needle would
touch single-crystalline regions of the S electrode, though
their crystallographic directions with respect to the con-
tact axis were unknown. In this way we performed direc-
tional spectroscopy of the Andreev reflection in
Mo Sb3 7 and could watch different (varying more than
fortyfold) order parameters in different contacts at practi-
cally invariant Tc . Thus, we have concluded that the pair-
ing in Mo Sb3 7 is not related to the s-type symmetry [5].
The design of the electrode holder allowed the relative
movement of the electrodes under an off-cryostat control.
It was thus possible to touch repeatedly different points
on the S-electrode surface during one measurement cycle.
The point-contact spectra dV/dI V( ) and dV/dI H( ) were
measured using the standard modulation technique at
487 Hz frequency. The magnetic field was produced with
a superconducting solenoid and was always perpendicu-
lar to the contact axis. To maintain the spectroscopic re-
gime, the size of the contact must be smaller than the
mean scattering path of charge carriers [6,7]. Unfortu-
nately, because of the lack of information about the elec-
tronic parameters of this new superconductor, we could
not estimate adequately the size of the contact and com-
pare it with the scattering length. Nevertheless, the high
and steady Andreev reflection currents observed up to bi-
ases over an order of magnitude exceeding the typical
gap-related voltages in the point contacts with nor-
mal-state resistance RN = 1–10
count in favor of a sta-
ble spectroscopic condition in them. Contacts with higher
resistance are less suitable for investigation as they show
worse stability against vibrations during several hours of
a complete measurement cycle.
Results and discussion
The measurements of point-contact spectra at different
points of the S electrode show that the order parameter �
can change over an order of magnitude from contact to
contact. The critical temperature found from the onset of the
superconducting transition Tc
on remained within 2.2–2.3 K.
The highest � reduced to zero temperature in accordance
with the BCS theory was � max( ) .0 0 31� meV, which
provides the characteristic ratio 2� max( ) / .0 3 2kTc � .
This is a little lower than � expected in the isotropic BCS
model �
BCS ( ) .0 0 35� meV. The discrepancy may be due
to the effects of pair breaking in this magnetic supercon-
ductor. The typical set of spectra (dV/dI V( ) characteris-
tics) measured on the same point contact with high � in
different magnetic fields is shown in Fig. 1 (solid lines).
1332 Fizika Nizkikh Temperatur, 2007, v. 33, No. 12
V.M. Dmitriev, L.F. Rybaltchenko, L.A. Ishchenko, E.V. Khristenko, Z. Bukowski, and R. Troæ
According to the BTK theory [8] modelling electron
scattering at the N–S boundary, the minima in spectra
near V � 0 in magnetic fields smaller than 8.36 kOe are
due to the processes of Andreev reflection in the
point-contact area (Fig. 1). The magnetic field in which
an appreciable dip first appears in spectrum was taken as
the upper critical field H c2 (H c2 8 3� . kOe for this con-
tact). � was found by fitting the formulas of the modified
BTK theory [9] to the experimental dV/dI V( ) curves. This
theory allows for the spectral line broadening near V � 0
through the so-called smearing parameter � which was
first introduced by Dynes et al. [10] to account for the fi-
nite lifetime of quasiparticle excitation at the Fermi level.
It is important that in actual practice the parameter � can
also include other factors, primarily, the inhomogeneous
distribution of � over the contact area and the effects of
pair breaking caused by spin-flip scattering of electrons.
Besides, the BTK theory contains another important pa-
rameter Z describing the elastic electron scattering di-
rectly at the N–S boundary. This scattering is caused by
defects of the surface layers of both the electrodes and by
the discrepancy between their Fermi momenta. Notice-
ably, the original BTK theory is strictly applicable only
for s-wave superconductors, whereas in a case of d-wave
symmetry the extended BTK should be used [11]. Mean-
while, the spectra calculated in either of these two models
for Z � 0 5. do not have strong distinctions. Therefore, the
results of fitting experimental spectra with small Z in both
cases should be close to each other, as was shown in [12].
This fact justifies the use of s-wave BTK model in our
work.
It should be noted that in each magnetic-field set of
dV/dI V( ) curves (similar to those in Fig. 1), only the
zero-field curve was fitted by three parameters �, �, and
Z. For the rest of the curves the fitting was performed with
Z invariant. The fitted curves are shown in Fig. 1 (dashed
curves). In general, the experimental and fitted curves
agree quite well, except for those measured in low fields
near V = 1 meV, where smeared maxima sometimes oc-
curred. Such maxima, typical for low-ohmic contacts, are
probably caused by the delay of the charge disbalance re-
laxation in the above-gap energy region. Meanwhile, cal-
culation of the spectra in BTK theory was done without
considering this fact. The order parameters � obtained in
different magnetic fields using this procedure are shown
in Fig. 2 (solid squares).
However, it is hardly possible to correlate our point
contact with the objects analyzed by known theories
which consider the order parameter as a function of the
magnetic field. It seems that �( )H measured in point-con-
tact experiments can be compared with the calculations
for type-II superconductors (Mo Sb3 7 belongs to this
class [1]), �( ) ( / ) /H H H c� �1 2
1 2 (e.g., see [13,14]).
However, the calculated dependence (not shown in
Fig. 2) runs much lower than the experimental one. The
reason for this significant discrepancy is that the
point-contact method of measuring the order parameter of
type-II superconductors in the magnetic field cannot
yield results similar to those obtained by other methods,
e.g., heat capacity measurement in which the measured
Andreev reflection study of a new magnetic superconductor Mo Sb3 7 in magnetic field
Fizika Nizkikh Temperatur, 2007, v. 33, No. 12 1333
–2 –1 0 1 2
8.36 kOe
7.38 kOe
6.52 kOe
5.40 kOe
4.15 kOe
2.63 kOe
1.65 kOe
H = 0
Ag–Mo Sb3 7
T = 1.6 K
d
V
/d
I(
V
),
re
l.
u
n
it
s
V, mV
Large order
parameter contact,
Fig. 1. Point-contact (PC) spectra dV/dI V( ) (solid lines) mea-
sured in different magnetic fields, indicated on each curve, of
an Ag–Mo Sb3 7 contact characterized by a relatively large order
parameter value �( ) .0 0 31� meV. The BTK fits are shown by
the dashed lines (Z = 0.15, � � 0 02. meV). For clarity, the
curves are shifted vertically.
0 1 2 3 4 5 6 7 8 9
0
0.05
0.10
0.15
0.20
0.25
Hc2
onset
Large order parameter contact
T = 1.6 K
H, kOe
experiment
Ginzburg–Landau theory
Fig. 2. Magnetic field dependence of the gap parameter �( )H
(solid squares) as compared to the Ginzburg–Landau theory
(dashed line) for the contact presented in Fig. 1.
values are averaged over a whole bulk volume. Mean-
while, the point-contact spectra account for only the prop-
erties of a thin surface layer of the sample. The thickness
of this layer is close to the contact diameter (usually
within 2–20 nm), which is much smaller than the London
penetration depth
L. In the applied magnetic field the
Abrikosov vortices that penetrate into the S electrode are
arranged so that the normal vortex core can never get into
the contact area (except for fields close to H c2) and can-
not contribute to the point-contact spectrum. (Note that in
our experiments the contact axis is perpendicular to the
magnetic field). It is therefore natural that our � values
exceed those obtained by other bulk-measurement tech-
niques.
The close agreement of the experimental curve �( )H
with the law �( ) ( ( / ) ) /H H H c� �1 2
2 1 2 (Fig. 2) calcu-
lated by the phenomenological Ginzburg–Landau (GL)
theory [15] for a thin film in the parallel field may be not
altogether casual, because such a film does not contain
normal regions either. Thus, the regimes realized in a
point contact and a thin film in a parallel field are in some
sense similar. The Ginzburg–Landau theory was later
confirmed by Gorkov’s basic microscopic relations of the
theory of superconductivity [16]. It appeared that the
equations of this theory held not only near Tc , as was ex-
pected earlier, but could work with quite good accuracy in
a much wider temperature interval. Later on the fact was
strengthened by Maki [17]. The comparison with other
theoretical dependences �( )H shows that our experimen-
tal results are less close to microscopic calculations
[17–19] than to the dependence following directly from
the Ginzburg–Landau theory (Fig. 2).
Note that in Fig. 2 the theoretical Ginzburg–Landau
dependence was fitted to the whole set of experimental
points, expect for the 8.3 kOe point. The critical field was
estimated at the point of intersection of the theoretical
curve and the abscissa. The obtained value H c2 7 4* .� kOe
is significantly lower than H c2 8 3� . kOe, which was de-
rived from the complete set of dV/dI V( ) curves taken in
different magnetic field and which accounts for the onset
of the superconducting transition. One of the reasons for
this discrepancy may be the smearing of the supercon-
ducting transition in magnetic field, which can be rather
large for materials with a complicated crystalline struc-
ture. Hence, the field value in the middle of the transition
would to some extent approach 7.4 kOe. Unfortunately,
it is impossible to find this mid-point straightforwardly
from the point-contact spectra. There is another reason
for the uncertainty in the critical field value. In many con-
tacts the gap minima registered near V = 0 do not vanish
completely after sharp decrease of their amplitudes in the
magnetic field, i.e., near the expected critical value of the
field. In many cases the low-intensity minima persist up
to H H c� 2 2. This effect is similar to that observed in
many high-Tc superconductors and is attributed to the
so-called pseudogap that appears in the spectrum of
quasiparticle excitation above Tc . (The effect is not dis-
cussed in this work.) The rather large amplitude of the
zero-bias minimum at H � 7 4. kOe (Fig. 1) may be a re-
sult of summing up the main, gap-like, and pseudogap
minima.
As noted above, many contacts have extremely low �
(down to � 0 01. meV), while the critical temperature re-
mains practically invariant to within several hundredths
of a Kelvin. The typical set of spectra taken on one of the
point contacts with rather low � (� 0 04. meV) is shown in
Fig. 3 (solid lines). The fitting of these spectra to the mo-
dified BTK theory [9] gives quite acceptable results
(Fig. 3, dashed lines). Nevertheless, the obtained depend-
ence �( )H differs appreciably of the one following from
the Ginzburg–Landau theory (Fig. 4). The fitting proce-
dure proves to be less successful when applied to contacts
with � � 0 04. meV, though it can be quite satisfactory for
curves measured in zero or comparatively low magnetic
fields (� 4 kOe). However, it is not applicable entirely to
curves measured in high fields because of the strange nar-
rowing of the gap minima. In such fields the calculated
1334 Fizika Nizkikh Temperatur, 2007, v. 33, No. 12
V.M. Dmitriev, L.F. Rybaltchenko, L.A. Ishchenko, E.V. Khristenko, Z. Bukowski, and R. Troæ
–2 –1 0 1 2
H = 0
1.32 kOe
2.63 kOe
3.95 kOe
5.27 kOe
6.59 kOe
7.24 kOe
7.90 kOe
8.56 kOe
9.22 kOe
T = 1.55 K
Small order
parameter contact
V, mV
d
V
/d
I(
V
),
re
l.
u
n
it
s
Fig. 3. Magnetic field set of the PC spectra (solid lines) for
Ag–Mo Sb3 7 contact with a small order parameter value
�( ) .0 0 04� meV (Z = 0.15, � � 0). The dashed lines present the
BTK fits.
curves are more broadened than the experimental ones no
matter how much the fitting parameters are varied.
A similar situation occured while measuring the tem-
perature dependence of the order parameter of Mo Sb3 7 in
[4], where it was assumed that this superconductor has
anisotropic symmetry of pairing, e.g., of the d- or sg-type.
So, the highest � is observed in the contacts oriented
along the crystallographic directions where the gap func-
tion has a maximum. In the other so-called nodal direc-
tions with zero or close-to-zero gap function the spectra
reveal the many times lower �. As before [4], we believe
that the behavior of � for the lobe directions (i.e., corre-
sponding to the maxima of gap function) with a change
of temperature or magnetic field is roughly similar to
that observed in conventional s-type superconductors
with an isotropic gap function. Indeed, the experimental
dependences �( )T (Fig. 2, [4]) and �( )H (Fig. 2, this
study) measured on contacts with nearly maximum �
deviate only slightly from the corresponding theoretical
curves suitable for conventional BCS superconductors.
The dependence of the magnetic field on temperature
(H–T phase diagram) and the upper critical field in Mo Sb3 7
were found using the magnetic field dependences of
the differential zero-bias resistance of the contacts
dV/dI H V( ) ( )�0 measured at different temperatures. Fi-
gure 5 shows the typical set of such curves for one of
the point contacts with �( , ) .0 0 0 22� meV and its zero-
field spectrum. The curves demonstrate suppression of
the Andreev current in the magnetic field. As this mag-
netic field increases, the superconducting electrode chan-
ges to the N state and the curves become saturated. De-
spite some smearing of the S–N transition near saturation
region, it is possible to estimate H c2 quite accurately for
each particular temperature. H c2 values were estimated at
the points of the largest curvature (e.g., see Fig. 5, the ar-
row at one of the curves). It should be noted that the N–S
transition is less smeared in our experiment than in mag-
netization measurement on the same material [1]. The
critical field H c2 estimated at �1 6. K for over 20 contacts
is within 7.9–8.9 kOe.
No correlation was found between H c2 and �. This is
not surprising because in the general case H c2 is highly
anisotropic only in layered superconductors, e.g., chal-
cogenides and copper oxide compounds whose critical
fields are three- or fourfold different along two main crys-
tallographic directions. Mo Sb3 7 has a cubic crystal lat-
tice, which itself cannot lead to anisotropy of H c2. Nor
is the anisotropic character of the gap function �( )k in
Mo Sb3 7 a sufficient factor to cause anisotropy of H c2.
This is evident from the analysis of published data on the
superconducting properties of borocarbide superconduc-
tors with an anisotropic �( )k function. Indeed, the aniso-
tropy of critical field is quite moderate in nonmagnetic
LuNi 2B 2C with the ratio � �min max ./ � 0 1 [20] and in
weakly paramagnetic YNi 2B 2C (� �min max ./ � 0 01)
[21]. For example, in LuNi 2B 2C the difference between
the H c2 values measured along the main crystallographic
directions was no more than 15%. In YNi 2B 2C no differ-
ence was registered within the measurement accuracy
[22]. It is known that H c2 is highly anisotropic in mag-
netic superconductors with large magnetic moments ori-
ented along certain crystallographic directions. Mo Sb3 7
does not belong to this group because it exhibits only a
weak paramagnetism (see below) and hence its magnetic
Andreev reflection study of a new magnetic superconductor Mo Sb3 7 in magnetic field
Fizika Nizkikh Temperatur, 2007, v. 33, No. 12 1335
0 1 2 3 4 5 6 7 8 9
0
0.01
0.02
0.03
0.04 T = 1.55 K
Small order
parameter contact
Hc2
onsetH, kOe
experiment
Ginzburg–Landau theory
Fig. 4. The experimental �( )H dependence (open circles) in
comparison with the Ginzburg–Landau law attached to the first
low-field experiment points (dashed lines) for the contact pre-
sented in Fig. 3.
0 2 4 6 8 10 12 14 16 18 20
–2 –1 0 1 2
2.18 K
2.20 K
2.23 K
2.1 K
2.0 K
1.9 K
1.8 K
1.7 K
1.6 K
1.55 K
0.2 W
R = 1.8N W
d
V
/d
I(
V
=
0
)
H, kOe
R = 1.8N W
T = 1.55 K
H = 0 0.2 W
V, mV
d
V
/d
I(
V
),
re
l.
u
n
it
s
Fig. 5. Zero-bias differential resistance vs magnetic field de-
pendences measured at different temperatures for Ag–Mo Sb3 7
contact with RN � 1 8.
(for clarity the curves are shifted ver-
tically). Hc2 values were taken at the points of the maximum
curvature, as indicated on the 2.0 K-curve by an arrow. The in-
set shows the PC spectrum dV/dI V( ) of this contact measured
in a zero magnetic field at 1.55 K (solid line), and BTK fitted
curve.
subsystem has no directionality. Thus, variations of the
critical field observed in this material can hardly be evi-
denced of its possible anisotropy. Most likely, they are a
consequence of inhomogeneous distribution of the criti-
cal parameters in the contact area.
Figure 6 illustrates the averaged H c2 values for se-
ven contacts with quite small scatter of critical fields
(8.2–8.5 kOe) (light circles). These data were obtained
from plots similar to those in Fig. 5. In addition, Fig. 6
carries the results of magnetization measurement (solid
square) [1]. The data of both sets exhibit a linear tempera-
ture dependence near Tc , which follows from the Wer-
thamer–Helfand–Honenberg (WHH) microscopic theory
[23] for conventional type-II superconductors. Earlier,
this behavior was predicted in the phenomenological GL
theory which holds a high accuracy in a narrow tempera-
ture interval near Tc . The results of Fig. 6 were fitted to
the empiric low H T H T Tc c c2 2
20 1( ) ( )[ ( / ) ]� � (solid and
dashed lines for our results and the data of Ref. 1, respec-
tively). The law is a good approximation (several percent
error) to the accurate microscopic equation with no tem-
perature limitation according to the WHH theory. The ob-
tained field H c2 0 16 5( ) .� kOe is quite close to 17.2 kOe
in Ref. 1.
We also estimated the slope of H Tc2( ) with respect
to the temperature axis (�dH /dTc2 ) near Tc . Its value
( .�12 9 kOe/K) is comparable with the corresponding
data for many intermetallic A-15 type superconductors.
Knowing this value, we can estimate the pair-breaking ef-
fect of the Pauli paramagnetism in the material investi-
gated. For this purpose we use a formula from Ref. 23
(a version of that in Ref. 24) that relates the dimensionless
pair-breaking parameter � and the slope (in Oe/K units)
� � ( . )( )5 28 10 5
2� �
�
�dH /dTc T Tc
. We thus arrive at � � 0 7. ,
which is typical for systems with moderate intensity of
spin-flip scattering.
Conclusion
The investigation of the Andreev reflection in the
magnetic superconductor Mo Sb3 7 has shown that the be-
havior of the order parameter � in the magnetic field is es-
sentially dependent on its own value. In our experiments
� varied widely, �( , ) . .0 0 0 01 0 31� � meV, in contacts with
different orientations at practically invariant Tc . No cor-
relation was found between � and H c2. When � is high,
its field dependence �( )H deviates slightly from the
known theoretical relation that apply to conventional su-
perconductors under point-contact conditions. However,
the deviation starts to increase with decreasing � and be-
comes very large in the region � min . Comparing this fact
with the similar behavior of �( )T in [4] we persist in the
belief that the gap function in Mo Sb3 7 is anisotropic. In
the context of this assumption � max can be registered in
contacts oriented along the crystallographic axes close
to the maxima in the gap function, which may have the
isotropic s-symmetry behavior in a limited interval of an-
gles. This assumption is helpful in explaining the nearly
standard dependences �( )H and �( )T . The lower
� max( ) .0 0 31� meV as against the BCS prediction
� BCS ( ) .0 0 35� meV can be attributed to the magnetic na-
ture of this material. Hence, the pair-breaking effect of
spin-flip scattering should not be neglected. The upper
critical fields H c2 values measured at different tempera-
tures and averaged over seven contacts were compared
with the quadratic dependence H Tc2( ) for type-II super-
conductors. On the basis of experimental dH/dT value and
the corresponding theoretical equation [23,24] we were
able to estimate the efficiency of the pair-breaking effect
caused by the Pauli paramagnetism. The effect has turned
out to be quite moderate.
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