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

Merits of QPscGW

No Z factor, easy to analyzeQP dispersion, full k-path...

Half-metal --- application

•Spin valve --- MRAM

•Spin OLED (organic light emitting diode)

DOS

EF

Half-metal↑

↓

↑ ↓ ↑

↓

Applications

Basic Idea

EF

↑↓

EF

↑↓

I↑

I↑

too simple...

Spin valve --- MRAM

-30%

Xiong et al., Nature 427, 821 (2004).

e↑

Alq=8-hydroxyquinoline aluminium

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

fp-LMTO calculation

La 4f

More accurate dispersion at higher energies

Majority spin

fp-LMTO

Minimum basis

O3s

O3p La7s

La6d Mn 5s

Mn 5p Mn4d

Double Hankel

La 5p(semicore)

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

Future problems

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

Next topic

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

input files of fp-LMTO

We made a prototype. Many tests are necessary to give better parameters!