111497850-ex3

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


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


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.


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.


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

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.


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


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)


Heusler Alloy

Heusler alloys that can be formed by combination of different elements in

periodic table


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)


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


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 (1)


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

′].”




Theorem (1)


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



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



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)



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



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



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


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



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.



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



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)



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)



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



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



WIEN2k Package


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




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




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

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]





-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

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]




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




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



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




Zooming DOS Figure – Example

-20

-10

0

10

DO

S[s

tate

s/eV

]

Minority




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

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





-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




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




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




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

2

4

6

8

10

12

Tot

al m

agne

tic m

omen

t (µ

B)


Fe3-x

MnxAl


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

2

4

6

8

10

12

Tot

al m

agne

tic m

omen

t (µ

B)


Fe3-x

MnxAl


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


8

10

12

14

16

18

20

Tot

al m

agne

tic m

omen

t (µ

B)


Fe3-x

MnxSb




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)




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


Conclution and Open issue

Conclusion

Fe rich compounds are metallic and have low spin polarization.



Conclusion


The metalloid atoms are not responsible for the origin of theband gap but lead to a shift in the fermi level.



Conclusion



Compounds beyond x > 0.75 are strong candidates ashalf-metals with high spin polarization.



Conclusion




Direct band gaps for the non-stoichiometric alloys.



Conclusion





Indirect band gaps along γ - X symmetry line for thestoichiometric alloys.



Conclusion





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.



Open issue

1 Investigation of the effect of disorder on the electric andmagnetic properties of Fe3−xMnxZ compounds.



Open issue


2 The optical properties of the Fe3−xMnxZ Heusler alloys.



Open issue



3 Elastic properties and magnetic shape memory alloy forFe3−xMnxZ.



Open issue




4 The transport properties and half-metallicity at elevatedtemperature of Fe3−xMnxZ compounds.



Open issue





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.



Open issue





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).


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


Thank You

111497850-ex3

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