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

LDA (use only the diagonal self-energy) Bare Exchange and Correlated parts (RPA, without vertex correction) made of and ++ GWA + GW method: first-principles (no parameter), correlation= RPA-level

QPscGW quasiparticle self-consistent GW one-body potential 1. Neglect frequency dependence of  (  ) 2.  =0, when self-consistency is achieved.

Merits of QPscGW No Z factor, easy to analyze QP dispersion, full k-path...

Half-metal --- application Spin valve --- MRAM Spin OLED (organic light emitting diode) DOS EFEF Half-metal ↑ ↓ ↑ ↓ ↑ ↓ Applications

Basic Idea EFEF ↑ ↓ EFEF ↑ ↓ 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 S0S0 S1S1 T1T1 L L+1 luminescencephosphorescence Organic semiconductor small Z: small L  S coupling long spin life time Change luminescence efficiency =0% h E.g. Davis and Bussmann, JAP 93, 7358 (2003). (slow)

La 0.7 Sr 0.3 MnO 3, (La 0.7 Ba 0.3 MnO 3,La 0.7 Ca 0.3 MnO 3 ) LaMnO 3 : collosal magnetoresistance oxides a strongly correlated system (intrinsic ramdomness) In theories LSDA: nonzero DOS at E F in minority spin component In experiments, many experiments: spin polarization: 35%-100% In this study, calculate La 0.7 Sr 0.3 MnO 3 beyond LSDA. estimate a band gap in the GW approximation.

Experimental results Non-zero DOS at E F = 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 E F =fully spin-polarized XPS, 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) Ionization energy e.g. GW improves bandgaps

LMTO-ASA virtual crystal approx. Mn e g Mn t 2g Mn e g Mn t 2g La Mn O Pm-3m LSDA results of La 0.7 Ba 0.3 MnO 3 Majority Mn e g <- Fermi level Minority Mn t 2g <- Fermi level Spin moment=3.55  B La 4f

fp-LMTO calculation La 4f More accurate dispersion at higher energies Majority spin

fp-LMTO Minimum basis O3s O3p La7s La6dMn 5s Mn 5pMn4d Double Hankel La 5p(semicore)

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 Minority spin, conduction bottom-E F =+0.9eV La 4f=+12eV, c.f., exp.(inverse photoemission) ~+8eV (Is screening insufficient?) (Previous result, conduction bottom-E F =+2eV) GW calculation 6x6x6 (20 irreducible) k-points, ~+100eV Spin moment=3.70  B (fully polarized)

Pickett and Singh, PRB 55, 8642 (1997) La 2/3 Ca 1/3 MnO 3 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 E F even in the presence of disorder La 2/3 Ca 1/3 Mn e g Mn t 2g Mn e g GW+randomness O2p 0.3eV Mn t 2g Effects of Mn potential distribution due to random La/Ca distribution

QPscGW, computational costs 1 cycle LDA and converting data to GW data~1hr exchange ~15hr polarization function ~8hr correlation~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=>plariton QP+plasmon=>plasmon+plasmaron?  E+Re(  ) Im(  ) A(  ) LDA qpGW LDA qpGW k=(000)

Future problems

Impurity level of semiconductors acceptor donor LDA orbital energy  quasiparticle energy unoccupied 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.

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 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-6.10 STRUC NBAS=5 NSPEC=3 NL=7 ALAT= PLAT= 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= ATOM=La POS= ATOM=O POS= ATOM=O POS= ATOM=O POS= HAM GMAX=11 SPEC ATOM= Mn Z= 25.0 R= 2.05 LMX= 6 LMXA= 4 KMXA= 3 A= EH= RSMH= P= IDMOD= ATOM= La Z= 56.7 R= 3.3 LMX= 6 LMXA= 4 KMXA= 3 A= EH= RSMH= EH2= RSMH2= P= IDMOD= ATOM= O Z= 8.0 R= 1.6 LMX= 6 LMX= 4 A= EH= RSMH= P= IDMOD= 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!