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INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
INVESTIGATION OF HALF-METALLICBEHAVIOR AND SPIN POLARIZATION FOR
THE HEUSLER ALLOYS Fe3−xMnxZ (Z= Al, Ge,
Sb): A FIRST PRINCIPLE STUDY
Said Moh’d Al Azar
Supervisor: Prof. Dr. Jamil KhalifehCo-supervisor: Dr. Bothina Hamad
August 5, 2011
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Outline
1 Overview
2 Half-Metallicity
3 Heusler Alloy
4 Density Functional Theory (DFT)
5 Full-Potential Linearized Augmented Plane-wave (FP-LAPW) MethodFormalismWIEN2k Package
6 Results and DiscussionStoichiometric Fe3−xMnxZ (Z= Al, Ge, Sb) SystemsNon-Stoichiometric Fe3−xMnxZ (Z= Al, Ge, Sb) Systems
7 Conclution and Open issue
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Overview
The Goal
The goal of this work is to study, with ab initio accuracy over awide concentration range, the effect of the main-group elements onthe electronic and magnetic structures of bulk Fe3−xMnxZ(Z=Al,Ge, Sb) alloys. Manganese concentration and the main-groupelements (Z) play an important role in the electronic and magneticstructures of these alloys. Furthermore, the half-metallic behavioris investigated.
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Overview
The Goal
The goal of this work is to study, with ab initio accuracy over awide concentration range, the effect of the main-group elements onthe electronic and magnetic structures of bulk Fe3−xMnxZ(Z=Al,Ge, Sb) alloys. Manganese concentration and the main-groupelements (Z) play an important role in the electronic and magneticstructures of these alloys. Furthermore, the half-metallic behavioris investigated.
Motivation
1 Fe2MnZ and Mn2FeZ have been proposed theoretically toshow half-metallicity.
2 An upsurge of interest in the ordered compound containing Fe.
3 Perspectives to use them in spintronics applications asspin-injection devices , spin-filters , tunnel junctions , GMRCMR and TMR devices.
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Half-Metallicity
What is Half-metallicity?
Definition
A half-metal is any materials that acts as a conductor to electronsof one spin orientation, but as an insulator or semiconductor tothose of the opposite orientation. Such materials exhibit nearlyfully spin polarized conduction electrons.
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Half-Metallicity
What is Half-metallicity?
Definition
A half-metal is any materials that acts as a conductor to electronsof one spin orientation, but as an insulator or semiconductor tothose of the opposite orientation. Such materials exhibit nearlyfully spin polarized conduction electrons.
Half-Metallicity Rules
Obey Slater-Pauling rule (integer total magnetic moment).
Kubler rule Mn atom have a high, localized magnetic moment.
Normally possible for alloys, typically 2 - 4 components.
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Half-Metallicity
Classifecation of half-metals after Coey and Venkatesan (2002)
Type DOS Conductivity Spin up Spin down Exampleelectrons at EF electrons at EF
IA half-metal metallic itinerant none CrO2 or NiMnSbIB half-metal metallic none itinerant Mn2VAlIIA half-metal nonmetallic localized noneIIB half-metal nonmetallic none localized Fe3O4
IIIA metal metallic itinerant localized (La0.7Sr0.3)MnO3
IIIB metal metallic localized itinerantIVA semimetal metallic itinerant localizedIVB semimetal metallic localized itinerant Tl2Mn2O7
VA semiconductor semiconducting few, itinerant none GaAsVB semiconductor semiconducting none few, itinerant
Example
Two types of Heusler
Some oxides
Manganites
Double perovskites
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Heusler Alloy
Full and Half Heusler alloys structure and their Wyckoff positions.
Wyckoff positions
For X2YZ (AlCu2Mn-type)X at 8c (14 ,
14 ,
14 )
Y and Z atoms at4a (0,0,0) and 4b (12 ,
12 ,
12 )
For XYZX at 4a (14 ,
14 ,
14)
Y and Z atoms at4b (0,0,0) and 4c (12 ,
12 ,
12)
Half-Heusler
α YX
Z
Z
YX
X
Void
XYZ [C1 ]b
X YZ [L2 ]2 1
Full-Heusler
For X2YZ (CuHg2Ti-type)X at 4a (0,0,0) and 4c (14 ,
14 ,
14)
Y and Z atoms at 4b (12 ,12 ,
12) and
4d (34 ,34 ,
34)
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Heusler Alloy
Heusler alloys that can be formed by combination of different elements in
periodic table
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Heusler Alloy
Hybridization and the origin of band gap and spin gap in full-Heusler alloys
V.B
C.B
EES
Eg
F
d − d hybridization
Determined by the X-X interaction only ( t1u - eu splitting)
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Heusler Alloy
The Slater-Pauling behavior of Heusler alloys
16 17 18 19 20 21 22 23 24 25
Number of valence electrons: Zt
−1
0
1
2
3
4
5
6
Tot
al s
pin
mom
ent:
Mt (
µ Β)
Half−Heusler Alloys
CoTiSb
CoVSb
NiMnTe
CoMnSb
NiMnSe
CoFeSbRhMnSb
FeMnSbCoCrSbNiVSb
IrMnSbNiCrSb
NiMnSbPdMnSbPtMnSb
M t=Z t−
18
NiFeSb
20 21 22 23 24 25 26 27 28 29 30 31 32
Number of valence electrons: Zt
−3
−2
−1
0
1
2
3
4
5
6
7
Tot
al s
pin
mom
ent:
Mt (
µ Β)
Full−Heusler Alloys
Mn2VAl
Fe2VAl
Fe2CrAl
Co2VAlFe2MnAl
Rh2MnGe
Co2FeAl
Co2MnSiCo2MnGe
Co2MnAlCo2MnGaRh2MnAlRh2MnGaRu2MnSb
Co2CrAlFe2MnSiRu2MnSiRu2MnGeRu2MnSn
Co2TiAl
Ni2MnAl
Co2MnAs
Co2FeSi
Rh2MnTl
Rh2MnSnRh2MnPb
M t=Z t−
24
Rh2MnIn
Co2TiSn
Mn2VGe
Co2MnSnCo2MnSb
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Density Functional Theory (DFT)
The Hohenberg-Kohn Theorems
Theorem (1)
“ It states that once you know the ground state electron density inposition space any ground state property is uniquely defined.”
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Density Functional Theory (DFT)
The Hohenberg-Kohn Theorems
Theorem (1)
“ It states that once you know the ground state electron density inposition space any ground state property is uniquely defined.”
Theorem (2)
“It states that once the functional that relates the electron densityin position space with the total electronic energy is known, one maycalculate it approximately by inserting approximate densities ρ′.Furthermore, just as for the variational method for wavefunctions,one may improve any actual calculation by minimizing Ee [ρ
′].”
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Density Functional Theory (DFT)
The Hohenberg-Kohn Theorems
Theorem (1)
“ It states that once you know the ground state electron density inposition space any ground state property is uniquely defined.”
Theorem (2)
“It states that once the functional that relates the electron densityin position space with the total electronic energy is known, one maycalculate it approximately by inserting approximate densities ρ′.Furthermore, just as for the variational method for wavefunctions,one may improve any actual calculation by minimizing Ee [ρ
′].”
The proof proceeds by reductio ad absurdum
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Density Functional Theory (DFT)
Schematic representation of Hohenberg-Kohn theorems.
Vext(r) n0(r)
Ψi(r) Ψ0(r)
HK
Schematic representation of Kohn-Sham ansatz .
Vext(r) n0(r) n0(r) VKS(r)
Ψi (r) Ψ0(r) Ψi=1,Ne(r) Ψi (r)
HK KS HK0
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Density Functional Theory (DFT)
The spin-polarized Kohn-Sham equations
(Hσ
KS − ǫσi )ψσ
i (r) = 0, (1)
where
Hσ
KS(r) = −1
2∇2 + V σ
KS(r), (2)
the spin-polarized Kohn-Sham potential Vσ
KS could be wirte by twoterms
φσ(r) = V σ
ext(r) +
∫
ρσ(r′)
|r− r′|dr′, (3)
and
µσxc(ρ) =δExc [ρ]
δρ(r, σ)= δ(ρσǫxc(ρ
σ))/δρσ (4)
where µσ is the spin-polarized exchange-correlation and the densityρ given by
ρ(r) =∑
σ
ρ(r, σ) =∑
σ
N∑
i=1
|ψσ
i (r)|2, (5)
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Density Functional Theory (DFT)
Exchange-correlation energy(Exc)
Definition
It is the different between the exact interacting many-body energyand the non-interacting one.
Exc [n(r)] = F [n(r)]− (Ts + EHartree)
= (Texact − Ts) + (Eint − EHartree) (6)
1 It is divided to Exc [n(r)] = Ex + Ec
2 Ec smaller in size relative to Ex
3 increase the Ex magnitude −→ lower the Etot
4 decrease the Ec magnitude −→ increase Etot
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Density Functional Theory (DFT)
LSDA versus GGA
Local Spin Density Approximation(LSDA)
1 Exc functional for ρ only
2 Favors density homogeneity
3 von Barth and Hedinparametrization
4 Desgined for slowly varyingdensities!
5 Orbital independent
6 Not self-interaction free
7 Dispertion interaction is notincluded
Generalized Gradient Approximation(GGA)
1 Exc functional for ρ and ∇ρ
2 Favors density inhomogeneity
3 Perdew, Burke and Ernzerhof(PBE96) parametrization
4 Orbital independent
5 Not self-interaction free
6 Dispertion interaction is notincluded
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Density Functional Theory (DFT)
Schematic flow-chart for self consistent functional calculations
Compute VKS(r)
Solve Single Particle Eqns.
Determine EF
Calculate ρout(r)
Mix ρout(r), ρin(r) Converged? Done
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Full-Potential Linearized Augmented Plane-wave (FP-LAPW) Method
Formalism
The historical progress of the FP-LAPW method flow chart
APW
(Slater 1937)
Unit cell divided into two regionsi) MT sphere
ii) Interstitial regionPlane-wave bases sets
LAPW
(Andersen 1975)
The energy dependence ofthe radial functions insideeach sphere is linearized
FP-LAPW
(Wimmer et al. 1981)No potential shape approximation
All-ellectron FP-LAPW
(Weinert et al. 1982)
The explicit algebraic cancellation ofthe nuclear Coulomb singularities in
the Kinetic and potential energy termswhich leads to good numerical stability
LAPW + LO
(Singh 1991)
Introduced local orbitals (LO’s)to augment the LAPW basis set
for certain l values
APW +lo
(Sjostedt et al. 2000)
Where APW’s are evaluated at a fixed energyand flexibility is added by including a type oflocal orbitals ( lo’s) combining a u and u
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Full-Potential Linearized Augmented Plane-wave (FP-LAPW) Method
Formalism
1 No shape approximations in charge density or potential
2 includes core orbitals
3 most precise method available
The FP-LAPW method enhanced the potential in LAPW andexpand it in the form:
Veff (r) =
∑|K |6Kpot
K Veff (K)e iK.r r ∈ I∑lmax
lm V lmeff (rα)Ylm(rα) r ∈ S
(7)
where Kpot and lmax determine the highest reciprocal latticevectors included in the sum.
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Full-Potential Linearized Augmented Plane-wave (FP-LAPW) Method
Formalism
LAPW assumptions
Sphere
Interstitial
(r), V(r) : Stars
(r) : Planewave
(r), V(r) : Lattice Harmonics
(r) : Atomic-like function
1 APW assumptions
2 ul is expanded by aTaylor expansionaround ǫl
3 Basis has moreflexibility insidesphere
4 No asymptoteproblem
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Full-Potential Linearized Augmented Plane-wave (FP-LAPW) Method
Formalism
APW and LAPW basis sets
The APW basis sets
φ(r) =
Ω− 12∑
G cGei(G+K).r r ∈ I
∑
lm Almul(r) r ∈ S(8)
The LAPW basis sets
φ(r) =
Ω− 12∑
G cGei(G+K).r r ∈ I
∑
lm[Almul(r) + Blmul(r)] r ∈ S(9)
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Full-Potential Linearized Augmented Plane-wave (FP-LAPW) Method
Formalism
LAPW+LO and APW+lo methods
The local orbitals basis sets in LAPW+LO method:
φ(r)LO =
0 r ∈ I
(aα,LOL u1l(r) + bα,LOL u1l(r) + cα,LOL u2l(r))YL(r) r ∈ S
(10)The local orbitals basis sets in APW+lo method:
φ(r)lo =
0 r ∈ I
(aα,loL u1l(r) + bα,loL u1l(r))YL(r) r ∈ S(11)
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Full-Potential Linearized Augmented Plane-wave (FP-LAPW) Method
Formalism
The pseudo-charge method for solving the Poisson equation
Calculate multipolesof the sphere charge
Calculate planewavecharge multipoles
Construct thepseudocharge
Calculate VPW
Synthesize VPW onthe sphere boundaries
Integrate Poisson’sEqn. in the spheres
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Full-Potential Linearized Augmented Plane-wave (FP-LAPW) Method
Formalism
The total energy per unit cell is
E =∑
i
ǫi −1
2
[
∫
ΩVc (~r )[ρ ↑ (~r ) + ρ ↓ (~r )]d~r +
∑
ν
Zν
⟨
1
r[ρ ↑ (~r) + ρ ↓ (~r )]
⟩
ν
]
−
∫
Ωµxc (~r )[ρ ↑ (~r ) + ρ ↓ (~r )]d~r −
1
2
∑
ν
Zν
Rnu[RνS0(Rν ) + Zν − Qν ]
+Exc [ρ ↑, ρ ↓]. (12)
where Vc is the Coulomb potential, EXC is exchange-correlation energy, µxc is the exchange-correlation energy
density per atom
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Full-Potential Linearized Augmented Plane-wave (FP-LAPW) Method
WIEN2k Package
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Results and Discussion
Stoichiometric Fe3−xMnxZ (Z= Al, Ge, Sb) Systems
3.5 3.55 3.6 3.65 3.7 3.75 3.8lattice parameter a (Å)
0
0.1
0.2
0.3
0.4
Tot
al e
nerg
y (e
V)
Fe3Al
3.45 3.5 3.55 3.6 3.65lattice parameter a (Å)
0
0.05
0.1
0.15
0.2
Tot
al e
nerg
y (e
V)
Fe2MnAl
3.5 3.55 3.6 3.65 3.7 3.75lattice parameter a (Å)
0
0.05
0.1
0.15
Tot
al e
nerg
y (e
V)
FeMn2Al
3.5 3.55 3.6 3.65 3.7 3.75 3.8lattice parameter a (Å)
0
0.05
0.1
0.15
0.2
Tot
al e
nerg
y (e
V)
Mn3Al
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Results and Discussion
Stoichiometric Fe3−xMnxZ (Z= Al, Ge, Sb) Systems
compound structure a(A) B (GPa) EV (max)(eV) EC(min)(eV) Eg (eV) ES (eV) P(%) Ref.
Fe3Al DO3 5.750 169.9 355.738 169.3 Lechermann et al. 025.820(exp) Bansal et al. 94
L12 3.653 169.43.651 174.9 Lechermann et al. 02
Fe2MnAl L21(Fm-3m) 5.683 200.9 0.740 1.205 0.465 815.670 Fujii et al. 955.850(exp) Vinesh et al. 09
Mn2FeAl L21(F-43m) 5.760 150.2 0.674 1.218 0.544 995.725 Luo et al. 08
Mn3Al DO3 5.806 143.9 0.555 1.098 0.543 0.116 1005.723 Fujii et al. 08
Fe3Ge DO3 5.736 167.7 205.760(exp) Zhou et al. 95
L12 3.642 179.63.667(exp) Zhou et al. 95
Fe2MnGe L21(Fm-3m) 5.703 217.6 0.845 1.392 0.547 96DO3 5.780(exp) Rodriquez-Carvajal 93
Mn2FeGe L21(F-43m) 5.718 214.4 0.893 1.376 0.482 875.675 Luo et al. 08
Mn3Ge DO3 5.765 197.2 0.828 1.326 0.497 965.749 Fujii et al. 08
L12 3.654 170.53.800(exp) Takizawa et al. 02
Fe3Sb DO3 5.996 159.5 285.900(exp) Bansal et al. 94
Fe2MnSb L21(Fm-3m) 5.955 192.6 0.979 1.668 0.689 82Mn2FeSb L21(F-43m) 5.999 141.2 0.731 1.127 0.396 0.063 100
5.925 Luo et al. 08Mn3Sb DO3 5.985 174.4 0.768 1.375 0.607 0.043 100
5.930 Fujii et al. 08L12 3.811 177.1
4.000(exp) Yamashita et al. 03
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Results and Discussion
Stoichiometric Fe3−xMnxZ (Z= Al, Ge, Sb) Systems
Total and atom-resolved DOS of the stoichiometric Fe3−xMnxSb
-10
-5
0
5
10Fe
3Sb - total
-3
0
3Fe[A,C]
-3
0
3
DO
S (
stat
es/e
V)
Fe[B]
-4 -2 0 2 4E-E
F (eV)
-1
0
1 Sb[D]
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Results and Discussion
Stoichiometric Fe3−xMnxZ (Z= Al, Ge, Sb) Systems
Total and atom-resolved DOS of the stoichiometric Fe3−xMnxSb
-10
-5
0
5
10Fe
3Sb - total
-3
0
3Fe[A,C]
-3
0
3
DO
S (
stat
es/e
V)
Fe[B]
-4 -2 0 2 4E-E
F (eV)
-1
0
1 Sb[D]
-10
-5
0
5 Fe2MnSb -Total
-8
-4
0
4 Fe[A,C]
-4-2024
DO
S (
stat
es/e
V)
Mn[B]
-4 -2 0 2 4E-E
F (eV)
-2
-1
0
1
2Sb[D]
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Results and Discussion
Stoichiometric Fe3−xMnxZ (Z= Al, Ge, Sb) Systems
Total and atom-resolved DOS of the stoichiometric Fe3−xMnxSb
-10
-5
0
5
10Fe
3Sb - total
-3
0
3Fe[A,C]
-3
0
3
DO
S (
stat
es/e
V)
Fe[B]
-4 -2 0 2 4E-E
F (eV)
-1
0
1 Sb[D]
-10
-5
0
5 Fe2MnSb -Total
-8
-4
0
4 Fe[A,C]
-4-2024
DO
S (
stat
es/e
V)
Mn[B]
-4 -2 0 2 4E-E
F (eV)
-2
-1
0
1
2Sb[D]
-8-4048
Mn2FeSb - Total
-3
0
3 Mn[A]
-3
0
3
DO
S (
stat
es/e
V)
Mn[B]
-3
0
3 Fe[C]
-3 0 3E-E
F (eV)
-1
0
1 Sb[D]
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Results and Discussion
Stoichiometric Fe3−xMnxZ (Z= Al, Ge, Sb) Systems
Total and atom-resolved DOS of the stoichiometric Fe3−xMnxSb
-10
-5
0
5
10Fe
3Sb - total
-3
0
3Fe[A,C]
-3
0
3
DO
S (
stat
es/e
V)
Fe[B]
-4 -2 0 2 4E-E
F (eV)
-1
0
1 Sb[D]
-10
-5
0
5 Fe2MnSb -Total
-8
-4
0
4 Fe[A,C]
-4-2024
DO
S (
stat
es/e
V)
Mn[B]
-4 -2 0 2 4E-E
F (eV)
-2
-1
0
1
2Sb[D]
-8-4048
Mn2FeSb - Total
-3
0
3 Mn[A]
-3
0
3
DO
S (
stat
es/e
V)
Mn[B]
-3
0
3 Fe[C]
-3 0 3E-E
F (eV)
-1
0
1 Sb[D]
-10
-5
0
5 Mn3Sb-Total
-10
-5
0
5 Mn[A,C]
-10
-5
0
5 Mn[B]
-4 -2 0 2 4E-E
F (eV)
-1
0
1 Sb[D]
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Results and Discussion
Stoichiometric Fe3−xMnxZ (Z= Al, Ge, Sb) Systems
The Fe[A,C] d-eg and d-t2g partial DOS
-2
-1
0
1
2
Fe[A,C] (d-eg)
Fe[A,C] (d-eg)
-2
-1
0
1
2
-2
-1
0
1
2
DO
S[s
tate
s/eV
]
-3 -2 -1 0 1 2E-E
F(eV)
-2
-1
0
1
2
Fe3Al
Fe[A,C] (d-t2g
)
Fe[A,C] (d-t2g
)
Fe2MnAl
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Results and Discussion
Stoichiometric Fe3−xMnxZ (Z= Al, Ge, Sb) Systems
The bandstructure and DOS
W L Γ X W K -10
-5
0
5
E-E
F (
eV)
Mn2FeSb
up
EF
W L Γ X W K -10
-5
0
5
E-E
F (
eV)
Mn2FeSb
down
EF
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Results and Discussion
Non-Stoichiometric Fe3−xMnxZ (Z= Al, Ge, Sb) Systems
Zooming DOS Figure – Example
-4 -2 0 2 4E - E
F
-30
-20
-10
0
10
20
30D
OS
[sta
tes/
eV]
Fe0.5
Mn2.5
GeMajority
Minority
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Results and Discussion
Non-Stoichiometric Fe3−xMnxZ (Z= Al, Ge, Sb) Systems
Zooming DOS Figure – Example
-20
-10
0
10
DO
S[s
tate
s/eV
]
Minority
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Results and Discussion
Non-Stoichiometric Fe3−xMnxZ (Z= Al, Ge, Sb) Systems
Spin-polarised DOS for Fe3−xMnxZ with different Mn concentration
-30-20-10
010203040
-30-20-10
0102030
DO
S [s
tate
s/eV
]
-8 -4 0 4E-E
F (eV)
-30-20-10
0102030
Fe1.5
Mn1.5
AlMajority
Minority
Fe1.25
Mn1.75
Al
Fe1.75
Mn1.25
Al
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Results and Discussion
Non-Stoichiometric Fe3−xMnxZ (Z= Al, Ge, Sb) Systems
Spin-polarised DOS for Fe3−xMnxZ with different Mn concentration
-30-20-10
010203040
-30-20-10
0102030
DO
S [s
tate
s/eV
]
-8 -4 0 4E-E
F (eV)
-30-20-10
0102030
Fe1.5
Mn1.5
AlMajority
Minority
Fe1.25
Mn1.75
Al
Fe1.75
Mn1.25
Al
-30-20-10
0102030
-30-20-10
0102030
DO
S[s
tate
s/eV
]
Fe0.75
Mn2.25
Ge
-12 -8 -4 0 4E-E
F (eV)
-30-20-10
0102030
Fe0.5
Mn2.5
Ge
Fe0.25
Mn2.75
Ge
Majority
Minority
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Results and Discussion
Non-Stoichiometric Fe3−xMnxZ (Z= Al, Ge, Sb) Systems
Spin-polarised DOS for Fe3−xMnxZ with different Mn concentration
-30-20-10
010203040
-30-20-10
0102030
DO
S [s
tate
s/eV
]
-8 -4 0 4E-E
F (eV)
-30-20-10
0102030
Fe1.5
Mn1.5
AlMajority
Minority
Fe1.25
Mn1.75
Al
Fe1.75
Mn1.25
Al
-30-20-10
0102030
-30-20-10
0102030
DO
S[s
tate
s/eV
]
Fe0.75
Mn2.25
Ge
-12 -8 -4 0 4E-E
F (eV)
-30-20-10
0102030
Fe0.5
Mn2.5
Ge
Fe0.25
Mn2.75
Ge
Majority
Minority
-20
0
20
40
-10
0
10
20
DO
S [s
tate
s/eV
]
-10 -5 0 5E - E
F (eV)
-40
-20
0
20
40
Majority
Minority
Fe2.75
Mn0.25
Sb
Fe2.5
Mn0.5
Sb
Fe2.25
Mn0.75
Sb
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Results and Discussion
Non-Stoichiometric Fe3−xMnxZ (Z= Al, Ge, Sb) Systems
Compound Space group a(A) B (GPa) Eg (eV) P(%)
Fe2.75Mn0.25Al Pm3m (221) 5.741 172.9 – 38.5Fe2.5Mn0.5Al P4/mmm (123) 4.059 132.7 – 40Fe2.25Mn0.75Al Pm3m (221) 5.726 197.4 0.405 100Fe1.75Mn1.25Al P43m (215) 5.694 194.1 0.311 88Fe1.5Mn1.5Al Pn3m (224) 5.698 180.8 0.274 100Fe1.25Mn1.75Al P43m (215) 5.731 157.6 0.356 98Fe0.75Mn2.25Al P43m (215) 5.726 134.3 0.349 100Fe0.5Mn2.5Al P42/nnm (134) 5.696 150.7 0.491 100Fe0.25Mn2.75Al P43m (215) 5.708 156.2 0.595 100
Fe2.75Mn0.25Ge Pm3m (221) 5.724 166.4 – 22Fe2.5Mn0.5Ge P4/mmm (123) 4.026 210.9 – 62Fe2.25Mn0.75Ge Pm3m (221) 5.701 213.0 0.447 100Fe1.75Mn1.25Ge P43m (215) 5.697 209.2 0.332 90Fe1.5Mn1.5Ge Pn3m (224) 5.703 205.9 0.282 95Fe1.25Mn1.75Ge P43m (215) 5.715 194.4 0.221 94Fe0.75Mn2.25Ge P43m (215) 5.729 180.9 0.243 90Fe0.5Mn2.5Ge P42/nnm (134) 5.751 190.4 0.389 94Fe0.25Mn2.75Ge P43m (215) 5.748 192.4 0.292 100
Fe2.75Mn0.25Sb Pm3m (221) 5.985 158.1 – 24.4Fe2.5Mn0.5Sb P4/mmm (123) 4.228 148.8 – 28Fe2.25Mn0.75Sb Pm3m (221) 5.978 160.2 0.063 88Fe1.75Mn1.25Sb P43m (215) 5.949 197.4 0.045 85Fe1.5Mn1.5Sb Pn3m (224) 5.981 188.4 0.057 86Fe1.25Mn1.75Sb P43m (215) 6.01 135.4 0.051 99Fe0.75Mn2.25Sb P43m (215) 5.992 157.7 0.079 95Fe0.5Mn2.5Sb P42/nnm (134) 5.975 164.6 0.499 100Fe0.25Mn2.75Sb P43m (215) 5.988 172.8 0.021 100
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Results and Discussion
Non-Stoichiometric Fe3−xMnxZ (Z= Al, Ge, Sb) Systems
structure MTOT (µB) ma(µB) mb(µB) mc(µB) md(µB) mg ,e1(µB) me2(µB) magnetic phase
Fe3Al 5.966 1.927 2.422 – -0.087 – – FMFe2.75Mn0.25Al 22.23 1.640Mn -0.09 2.410 -0.08 1.810 FMFe2.5Mn0.5Al 10.72 2.420 -0.07 -0.07 1.74Mn 1.760 FMFe2.25Mn0.75Al 9.00 2.62 0.000 -0.013 2.39Mn -0.09 FM∗
Fe2MnAl 2.003 -0.152 2.32Mn – -0.015 FMFe1.75Mn1.25Al 7.13 -0.04 -1.49Mn -0.04 -0.24 2.38Mn -0.01 FM∗
Fe1.5Mn1.5Al 5.99 -1.66 2.429 -0.004 -0.07Fe FMFe1.25Mn1.75Al 5.01 0.200 -0.31 0.050 -1.71Mn 0.00 2.54Mn FM∗
FeMn2Al 0.999 0.15Fe 2.669 -1.798 -0.006 – – FM∗
Fe0.75Mn2.25Al 2.99 -1.47 -1.64 0.30Fe -1.55 2.49 -0.002 FM∗
Fe0.5Mn2.5Al 1.99 0.38Fe 0.00 2.44 -1.41 FM∗
Fe0.25Mn2.75Al 2.99 1.42Fe -0.011 -2.56 -0.005 1.16 FM∗
Mn3Al 0.000 -1.415 2.826 – 0.012 – AF
Fe3Ge 5.624 1.624 2.575 – -0.057 FMFe2.75Mn0.25Ge 19.9 2.34Mn -0.04 2.59 -0.06 1.32 FMFe2.5Mn0.5Ge 8.19 2.61 -0.03 -0.03 2.26Mn 0.88 FMFe2.25Mn0.75Ge 12.99 2.70 -0.02 -0.02 2.36Mn 0.44 FMFe2MnGe 3.024 0.209 2.626 – -0.012 – – FMFe1.75Mn1.25Ge 11.05 0.30 -1.34Mn 0.26 0.29 2.60Mn -0.004 FM∗
Fe1.5Mn1.5Ge 10.09 -0.96 2.54 0.007 0.28Fe FM∗
Fe1.25Mn1.75Ge 9.01 0.003 2.41Fe 0.01 2.47 0.76Fe -0.98 FM∗
FeMn2Ge 2.013 0.506 2.562 -1.080 0.010 – – FM∗
Fe0.75Mn2.25Ge 7.12 -0.83 -1.19 0.60Fe -1.14 2.63 0.02 FM∗
Fe0.5Mn2.5Ge 6.03 0.59Fe -1.02 -1.02 0.03 2.68 FM∗
Fe0.25Mn2.75Ge 4.99 2.47Fe 0.03 2.66 0.04 -0.73 FM∗
Mn3Ge 1.002 -0.918 2.750 – 0.044 – – FM∗
Fe3Sb 6.116 1.789 2.730 – -0.028 – – FMFe2.75Mn0.25Sb 23.83 2.83Mn -0.02 2.72 -0.04 1.69 FMFe2.5Mn0.5Sb 11.27 2.72 -0.04 -0.03 2.78Mn 1.52 FMFe2.25Mn0.75Sb 17.14 3.04 -0.03 -0.02 2.90Mn 0.74 FMFe2MnSb 4.140 0.670 2.875 – -0.02 – – FMFe1.75Mn1.25Sb 15.55 1.27 -2.01Mn 0.76 1.03 2.79Mn -0.01 FM∗
Fe1.5Mn1.5Sb 14.07 -1.46 2.78 -0.003 0.96Fe FM∗
Fe1.25Mn1.75Sb 13.01 0.02 2.81Fe 0.02 2.92 1.29Fe -0.94 FM∗
FeMn2Sb 3.000 1.164 2.948 -1.141 0.017 – – FM∗
Fe0.75Mn2.25Sb 10.96 3.05 0.02 0.03 2.65Fe 0.04 FM∗
Fe0.5Mn2.5Sb 10.00 0.91Fe 0.02 2.91 -0.62 FM∗
Fe0.25Mn2.75Sb 8.98 2.70Fe 0.023 2.78 0.025 -0.29 FM∗
Mn3Sb 2.000 -0.472 2.856 – 0.028 – FM∗
FM: Ferromagnetic FM∗: Ferrimagnetic AF: Antiferromagnetic
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Results and Discussion
Non-Stoichiometric Fe3−xMnxZ (Z= Al, Ge, Sb) Systems
Relation between spin magnetic moment and Mn concentration
0 0.5 1 1.5 2 2.5 3Mn concentration
0
2
4
6
8
10
12
Tot
al m
agne
tic m
omen
t (µ
B)
Generalized Slater-Pauling ruleCalculated total magnetic moment
Fe3-x
MnxAl
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Results and Discussion
Non-Stoichiometric Fe3−xMnxZ (Z= Al, Ge, Sb) Systems
Relation between spin magnetic moment and Mn concentration
0 0.5 1 1.5 2 2.5 3Mn concentration
0
2
4
6
8
10
12
Tot
al m
agne
tic m
omen
t (µ
B)
Generalized Slater-Pauling ruleCalculated total magnetic moment
Fe3-x
MnxAl
0 0.5 1 1.5 2 2.5 3Mn concentration
4
6
8
10
12
14
16
Tot
al m
agne
tic m
omen
t (µ
B)
Generalized Slater-Pauling rulecalculated total magnetic moment
Fe3-x
MnxGe
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Results and Discussion
Non-Stoichiometric Fe3−xMnxZ (Z= Al, Ge, Sb) Systems
Relation between spin magnetic moment and Mn concentration
0 0.5 1 1.5 2 2.5 3Mn concentration
0
2
4
6
8
10
12
Tot
al m
agne
tic m
omen
t (µ
B)
Generalized Slater-Pauling ruleCalculated total magnetic moment
Fe3-x
MnxAl
0 0.5 1 1.5 2 2.5 3Mn concentration
4
6
8
10
12
14
16
Tot
al m
agne
tic m
omen
t (µ
B)
Generalized Slater-Pauling rulecalculated total magnetic moment
Fe3-x
MnxGe
0 0.5 1 1.5 2 2.5 3Mn concentration
8
10
12
14
16
18
20
Tot
al m
agne
tic m
omen
t (µ
B)
Generalized Slater-Pauling ruleCalculated total magnetic moment
Fe3-x
MnxSb
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Results and Discussion
Non-Stoichiometric Fe3−xMnxZ (Z= Al, Ge, Sb) Systems
Magnetic hyperfine field on Z atoms
0 0.5 1 1.5 2 2.5 3Mn concentration (%)
-50
0
50
100
150
200
250
300
350
400
450
500
550
600
Mag
netic
hyp
erfin
e fie
ld o
n Z
(K
G)
Fe3-x
MnxAl
Fe3-x
MnxGe
Fe3-x
MnxSb
Hyperfine fields (contact + dipolar + orbitals contribution)
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Results and Discussion
Non-Stoichiometric Fe3−xMnxZ (Z= Al, Ge, Sb) Systems
Magnetic hyperfine field on the B-site
0 0.5 1 1.5 2 2.5 3 concentration x
-400
-300
-200
-100
0
HF
F o
n B
site
(K
Gau
ss)
Fe3-x
MnxAl
Fe3-x
MnxGe
Fe3-x
MnxSb
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Conclution and Open issue
Conclusion
Fe rich compounds are metallic and have low spin polarization.
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Conclution and Open issue
Conclusion
Fe rich compounds are metallic and have low spin polarization.
The metalloid atoms are not responsible for the origin of theband gap but lead to a shift in the fermi level.
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Conclution and Open issue
Conclusion
Fe rich compounds are metallic and have low spin polarization.
The metalloid atoms are not responsible for the origin of theband gap but lead to a shift in the fermi level.
Compounds beyond x > 0.75 are strong candidates ashalf-metals with high spin polarization.
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Conclution and Open issue
Conclusion
Fe rich compounds are metallic and have low spin polarization.
The metalloid atoms are not responsible for the origin of theband gap but lead to a shift in the fermi level.
Compounds beyond x > 0.75 are strong candidates ashalf-metals with high spin polarization.
Direct band gaps for the non-stoichiometric alloys.
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Conclution and Open issue
Conclusion
Fe rich compounds are metallic and have low spin polarization.
The metalloid atoms are not responsible for the origin of theband gap but lead to a shift in the fermi level.
Compounds beyond x > 0.75 are strong candidates ashalf-metals with high spin polarization.
Direct band gaps for the non-stoichiometric alloys.
Indirect band gaps along γ - X symmetry line for thestoichiometric alloys.
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Conclution and Open issue
Conclusion
Fe rich compounds are metallic and have low spin polarization.
The metalloid atoms are not responsible for the origin of theband gap but lead to a shift in the fermi level.
Compounds beyond x > 0.75 are strong candidates ashalf-metals with high spin polarization.
Direct band gaps for the non-stoichiometric alloys.
Indirect band gaps along γ - X symmetry line for thestoichiometric alloys.
Hyperfine fields on transition atoms are decreasing inmagnitude with increasing Mn concentration, while theoppsite for metaloids.
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Conclution and Open issue
Open issue
1 Investigation of the effect of disorder on the electric andmagnetic properties of Fe3−xMnxZ compounds.
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Conclution and Open issue
Open issue
1 Investigation of the effect of disorder on the electric andmagnetic properties of Fe3−xMnxZ compounds.
2 The optical properties of the Fe3−xMnxZ Heusler alloys.
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Conclution and Open issue
Open issue
1 Investigation of the effect of disorder on the electric andmagnetic properties of Fe3−xMnxZ compounds.
2 The optical properties of the Fe3−xMnxZ Heusler alloys.
3 Elastic properties and magnetic shape memory alloy forFe3−xMnxZ.
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Conclution and Open issue
Open issue
1 Investigation of the effect of disorder on the electric andmagnetic properties of Fe3−xMnxZ compounds.
2 The optical properties of the Fe3−xMnxZ Heusler alloys.
3 Elastic properties and magnetic shape memory alloy forFe3−xMnxZ.
4 The transport properties and half-metallicity at elevatedtemperature of Fe3−xMnxZ compounds.
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Conclution and Open issue
Open issue
1 Investigation of the effect of disorder on the electric andmagnetic properties of Fe3−xMnxZ compounds.
2 The optical properties of the Fe3−xMnxZ Heusler alloys.
3 Elastic properties and magnetic shape memory alloy forFe3−xMnxZ.
4 The transport properties and half-metallicity at elevatedtemperature of Fe3−xMnxZ compounds.
5 The effect of lowering the dimension of Fe3−xMnxZcompounds may be studied.( surfaces and interfaces)
6 The electronic and magnetic properties of Mn2FeAl1−xGexquaternary Heusler alloys could be investigated.
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Conclution and Open issue
Open issue
1 Investigation of the effect of disorder on the electric andmagnetic properties of Fe3−xMnxZ compounds.
2 The optical properties of the Fe3−xMnxZ Heusler alloys.
3 Elastic properties and magnetic shape memory alloy forFe3−xMnxZ.
4 The transport properties and half-metallicity at elevatedtemperature of Fe3−xMnxZ compounds.
5 The effect of lowering the dimension of Fe3−xMnxZcompounds may be studied.( surfaces and interfaces)
6 The electronic and magnetic properties of Mn2FeAl1−xGexquaternary Heusler alloys could be investigated.
7 The half-metallicity search in Ti1+xFeSb Heusler alloys (x= 0,0.25, 0.5, 0.75, 1).
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Acknowledgement
My deepest acknowledgement to:
My supervisor Dr. Jamil khalifeh and co-supervisor Dr.Bothina Hamad
The examination committee
My colleagues, co-workers and friends
Audience
INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe3−xMnxZ (Z=
Thank You