Ab initio study for the structural, electronic, magnetic, optical, and thermoelectric properties of K2OsX6 (X = Cl, Br) compounds

Abstract

Density-functional theory based, first-principles spin-polarized calculations of the structural, electronic, magnetic, optical, and thermoelectric characteristics of K2OsX6 (X = Cl, Br) are presented. Structural optimization confirms the stability of these compounds in ferromagnetic phase with curie temperatures of 726 K (K2OsCl6) and 557 K (K2OsBr6). The calculated formation and cohesive energies present K2OsX6 compounds as thermodynamically stable and strongly bonded. Computed electronic properties explore both the compounds as halfmetallic. In the spin-up channel, they exhibit semiconducting nature, having direct band gap values of 2.69 eV (K2OsCl6) and 2.1 eV (K2OsBr6), while in spin-down configuration, they turn into metals. The calculated ferromagnetic total spins magnetic moment per formula unit is 2.00 μB for both the compounds with major contributions from Os-t2g states. The reasonable values of optical parameters like optical conductance, absorption factor, refractive index, and reflectivity potentially dedicate these compounds for optoelectronic applications. The calculated positive Seebeck coefficient with maximum values of 76.4 μV/K, for K2OsCl6, and 99.9 μV/K, for K2OsBr6, represent these compounds as p-type materials. The proposed compounds may achieve consideration in spintronic, thermoelectric, and optoelectronic devices.

Full text

RESEARCH ARTICLE
Ab initio study for the structural, electronic, magnetic,
optical, and thermoelectric properties of K
2
OsX
6
(X = Cl, Br) compounds
Rehan Ullah
1
| Malak Azmat Ali
1
| G. Murtaza
2
| Afzal Khan
3
|
Asif Mahmood
4
1
Department of Physics, Government Post
Graduate Jahanzeb College Saidu Sharif,
Swat, Pakistan
2
Materials Modeling Lab, Department of
Physics, Islamia College, Peshawar,
Pakistan
3
Department of Physics, University of
Peshawar, Peshawar, Pakistan
4
Chemical Engineering Department,
College of Engineering, King Saud
University, Riyadh, Saudi Arabia
Correspondence
Malak Azmat Ali, Department of Physics,
Government Post Graduate Jahanzeb
College Saidu Sharif, Swat 19130, Khyber
Pakhtunkhwa, Pakistan.
Email: azmatupesh@gmail.com, azmat@
jc.edu.pk
Summary
Density-functional theory based, first-principles spin-polarized calculations of
the structural, electronic, magnetic, optical, and thermoelectric characteristics
of K
2
OsX
6
(X = Cl, Br) are presented. Structural optimization confirms the sta-
bility of these compounds in ferromagnetic phase with curie temperatures of
726 K (K
2
OsCl
6
) and 557 K (K
2
OsBr
6
). The calculated formation and cohesive
energies present K
2
OsX
6
compounds as thermodynamically stable and strongly
bonded. Computed electronic properties explore both the compounds as half-
metallic. In the spin-up channel, they exhibit semiconducting nature, having
direct band gap values of 2.69 eV (K
2
OsCl
6
) and 2.1 eV (K
2
OsBr
6
), while in
spin-down configuration, they turn into metals. The calculated ferromagnetic
total spins magnetic moment per formula unit is 2.00 μ
B
for both the com-
pounds with major contributions from Os-t
2g
states. The reasonable values of
optical parameters like optical conductance, absorption factor, refractive index,
and reflectivity potentially dedicate these compounds for optoelectronic appli-
cations. The calculated positive Seebeck coefficient with maximum values of
76.4 μV/K, for K
2
OsCl
6
, and 99.9 μV/K, for K
2
OsBr
6
, represent these com-
pounds as p-type materials. The proposed compounds may achieve consider-
ation in spintronic, thermoelectric, and optoelectronic devices.
KEYWORDS
curie temperatures, ferromagnetic, optical properties, Seebeck coefficient, thermoelectric
properties
1|INTRODUCTION
Nowadays, investigation of half-metallic ferromagnetic
compounds has been a subject of great interest because
of their wide range of applications in spintronics and sen-
sors industry.
1
Half-metallic ferromagnets were intro-
duced by de Groot and his coworkers in early 1983.
2
Ideally, these compounds have two spin channels. In one
of these, a ferromagnet exhibits metallic band character.
While other channel makes its electronic nature as semi-
conducting or insulating. This special character results in
quantized magnetic moments, zero spin susceptibility,
and 100% spin-polarizability at Fermi level.
3
High Curie
temperature, magnetic moments, and tunable electronic
structure make these materials suitable for the device
based applications.
4
The most advantageous factor of
half-metallic ferromagnetic materials is the ability of
maintaining their spin polarizability up to a certain
Received: 27 February 2020 Revised: 26 April 2020 Accepted: 13 May 2020
DOI: 10.1002/er.5613
Int J Energy Res. 2020;44:9035–9049. wileyonlinelibrary.com/journal/er © 2020 John Wiley & Sons Ltd 9035

temperature limit (Curie temperature).
3
Therefore, these
compounds can be potential candidates for industrial-
based spin valves, spin filters, magnetic sensors, and
magnetic memories.
5,6
Recently, half-metallic ferromag-
netic behavior has been reported in different compounds
such as perovskites,
7–12
rock salts,
13, 14
Heusler,
15–20
half-
Heusler,
21,22
CrO
2,23
Fe
3
O
4
,
24
and double perovskites
25-31
etc. In addition, the shift of the electronic nature of a mate-
rial to half-metallic has been reported by doping factor.
32
However, presently, the major problem is that the avail-
able spin-based polarizability is insufficient for more effi-
cient spintronics based devices. The researchers all over
the world are investigating new ferromagnetic materials
having high enough spin polarizability with excellent opti-
cal and thermoelectric properties. In this regard, variant
perovskite compounds may play an important role. In this
family, ferromagnetism was experimentally reported in
Rb
2
CoF
6
and Cs
2
CoF
6
compounds.
33
While on the theo-
retical side, K
2
MoCl
6
,Cs
2
MoCl
6
, and Cs
2
NpBr
6
were
explored as half metallic ferromagnets with excellent
physical properties.
34-36
These studies approve the use of
variant perovskites in spintronics and related fields.
Therefore, we got the motivation to carry a research on
K
2
OsX
6
(X = Cl, Br) compounds in variant perovskites
family. These compounds were studied in few experimen-
tal
37,38
and theoretical
39,40
studies for structural stuff only.
While, for calculation of electronic, magnetic, optical, and
thermoelectric properties further experimental and theo-
retical studies are required. To cover the theoretical side,
we present our density functional theory
41
based calcula-
tions of the above properties. We hope that our computed
results will be useful in further experimental studies on
K
2
OsX
6
compounds for possible device based applications.
2|COMPUTATIONAL
METHODOLOGY
Spin-polarized computations of the physical properties for
K
2
OsX
6
(X = Cl, Br) are carried out in three steps: first step
involves the optimization of lattice constants and other
structural parameters; in the second step, the band struc-
tures, magnetic properties, and optical properties are calcu-
lated. These two steps were executed using the first-
principles FPLAPW (full potential linearized augmented
plane wave) Scheme
42
based on DFT
41
using Wien2k simu-
lation code.
43
Where relaxed lattice constants and other
structural parameters in NM (non-magnetic), FM (ferro-
magnetic), and AFM (anti-ferromagnetic) phases are calcu-
lated through optimization process, followed by the
investigation of electronic, magnetic, and optical properties.
In the third step, thermoelectric parameters are computed
using BoltzTrap package, based on semi-classical
Boltzmann theory.
44
According to the requirements of
DFT, GGA (generalized gradient approximation) of Wu-
Cohen
45
is used as exchange correlation potential. Usually,
GGA underestimates the exchange correlation effect in
strongly correlated electron systems and results in inconsis-
tent calculations. To overcome this problem, we used the
corrected correlation approximation GGA + U,
46
where U
is the Hubbard/C parameter. The value of the U parameter
(0.35 eV) is calculated by the linear response method.
47
The
cut-off parameter is used as R
MT
×K
max =
7, where R
MT
and
K
max
represent the smallest muffin tin radii and largest k-
value in momentum space, respectively. A dense mesh of
1000 k points is used for Brillouin zone (BZ) integration in
momentum space.
3|RESULTS AND DISCUSSION
3.1 |Thermodynamic stability, cohesive
energy, and structural parameters
K
2
OsX
6
compounds are reported to crystallize into anti-
fluorite cubic structure with space group No. 225 (Fm-
3m).
37
Each unit cell consists of nine atoms with a unit
cell edge of 9.729 and 10.30 Å for K
2
OsCl
6
and K
2
OsBr
6
,
respectively.
34
Potassium (K) and Osmium (Os) cations
occupy 8e (1/4, 1/4, 1/4) and 4b (0, 0, 0) Wyckoff's sites,
respectively, while X (Cl, Br) anions occupy octahedral
site 24a (u, 0, 0). u is an anion displacement parameter
having a value of 0.243 ± 0.002 for K
2
OsCl
6
and
0.244 ± 0.001 for K
2
OsBr
6.34
The structure of these com-
pounds is given in Figure 1.
Thermodynamic stabilities of K
2
OsX
6
are confirmed
by calculating the values of enthalpy of formation (H
f
)by
the relation (taken idea from).
48
ΔHf=ETotal K2OsX6
ðÞ−2EK−EOs −6EX:ð1Þ
FIGURE 1 Crystal structure of K
2
OsX
6
(X = Cl, Br) [Colour
figure can be viewed at wileyonlinelibrary.com]
9036 ULLAH ET AL.

Here, E
Total
(K
2
OsX
6
) represents the total ground
energy of K
2
OsX
6
, and E
K
,E
Os
, and E
X (X = Cl, Br)
are gro-
und state energies of the K (body center cubic), Os (hex-
agonal), and X (orthorhombic) in bulk form. The
calculated values of H
f
for K
2
OsCl
6
and K
2
OsBr
6
are
−25.95 and −20.89 eV, respectively. These energies favor
the thermodynamic stability of the studied compounds.
49
Moreover, the negative sign shows that during the forma-
tion of K
2
OsX
6
compounds, heat energy is released to the
outside environment. Therefore, the formation reaction
is exothermic.
Knowing how strongly the individual atoms are held
together in solids is helpful in determining the stability of
any material. This can be indicated from the values of
cohesive energies. The cohesive energy per atom of a
material A
x
B
y
, where x and y represent the number of A
and B atoms, respectively, can be calculated by the fol-
lowing relation.
50
EAxby
Coh =xEA
atom +yE
B
atom

−EAxBy
x+y:ð2Þ
Therefore, cohesive energies per atom for K
2
OsX
6
compounds were calculated by the below relation
EK2OsX6
Coh =2EK
atom +EOs
atom +6EX
atom

−EK2OsX6
9,ð3Þ
where EK
atom ,EOs
atom , and EX
atom represent isolated atomic
energies of K, Os, and X atoms, respectively. The calcu-
lated cohesive energies are 2.88 eV for K
2
OsCl
6
and
2.32 eV for K
2
OsBr
6
. These high values clearly indicate
that the individual atoms are strongly held together in
the crystal lattice of the studied compounds.
For the investigation of structural phase stability
on the basis of magnetism, the volume optimization
process is carried out in NM (non-magnetic), FM
(ferromagnetic), and AFM (anti-ferromagnetic) config-
urations. The plots of energy vs volume of the optimi-
zation process are given in Figure 2A,B. These plots
make it clear that both the K
2
OsX
6
compounds are sta-
ble in the FM phase. Therefore, we calculated the
structural stuff only in the FM phase. For which, the
values of energies and volumes of the figures (only FM
state) are fitted in the equation of state given by Birch-
Murnaghan (Equation [4])
51
in order to attain lattice
parameters like lattice constant, a

,unitcellground
state energy, E
o
, bulk modulus, B, and its pressure deri-
vate, B
/
.
EVðÞ=Eο+9VoBo
16
Vo
V

−1

Bo

+Vo
V

2
3
−1
()
2
6−4Vo
V

2
3
()#
:ð4Þ
The computed lattice parameters are listed in Table 1
along with available theoretical and experimental values
for comparison. This comparison favors our calculated
values of lattice constants, as these are in the range of
previously calculated values.
Thus, the FM phase stability of both compounds is
confirmed above. Therefore, Curie temperatures (T
C
)of
these compounds are calculated by the classical Heisen-
berg model in mean-field approximation, that is,
K
B
Tc =2ΔE/3x. Here, ΔEis the difference of energy
between the FM and AFM phases; K
B
represents the
Boltzmann constant while x represents the concentration
of doping atoms. The calculated values of T
C
for K
2
OsCl
6
FIGURE 2 Energy vs volume curves for non-magnetic (NM), ferromagnetic (FM), and anti-ferromagnetic phases of A, K
2
OsCl
6
B,
K
2
OsBr
6
[Colour figure can be viewed at wileyonlinelibrary.com]
ULLAH ET AL.9037

TABLE 1 Calculated value of
lattice constant (a
o
), Bulk modulus (B),
and pressure derivative (B0) under GGA
scheme for K
2
OsX
6
(X = Cl, Br) in
stability (ferromagnetic) phase
Compound Status a
o
(Å) B (GPa) B
/
E(Ry)
K
2
OsCl
6
Present 9.6452 49.99 5.00 −42 504.3707
Experimental 9.729
37
-- -
Theoretical 9.819
39
-- -
9.774
40
K
2
OsBr
6
Present 10.20 41.25 5.00 −68 242.9675
Experimental 10.30
37
-- -
Theoretical - - - -
FIGURE 3 Calculated band plots of K
2
OsCl
6
within GGA and GGA + U [Colour figure can be viewed at wileyonlinelibrary.com]
9038 ULLAH ET AL.

and K
2
OsBr
6
are 726 and 557 K, respectively. These high
values make K
2
OsX
6
compounds ideal for spintronic
devices.
3.2 |Electronic properties
Valuable information in regard to electronic properties of
K
2
OsX
6
compounds was evaluated via calculation of
band structures, total and partial density of states (TDOS
and PDOS). The computed spin-polarized band plots
through GGA and GGA + U along different symmetry
directions are shown in Figure 3 (for K
2
OsCl
6
) and
Figure 4 (for K
2
OsBr
6
). The figure shows that in spin-
down configuration the Fermi level remains completely
occupied and hence implies the metallic nature for the
K
2
OsX
6
compound, and for spin-up states, the Fermi
level remains vacant, dropping in a gap, and thus offering
FIGURE 4 Calculated band plots of K
2
OsBr
6
within GGA and GGA + U [Colour figure can be viewed at wileyonlinelibrary.com]
ULLAH ET AL.9039

the semi-conducting nature for K
2
OsX
6
compounds. In
the semiconducting configuration, the conduction band
minimum and valence band maxima lie at the same sym-
metry point X. Therefore, these compounds are basically
direct band gap semiconductors. Table 2 enlists the band
values of K
2
OsX
6
(X = Cl, Br). We have lack of experi-
mental values. Therefore, we cannot give a guarantee of
the accuracy of any approximation used. However, the
addition of Hubbard term (U) enhances the band gap
and makes them closer to experimental values.
52
Hence
we will use the values of GGA + U for further
calculations.
The TDOS in Up and Down spin states within GGA
and GGA+ U of K
2
OsCl
6
and K
2
OsBr
6
compounds are
presented in Figures 5A,B and 6A,B, respectively. It is
observed from plots that in the Up-spin configuration the
Fermi level remains empty while in spin-down configura-
tion, it remains occupied, resulting 100% polarizability
(P) in the case of both compounds. The percentage of P is
calculated from the below relation.
53
P=N"EF
ðÞ−N#EF
ðÞ
N"EF
ðÞ+N#EF
ðÞ
×100%,ð5Þ
where N
"
(E
F
) and N
#
(E
F
) are Fermi level TDOS in up
and down spin states, respectively.
The elemental contribution toward band structures
was investigated by computing spin-polarized PDOS
through GGA + U, as shown in Figure 7A,B. The figure
clearly shows that the valence band, extended from −4to
0 eV, is majorly occupied by Os-d, Cl-pstates with minor
contribution of K-dstates, whereas the conduction band
from 0 to 12 eV is majorly populated by K-d, Os-d, Cl-p,
and Cl-dstates. Valence band minimum and maximum
in K
2
OsX
6
are majorly composed of by X-pand Os-d
states, respectively. Conduction band maximum of both
compounds is majorly occupied by K-dstates. Moreover,
from the figures, it can be seen that in-spin down config-
uration the metallic nature of K
2
OsX
6
is due to the pres-
ence of Os-dstates on Fermi level with feeble
involvement of X-pstates, while in the case of spin-down
configuration, these states are drawn deep into the
valence band, thus generating a gap and turning the com-
pounds as semiconducting.
3.3 |Magnetic properties and
ferromagnetic origin
The magnetic properties are the most significant factor
for suitability of a material in spintronics. There are two
possible exchanges that are responsible for magnetism in
compounds, the double-exchange and the super
exchange.
54
Super exchange is coupling between two
nearby cations in a compound via non-magnetic anions.
Where d-orbitals of both atoms have the same localized
electrons or differ by 2. On the contrary, double exchange
is magnetic interaction in which one electron moves from
one atom to another in a compound by retaining its spin
motion.
55
It differs from super exchange by the fact that
no bridging is required for the transfer of electron. Super
exchange causes anti-ferromagnetism
56
while double
exchange is responsible for producing ferromagnetism in
compounds.
55,57
Here, in our case, we already confirmed
the FM nature K
2
OsX
6
compounds through optimization.
In addition, the positive values of total difference of
energy between the FM phase and AFM phase
(ΔE=E
AFM
−E
FM
) are the evidence of FM nature of
these materials. Therefore, double exchange mechanism
is responsible for the observed ferromagnetism in cubic
K
2
OsX
6
, in which one electron of Os-dorbital moves and
interacting with X-porbitals. To find the ferromagnetic
strength of these compounds, we computed unit cell
magnetic moments for interstitial region, individual
atoms, and total magnetic moments, M
Tot
, in Bohr's mag-
neton (μ
B
) via GGA and GGA + U and presented in
Table 3. The M
Tot
per formula unit was computed from
the difference between the number of spin-down (#) and
the spin-up (") occupied states, which include the contri-
bution from the interstitial region, K, Os, and X ions. Our
calculated total magnetic moment per formula unit is
2.00 μ
B
for both K
2
OsX
6
compounds. Form Table 3, it can
be seen that Os atom and interstitial region majorly con-
tribute to the M
Tot
. The reason behind the higher values
TABLE 2 Calculated values of
band gap at different symmetries for
K
2
OsX
6
(X = Cl, Br) using GGA and
GGA + U
Compound Configuration
Band Gap (eV)
E
g
(L-L)E
g
(Γ-Γ)E
g
(X-X)E
g
(W-W)
K
2
OsCl
6
GGA 3.11 3.84 1.93 2.25
GGA + U 3.87 4.43 2.69 2.99
K
2
OsBr
6
GGA 2.84 3.45 1.56 1.91
GGA + U 3.53 3.57 2.1 2.49
9040 ULLAH ET AL.

of magnetic moments in interstitial region is the strong
hybridization of Os-dand X-pstates on Fermi level
(Figure 9) at the octahedral site, OsX
6
. The pand dstates
hybridization shrinks the local magnetic moments
49,58
and increases corresponding interstitial magnetic
moments. The investigated values are in the range of
magnetic moments of other related compounds.
59
To deeply apprehend the mechanism of ferromagne-
tism in K
2
OsX
6
, we have to go deep inside into the
crystal-field-splitting and spin-splitting. As discussed
FIGURE 5 Calculated total density of states of K
2
OsCl
6
within A, GGA and B, GGA + U [Colour figure can be viewed at
wileyonlinelibrary.com]
FIGURE 6 Calculated total density of states of K
2
OsBr
6
within A, GGA and B, GGA + U [Colour figure can be viewed at
wileyonlinelibrary.com]
TABLE 3 Calculated values of
total and atomic magnetic moments
(μ
B
) for K
2
OsX
6
(X = Cl, Br) using GGA
and GGA + U
Compound Configuration M
Int
M
K
M
Os
M
x
M
Tot
X = Cl X = Br
K
2
OsCl
6
GGA 0.3046 0.0023 1.6325 0.0606 2.00
GGA + U 0.2393 0.0017 1.7072 0.0518 2.00
K
2
OsBr
6
GGA 0.3267 0.0022 1.6104 0.0607 2.00
GGA + U 0.2560 0.0019 1.6914 0.0507 2.00
ULLAH ET AL.9041

above in Figure 7 that in both up and down spin chan-
nels the total DOS is mainly composed of Os-dstates
around the Fermi level. So, we paid more attention to Os-
dstates of both compounds. In view of DOS peaks near
the Fermi level, the electrostatic field due to the octahe-
dral six X ions around Os site split the Os-dstates into
the doubly degenerate e
g
states, having high energy, and
the triply degenerate t
2g
states residing at low energy,
which occurs due to the Coulomb repulsion experienced
by the negative charge on the non-bonding electrons of
anions compared with the electrons away from the
anions.
60
Such coulomb repulsion, in turn, split the e
g
states into d
z2,
d
x2-y2
states, and t
2g
states into d
xy
,d
yz
,
and d
zx
,inbothup(") and down (#) spin channels. The
results of e
g
states splitting is the lowering of energy of
d
z2
state at the expenditure of a raise in the energy of
d
x2-y2
states, while for t
2g
,d
xy
is shifted to a higher energy
as compared with d
zx
and d
yz
states as shown in Figure 8.
The spin splitting of about 1.4 eV in both studied com-
pounds makes the spin-down states of the triply degener-
ate t
2g
cross the Fermi level, resulting in the partial
occupation, and spin-up t
2g
states are not occupied and
lie at about −1.1 eV (K
2
OsCl
6
) and 0.9 eV (K
2
OsBr
6
)
under the Fermi level. The e
g
states of up and down spin
channels of K
2
OsCl
6
lying, respectively, at about 1.7 and
2.2 eV both are not occupied, similar is the case for
K
2
OsBr
6
as shown in Figure 9. So the chief involvement
to the total magnetic moments comes from the Os-t
2g
states. The considerable contribution of the six X atoms
to the total moment consequences from the hybridization
between the X-pand the Os-t
2g
states around Fermi level
as indicated in Figure 9.
3.4 |Optical properties
The response of K
2
OsX
6
(X = Cl, Br) compounds to the
incident electromagnetic radiations was checked by cal-
culating the optical properties like optical conductivity
σ(ω), absorption coefficient α(ω), refractive index n(ω),
and reflectivity R(ω) in the spin-up channel (for semicon-
ductor structure). All these optical functions were investi-
gated within energy limits of 0 to 6 eV and illustrated in
Figure 10. While, the corresponding important values are
given in Table 4.
The optical conductance, σ(ω), and absorption factor,
α(ω), possibly can be calculated by the relations.
61
σωðÞ=2WCV ℏω
E∘2
!;αωðÞ=4πkωðÞ
λ,ð6Þ
where W
CV
represents transition probability per unit
time and k(ω) is frequency-dependent extension coeffi-
cient. The optical conductivity is actually the extension of
the electrical transport to optical frequencies. The simu-
lated optical conductance for the K
2
OsX
6
compounds is
shown in Figure 10A. Optical conductance starts approxi-
mately at fundamental band gap for both compounds.
Peak values of σ(ω) were observed at 2.99 eV (K
2
OsCl
6
)
and 2.49 eV (K
2
OsBr
6
). This may be attributed to the
transition of charge along the W symmetry point in case
of both compounds. The maximum values of optical con-
ductivities lie in the visible range. Thus, these com-
pounds can be used effectively for solar cells application.
Absorption coefficient α(ω) is a valuable optical
parameter, which quantifies how far a light of a specific
FIGURE 7 Calculated partial density of states of A, K
2
OsCl
6
and B, K
2
OsBr
6
within GGA + U [Colour figure can be viewed at
wileyonlinelibrary.com]
9042 ULLAH ET AL.

wavelength can penetrate into a material before it is
absorbed. Figure 10B shows the simulated plot for
absorption coefficients. From the figure, it is clear that
the absorption curves follow the same trend as σ(ω)
because on absorption of photons, the charges become
available for conduction.
Refractive index n(ω) illustrates the refraction behav-
ior of a compound for its applicability in optical instru-
ments suchlike waveguides, photonic crystals, detectors,
and solar cells.
62
One can calculate n(ω) using the below
Equation
61
:
nωðÞ=1
21
=
2ε1ωðÞ
2+ε2ωðÞ
2

1=2
−ε1ωðÞ
hi
1
=
2:ð7Þ
Figure 10C shows the computed refractive indices for
K
2
OsX
6
compounds with respect to the incident energy
of electromagnetic radiations. The calculated important
FIGURE 8 Distribution of Os-d
states in K
2
OsX
6
(X = Cl, Br) at
octahedral site [Colour figure can be
viewed at wileyonlinelibrary.com]
FIGURE 9 Investigated crystal
field splitting of Os-dstates in K
2
OsX
6
(X = Cl, Br) [Colour figure can be
viewed at wileyonlinelibrary.com]
ULLAH ET AL.9043

values are presented in Table 4. Figure 10C specifies that
the refractive indices of K
2
OsX
6
increases with photon
energies and reach the maximum peak values of 4.1 for
K
2
OsCl
6
, and 4 for K
2
OsBr
6
. Beyond maximum value, the
refractive index of both compounds starts decreasing and
becomes lower as below one in specific energy limits.
The value of refractive index lesser than one gives indica-
tions of increase in group velocity of the falling electro-
magnetic radiation beyond c (Vg = c/n). In these energy
ranges, the material becomes superluminal.
63
Reflectivity quantifies the reflection of incident light
from a surface of materials as given by the following
relation
61
;
RωðÞ=
n−1

n+1

2
:ð8Þ
The computed reflectivities for K
2
OsX
6
compounds
are shown in Figure 10D. The zero-frequency reflectivity
starts around from 0.12 and 0.17 for K
2
OsCl
6
and
K
2
OsBr
6
, respectively. The reflectivity increases as the
energy gets increased and achieves a maximum value of
60% (for K
2
OsCl
6
) and 56% (for K
2
OsBr
6
). In high reflec-
tivity energy ranges, the studied material reflects most of
the incident electromagnetic radiations, thus shows
metallic behavior. Moreover, the compounds in this
range of energy can be used for shielding purposes where
the variation occurs in the magnitude of reflectivity with
the frequency of incident radiations, which is suitable for
Bragg's Reflector.
64
From the figure it can be seen that
the reflectivity peak decreases from Cl to Br. This
decreasing trend was also reported in other correlated
compounds.
65
On the basis of present calculations, K
2
OsX
6
com-
pounds are recommended for use in various optical and
optoelectronic devices.
3.5 |Thermoelectric response
The ever increasing demand of energy has compelled the
scientific researchers to search for novel materials and
devices that are highly efficient for the conversion of
thermal energy into electrical energy. Thermoelectric
(TE) materials can be used in this perspective. These
materials work on Seebeck or Peltier effect
66
and are
FIGURE 10 Computed A, optical conductivity, B, absorption coefficient, C, refractive index, and D, reflectivity for K
2
OsX
6
(X = Cl, Br)
[Colour figure can be viewed at wileyonlinelibrary.com]
TABLE 4 Calculated values of optical parameters under
GGA + U Scheme for K
2
OsX
6
(X = Cl, Br)
Compound σ(ω)
max
α(ω)
max
n(ω)
max
R(ω)
max
K
2
OsCl
6
7642 94.4 4.01 0.60
K
2
OsBr
6
5718 71.58 3.96 0.56
9044 ULLAH ET AL.

useful for power generation. Consequently, TE materials
have diverse applications in energy devices.
67,68
Ideal thermoelectric material has low thermal
conductivity K (W/mK), high electronic conductivity
σ(Ωm)
−1
, and high Seebeck coefficient, S (μV/K).
69
On
the other side, the thermal conversion power can be
deduced from the power factor (PF) = S
2
σand figure of
merit (ZT). In this work, carrier concentration n,σ,
k
e
, S, PF, and Figure of merit (ZT) are elucidated for
K
2
OsX
6
(X = Cl, Br) using semiclassical Boltzmann
transport theory encoded in BoltzTrap package
44
while
the lattice thermal conductivity K
l
is calculated via
Slack's Equation.
70
Theseparametersareplottedasthe
function of temperature in Figures 11 and 12 and corre-
lated values at room temperature are tabulated in
Table 5. As these properties are sensitive to Brillouin
zone sampling, so, for the accurate convergence we have
manipulated constant relaxation time (10
−14
)approxi-
mation with a dense mesh of 100 000 k-points in
Brillouin zone.
FIGURE 11 Computed temperature dependent plots of A,
electrical conductivity, B, electronic thermal conductivity, and C,
lattice thermal conductivity of K
2
OsX
6
(X = Cl, Br) [Colour figure
can be viewed at wileyonlinelibrary.com]
FIGURE 12 Computed temperature dependent plots of A,
Seebeck coefficient and B, power factor of K
2
OsX
6
(X = Cl, Br)
[Colour figure can be viewed at wileyonlinelibrary.com]
ULLAH ET AL.9045

σdescribes the flow of free electrons in compounds.
Energy band theory illustrates that conductors have free
charges for conduction while semiconductors require
external energy for the charges generation. The computed
plots of σfor K
2
OsX
6
compounds within temperature
range of 200 K to 900 K are presented in Figure 11A. The
figure shows that σdecreases with increase in temperature
from 1.27 ×10
6
(Ωm)
−1
to 0.47 ×10
6
(Ωm)
−1
for K
2
OsCl
6
and from 1.01 ×10
6
(Ωm)
−1
to 0.44 ×10
6
(Ωm)
−1
for
K
2
OsBr
6
. Thus, both the materials have high capability of
convergence of thermal into electrical energy. The room
temperature values of σarelistedinTable5.
The calculated electronic thermal conductivity, k
e
, for
K
2
OsX
6
compounds is plotted as shown in Figure 11B.
From the plot, it can be supposed that the k
e
of both
investigated compounds is a direct function of tempera-
ture. For K
2
OsCl
6
, it increased from 0.0939 to 5.25
(W/mK), and for K
2
OsBr
6
, it increased from 0.104 to 5.03
(W/mK). Another correlated compound
69
also exhibits
such type of behavior. The excellent TE material should
have high σand low k
e
. Herein, our investigated com-
pounds obey the criteria of an excellent TE material.
The lattice thermal conductivity, k
l
, is an essential
thermal property of solids, which describe the conduction
of heat through the vibration of lattice ions (phonons)
within materials. We have used the famous Slack's
model
70
(Equation [9]) for the calculation of k
l
for
K
2
OsX
6
(X = Cl, Br) within the temperature range from
200 to 900 K, as shown in Figure 11C. The resulted values
at room temperature are given in Table 5.
Kl=AΘ3
DV
1
3
totM
γ2n2
3T,ð9Þ
where γis the Grüneisen parameter, Ais γreliant coeffi-
cient (3.1 ×10
−6
for K
l
in W/mK),
71
Mis the average
atomic mass of all the atoms (in unit of amu), Vis the aver-
age atomic volume (in unit of Å
3
) in the primitive unit cell,
Tis the absolute temperature, nis the total number of
atoms per unit cell, and θ
D
is Debye temperature (in unit
of K).
70
θ
D
(320.10 for K
2
OsCl
6
and 241.16 for K
2
OsBr
6
)
and γ(2.33 for both K
2
OsX
6
compounds) are calculated
through Quasi-harmonic Debye approximation.
72
Because
this model gives values of θ
D
and γat 0 GPa pressure and
0 K temperature as calculated from elastic constants.
73
From Figure 11C, it can be seen that the k
l
of both
compounds decreases with rise in temperature. This indi-
cates less phonon-phonon interaction at lower tempera-
tures ranges. At high temperatures, the phonon
interaction increases, thus results in lowering the k
l
values. Another essential TE parameter that explains the
thermoelectric conversion of a material is its S. This can
be calculated via the following relation
74
:
S=8
3eh2π2K2
BmTπ
3n

1
2,ð10Þ
where k
B
,h,e,T,n, and m* are the Boltzmann constant,
Planck constant, electronic charge, absolute temperature,
carrier concentration, and effective mass of charges,
respectively. The computed temperature-dependent S of
the studied compounds is plotted against temperature
from and shown in Figure 12A. The figure shows that the
calculated values of S are positive in the entire range of
temperature, revealing the presence of p-type charge car-
riers in both compounds. Moreover, for both K
2
OsX
6
compounds, S increases with rise in temperature.
The thermoelectric device performance can be illus-
trated from the product of S
2
and σ, generally termed as
power factor (PF = S
2
σ).
75
Figure 12B shows that PF has
the same trend as S for both compounds.
The potential of the material in thermoelectric appli-
cations is not only determined by PF value but more
accurately from figure of merit (ZT = S
2
σT/κ) value. The
computed ZT plots of the studied compounds are shown
in Figure 12C. The maximum ZT value of K
2
OsCl
6
(0.49)
and K
2
OsBr
6
(0.8) suggests that these compounds have
promising thermoelectric applications.
Overall values of S and FP and ZT make K
2
OsX
6
com-
pounds attractive for green energy generation.
4|CONCLUSION
In this work, a comprehensive spin-resolved calculations
of structural, electronic, magnetic, optical, and thermo-
electric properties of K
2
OsX
6
(X = Cl, Br) are carried out
within highly precise DFT using FPLPAW method
encoded in Wein2k. Structural optimization established
the stability of these compounds in the ferromagnetic
TABLE 5 Computed values of transport parameters of K
2
OsX
6
(X = Cl, Br) at room temperature (300 K)
Compound σ(Ωm)
−1
k (W/mK) K
p
(W/mK) S (μV/K) S
2
σ(mW/mK
2
)ZT
K
2
OsCl
6
0.89 ×10
6
0.9 3.50 6.05 0.0314 1.06 ×10
−2
K
2
OsBr
6
0.69 ×10
6
1 2.46 10.0 0.0580 1.75 ×10
−2
9046 ULLAH ET AL.

phase. The computed lattice parameters are found in
close resemblance with available experimental results.
The calculated negative formation energies show that the
reaction involved in the formation of both the com-
pounds is exothermic. Moreover, high values of cohesive
energies predict strong bonding between constituent
atoms in these compounds. The computed spin-resolved
electronic properties suggest the semiconducting nature
of the investigated compounds in spin-up configuration
and metallic in spin-down configuration. From magnetic
investigations it is concluded that the ferromagnetism of
K
2
OsX
6
compounds, originated from indirect exchange
between Os atoms via X (Cl, Br) atoms. Moreover, the
crystal field splitting study shows that the Os-t
2g
sates are
responsible for the half metallic behavior. Our calculated
optical coefficients clarify that K
2
OsX
6
materials have
high absorption coefficient visible range of electromag-
netic spectrum. Boltzmann theory and Slack's model-
based computed thermal characteristics specified high
electrical conductivity and low lattice thermal conductiv-
ity of K
2
OsX
6
compound at low temperatures. The data
obtained in this work recommend the studied com-
pounds for spintronic, optoelectronic, thermo-electronic,
and magneto-electronic based devices. Keeping in view
the proper format of the paper, we could not investigate
some properties like elastic, mechanical, acoustical, and
detailed thermodynamic. These properties should be
investigated in future to disclose the furthermore prolific
characteristic of these compounds for the industrial use.
ACKNOWLEDGMENT
One of the authors (A. Mahmood) extend their apprecia-
tion to Deanship of Scientific Research King Saud Uni-
versity for funding the work through the research group
project No. RGP-311.
ORCID
Malak Azmat Ali https://orcid.org/0000-0002-6290-
0317
REFERENCES
1. Prinz GA. Magnetoelectronics. Science. 1998;282:1660-1663.
2. de Groot RA, Mueller FM, Engen PGV. New class of materials:
half-metallic ferromagnets. Phys Rev Lett. 1983;50:2024.
3. Li L, Gao Q, Lei G, Xie HH, Deng JB, Hu XR. First-principles
investigations on electronic and thermodynamic properties of
double perovskite Sr
2
XMoO
6
(X=Ge and Si). J Phys Chem
Solids. 2016;94:30.
4. Kubler J, Williams AR, Sommers CB. Formation and coupling
of magnetic moments in Heusler alloys. Phys Rev B. 1983;28:
1745-1755.
5. Katsnelson MI, Irkhin VY, Chioncel L, Lichtenstein AI, De
Groot RA. Half-metallic ferromagnets: from band structure to
many-body effects. Rev Mod Phys. 2008;80:315-378.
6. Atsufumi H, Koki T. Future perspectives for spintronic devices.
J Phys D. 2014;47:193001.
7. Bouadjemi B, Bentata S, Abbad A, Benstaali W, Bouhafs B.
Half-metallic ferromagnetism in PrMnO
3
perovskite from first
principles calculations. Solid State Commun. 2013;168:6-10.
8. Abbad A, Benstaali W, Bentounes HA, Bentata S,
Benmalem Y. Search for half-metallic ferromagnetism in
orthorhombic Ce(Fe/Cr)O
3
perovskites. Solid State Commun.
2016;228:36-42.
9. Park JH, Vescovo E, Kim HJ, Kwon C, Ramesh R,
Venkatesan T. Direct evidence for a half-metallic ferromagnet.
Nature. 1998;392:794-796.
10. Dar SA, Khandy SA, Islam I, et al. Temperature and pressure
dependent electronic, mechanical and thermal properties of
f-electron based ferromagnetic barium neptunate. Chin J Phys.
2017;55:1769-1779.
11. Hamlat M, Boudia K, Amara K, Khelfaoui F, Marbouh N. Half-
metallic stability of the cubic Perovskite KMgO
3
.Comput Con-
dens Matter. 2020;23:e00456.
12. Khandy SA, Gupta DC. Investigation of the transport, struc-
tural and mechanical properties of half-metallic REMnO
3
(RE = Ce and Pr) ferromagnets. RSC Adv. 2016;6:97641.
13. Zhang W, Song Z, Peng B, Zhang W. Electronic structure and
magnetism in M(=IA, IIA)C compounds with the rocksalt
structure. J Appl Phys. 2012;112:043905.
14. Lei G, Liu XX, Xie HH, Li L, Gao Q, Deng JB. First-principle
study of half-metallic ferromagnetism in rocksalt XO (X=Li, K,
Rb, Cs). J Magn Magn Mater. 2016;397:176.
15. Khandy SA, Chai JD. Robust stability, half-metallic ferrimagne-
tism and thermoelectric properties of new quaternary Heusler
material: a first principles approach. J Magn Magn Mater. 2020;
502:166562.
16. Liu GD, Dai XF, Liu HY, et al. Mn
2
CoZ(Z=Al,Ga,in,Si,Ge,Sn,
Sb) compounds: structural, electronic, and magnetic properties.
Phys Rev B. 2008;77:014424.
17. Caraballo-Vivas RJ, Tedesco JCG, Checca NR, et al. Experi-
mental and theoretical evidences that atomic disorder sup-
presses half-metallicity of Heusler compounds. Intermetallics.
2019;111:106502.
18. Khandy SA, Islam I, Gupta DC, Laref A. Full Heusler alloys
(Co
2
TaSi and Co
2
TaGe) as potential spintronic materials
with tunable band profiles. JSolidStateChem. 2019;270:
173-179.
19. Liu W, Zhang X, Jia H, Khenata R, Dai X, Liu G. Theoretical
investigations on the mechanical, magneto-electronic proper-
ties and half-metallic characteristics of ZrRhTiZ (Z = Al, Ga)
quaternary Heusler compounds. Appl Sci. 2019;9:883.
20. Pourebrahim G, Ahmadian F, Momeni P. Robust half-
Metallicity in quaternary Heusler compounds KSrNZ (Z = O,
S, and se). J Supercond Nov Magn. 2019;32:3305-3314.
21. Singh M, Saini HS, Kumar S, Kashyap MK. Effect of substitut-
ing sp-element on half metallic ferromagnetism in NiCrSi
Heusler alloy. Comput Mater Sci. 2012;53:431-435.
22. Özdemir EG, Merdan Z. First principle predictions on half-
metallic results of MnZrX (X = In, Tl, C, Si, Ge, Sn, Pb, N, P,
As, Sb, O, S, Se, Te) half-Heusler compounds. J Supercond Nov
Magn. 2019;491:165567.
23. Schwarz K. CrO
2
predicted as a half-metallic ferromagnet.
J Phys F. 1986;16:L211-L215.
ULLAH ET AL.9047

24. Jeng HT, Guo GY. First-principles investigations of the elec-
tronic structure and magnetocrystalline anisotropy in strained
magnetiteFe3O4. Phys Rev B. 2002;65:094429.
25. Berri S. First-principles study on half-metallic properties of the
Sr
2
GdReO
6
double perovskite. J Magn Magn Mater. 2015;
385:124.
26. Koepernik K, Eschrig H. Full-potential nonorthogonal local-
orbital minimum-basis band-structure scheme. Phys Rev B.
1999;59:1743-1757.
27. Djefal A, Amari S, Obodo KO, et al. Half-metallic ferromagne-
tism in double perovskite Ca
2
CoMoO
6
compound: DFT+U cal-
culations. Spin. 2017;7:1750009.
28. Khandy SA, Gupta DC. Electronic structure, magnetism and
thermoelectricity in layered perovskites: Sr
2
SnMnO
6
and
Sr
2
SnFeO
6
.J Supercond Nov Magn. 2017;441:166.
29. Kato H, Okuda T, Okimoto Y, et al. Metallic ordered double-
perovskite Sr
2
CrReO
6
with maximal curie temperature of
635 K. Appl Phys Lett. 2002;81:328-330.
30. Hauser AJ, Williams RE, Ricciardo RA, et al. Unlocking the
potential of half-metallic Sr
2
FeMoO
6
films through controlled
stoichiometry and double-perovskite ordering. Phys Rev B.
2011;83:014407.
31. Haid S, Bouadjemi B, Houari M, et al. Investigation of DFT+U
effect of holmium rare-earth on the electronic, magnetic and
the half-metallic ferromagnetic properties' of double perovskite
Ba
2
HoReO
6
.Solid State Commun. 2019;294:29-35.
32. Wang X, Chen X, Dong R, Huang Y, Lu W. Ferromagnetism in
carbon-doped ZnO films from first-principle study. Phys Lett A.
2009;373:3091-3096.
33. Quail JW, Rivett GA. Complex fluorides of tetravalent cobalt.
Can J Chem. 1972;50:2447-2450.
34. Faizan M, Khan SH, Murtaza G, Khan A, Laref A. Electronic
and magnetic properties of alkali metal chlorides A
2
MC
l6
(A = K, Rb, Cs; M = Mn, Mo): a density functional theory
study. Int J Mod Phys B. 2019;33:1950072.
35. Faizan M, Khan SH, Khan A, Laref A, Murtaza G. Ab-initio
prediction of structural, electronic and magnetic properties of
hexafluoromanganete(IV) complexes. Int J Mod Phys B. 2018;
32:1850270.
36. Ali MA, Murtaza G, Laref A. Exploring the ferromagnetic half
metallic nature of Cs
2
NpBr
6
via spin polarized density func-
tional theory. Chin J Phys. 2020;29:066102. https://doi.org/10.
1088/1674-1056/ab7da4.
37. McCullough JD. The crystal structure of Potassium
chlorosmate, K
2
OsCl
6
, and of potassium bromosmate, K
2
OsBr
6
.
Z Kristallogr - Cryst Mater. 1936;94:143.
38. Turner AG, Clifford AF, Rao CR. Crystallographic data. 174.
Potassium hexachloro-osmate, K
2
OsCl
6
, and potassium
hexabromo-osmate, K
2
OsBr
6
.Anal Chem. 1958;30:1708.
39. Brik MG, Kityk IV, Phys J. Modeling of lattice constant and
their relations with ionic radii and electronegativity of consti-
tuting ions of A
2
XY
6
cubic crystals (A=K, Cs, Rb, Tl; X=tetra-
valent cation, Y=F, Cl, Br, I). J Phys Chem Solids. 2011;72:
1256-1260.
40. Sidey V. A simplified empirical model for predicting the lattice
parameters for the cubic perovskite-related inorganic A
2
BX
6
halides. J Phys Chem Solids. 2019;126:310.
41. Hohenberg P, Kohn W. Inhomogeneous electron gas. Phys Rev.
1964;136:B864.
42. Perdew P, Wang Y. Accurate and simple analytic representa-
tion of the electron-gas correlation energy. Phys Rev B. 1992;45:
13244.
43. P. Blaha, et al., (2001). WIEN2k: An augmented plane wave+
local orbitals program for calculating crystal properties.
44. Madsen GKH, Schwarz K, Singh DJ. BoltzTraP. A code for cal-
culating band-structure dependent quantities. Comput Phys
Commun. 2006;175:67-71.
45. Wu Z, Cohen RE. More accurate generalized gradient approxi-
mation for solids. Phys Rev B. 2006;73:235116.
46. Dar SA, Srivastava V, Sakalle UK, Parey V, Pagare G. DFT
investigation on electronic, magnetic, mechanical and thermo-
dynamic properties under pressure of some EuMO3(M = Ga,
in) perovskites. Mater Res Exp. 2017;4:106104.
47. Cococcioni M, De Gironcoli S. Linear response approach to the
calculation of the effective interaction parameters in theLDA
+Umethod. Phys Rev B. 2005;71:035105.
48. Sharma R, Dar SA, Mishra AB. Structure, electronic, magnetic
and optical properties of cubic Hf1-x(TM)xO
2
(X = 0, 0.25,
TM = Mn, Fe, Co, Ni): a first principle investigation. J Alloys
Compd. 2019;791:983-993.
49. Sabir B, Murtaza G, Mahmood Q, Ahmad R, Bhamu KC. First
principles investigations of electronics, magnetic, and thermo-
electric properties of rare earth based PrYO
3
(Y=Cr, V) perov-
skites. Curr Appl Phys. 2017;17:1539-1546.
50. Yakoubi A, Baraka O, Bouhafs B. Structural and electronic
properties of the laves phase based on rare earth type BaM
2
(M=Rh, Pd, Pt). Results Phys. 2012;2:58-65.
51. Murnaghan FD. The compressibility of media under extreme
pressures. Proc Natl Acad Sci U S A. 1944;30:244-247.
52. Singh KD, Pandit R, Kumar R. Effect of rare earth ions on
structural and optical properties of specific perovskite
orthochromates; RCrO
3
(R = La, Nd, Eu, Gd, Dy, and Y). Solid
State Sci. 2018;85:70-75.
53. Hoat D. Investigation on new equiatomic quaternary Heusler
compound CoCrIrSi via FP-LAPW calculations. Chem Phys.
2019;523:130-137.
54. Blundell S. Magnetism in Condensed Matter. New York, NY:
Oxford University Press; 2001.
55. Zener C. Interaction between the d-shells in the transition
metals. II. Ferromagnetic compounds of manganese with
perovskite structure. Phys Rev. 1951;82:403-405.
56. Sasioglu E, Sandratskii LM, Bruno P. First-principles calcula-
tion of the intersublattice exchange interactions and Curie tem-
peratures of the full Heusler alloysNi2MnX(X=Ga,In,Sn,Sb).
Phys Rev B. 2004;70:024427.
57. de Gennes PG. Effects of double exchange in magnetic crystals.
Phys Rev. 1960;118:141-154.
58. Zhang H, Liu W, Lin T, Wang W, Liu G. Phase stability and
magnetic properties of Mn
3
Z (Z = Al, Ga, In, Tl, Ge, Sn, Pb)
Heusler alloys. Appl Sci. 2019;9:964.
59. Jeng HT, Guo GY. First-principles investigations of orbital
magnetic moments and electronic structures of the double
perovskites Sr
2
FeMoO
6
,Sr
2
FeReO
6
, and Sr
2
CrWO
6
.Phys Rev B.
2003;67:094438.
60. Mahmood Q, Hassan M, Ahmad SHA, Bhamu KC,
Mahmood A, Ramay SM. Study of electronic, magnetic and
thermoelectric properties of AV
2
O
4
(A = Zn, Cd, Hg) by using
DFT approach. J Phys Chem Solids. 2019;128:283-290.
9048 ULLAH ET AL.

61. Murtaza G, Ahmad I. First principle study of the structural and
optoelectronic properties of cubic perovskites CsPbM
3
(M=Cl,
Br, I). Phys B Condens Matter. 2011;406:3222-3229.
62. Chettri S, Rai DP, Shankar A, et al. GGA + U and mBJ + U
study of the optoelectronic, magnetic and thermoelectric prop-
erties of the SmAlO
3
compound with spin–orbit coupling. Int J
Mod Phys B. 2016;30:1650078.
63. Mugnai D, Ranfagni A, Ruggeri R. Observation of
superluminal behaviors in wave propagation. Phys Rev Lett.
2000;84:4830-4833.
64. Amin B, Ahmad I, Maqbool M. Conversion of direct to indi-
rect bandgap and optical response of B substituted InN for
novel optical devices applications. J Light Wave Technol. 2010;
28:223.
65. Heidrich K, Schafer W, Schreiber M, et al. Electronic structure,
photoemission spectra, and vacuum-ultraviolet optical spectra
of CsPbCl
3
and CsPbBr
3
.Phys Rev B. 1981;24:5642-5649.
66. Souadia Z, Bouhemadou A, Bin-Omran S, Khenata R, Al-
Douri Y, Al-Essa S. Electronic structure and optical properties
of the dialkali metal monotelluride compounds: ab initio study.
J Mol Graph Model. 2019;90:77-86.
67. Goldsmid HJ, Douglas RW. The use of semiconductors in ther-
moelectric refrigeration. J Appl Phys. 1954;5:386.
68. Tritt TM. Thermoelectric phenomena, materials, and applica-
tions. Rev Mater Res. 2011;41:433-448.
69. Ruleovaa P, Drasar C, Lostak P, Li CP, Ballikaya S, Uher C.
Thermoelectric properties of Bi
2
O
2
Se. Mater Chem Phys. 2010;
119:2991.
70. Slack GA. The thermal conductivity of nonmetallic crystals.
Solid State Phys. 1979;34:1.
71. Morelli DT, Jovovic V, Heremans JP. Intrinsically minimal
thermal conductivity in CubicI−V−VI2Semiconductors. Phys
Rev Lett. 2008;101:035901.
72. Blanco MA, Francisco E, Luania V. GIBBS: isothermal-isobaric
thermodynamics of solids from energy curves using a quasi-
harmonic Debye model. Comput Phys Commun. 2004;158:57-72.
73. Dar SA, Srivastava V, Sakalle UK, Khandy SA. Ab initio inves-
tigation on electronic, magnetic, mechanical, and thermody-
namic properties of AMO
3
(A = Eu, M = Ga, In) Perovskites.
J Supercond Nov Magn. 2018;31:1549-1558.
74. Yousaf S, Gupta DC. Investigation of electronic, magnetic and
thermoelectric properties of Zr
2
NiZ (Z = Al, Ga) ferromagnets.
Mater Chem Phys. 2017;192:33-40.
75. Ramachandran T, Rajeevan NE, Pradyumnan PP. Enhanced
thermoelectric properties of BiCoO
3
by nickel substitution.
Mater Sci Appl. 2013;4:816-821.
How to cite this article: Ullah R, Ali MA,
Murtaza G, Khan A, Mahmood A. Ab initio study
for the structural, electronic, magnetic, optical, and
thermoelectric properties of K
2
OsX
6
(X = Cl, Br)
compounds. Int J Energy Res. 2020;44:9035–9049.
https://doi.org/10.1002/er.5613
ULLAH ET AL.9049