Original Articlecompounds Saadi Berria,b,* a Laboratory for Developing New Materials and Their Characterizations, University of Setif 1, Algeria b Faculty of Science, University of M'sil
Trang 1Original Article
compounds
Saadi Berria,b,*
a Laboratory for Developing New Materials and Their Characterizations, University of Setif 1, Algeria
b Faculty of Science, University of M'sila, Algeria
a r t i c l e i n f o
Article history:
Received 18 January 2018
Received in revised form
10 March 2018
Accepted 22 March 2018
Available online 29 March 2018
Keywords:
Half-metallic
Optical properties
Electronic properties
Magnetic properties
Ferromagnetic materials
a b s t r a c t The structural, electronic, magnetic and optical properties of suggested XAlO3(X¼ Cs, Rb and K) pe-rovskites under pressure effects are investigated by means of thefirst-principles calculations with the technique of the Full Potential Linearly Augmented Plane Wave (FP-LAPW) implemented within Wien2k computer package The electronic exchange correlation energy is determined by using Generalized Gradient Approximation together with SpineOrbit Interaction (GGA þ SOI) The lattice constant, bulk modulus and its pressure derivative are calculated Half-metallicity was preserved at ranges of 4.03 e4.19 Å, 4.03e4.18 Å and 3.74e4.09 Å for the CsAlO3, RbAlO3and KAlO3compounds, respectively The largest spin-flip gaps are found in the spin up channel, corresponding to a magnetic moment of 2mB/f.u Optical properties are also studied Dielectric function, refractive index, and loss energy are calculated and discussed The present work presents thefirst theoretical study of the perovskites of interest and still awaits experimental confirmations
© 2018 The Author Publishing services by Elsevier B.V on behalf of Vietnam National University, Hanoi This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)
1 Introduction
Numerous investigations have been extensively done regarding
the perovskite structure with different compositions and
struc-tures, motivated by their possible applications in numerous
many interesting properties such as mixed-conducting oxides for
In the present paper, the magnetic, electronic and optical
the electronic structure, magnetic and optical properties of ma-terials are concerned; these features play a crucial role in determining their magneto-optic properties for devices There-fore, accurate knowledge of these properties is very important for the application The aim of this work is to examine the
The calculations are performed using ab initio a full relativistic version of the full-potential augmented plane-wave scheme
interaction The rest of the paper is organized as follows: The
2 Method of calculations Ab-initio calculations are executed using DFT as implemented
full-potential linearized augmented plane wave (FP-LAPW) plus local
* Laboratory for Developing New Materials and Their Characterizations,
Univer-sity of Setif 1, Algeria.
E-mail address: berrisaadi12@yahoo.fr
Peer review under responsibility of Vietnam National University, Hanoi.
Journal of Science: Advanced Materials and Devices
https://doi.org/10.1016/j.jsamd.2018.03.001
2468-2179/© 2018 The Author Publishing services by Elsevier B.V on behalf of Vietnam National University, Hanoi This is an open access article under the CC BY license
Trang 2orbitals method through a density functional theory approach
[22,23] The linearized augmented plane waves (LAPW) will be:
lðEl;
l ; aa
in the spherical harmonics form inside the atom spheres Plane
wave expansion is used in the interstitial regions of atoms inside
to the corresponding ionic radii The energy between successive
iterations is converged to 0.0001 Ry and forces are minimized to
Brillouin zone integrations Exchange-correlation effects are
treated using generalized gradient approximation (GGA) as
interaction (SOI) during the calculations A dense k-mesh with
linear optical properties Anyway, the optical prosperities such as
and energy loss as functions of photon energy are presented
We present the structural, electronic, Half-metallic and optical
elevated pressures The perovskite alkali metal aluminum oxygen
as follows: X atom at (0, 0, 0), Al atom at (0.5, 0.5, 0.5), and O atoms
at (0, 0.5, 0.5), (0.5, 0, 0.5), (0.5, 0.5, 0)
Optical properties of a solid are usually described in terms of the
between the occupied and unoccupied wave functions within the
ε2ðuÞ ¼16u p2e2
X
s !l
〈Ojnecnjs〉2
d
uU2
(2)
ε1ðuÞ ¼ 1 þ2P
p
Z∞
0
Xu0ε2ðu0Þ
u02u2
2
transition matrix from valence to conduction states and P is the
principal value of the integral and the integral is over irreducible Brillouin zone The optical constants such as a refractive index n(w), are calculated in terms of the real and the imaginary parts of the
nðuÞ ¼
ε1ðuÞ þ ε2ðuÞ þ ε2ðuÞ1
1
ffiffiffi 2
The energy loss function L(w) solid at normal incidence can be derived by the following equation
LðuÞ ¼ Im
1
εðuÞ
¼ ε2ðuÞ
ε2ðuÞ2þ ε1ðuÞ2 (5)
compounds
Ef ¼hETotXAlO
3 Ebulk
X þ Ebulk
Al þ 3Ef
O
i
(6)
KAlO 3, Etot RbAlO 3and Etot
CsAlO 3are the equilibrium total energies
K , Ebulk
Rb , Ebulk
to the total energy per atom of solid for the K, Rb, Cs and Al atoms, respectively During calculation, Cs and Rb are taken as body-centered cubic structure (space group Im-3m) and K and Al are taken as cubic close-packed (space group Fm-3m) The vacancy
3 Results and discussion The main objective in this work is to calculate the total energy as
a function of the unit-cell volume in both ferromagnetic (FM) and
prop-erties, such as equilibrium lattice constant a(Å), bulk modulus B(GPa) and its pressure derivative B' The calculated structural
The lattice constant increase with increasing atomic radii of alkali
crystal rigidity can be measured by the bulk modulus B, so a large B represents high crystal rigidity The bulk modulus was found to be
This increasing trend reveals that the compressibility as well as the hardness of the material increases in the same sequence On the
fk;iðxÞ ¼
8
>
>
U 1 e i ð Giþk Þ x /outsid …esphere X
lm
aalmualðEl; raÞ þ ba
lm_ua
lðEl; raÞ Ylm
Trang 3material than RbAlO3 and CsAlO3 Until now, experimental or
theoretical lattice parameters, the bulk modulus and its pressure
derivative value have not been reported At an equilibrium lattice
of the paramagnetic one
InTable 1, we have given the values of formation energy per
fabri-cated experimentally
The self-consistent scalar relativistic band structures as well as
the various symmetry lines within the GGA method, are given in
Fig 2 Note that, there is an overall topological resemblance for both
compounds For these compounds, the minority spin band is
metallic, while the majority spin band shows a semiconducting gap around the Fermi level of 6.62, 6.14, and 4.98 eV, respectively From
compounds exhibit a half-metallic character
The half-metallic gap, which is the minimum between the ab-solute values of the valence band maximum (VBM) and the con-duction band minimum (CBM), represents the same variation law,
absence of the transition-metal atoms makes these compounds important model systems for the study of the origin and properties
in orbitals on the same atom or nearest neighbor atoms but longer-ranged interactions can occur via intermediary atoms and this is
type of a magnetic exchange that may arise between ions in
-6900,26
-6900,25
-6900,24
-6900,23
-6900,22
340 360 380 400 420 440 460 480 500 -16517,81
-16517,80 -16517,79 -16517,78 -16517,77 -16517,76 -16517,75 -16517,74
-2141,60 -2141,59 -2141,58 -2141,57 -2141,56 -2141,55
PM
FM PM
FM
PM
FM
Fig 1 Calculated total energy as a function of volume for XAlO 3 (X ¼ Cs, Rb and K) compounds.
Table 1
Lattice constant a (Å), bulk modulus B (in GPa), and pressure derivative of bulk modulus B0, total, partial magnetic moment (inmB ) and formation energy for XAlO 3 (X ¼ Cs, Rb and K) compounds.
Trang 4different oxidation states First proposed by Clarence Zener[32]
agreed to provide a description of the FM ground state, but this
theory predicts the relative ease with which an electron may be
exchanged between two species
In the next stage, we presented the partial densities of states of
Fermi level was set as 0 eV Basically, for these compounds, the DOS can be divided into four parts, at lower energy core states where we find the contribution of X-s states in the core states; the second part
-8 -6 -4 -2 0 2 4 6 8
-8 -6 -4 -2 0 2 4 6 8
CsAlO3 CsAlO3
-8 -6 -4 -2 0 2 4 6 8 -6
-4 -2 0 2 4 6
-8 -6 -4 -2 0 2 4 6 8 -6
-4 -2 0 2 4 6
-8 -6 -4 -2 0 2 4 6 8
b) a)
-8 -6 -4 -2 0 2 4 6 8 -6
-4 -2 0 2 4 6
RbAlO3 KAlO3
RbAlO3 Energy (eV)
KAlO3
Fig 2 Spin-polarized a) band structure and b) total densities of states (TDOS).
-24 -18 -12 -6 0 6 12 -1,5
-1,0 -0,5 0,0 0,5 1,0 1,5 2,0
Energy (eV) Energy (eV)
Energy (eV)
-24 -18 -12 -6 0 6 12 -0,4
-0,2 0,0 0,2 0,4
Al-p K-s
K-d
K-p
-24 -18 -12 -6 0 6 -1,0
-0,5 0,0 0,5 1,0
O-s
O-p
O-s
-24 -18 -12 -6 0 6 12
-2,20
-1,65
-1,10
-0,55
0,00
0,55
1,10
1,65
Energy (eV)
Energy (eV)
Energy (eV) -24 -18 -12 -6 0 6 12
-0,4 -0,2 0,0 0,2 0,4
Al-p Rb-s
Rb-d
Rb-p
-24 -18 -12 -6 0 6 -1,0
-0,5 0,0 0,5 1,0
O-s
O-p
O-s
-24 -18 -12 -6 0 6 12
-2,5 -2,0 -1,5 -1,0 -0,5 0,0 0,5 1,0 1,5 2,0
Energy (eV) Energy (eV)
Energy (eV)
-24 -18 -12 -6 0 6 12
-0,4 -0,2 0,0 0,2 0,4
Al-p Cs-s
Cs-d
Cs-p
-24 -18 -12 -6 0 6
-1,0 -0,5 0,0 0,5 1,0
O-s
O-p
O-s
Trang 5is from12 to 5 eV that is mainly derived from X-p states, the
third part which is beyond the Fermi level, which represents the
contribution of the s and p orbitals of O atoms hybridized with Al p
states For unoccupied states above the Fermi level, which
repre-sents the contribution of the p orbitals of Al atoms hybridized with
X-d electrons is principally for the highest conduction bands (CB)
In a practical application, the external stress is one of the
important factors to destroy half-metallicity The energy values of
the conduction band minimums (CBM) and the valence band
maximums (VBM) are used to characterize the half-metallicity
external stress on the half-metallicity, the band structures of
clear change of the Fermi level position is observed The band structures at different lattice constants were presented only for
might be expected to be less important since the magnetic
-4 -2 0 2 4
Γ
M
R X Γ R Γ X M Γ
-4 -2 0 2 4
-4 -2 0 2 4
Γ
M
R X Γ R Γ X M Γ
-4 -2 0 2 4
-4 -2 0 2 4
Γ
M
R X Γ R Γ X M Γ
-4 -2 0 2 4
-4 -2 0 2 4
Γ
M
R X Γ R Γ X M Γ
-4 -2 0 2 4
-4
-2
0
2
4
Γ
M
R X Γ R Γ X M Γ
-4 -2 0 2 4
Fig 4 The calculated band structure of RbAlO 3 as a function of the lattice constant.
[ and total magnetic moment as a function of the lattice constant.
Trang 6properties are governed by p electrons which experience fewer
correlations than d electrons Meanwhile, one can see that the
both compounds, in both spin directions, the band structure shows
respectively
in a PM state at the equilibrium lattice constants In WIEN2k,
to calculate the eigenvalues and eigenvectors using the scalar relativistic wave functions The similar features of band structure
compound, the results show considerable differences in the
The calculated total and atom-resolved magnetic moments for
fu for both compounds are close to an integer, which agrees with the half metallicity of these materials Here, the main source of
-20
-19
-18
-17
-16
-8
-7
-6
-5
-4
Γ
M
-20 -19 -18 -17 -16 -8 -7 -6 -5 -4
-20 -19 -18 -17 -16 -11 -10 -9 -8 -7 -6 -5
-4
KAlO 3 RbAlO 3
CsAlO 3
Fig 6 The calculated band structures of the perovskites using GGA and GGA þ SOC methods.
Fig 7 The real part ε (u) and imaginary part ε (u) of dielectric constant ε(u) for the perovskites XAlO (X ¼ Cs, Rb and K) in the PM state at the equilibrium lattice constants.
Trang 7magnetization in these compounds is thus two contributions one
each from the oxygen atoms and the interstitial region, whereas the
moments of the alkali metal and aluminum are small The nature of
splitting
behavior of linear response of a material to the electromagnetic
that material The real part of the dielectric function describes how
much material polarized as a result of induced electric dipole
indicates how much material absorbs photon energy There are two
tran-sitions The contribution from intraband transitions is important
only for metals The interband transitions can further be split in to
direct and indirect transitions We neglect the indirect interband
transitions, which involve scattering of phonons and are expected
InFig 7we present the dielectric function of RbAlO3, KAlO3and
waves are possible For energies up to 6 eV, based on our calculated band structure it would be worthwhile to identify the interband
remark that the material possesses a high dielectric function within Near infrared NIR region and decreases at higher energy in the Near
respectively These points are mainly coming from the electron transition from the O-p (VB), O-s (VB) and X-p (VB) to X-d (CB) orbitals
The refractive index is a quantity that describes how much light
and then decreases with photon energy The energy loss function of
describes the energy loss of a fast electron traversing the material It
is observed that the prominent peaks are found at 2.66(3.31) eV,
represent the characteristic associated with the plasma resonance and the corresponding frequency is the so-called plasma frequency
incident photon energy is higher than 2.66 (3.31) eV, 2.88 (3.51) eV
respectively
Table 2
Position of the principal peaks of the imaginary part of the dielectric function for
XAlO 3 (X ¼ Cs, Rb and K) compounds.
0 4 8 12
3
0 4 8
0 4 8
0 4 8 12
16
20
24
0 2 4 6 8
0 4 8
b) a)
Fig 8 The reflective index n(u) and energy loss function L(u) for the perovskite compounds XAlO 3 (X ¼ Cs, Rb and K) in the PM state at the equilibrium lattice constants.
Trang 84 Conclusion
electronic, magnetic and optical properties under various pressures
have been reported using the full potential augmented plane wave
derivative of these perovskites are calculated Half-metallically is
half-metallicity characteristic exists in the relatively wide ranges of
calculated and analyzed The dielectric function, refractive index,
and loss energy are calculated and discussed
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