Transcript GW study of half-metallic electronic structure of La0.7Sr0

Quasiparticle Self-consistent GW
Study of LSMO
and future studies
Hiori Kino
Half-metal: Important materials for spin-electronics
Future targets:
Semiconductor: Impurity problem
Antiferromagnetic Mott insulators: positions of oxigen levels
GW method: first-principles (no parameter), correlation= RPA-level
LDA
 p2
 LDA
n( r ' )
LDA
LDA
LDA

v

dr
'

v
(
n
(
r
))




ext
XC
kn
kn

 kn

| r  r '|
 2m

GWA
(RPA, without vertex correction)
LDA
Ekn   knLDA  kn |  ( Ekn )  VXC
| kn
(use only the diagonal self-energy)
+
+
+
Bare Exchange and Correlated parts
made of
v(q)
 knLDA
and
 knLDA
QPscGW
quasiparticle self-consistent GW
one-body potential
 p2
 1
n( r ' )
1
1 1

V

dr
'

V
(
n
(
r
))


(
E
)


E
atom
XC
ik
ik  ik
ik ik


| r  r '|
 2m

1
 ik ( Eik )  ik | ( Eik )  VXC
| ik
n(r ) 
 nik (r) 
Eik  EF
1
2
|

(
r
)
|
 ik
Eik  EF
1. Neglect frequency dependence of (w)
LDA
 |  ik1
2. =0, when self-consistency is achieved.  |  ik
Merits of QPscGW
No Z factor, easy to analyze
QP dispersion, full k-path
...
Half-metal --- application
DOS
↑
↓
EF
↑
Half-metal
↓
Applications
•Spin valve --- MRAM
•Spin OLED (organic light emitting diode)
↑
↓
Basic Idea
I↑
↑
↓
EF
↑
↓
EF
I↑
too simple...
Spin valve --- MRAM
e↑
Alq=8-hydroxyquinoline aluminium
-30%
Xiong et al., Nature 427, 821 (2004).
Spin OLED (organic light emitting diode)
---Organic EL (electroluminescence)
Change luminescence efficiency
luminescence
phosphorescence
hn
L+1
hn
(slow)
L
S1 |  |
S0
h↑
e↑
semiconductor
=0%
T1
Organic semiconductor
•small Z: small LS coupling
•long spin life time
E.g. Davis and Bussmann, JAP 93, 7358 (2003).
La0.7Sr0.3MnO3,
(La0.7Ba0.3MnO3,La0.7Ca0.3MnO3)
LaMnO3: collosal magnetoresistance oxides
a strongly correlated system
(intrinsic ramdomness)
In theories
LSDA: 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
For the Minority spin state
Non-zero DOS at EF = partially spin-polarized
Andreev 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-polarized
XPS, Park et al.
resistivity, Zhao et al. (bulk)
tunnel, Wei et al. (bulk)
e.g. GW improves bandgaps

LDA
i
E

 Ionization energy  E ( N  1)  E ( N )
ni
L. Hedin, J. Phys. Condens. Matter 11,R489(1999)
LSDA results of La0.7Ba0.3MnO3
•LMTO-ASA
•virtual crystal approx.
La
O
Majority Mn eg <- Fermi level
Minority Mn t2g <- Fermi level
Mn
Pm-3m
La 4f
Mn eg
Mn t2g
Spin moment=3.55mB
Mn eg
Mn t2g
fp-LMTO calculation
Majority spin
La 4f
More accurate dispersion
at higher energies
fp-LMTO
Double Hankel
O3s
Minimum basis
O3p
La7s
La 5p(semicore)
La6d
Mn 5s
Mn 5p
Mn4d
1st iteration GW result
GW 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
GW calculation 6x6x6 (20 irreducible) k-points, ~+100eV
Spin moment=3.70mB (fully polarized)
Minority spin, conduction bottom-EF=+0.9eV
(Previous result, conduction bottom-EF=+2eV)
La 4f=+12eV,
c.f., exp.(inverse photoemission) ~+8eV (Is screening insufficient?)
Effects of Mn potential distribution
due to random La/Ca distribution
La 2/3 Ca 1/3
•La2/3Ca1/3MnO3
•LSDA
•random distribution of La/Ca
•Mn potential distribution
=0.6eV
GW+randomness
Mn eg
Mn t2g
Mn eg
0.3eV
Mn t2g
Pickett and Singh, PRB 55, 8642 (1997)
O2p
•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
QPscGW, computational costs
LSMO, 5 atoms, upto ~100eV(~100bands), 20 k-points,
SR11000, 4CPU
1 cycle
LDA and converting data to GW data
exchange
polarization function
correlation
~1hr
~15hr
~8hr
~74hr
1day for LDA+exchange+polarization (1 q4L job)
1day for correlation (4 q4L jobs simultaneously)
About 10 cycles to be converged ~20days (2.5 q4L jobs per day)
Disk: ~10Gbyte
GW Tetrahedron DOS
k=(000)
An example of diamond-Si
Im()
A(w)
w
QP
Lambin & Vigneron, RPB 29, 3430 (1984)
A(w ) ~ Im[G]  1 /(w  E  (w))
E+Re((w))
Phonon+photon=>plariton
QP+plasmon=>plasmon+plasmaron?
Plasmaron? plasmon
LDA
qpGW
Z~0.75
LDA
qpGW
Future problems
Impurity level of semiconductors
donor
acceptor
Si
GW Direct
LDA orbital energyquasiparticle energy
determination of
unoccupied energy level: underestimated
acceptor and
donor levels
Antiferromagnetic Mott insulators:
positions of oxigen levels
•In the AF Mott insulators, AF spin-up and -down bands corresponds
to the upper and lower Hubbard bands.
• |  LDA  |  1
ik
ik
LDA
GW
M↓
M↓
M↑
O
?
O
Oxygen level is too low
M↑
Some improvement on the
energy level of ogygen?
Next topic
Complementing input files of fp-LMTO
H. Kino and H. Kotani
fpLMTO is
fullpotential
efficient, 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
wavefunctions
potential
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
input files of fp-LMTO
We made scripts to complement input files of fpLMTO
A minimum input file
HEADER LSMO
VERS LMF-6.10 LMASA-6.10
STRUC NBAS=5 NSPEC=3 NL=7
ALAT=7.3246
PLAT=1 0 0
010
001
SYMGRP find
SPEC
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=0.015
SITE 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
Complement each section
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
Keywords to control accuracy
input files of fp-LMTO
We made a prototype.
Many tests are necessary to give better
parameters!