Temperature dependent electroniccorrelation effects in GdN
Anand Sharma
Lehrstuhl Festkorpertheorie, Institut fur PhysikHumboldt Universitat zu Berlin
December 20, 2007
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
Summary
Outline
1 Introduction
2 Theoretical evaluationGreen function methodMulti- band self- energyPhysical properties
3 ab-initio calculationKinetic energyIntra-atomic exchange
4 Results
5 Summary
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
Summary
Outline
1 Introduction
2 Theoretical evaluationGreen function methodMulti- band self- energyPhysical properties
3 ab-initio calculationKinetic energyIntra-atomic exchange
4 Results
5 Summary
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
Summary
Spintronics
It is a technology which exploits the quantum spin as well ascharge states of electrons
Spin- polarized electrontransport.Giant MagnetoResistance(GMR) effect
considered as birth of thistechnology.Prof. A.Fert (France) andProf. P.Grunberg (Germany)shared the 2007 Nobel prizein Physics.
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
Summary
Spintronics
It is a technology which exploits the quantum spin as well ascharge states of electrons
Spin- polarized electrontransport.Giant MagnetoResistance(GMR) effect
considered as birth of thistechnology.Prof. A.Fert (France) andProf. P.Grunberg (Germany)shared the 2007 Nobel prizein Physics.
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
Summary
Spintronics
ApplicationsRead heads in magnetic diskrecorders.”Non-volatile” memories.Magnetic tunnel junction.
FutureIn search of materials exploiting100% spin- polarization of chargecarriers. Thus giving a newdirection to the field of electronics.
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
Summary
Spintronics
ApplicationsRead heads in magnetic diskrecorders.”Non-volatile” memories.Magnetic tunnel junction.
FutureIn search of materials exploiting100% spin- polarization of chargecarriers. Thus giving a newdirection to the field of electronics.
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
Summary
Real Materials
Examples (of currently studied substances)Composite of thin films : magnetic semiconductors(Europium chalcogenides and Gadolinium pnictides) withtransition metals (Fe) and local moments (Gd).Family of Heusler alloys.Diluted Magnetic Semiconductors (DMS) : transition metaland rare earth doped III-V and II-VI semiconductors.Manganites like A1−xBxMnO3 where A=La,Pr,Nd andB=Sr,Ca,Ba,Pb).
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
Summary
Real Materials
Examples (of currently studied substances)Composite of thin films : magnetic semiconductors(Europium chalcogenides and Gadolinium pnictides) withtransition metals (Fe) and local moments (Gd).Family of Heusler alloys.Diluted Magnetic Semiconductors (DMS) : transition metaland rare earth doped III-V and II-VI semiconductors.Manganites like A1−xBxMnO3 where A=La,Pr,Nd andB=Sr,Ca,Ba,Pb).
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
Summary
Real Materials
Examples (of currently studied substances)Composite of thin films : magnetic semiconductors(Europium chalcogenides and Gadolinium pnictides) withtransition metals (Fe) and local moments (Gd).Family of Heusler alloys.Diluted Magnetic Semiconductors (DMS) : transition metaland rare earth doped III-V and II-VI semiconductors.Manganites like A1−xBxMnO3 where A=La,Pr,Nd andB=Sr,Ca,Ba,Pb).
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
Summary
Real Materials
Examples (of currently studied substances)Composite of thin films : magnetic semiconductors(Europium chalcogenides and Gadolinium pnictides) withtransition metals (Fe) and local moments (Gd).Family of Heusler alloys.Diluted Magnetic Semiconductors (DMS) : transition metaland rare earth doped III-V and II-VI semiconductors.Manganites like A1−xBxMnO3 where A=La,Pr,Nd andB=Sr,Ca,Ba,Pb).
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
Summary
Kondo Lattice model
Also known as s-d , s-f andferromagnetic Kondo lattice model
DefinitionIt describes a ferromagnetic spin- exchange interactionbetween band of itinerant electrons and a system of localizedspins.
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
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Many body theoretical model
T αβij : electron hopping matrix
c†iασ, ciασ : electron creation andannihilation operatorsJ : intra- atomic exchangeSz
i ,Sσi = Sx
i + izσSyi : spin operators
z↑ = +1, z↓ = −1
Multi- band Hamiltonian
H = Hkin + Hint
=∑ijαβσ
T αβij c†iασcjβσ −
J2
∑iασ
(zσSzi c†iασciασ + Sσ
i c†iα−σciασ)
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
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Many body theoretical model
T αβij : electron hopping matrix
c†iασ, ciασ : electron creation andannihilation operatorsJ : intra- atomic exchangeSz
i ,Sσi = Sx
i + izσSyi : spin operators
z↑ = +1, z↓ = −1
Multi- band Hamiltonian
H = Hkin + Hint
=∑ijαβσ
T αβij c†iασcjβσ −
J2
∑iασ
(zσSzi c†iασciασ + Sσ
i c†iα−σciασ)
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
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Green function methodMulti- band self- energyPhysical properties
Outline
1 Introduction
2 Theoretical evaluationGreen function methodMulti- band self- energyPhysical properties
3 ab-initio calculationKinetic energyIntra-atomic exchange
4 Results
5 Summary
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
Summary
Green function methodMulti- band self- energyPhysical properties
Analytical approach
Green function :
Gµνlmσ(E) = 〈〈clµσ; c†mνσ〉〉E
Equation of motion :
EGµνlmσ(E) = δlmδµν +
∑jβ
T µβlj Gβν
jmσ(E)− J2
[zσΓµνllmσ(E) + Fµν
llmσ(E)]
Higher order Green functions :
Ising function Γµνklmσ(E) = 〈〈Sz
k clµσ; c†mνσ〉〉E
Spin- flip function Fµνklmσ(E) = 〈〈S−σ
k clµ−σ; c†mνσ〉〉E
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
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Green function methodMulti- band self- energyPhysical properties
Analytical approach
The electronic self- energy can be understood as :
〈〈[clµσ,Hint ]; c†mνσ〉〉 =∑pγ
Σµγlpσ(E)Gγν
pmσ(E)
which gives the required solution :
Gkσ(E) = [(E + i0+)I − ε(k)− Σkσ(E)]−1
ProblemHow to obtain the self- energy ?Is it possible to guess from the limiting case of the model ?
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
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Green function methodMulti- band self- energyPhysical properties
Analytical approach
The electronic self- energy can be understood as :
〈〈[clµσ,Hint ]; c†mνσ〉〉 =∑pγ
Σµγlpσ(E)Gγν
pmσ(E)
which gives the required solution :
Gkσ(E) = [(E + i0+)I − ε(k)− Σkσ(E)]−1
ProblemHow to obtain the self- energy ?Is it possible to guess from the limiting case of the model ?
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
Summary
Green function methodMulti- band self- energyPhysical properties
Analytical approach
The electronic self- energy can be understood as :
〈〈[clµσ,Hint ]; c†mνσ〉〉 =∑pγ
Σµγlpσ(E)Gγν
pmσ(E)
which gives the required solution :
Gkσ(E) = [(E + i0+)I − ε(k)− Σkσ(E)]−1
ProblemHow to obtain the self- energy ?Is it possible to guess from the limiting case of the model ?
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
Summary
Green function methodMulti- band self- energyPhysical properties
Limiting case : T = 0 and empty bands
The spin- dependent (k-independent) form of self- energy is :
Σσ(E) = −JSzσ
2I
+J2S(zσ − 1)
4Gσ
(E − JSzσ
2
)[I − J
2Gσ
(E − JSzσ
2
)]−1
where
Gσ
(E − JSzσ
2
)=
1N
∑q
[(E − JSzσ
2
)I − ε(k-q)
]−1
Interpolating self- energy approach for one-band KLM[W.Nolting et al, PRB 64, 155109 (2001)]
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
Summary
Green function methodMulti- band self- energyPhysical properties
Limiting case : T = 0 and empty bands
The spin- dependent (k-independent) form of self- energy is :
Σσ(E) = −JSzσ
2I
+J2S(zσ − 1)
4Gσ
(E − JSzσ
2
)[I − J
2Gσ
(E − JSzσ
2
)]−1
where
Gσ
(E − JSzσ
2
)=
1N
∑q
[(E − JSzσ
2
)I − ε(k-q)
]−1
Interpolating self- energy approach for one-band KLM[W.Nolting et al, PRB 64, 155109 (2001)]
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
Summary
Green function methodMulti- band self- energyPhysical properties
Electronic self- energy
The multi- band self- energy ansatz :
Σσ(E) = −J2
Mσ I+J2
4aσGσ
(E−J
2Mσ
) [I − J
2Gσ
(E − J
2Mσ
)]−1
where
Mσ = zσ〈Sz〉; aσ = S(S + 1)−Mσ(Mσ + 1).
and the non- interacting Green function is :
Gσ(E) =1N
∑k
[(E + i0+)I − ε(k)]−1
Anand Sharma Temperature dependent correlation effects in GdN
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Green function methodMulti- band self- energyPhysical properties
If hopping matrix, ε(k), intra- atomic exchange, J and spinquantum number, S are known
Gσ(E) −→ Σσ(E) −→ Gkσ(E)
Quasi- particle spectral density :
Skσ(E) = −1π
ImTr(Gkσ(E))
Quasi- particle density of states :
ρσ(E) =1N
∑k
Skσ(E)
Anand Sharma Temperature dependent correlation effects in GdN
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Kinetic energyIntra-atomic exchange
Outline
1 Introduction
2 Theoretical evaluationGreen function methodMulti- band self- energyPhysical properties
3 ab-initio calculationKinetic energyIntra-atomic exchange
4 Results
5 Summary
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
Summary
Kinetic energyIntra-atomic exchange
Density Functional Theory (DFT)
Two theorems by Hohenberg and Kohn [PR 136, B864 (1964)].
F [ρ(r)] = T [ρ(r)] +
∫Vext(r)ρ(r)d3r
+12
∫ρ(r)ρ(r′)| r− r′ |
d3rd3r′ + Exc[ρ(r)]
[−~2
2m4+ VKS(r)
]ψi(r) = εiψi(r)
VKS(r)[ρ(r)] = Vext(r) +
∫ρ(r′)
| r− r′ |d3r′ +
δExc[ρ(r)]δρ(r)
ρ(r) =∑
i
f (εi) | ψi(r) |2
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
Summary
Kinetic energyIntra-atomic exchange
Density Functional Theory (DFT)
Two theorems by Hohenberg and Kohn [PR 136, B864 (1964)].
F [ρ(r)] = T [ρ(r)] +
∫Vext(r)ρ(r)d3r
+12
∫ρ(r)ρ(r′)| r− r′ |
d3rd3r′ + Exc[ρ(r)]
[−~2
2m4+ VKS(r)
]ψi(r) = εiψi(r)
VKS(r)[ρ(r)] = Vext(r) +
∫ρ(r′)
| r− r′ |d3r′ +
δExc[ρ(r)]δρ(r)
ρ(r) =∑
i
f (εi) | ψi(r) |2
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
Summary
Kinetic energyIntra-atomic exchange
Density Functional Theory (DFT)
Two theorems by Hohenberg and Kohn [PR 136, B864 (1964)].
F [ρ(r)] = T [ρ(r)] +
∫Vext(r)ρ(r)d3r
+12
∫ρ(r)ρ(r′)| r− r′ |
d3rd3r′ + Exc[ρ(r)]
[−~2
2m4+ VKS(r)
]ψi(r) = εiψi(r)
VKS(r)[ρ(r)] = Vext(r) +
∫ρ(r′)
| r− r′ |d3r′ +
δExc[ρ(r)]δρ(r)
ρ(r) =∑
i
f (εi) | ψi(r) |2
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
Summary
Kinetic energyIntra-atomic exchange
Density Functional Theory (DFT)
Two theorems by Hohenberg and Kohn [PR 136, B864 (1964)].
F [ρ(r)] = T [ρ(r)] +
∫Vext(r)ρ(r)d3r
+12
∫ρ(r)ρ(r′)| r− r′ |
d3rd3r′ + Exc[ρ(r)]
[−~2
2m4+ VKS(r)
]ψi(r) = εiψi(r)
VKS(r)[ρ(r)] = Vext(r) +
∫ρ(r′)
| r− r′ |d3r′ +
δExc[ρ(r)]δρ(r)
ρ(r) =∑
i
f (εi) | ψi(r) |2
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
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Kinetic energyIntra-atomic exchange
DFT-LDA and TB-LMTO-ASA
For Vext(r) : Muffin Tin (MT) potential
Vext(r) ≈ VMT = V (r - R) r ≤ R= V0 r > R
In Atomic Sphere Approximation (ASA), the muffin tinspheres are allowed to overlap with each other.The Tight Binding (TB) formalism minimizes this overlap.For Exc[ρ(r)] : Local Density Approximation (LDA)
Exc[ρ(r)] ≈ Ehomxc [ρ(r)]
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
Summary
Kinetic energyIntra-atomic exchange
DFT-LDA and TB-LMTO-ASA
For Vext(r) : Muffin Tin (MT) potential
Vext(r) ≈ VMT = V (r - R) r ≤ R= V0 r > R
In Atomic Sphere Approximation (ASA), the muffin tinspheres are allowed to overlap with each other.The Tight Binding (TB) formalism minimizes this overlap.For Exc[ρ(r)] : Local Density Approximation (LDA)
Exc[ρ(r)] ≈ Ehomxc [ρ(r)]
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
Summary
Kinetic energyIntra-atomic exchange
DFT-LDA and TB-LMTO-ASA
For Vext(r) : Muffin Tin (MT) potential
Vext(r) ≈ VMT = V (r - R) r ≤ R= V0 r > R
In Atomic Sphere Approximation (ASA), the muffin tinspheres are allowed to overlap with each other.The Tight Binding (TB) formalism minimizes this overlap.For Exc[ρ(r)] : Local Density Approximation (LDA)
Exc[ρ(r)] ≈ Ehomxc [ρ(r)]
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
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Kinetic energyIntra-atomic exchange
GdN : experimental details
Electronic ground state is unconfirmed : Half- metal orsemiconductor ?Ferromagnet having Curie temperature ranging from 58 -90 K.4f7- local moments =⇒ S = 7
2NaCl structure with lattice constant, a = 4.99 A along withatomic positions act as input parameters in theTB-LMTO-ASA program :
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
Summary
Kinetic energyIntra-atomic exchange
GdN : experimental details
Electronic ground state is unconfirmed : Half- metal orsemiconductor ?Ferromagnet having Curie temperature ranging from 58 -90 K.4f7- local moments =⇒ S = 7
2NaCl structure with lattice constant, a = 4.99 A along withatomic positions act as input parameters in theTB-LMTO-ASA program :
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
Summary
Kinetic energyIntra-atomic exchange
GdN : experimental details
Electronic ground state is unconfirmed : Half- metal orsemiconductor ?Ferromagnet having Curie temperature ranging from 58 -90 K.4f7- local moments =⇒ S = 7
2NaCl structure with lattice constant, a = 4.99 A along withatomic positions act as input parameters in theTB-LMTO-ASA program :
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
Summary
Kinetic energyIntra-atomic exchange
GdN : experimental details
Electronic ground state is unconfirmed : Half- metal orsemiconductor ?Ferromagnet having Curie temperature ranging from 58 -90 K.4f7- local moments =⇒ S = 7
2NaCl structure with lattice constant, a = 4.99 A along withatomic positions act as input parameters in theTB-LMTO-ASA program :
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
Summary
Kinetic energyIntra-atomic exchange
T = 0 bandstructure (DFT-LDA)
The hopping matrix, ε(k) : GdN 5d conduction band
Anand Sharma Temperature dependent correlation effects in GdN
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Kinetic energyIntra-atomic exchange
T = 0 density of states (DFT-LDA)
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
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Kinetic energyIntra-atomic exchange
T = 0 density of states (DFT-LDA)
∆E = 1.237eV= JS
J = 0.35 eV
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
Summary
Outline
1 Introduction
2 Theoretical evaluationGreen function methodMulti- band self- energyPhysical properties
3 ab-initio calculationKinetic energyIntra-atomic exchange
4 Results
5 Summary
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
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Summary
T = 0 density of states : LDA, ISA
↑ - spectrum is free fromcorrelation (absence of spin-flip processes) but is rigidlyshifted (JS
2 ).compensation of rigid shiftfulfills the exact (T = 0, σ =↑)limiting case and avoids thedouble counting of interaction.↓ - spectrum demonstratescorrelation effects even atT = 0 K.
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
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Magnon emission :
Magnetic polaron :
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
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Magnon emission :
Magnetic polaron :
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
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Quasi- particle bandstructure
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
Summary
Quasi- particle bandstructure
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
Summary
Quasi- particle bandstructure
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
Summary
Quasi- particle bandstructure
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
Summary
Quasi- particle spectral density
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
Summary
Quasi- particle spectral density
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
Summary
Quasi- particle spectral density
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
Summary
Quasi- particle spectral density
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
Summary
Quasi- particle spectral density
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
Summary
Quasi- particle spectral density
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
Summary
Quasi- particle density of states
Redshift of opticalabsorption edge for anelectronic transition i.e.shift to lower energiesupon cooling fromT=Tc → T=0.
Anand Sharma Temperature dependent correlation effects in GdN
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Red- shift
Theoretical [A.S and W.NoltingJPCM 18, 7337 (2006)] = 0.34 eVTheoretical [W.Lambrecht, PRB62, 13538 (2000)] = 0.30 eVTheoretical [S.Bhattacharjee andS.M.Jaya EPJB 49, 305 (2006)] =0.49 eVExperimental [F.Leuenberger etal PRB 73, 214430 (2006)] = 0.40eV
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
Summary
Red- shift
Theoretical [A.S and W.NoltingJPCM 18, 7337 (2006)] = 0.34 eVTheoretical [W.Lambrecht, PRB62, 13538 (2000)] = 0.30 eVTheoretical [S.Bhattacharjee andS.M.Jaya EPJB 49, 305 (2006)] =0.49 eVExperimental [F.Leuenberger etal PRB 73, 214430 (2006)] = 0.40eV
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
Summary
Red- shift
Theoretical [A.S and W.NoltingJPCM 18, 7337 (2006)] = 0.34 eVTheoretical [W.Lambrecht, PRB62, 13538 (2000)] = 0.30 eVTheoretical [S.Bhattacharjee andS.M.Jaya EPJB 49, 305 (2006)] =0.49 eVExperimental [F.Leuenberger etal PRB 73, 214430 (2006)] = 0.40eV
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
Summary
Red- shift
Theoretical [A.S and W.NoltingJPCM 18, 7337 (2006)] = 0.34 eVTheoretical [W.Lambrecht, PRB62, 13538 (2000)] = 0.30 eVTheoretical [S.Bhattacharjee andS.M.Jaya EPJB 49, 305 (2006)] =0.49 eVExperimental [F.Leuenberger etal PRB 73, 214430 (2006)] = 0.40eV
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
Summary
Outline
1 Introduction
2 Theoretical evaluationGreen function methodMulti- band self- energyPhysical properties
3 ab-initio calculationKinetic energyIntra-atomic exchange
4 Results
5 Summary
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
Summary
Summary
Multi- band self- energy ansatz is formulated.The kinetic (hopping) term is in the form of a matrix.The many body theoretical evaluation is combined withab-initio calculation.Quasi- particle spectral densities and density of states arecalculated.Temperature dependent strong electronic correlationeffects are observed.Theoretically calculated red- shift energy is in closecomparison with experimentally measured value.
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
Summary
Summary
Multi- band self- energy ansatz is formulated.The kinetic (hopping) term is in the form of a matrix.The many body theoretical evaluation is combined withab-initio calculation.Quasi- particle spectral densities and density of states arecalculated.Temperature dependent strong electronic correlationeffects are observed.Theoretically calculated red- shift energy is in closecomparison with experimentally measured value.
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
Summary
Summary
Multi- band self- energy ansatz is formulated.The kinetic (hopping) term is in the form of a matrix.The many body theoretical evaluation is combined withab-initio calculation.Quasi- particle spectral densities and density of states arecalculated.Temperature dependent strong electronic correlationeffects are observed.Theoretically calculated red- shift energy is in closecomparison with experimentally measured value.
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
Summary
Summary
Multi- band self- energy ansatz is formulated.The kinetic (hopping) term is in the form of a matrix.The many body theoretical evaluation is combined withab-initio calculation.Quasi- particle spectral densities and density of states arecalculated.Temperature dependent strong electronic correlationeffects are observed.Theoretically calculated red- shift energy is in closecomparison with experimentally measured value.
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
Summary
Summary
Multi- band self- energy ansatz is formulated.The kinetic (hopping) term is in the form of a matrix.The many body theoretical evaluation is combined withab-initio calculation.Quasi- particle spectral densities and density of states arecalculated.Temperature dependent strong electronic correlationeffects are observed.Theoretically calculated red- shift energy is in closecomparison with experimentally measured value.
Anand Sharma Temperature dependent correlation effects in GdN
IntroductionTheoretical evaluation
ab-initio calculationResults
Summary
Summary
Multi- band self- energy ansatz is formulated.The kinetic (hopping) term is in the form of a matrix.The many body theoretical evaluation is combined withab-initio calculation.Quasi- particle spectral densities and density of states arecalculated.Temperature dependent strong electronic correlationeffects are observed.Theoretically calculated red- shift energy is in closecomparison with experimentally measured value.
Anand Sharma Temperature dependent correlation effects in GdN