INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe 3-x Mnx Z (Z= INVESTIGATION OF HALF-METALLIC BEHAVIOR AND SPIN POLARIZATION FOR THE HEUSLER ALLOYS Fe 3−x Mn x Z (Z= Al, Ge, Sb): A FIRST PRINCIPLE STUDY Said Moh’d Al Azar Supervisor: Prof. Dr. Jamil Khalifeh Co-supervisor: Dr. Bothina Hamad August 5, 2011
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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=
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
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=