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Quasiparticle Self-consistent GW Study of LSMO and future studies
Hiori Kino
Half-metal: Important materials for spin-electronics
Future targets:Semiconductor: Impurity problemAntiferromagnetic Mott insulators: positions of oxigen levels
LDA
knVEknE LDAXCkn
LDAknkn |)(|
(use only the diagonal self-energy)
Bare Exchange and Correlated parts
(RPA, without vertex correction)
made of and
)(qv
LDAkn LDA
kn
+ +
LDAkn
LDAkn
LDAkn
LDAXCext rnv
rr
rndrv
m
p
))((
|'|
)'('
2
2
GWA
+
GW method: first-principles (no parameter), correlation= RPA-level
ikVEikE XCikikik |)(|)( 1
Fik
ik
Fik EEEEik rrnrn 21 |)(|)()(
11112
)())((|'|
)'('
2 ikikikikikXCatom EErnVrr
rndrV
m
p
QPscGWquasiparticle self-consistent GW
one-body potential
1. Neglect frequency dependence of ()2. =0, when self-consistency is achieved. 1|| ik
LDAik
Half-metal --- application
•Spin valve --- MRAM
•Spin OLED (organic light emitting diode)
DOS
EF
Half-metal↑
↓
↑ ↓ ↑
↓
Applications
Spin OLED (organic light emitting diode)
---Organic EL (electroluminescence)
e↑
h↑
h
semiconductor
S0 S1T1
L
L+1
luminescence phosphorescence
Organic semiconductor•small Z: small LS coupling•long spin life time
Change luminescence efficiency
=0%
h
E.g. Davis and Bussmann, JAP 93, 7358 (2003).
(slow)
||
La0.7Sr0.3MnO3, (La0.7Ba0.3MnO3,La0.7Ca0.3MnO3)
LaMnO3: collosal magnetoresistance oxidesa strongly correlated system(intrinsic ramdomness)
In theoriesLSDA: nonzero DOS at EF in minority spin component
In experiments, many experiments: spin polarization: 35%-100%
In this study, calculate La0.7Sr0.3MnO3 beyond LSDA. estimate a band gap in the GW approximation.
Experimental results
Non-zero DOS at EF = partially spin-polarizedAndreev reflection, Soulen Jr. et al.,tunnel junction, Lu et al., Worledge et al., Sun et al.,residual resistivity, Nadgomy et al. (bulk)
Zero DOS at EF=fully spin-polarizedXPS, Park et al.resistivity, Zhao et al. (bulk)tunnel, Wei et al. (bulk)
For the Minority spin state
L. Hedin, J. Phys. Condens. Matter 11,R489(1999)
i
LDAi n
E Ionization energy )()1( NENE
e.g. GW improves bandgaps
•LMTO-ASA•virtual crystal approx.
Mn eg Mn t2g
Mn eg
Mn t2g
La
Mn
O
Pm-3m
LSDA results of La0.7Ba0.3MnO3
Majority Mn eg <- Fermi levelMinority Mn t2g <- Fermi level
Spin moment=3.55B
La 4f
1st iteration GW resultGW calculation 6x6x6 (20 irreducible) k-points, ~+100eV
Not easy to see what happens from the figure…
It looks that a gap opens in the minority band and spin is fully polarized.
QPscGW result
Minority spin, conduction bottom-EF=+0.9eV
La 4f=+12eV, c.f., exp.(inverse photoemission) ~+8eV (Is screening insufficient?)
(Previous result, conduction bottom-EF=+2eV)
GW calculation 6x6x6 (20 irreducible) k-points, ~+100eV
Spin moment=3.70B (fully polarized)
Pickett and Singh, PRB 55, 8642 (1997)
•La2/3Ca1/3MnO3
•LSDA•random distribution of La/Ca•Mn potential distribution =0.6eV
•0.9eV(GW minority-spin band edge)-0.3eV(Mn potential distribution)=+0.3eV
•no QP state in the minority spin component at EF even in the presence of disorder
La 2/3 Ca 1/3
Mn eg
Mn t2g
Mn eg
GW+randomness
O2p
0.3eVMn t2g
Effects of Mn potential distribution due to random La/Ca distribution
QPscGW, computational costs
1 cycleLDA and converting data to GW data ~1hrexchange ~15hrpolarization function ~8hrcorrelation ~74hr
1day for LDA+exchange+polarization (1 q4L job)1day for correlation (4 q4L jobs simultaneously)
LSMO, 5 atoms, upto ~100eV(~100bands), 20 k-points, SR11000, 4CPU
About 10 cycles to be converged ~20days (2.5 q4L jobs per day)
Disk: ~10Gbyte
GW Tetrahedron DOS
Plasmaron? plasmon
QP
Lambin & Vigneron, RPB 29, 3430 (1984)
Z~0.75
An example of diamond-Si
Phonon+photon=>plaritonQP+plasmon=>plasmon+plasmaron?
E+Re()
Im()A()
LDA
qpGW
LDA
qpGW
k=(0
00)
))(/(1]Im[~)( EGA
Impurity level of semiconductors
acceptor
donor
LDA orbital energyquasiparticle energyunoccupied energy level: underestimated
GW
Si
Direct determination of acceptor and donor levels
Antiferromagnetic Mott insulators:
positions of oxigen levels
Oxygen level is too low Some improvement on the energy level of ogygen?
M↑
M↓
O
LDA
M↑
M↓
O
GW
?
•In the AF Mott insulators, AF spin-up and -down bands corresponds to the upper and lower Hubbard bands.• 1|| ik
LDAik
Complementing input files of fp-LMTO
H. Kino and H. Kotani
fpLMTO is fullpotentialefficient, fast, for bulk systems
We distribute the GW programs and would like to make it popular.
The present GW program strongly depends on the fpLMTO program. But, it is hard to write input files of fpLMTO. People do not use such a program.
Interstitial region of fpLMTO
Interstitial region is expanded via Hunkel functions, Parameters of Hunkel functions are necessary. But it is not easy for beginners of fpLMTO to give good values. What kind of values are optimal? E.g. plane wave ~ cutoff energy
potential
wavefunctions
input files of fp-LMTO
HEADER LSMO VERS LMF-6.10 LMASA-6.10STRUC NBAS=5 NSPEC=3 NL=7 ALAT=7.3246 PLAT=1 0 0 0 1 0 0 0 1 SYMGRP findSPEC ATOM=Mn Z=25.0 R=2.05 LMX=6 quality=low ATOM=La Z=56.7 R=3.3 LMX=6 quality=gw1 ATOM=O Z= 8.0 R=1.6 LMX=6 MTOQ=s,s,0,0,0 LMX=4 A=0.015SITE ATOM=Mn POS=0.0 0.0 0.0 ATOM=La POS=0.5 0.5 0.5 ATOM=O POS=0.5 0.0 0.0 ATOM=O POS=0.0 0.5 0.0 ATOM=O POS=0.0 0.0 0.5 HAM GMAX=11
SPEC ATOM= Mn Z= 25.0 R= 2.05 LMX= 6 LMXA= 4 KMXA= 3 A= 0.016 EH= -1.00 -1.00 -1.00 RSMH= 1.37 1.37 0.91 P= 4.59 4.35 3.88 4.17 5.10 IDMOD= 0 0 0 1 1 ATOM= La Z= 56.7 R= 3.3 LMX= 6 LMXA= 4 KMXA= 3 A= 0.016 EH= -1.00 -1.00 -1.00 -0.20 RSMH= 2.20 2.20 1.81 1.40 EH2= -0.20 -0.20 -0.20 RSMH2= 2.20 2.20 1.81 P= 6.57 6.21 5.85 4.13 5.13 IDMOD= 0 0 0 1 1 ATOM= O Z= 8.0 R= 1.6 LMX= 6 LMX= 4 A= 0.015 EH= -1.30 -1.00 RSMH= 0.87 0.81 P= 2.88 2.85 3.26 4.13 5.09 IDMOD= 0 0 1 1 1
We made scripts to complement input files of fpLMTO
A minimum input file Complement each section
Keywords to control accuracy
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