Physical property and electronic structure characterization of bulk superconducting Bi3Ni
ABSTRACT We report the experimental and theoretical study of the magnetic nature of the Bi3Ni system. The structure is found to be orthorhombic (Pnma) with lattice parameters a = 8.879 Å, b = 4.0998 Å and c = 4.099 Å. The title compound is synthesized via a solid state reaction route by quartz vacuum encapsulation of 5 N purity stoichiometric ingredients of Ni and Bi. The superconducting transition temperature is found to be 4.1 K as confirmed from magnetization and specific heat measurements. The lower critical field (Hc1) and irreversibility field (Hirr) are around 150 and 3000 Oe respectively at 2 K. Upper critical field (Hc2), as determined from in-field (up to 4 T) ac susceptibility, is found to be around 2 T at 2 K. The normal state specific heat is fitted using the Sommerfeld–Debye equation C(T) = γT + βT3 + δT5 and the parameters obtained are γ = 11.08 mJ mol − 1 K − 2, β = 3.73 mJ mol − 1 K − 4 and δ = 0.0140 mJ mol − 1 K − 6. The calculated electronic density of states (DOS) at the Fermi level N(EF) and Debye temperature ΘD are 4.697 states/eV/f.u. and 127.7 K respectively. We also estimated the value of the electron–phonon coupling constant (λ) to be 1.23, which when substituted in the MacMillan equation gives Tc = 4.5 K. Density functional theory (DFT) based calculations for experimentally determined lattice parameters show that Ni in this compound is non-magnetic and ferromagnetic interactions seem to play no role. The Stoner condition IN(EF) = 0.136 per Ni atom also indicates that the system cannot have any ferromagnetism. The fixed spin moment (FSM) calculations, by fixing total magnetic moment on the unit cell, also suggested that this system does not exhibit any signatures of ferromagnetism.
Physical property and electronic structure characterization of bulk superconducting
Jagdish Kumar1,2, Anuj Kumar1, Arpita Vajpayee1, Bhasker Gahtori1, Devina Sharma1,3, P.K.
Ahluwalia2, S. Auluck1, and V.P.S. Awana1,*
1Quantum Phenomena and Application Division, National Physical Laboratory (CSIR)
New Delhi-110012, India
2Department of Physics, Himachal Pradesh University, Summerhill, Shimla-171005, India
3Department of Physics, Punjab University, Chandigrah 160014, India
We report the experimental and theoretical study on magnetic nature of Bi3Ni system.
The structure is found to be orthorhombic (Pnma) with lattice parameters a = 8.879Å b =
4.0998Å and c = 4.099Å. The title compound is synthesized via a solid state reaction route by
quartz vacuum encapsulation of 5N purity stoichiometric ingredients of Ni and Bi. The
superconducting transition temperature is found to be 4.1 K as confirmed from magnetization
and specific heat measurements. The lower critical field (Hc1) and irreversibility field (Hirr) are
around 150 and 3000Oe respectively at 2K. Upper critical field (Hc2) as determined from in field
(up to 4 Tesla) ac susceptibility is found to be around 2 Tesla at 2K. The normal state specific
heat is fitted using Sommerfeld-Debye equation C(T) = γT + βT3+δT5 and the parameters
obtained are γ= 11.08mJ/mol-K2, β= 3.73mJ/mol-K4 and δ= 0.0140mJ/mol-K6. The calculated
electronic density of states (DOS) at Fermi level N(EF) and Debye temperature ΘD are 4.697
states/eV per formula unit and 127.7K respectively. We also estimated the value of electron
phonon coupling constant (λ) to be 1.23, which when substituted in MacMillan equation gives Tc
= 4.5K. Density functional (DFT) based calculations for experimentally determined lattice
parameters show that Ni in this compound is non-magnetic and ferromagnetic interactions seem
to play no role. The Stoner condition I*N(EF) = 0.136 per Ni atom also indicates that system
cannot have any ferromagnetism. The fixed spin moment (FSM) calculations by fixing total
magnetic moment on the unit cell also suggested that this system does not exhibit any signatures
Key Words: Bi3Ni, Structure, Magnetization, Superconductivity, Heat Capacity, and Density
PACS: 74.25.-q, 74.62.Bf, 74.62.Dh
Dr. V.P.S. Awana
Fax No. 0091-11-45609310: Phone No. 0091-11-45608329
These are rich days for the search of new superconducting materials. This is because
often new superconducting compounds keep on adding, which provide clues to the theoreticians
to solve the puzzle of high Tc superconductivity beyond 40K. The quest slightly speeded up once
again (post high Tc superconductivity (HTSc) avalanche ) with the discovery of
superconductivity in MgB2  and Fe based oxy-pnictides . The Tc of latest entrants i.e., oxy-
pnictides was raised by applying pressure (Tconset = 43 K)  or substitution of smaller rare earth
ion for the La site (Tc = 55 K for SmFeAsO1-xFx) . Soon after researchers reported other
crystal structure types of layered Fe compounds to be superconducting, including Ba1−xKxFe2As2
, Li1−xFeAs  and FeSe . Fe based oxy-pnictides crystallize in ZrCuSiAs-type structure
with space group P4/nmm [3-5]. Very recently, a similar structure (ZrCuSiAs-type) Ni
containing compound (CeNi0.8Bi2) is reported  from the consortium of the oxy-pnictide
inventors  group. At this stage, we focused on another interesting Ni containing Bi compound
i.e., Bi3Ni, which is though known to be superconducting since 1951 , but only a few scant
reports [11-13] do exist on its superconductivity. Tunneling spectroscopy results revealed that
Bi3Ni is a strongly coupled superconductor . The latest one exists in year 2000 by Y.
Fujimori et al. . More recently Bi3Ni is synthesized by vacuum encapsulation technique and
possibility of co-existence of magnetism and superconductivity in this compound is addressed
. Keeping this in view, we synthesized Bi3Ni via an easy and versatile synthesis route,
instead of conventional “arc melting”. The studied compound is synthesized by sealing in quartz
and vacuum annealing at 1000oC for 24 hours and slowly cooled to room temperature. This is
one shot heat treatment and post annealing etc. is not required. The resultant compound is
superconducting below 4.1K and the Ni is non-magnetic. The non magnetic character of Ni in
Bi3Ni is similar to that as observed earlier for the famous Ni Boro-Carbides viz. Y-Ni-B-C 
and MgCNi3 . Detailed specific heat analysis and DFT calculations revealed that this
compound is having electron-phonon coupling constant of around 1.23 and Ni is non magnetic.
Further it is concluded that ferromagnetic interactions play no role in superconductivity of Bi3Ni.
This is in contrast to a recent report  related to possibility of coexistence of
superconductivity and magnetism in Bi3Ni. Our results will surely attract more researchers to
work on superconductivity of this and similar Ni containing compounds.
Samples of nominal composition Bi3Ni are synthesized by solid state reaction route. The
stoichiometric amounts of high purity (> 5N) Bi and Ni are ground thoroughly with help of an
agate and mortar for around an hour. The mixed and pulverized powders are pressed into the
form of a rectangular bar and are encapsulated in an evacuated quartz tube. The encapsulated
tube was then heated at 1000oC for over 24 hours and slowly cooled to room temperature. The
X-ray diffraction patterns of the samples were obtained with the help of a Rigaku diffractometer
using CuKα radiation. All physical property measurements including magneto-transport R(T)H,
thermoelectric power S(T), heat capacity Cp(T)H and magnetization (AC and DC) were carried
out using Quantum Design PPMS (Physical Property Measurement System).
Results and Discussion
Fig. 1 depicts the room temperature X-ray diffraction (XRD) plot of the studied Bi3Ni.
The resultant compound is mainly single phase, with minor impurity of Bi at 27.20. The fitted
and observed Reitveld parameters are shown in Table 1. Bi3Ni crystallizes in orthorhombic
structure with space group Pnma, The lattice parameters are a = 8.878(5)Å, b = 4.102(1)(5)Å,
and c = 11.479(1)Å. These lattice parameters are in agreement with earlier reports [10-14]. For
Bi3Ni, there are three Bi sites namely Bi1, Bi2 and Bi3 having fixed y at ¼ and varying x and z
coordinates . For Ni as well the y is fixed at ¼ and x and z coordinates are varied. So in
effect there are four coordinate sites i.e., three for Bi and one for Ni in unit cell of Bi3Ni. Further,
one unit cell of Bi3Ni consists of four sub unit cells. The representative unit cell being
determined from Reitveld analysis of the studied Bi3Ni is given in Fig. 1(b).
The DC and AC magnetic susceptibility plots of studied Bi3Ni are shown in Fig. 2 and 3
respectively. Namely, Fig. 2(a) depicts the DC magnetic susceptibility (χ) in both zero-field-
cooled (FC) and field-cooled (FC) situations in temperature range of 2K to 10K. The applied
field is 10Oe. Superconductivity is observed at 4.1K with a sharp diamagnetic transition in
magnetic susceptibility (χ) in both ZFC and FC situations. The superconducting volume fraction
seems to be around 87.6% as calculated from FC (χ). This is slightly higher than as reported in
ref. 13.Though an estimated value is given, still we believe estimating superconducting volume
fraction without exactly knowing the pinning properties is not correct. What one can safely
conclude from Fig. 2(a) is that the studied Bi3Ni is a bulk superconductor with superconducting
transition temperature (Tc) at 4.1K. The AC susceptibility of Bi3Ni in both real (χ/) and imaginary
(χ//) parts at frequency of 333Hz and amplitude of 1.0Oe is shown in Fig. 2(b). We also studied
the AC susceptibility of Bi3Ni in both real (χ/) and imaginary (χ//) parts at various amplitude of 3-
11 Oe and fixed frequency of 33 Hz. These results are depicted in Fig. 3. Basically there is
nearly no shift in the peak position temperature with increase in AC drive field. This is unlike
high Tc superconductors (HTSc)  or the recently invented pnictides . Fundamentally this
shows that the superconducting grains are strongly coupled in Bi3Ni and hence inter/intra grains
superconductivity characteristic of this compound must be good enough for practical
The isothermal magnetization M(H) plots for studied Bi3Ni at various fields and
temperatures are depicted in Figs. 4(a-d). The low field (< 200Oe) isothermal M(H) plots of
Bi3Ni at T = 2, 2.5, 3 and 3.5K are shown in Fig. 4(a). The inversion of these M(H) marks the
lower critical field (Hc1) for studied Bi3Ni superconductor. The Hc1 is around 150Oe at 2K and
decreases monotonically with increase in T to 30Oe at 3.5K. These values of Hc1 for studied
Bi3Ni are in good agreement with an earlier report [13, 14].
Fig. 4(b) depicts the isothermal M (H) plot for real part of AC susceptibility (M/) with
applied field of up to 5 kOe at 2K. This is done to know the extent of complete flux inclusion
into the superconductor. This field roughly coincides with the upper critical field (Hc2) of the
superconductor at the particular temperature. As seen from Fig. 4(b), the complete inclusion of
the flux takes place at above 3 kOe. The 10%, 50% and 90% of the same is marked in the Fig.
4(b). By definition one takes the upper critical field (Hc2), to be 50% of externally excluded field,
instead of full exclusion i.e. 100%. This is done in accordance with ref. 13. The upper critical
field value of Bi3Ni thin films  is slightly higher than our value for studied bulk Bi3Ni
Complete (all four quadrants) isothermal M(H) loops for studied Bi3Ni are shown in Fig.
4(c) at T = 2, 2.5, 3 and 3.5K with in +3000 to – 3000Oe applied fields. The M(H) plots exhibit
expected symmetric superconducting loops with their closing at above 2000 Oe. This means the
irreversibility field (Hirr) is close to 2000Oe. Interestingly a careful close look of these plots
shows some magneto-superconductivity like asymmetry. To elaborate on this, we zoom Fig. 5(c)
and the result is shown in Fig. 4(d). It is clear from Fig. 5(d) that all the superconducting M(H)
loops are closed below and above base line in first and fourth quadrants respectively. This is
unusual, because in normal course (with out magnetic background) the isothermal M(H) loops
for a superconductor meet/close at the base/zero line. The external field matching with closing of
the isothermal M(H) loops corresponds to the irreversibility field (Hirr), which is at around
2000Oe at 2K and is marked in Fig. 4(d). Hence as far as the irreversibility field (Hirr) is
concerned, the same is around 2000Oe at 2K and is clear from both Fig. 4(d).
The moot question remains is that whether the slight asymmetry in M(H) loops is due to
magnetic background or some other possible reasons like small grain size. To look for the
possibility of either intrinsic (Ni in Bi3Ni structure magnetic) or extrinsic (un-reacted Ni)
magnetism in studied Bi3Ni, we carried out the moment versus temperature M(T) experiments
and the results are shown in Fig. 5. The M(T) is carried out at an applied field of 100 Oe in both
Zero-field-cooled (ZFC) and Field-cooled (FC) situations. The temperature range is 2-300K. As
evidenced from the M(T) results of Fig. 5, studied Bi3Ni is superconducting below 4.1K with
sufficient superconductivity shielding fraction and the normal state i.e. 4.1 to 300K, is non-
magnetic. This is interesting, because despite being full occupancy of Ni in studied compound
Bi3Ni, no sign of magnetic ordering or even the moment of Ni is seen. The normal state M(T) of
studied Bi3Ni clearly demonstrates that Ni is non magnetic in Bi3Ni structure. This is consistent
with our DFT calculations.
To further investigate the normal state magnetism of Ni in Bi3Ni, we did isothermal
magnetization M(H) on studied Bi3Ni. The M(H) done at 200K in -3000 to +3000 Oe in all four
quadrants is depicted in inset of Fig. 5. Clearly the M(H) shown in inset of Fig. 5 is linear and
thus rules out any magnetic ordering. Further the moment is also very small i.e., 0.002 emu/g at
3000Oe field. The calculated moment per Ni atom is in fact negligible (10-4 µB). At this point we
conclude Ni is non-magnetic in Bi3Ni superconductor. This is similar to another Ni based
superconductor MgCNi3 . As far as the small asymmetry of M(H) loops (Fig. 4d) is
concerned, the same can be caused by grains size distribution as well. Remember, the presently
studied sample of Bi3Ni is synthesized by an easy versatile method of vacuum encapsulation
instead of the arc melting [10-12]. A representative SEM (scanning electron microscope) picture
of the studied Bi3Ni compound is shown in Fig. 6. The typical grain size is laminar slab like and
quite inhomogeneous, and this could be the reason behind slightly asymmetric M(H) plots shown
in Fig. 4(d). We recently observed a similar effect in particle size controlled La1.8Sr.15CuO4
superconductor . Because we did not find any conclusive evidence for magnetic
contributions from Ni in Bi3Ni superconductor, hence we believe the slight asymmetry in M(H)
plots is due to inhomogeneous grain size and not due to magneto-superconductivity.
The temperature dependence of specific heat C(T) is measured in zero field and for 1
Tesla applied on Quantum design PPMS and is shown in Figure 7. The jump in electronic
specific heat anomaly is clearly visible in zero magnetic field at around 4.2K. The value of jump
is found to be 6.23×10-2J/mol-K, see upper inset of Fig. 7. The normalized value of jump (Ces-
γTc)/γTc is found to be 1.50 that is close to BCS value of 1.43. The low temperature specific heat
was fitted to Somerfield-Debye expression
C (T) = γT + βT3 + T5
where T5 term represents the anharmonic contribution. From this fitting the values of
Sommerfeld constant (γ) and are obtained. The γ and give the value of electronic density of
states and approximate value of Debye temperature respectively. The values obtained are
= 11.08mJ/mol-K2, = 3.73mJ/mol-K4 and = 0.0140mJ/mol-K6. The fitting is shown in
lower inset of Fig. 8. These values are in good agreement with other reported values . The
small difference in the values can possibly be because of little Bismuth impurity in our sample.
From the value of we calculated the value of Debye temperature using ΘD = (234zR/β) 1/3 here
z being number of atoms per formula unit and R is gas constant. The value of ΘD is found to be
127.77K. From the value of Sommerfeld constant we have calculated value of electronic Density
of states at Fermi level N (Ef) using formula:
The value of is N(Ef) found to be 4.697 states/eV-fu.
To further investigate the magnetic nature and detailed microscopy of this compound we
perform the density functional based calculations using the Full Potential Linear Augmented
Plane Wave (FP-LAPW) as implemented in WIEN2k. To describe the exchange and correlation
in the crystal Hamiltonian, we use the local density approximation (LDA). The LAPW sphere
radii for Bi and Ni were chosen as 2.50 a.u. and 2.00 a.u., respectively. The total energy was
converged for 96 k-points in the irreducible BZ. The experimental lattice parameters were used.
The unit cell (u.c.) consists of four formula units (fu) with total of 16 atoms (4-Ni and 12-Bi).
Each Ni atom is surrounded by six Bi atoms and two Ni atoms. We relaxed the internal
coordinates of the Bi ions via force minimization technique to a maximum force of 1mRy/a.u.
Force minimization to determine the lattice coordinates yields consistent values with the
experiments. In Fig.8(a), we show the electronic density of states (DOS) of Bi3Ni for the fully
relaxed structure. As revealed in Fig.8(a), we find that the Ni-d and Bi-p states are distributed
over the large energy range suggesting strong covalent bonding in Ni-d and Bi-p states. The
bands in lower valance band (-13.8 to -9.6eV) consists mainly of Bi-s states with small
contribution of Ni states. Then follows a gap in DOS of about 3.6eV and upper part of valance
band (-6.0eV to Fermi level) is dominated by Ni-d states. The uniform spread of DOS over large
energy range suggests covalent nature of bonding. To further investigate the details of Ni states,
we have calculated the l-resolved Ni projected density of states (PDOS), which shows that most
of Ni states come from Ni-d orbitals. At Fermi level the total states are dominated mostly from
Ni-d with relatively smaller contribution from Bi-p states. The value of DOS at Fermi level is
around 10.2 States/eV-u.c. (2.55 states/eV-fu), which shows that system is metallic. Non
magnetic nature is confirmed from total DOS for spin up and spin down states bring overlapping
exactly. Since spin-orbit coupling (SOC) plays important role in Bi based compounds, we have
done the same calculations by incorporating SOC. The stabilization of the energy with SOC was
lower by ~35.47mRy per atom, which is quite large. However this is expected as bismuth has
strong SOC . The Fermi level is on a broad peak (see inset of Fig. 8a), ruling out any
possibility of doping dependent enhancement in Tc as per BCS criteria. The value of electronic
density of states at Fermi level N(EF) with SOC is decreased to 2.11 States/eV/f.u. The main
features of DOS remain unaltered by SOC.
From the value of calculated DOS at Fermi level and that obtained from low temperature
specific heat we have estimated the value of electron phonon coupling constant λ using relation
From equation (2) we have
Thus equation (3) is equivalent to
, whence λ=0.842 that shows Bi3Ni is an intermediate
coupling superconductor. When we use Ncalc.(EF) being obtained considering SOC, the λ comes
out to be 1.23. It is known that BCS superconductors can be well described using MacMillan
where D is Debye temperature and is determined from specific heat measurements and
μ* is Coulomb coupling constant. The standard value of μ*=0.13 gives a Tc of 4.5 K for λ=0.842
which is in good agreement with corresponding experimental value of 4.1K. However for the
case with SOC, λ=1.23 (as should be actually considered), the Tc is overestimated to ~8.6K for
μ*=0.13, which is more than double of the experimental value. To obtain experimental Tc one
has to take μ*~0.26, which is quite a large value. It is interesting to see the larger value of μ* to
reproduce experimental Tc in case of SOC. Such a large value for μ* have been recently reported
for solid picene (C22H14)  by Subedi et. al. Thus dependence of μ* on SOC is interesting to
investigate in future.
The non magnetic character of Bi3Ni is also evident from Stoner condition i.e., I*N(EF), I
is Stoner parameter , N(EF) is total density of states at Fermi level due to d states of magnetic
elements, which here are 4-Ni atoms. We found I*N(EF) here to be~0.55 per unit cell, which for
per Ni atom is ~0.136. For ferromagnetism the value must be close to or greater than 1, which is
not the case for Bi3Ni. The value is so small (comparable to Al with 0.126 ) that any
possibility of ferromagnetism in this compound can be overruled. To further ensure the
possibility of any local minima near zero magnetic moment, we did fixed spin moment (FSM)
calculations by fixing total magnetic moment on the unit cell and observe corresponding energy.
The so obtained magnetic energy is then fitted to sixth order Ginzburg Landau (GL) equation
that gives us
B=0.155±0.0.035mRy/μ4B, C=-0.02053±0.0091 mRy/μ6B per Ni atom. Thus fitted plot for
moment per unit cell (4 fu i.e. 4Ni) versus energy is shown in Fig. 8(b). These values suggest that
system does not exhibit any signatures of ferromagnetism.
Summarily, we synthesized Bi3Ni superconductor by an easy solid state synthesis route
with Tc of 4.1K. Various physical properties of the compound including structure, AC/DC
magnetization and heat capacity etc. are presented and discussed. Detailed specific heat analysis
and DFT calculations revealed that this compound is having moderate electron-phonon coupling
constant of around 1.23 and Ni is non magnetic. Further it is concluded that ferromagnetic
interactions play no role in superconductivity of Bi3Ni. Further, the value of μ*=0.26 is required
to reproduce experimental value of Tc as per McMillan equation, while considering the strong
SOC character of Bi. This adds to the future scope to investigate the detailed SOC dependence of
μ* in Bi3Ni.
Jagdish Kumar, Anuj Kumar, and Arpita Vajpayee would like to thank the CSIR for the
award of Senior Research Fellowship to pursue their Ph. D degree. Authors thank Prof. R.C.
Budhani, DNPL and Dr. Hari Kishan, HOD for their keen interest and encouragement for
Table 1 Rietveld refined structure parameters of Bi3Ni
[a = 8.878(5)Å, b = 4.102(1)(5)Å, c = 11.479(1))Å, Rp = 7.03, Rwp= 9.88, Rexp= 3.50,2= 2.37 ,
Vol = 418.081A3]
Atom x y z
Bi1 0.293(5) 1/4 0.890(8)
Bi2 0.378(2) 1/4 0.588(7)
Bi3 0.407(1) 1/4 0.177(6)
Ni 0.069(5) 1/4 0.513(2)
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Figure 1(a) X-ray diffraction (XRD) pattern of studied Bi3Ni, the impurity Bi line is
Figure 1(b) Schematic unit cell of Bi3Ni.
Figure 2(a) DC magnetic susceptibility M(T) in ZFC (Zero-Field-Cooled) and FC (Field-
Cooled) situations at 10Oe for Bi3Ni.
Figure 2(b) AC magnetic susceptibility in both real (M/) and imaginary (M//) situations at
333Hz and 1Oe amplitude for Bi3Ni.
Figure 3 AC magnetic susceptibility in both real (M/) and imaginary (M//) situations at
fixed frequency of 33Hz and varying Amplitudes of 3-11Oe for Bi3Ni.
Figure 4(a) Isothermal magnetization (MH) plots at 2, 2.5, 3 and 3.5K in low field range
of <200Oe for Bi3Ni, the lower critical field (Hc1) is marked.
Figure 4(b) Isothermal magnetization (MH) for real part of AC susceptibility (M/) with
applied field of up to 5 kOe at 2K Bi3Ni, the upper critical field (Hc2) is marked.
Figure 4(c) Isothermal magnetization (MH) plots at 2K in high field range of up to
2500Oe in four quadrants for Bi3Ni.
Figure 4(d) Expanded MH plots at 2K in high field range of up to 2500Oe in four
quadrants for Bi3Ni, the Hirr is marked.
Figure 5 M(T) in both ZFC and FC situations at 10Oe for Bi3Ni in temperature range of
2 to 300K, the inset shows the M(H) at 20K with in 3000Oe in all four quadrants.
Figure 6 Typical Scanning Electron Microscope (SEM) picture of studied Bi3Ni.
Figure 7 Specific heat versus temperature plot CP(T) in temperature range of 2-100K for
studied Bi3Ni, the upper and lower insets show the electronic specific heat anomaly at Tc
and he fitting parameters respectively.
Figure 8(a) Calculated electronic density of states (DOS) for the fully relaxed structure
Bi3Ni, inset shows the DOS with and without SOC around Fermi level.
Figure 8(b) Fixed spin moment calculations of Bi3Ni
I (arb. unit)
S.G.= P n m a
Figure 3 (a)
H = 10Oe
Figure 3 (b)
Hac = 1Oe
f = 333Hz