Quasiparticle Selfconsistent GW Study of LSMO and future

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 GWA (RPA, without vertex correction) (use only the diagonal self-energy) + + + Bare Exchange and Correlated parts made of and

QPsc. GW quasiparticle self-consistent GW one-body potential 1. Neglect frequency dependence of S(w) 2. DS=0, when self-consistency is achieved.

Merits of QPsc. GW 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 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 hn L+1 L phosphorescence hn (slow) S 0 T 1 S 1 h↑ e↑ semiconductor =0% Organic semiconductor • small Z: small L S coupling • long spin life time E. g. Davis and Bussmann, JAP 93, 7358 (2003).

La 0. 7 Sr 0. 3 Mn. O 3, (La 0. 7 Ba 0. 3 Mn. O 3, La 0. 7 Ca 0. 3 Mn. O 3) La. Mn. O 3: 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 La 0. 7 Sr 0. 3 Mn. O 3 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 Ionization energy L. Hedin, J. Phys. Condens. Matter 11, R 489(1999)

LSDA results of La 0. 7 Ba 0. 3 Mn. O 3 • LMTO-ASA • virtual crystal approx. La O Mn Pm-3 m La 4 f Mn eg Mn t 2 g Spin moment=3. 55 m. B Majority Mn eg <- Fermi level Minority Mn t 2 g <- Fermi level Mn eg Mn t 2 g

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

fp-LMTO Double Hankel O 3 s Minimum basis O 3 p La 5 p(semicore) La 7 s La 6 d Mn 5 s Mn 5 p Mn 4 d

1 st iteration GW result GW calculation 6 x 6 x 6 (20 irreducible) k-points, ~+100 e. V Not easy to see what happens from the figure… It looks that a gap opens in the minority band spin is fully polarized.

QPsc. GW result GW calculation 6 x 6 x 6 (20 irreducible) k-points, ~+100 e. V Spin moment=3. 70 m. B (fully polarized) Minority spin, conduction bottom-EF=+0. 9 e. V (Previous result, conduction bottom-EF=+2 e. V) La 4 f=+12 e. V, c. f. , exp. (inverse photoemission) ~+8 e. V (Is screening insufficient? )

Effects of Mn potential distribution due to random La/Ca distribution La 2/3 Ca 1/3 • La 2/3 Ca 1/3 Mn. O 3 • LSDA • random distribution of La/Ca • Mn potential distribution =0. 6 e. V GW+randomness Mn eg Mn t 2 g Mn eg 0. 3 e. V Mn t 2 g Pickett and Singh, PRB 55, 8642 (1997) O 2 p • 0. 9 e. V(GW minority-spin band edge)-0. 3 e. V(Mn potential distribution)=+0. 3 e. V • no QP state in the minority spin component at EF even in the presence of disorder

QPsc. GW, computational costs LSMO, 5 atoms, upto ~100 e. V(~100 bands), 20 k-points, SR 11000, 4 CPU 1 cycle LDA and converting data to GW data exchange　 polarization function correlation ~1 hr ~15 hr ~8 hr ~74 hr 1 day for LDA+exchange+polarization (1 q 4 L job) 1 day for correlation (4 q 4 L jobs simultaneously) About 10 cycles to be converged ~20 days (2. 5 q 4 L jobs per day) Disk: ~10 Gbyte

GW Tetrahedron DOS k=(000) An example of diamond-Si Im(S) A(w) w QP E+Re(S(w)) Lambin & Vigneron, RPB 29, 3430 (1984) Phonon+photon=>plariton QP+plasmon=>plasmon+plasmaron? Plasmaron? plasmon LDA qp. GW Z~0. 75 LDA qp. GW

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 GW M↓ M↓ M↑ O ? Oxygen level is too low O M↑ Some improvement on the energy level of ogygen?

Next topic

Complementing input files of fp-LMTO H. Kino and H. Kotani fp. LMTO 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 fp. LMTO program. But, it is hard to write input files of fp. LMTO. People do not use such a program.

Interstitial region of fp. LMTO wavefunctions potential Interstitial region is expanded via Hunkel functions, Parameters of Hunkel functions are necessary. But it is not easy for beginners of fp. LMTO 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 fp. LMTO 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=gw 1 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 ATOM=La POS=0. 5 ATOM=O POS=0. 5 0. 0 ATOM=O POS=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 RSMH= 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 -0. 20 RSMH= 2. 20 1. 81 1. 40 EH 2= -0. 20 RSMH 2= 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= 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!