Yoshida Laboratory Mino Yoshitaka. Contents Introduction – Material properties of La 2-x Sr x CuO 4 (LSCO) – Purpose of my study Calculation method –

Yoshida Laboratory Mino Yoshitaka

Electronic structure of La2-xSrxCuO4 calculated by the

self-interaction correction method

Contents

• Introduction– Material properties of La2-xSrxCuO4 (LSCO)– Purpose of my study

• Calculation method– Local density approximation (LDA)– Self-Interaction Correction (SIC)

• Results– Calculated electronic structure of LSCO– Stability of anti-ferromagnetic state(The calculation code is MACHIKANEYAMA and the SIC program is developed by Toyoda.)

• Discussion• Summary• Future work

Introduction

AFM ： anti-ferromagnetism, PM : paramagnetic, SG : spin glass, I : insulator, M : metal, N : normal conductivity, SC : superconductivity, T : tetragonal, O : orthorhombic

Warren E. Pickett ; Rev. Mod. Phys. 61, 433 (1989)

La2CuO4

Experiment

Neel temperature TN 200 ～ 300 KLocal magnetic moment on Cu 0.3 ～ 0.5μB

Concentration x when the anti-ferromagnetism disappears.

x=0.02

Tc at the optimal doping 50 K

Concentration x at the optimal doping. x=0.15Cu

La

Oz

Oxy

IntroductionLa2CuO4

TN:200 ～ 300 K

x=0.02

Cu

La

Oz

Oxy

La2CuO4 is one of the transitional-metal oxides (TMO). The electronic structure of the TMO is not well

described by the band structure method based on the local density approximation (LDA)

The purpose of my study is to reproduce the magnetic phase diagram with the self-interaction correction (SIC) method in the first principle calculation.

AFM ： anti-ferromagnetism, PM : paramagnetic, SG : spin glass, I : insulator, M : metal, N : normal conductivity, SC : superconductivity, T : tetragonal, O : orthorhombic

Warren E. Pickett ; Rev. Mod. Phys. 61, 433 (1989)

La2-xSrxCuO4

veff(r) : effective potentialψi(r) : wave function

Kohn-Sham theoryWe map a many body problem on one electron problem with effective potential.

veff(r)

ψi(r)

Kohn-Sham equation

Schrodinger equation

W. Kohn, L. J. Sham ; Phys. Rev. 140, A1133 (1965)

Local Density Approximation (LDA) We do not know the μxc and we need approximate expressions of them to perform

electronic structure calculations. For a realistic approximation, we refer homogeneous electron gas.

When the electron density changes in the space, we assume that the change is moderate and the electron density is locally homogeneous.

Local Density Approximation (LDA)

We call this “exchange correlation potential”.

External potential Coulomb potential from electron density

effective potential

Systematic error of LDALDA has some errors in predicting material properties.

Underestimation of lattice constant.

Overestimation of cohesion energy.

Overestimation of bulk modulus.

Underestimation of band gap energy.

Predicting occupied localize states (d states) at too high energy.

...

Self-interaction correction (SIC)

LDA

Self Coulomb interaction and self exchange correlation interaction don’t cancel each other perfectly.

We need self-interaction correction (SIC) .

exchange correlation potential

External potential Coulomb interaction between electrons

effective potential

J. P. Perdew, Alex Zunger; Phys. Rev. B23, 5048 (1981)

Alessio Filippetti and Nicola A. Spaldin; Phys. Rev. B67, 125109 (2003)

Cu 3d

Cu 3d

Cu 3d

O 2p

O 2p

Cu 3d

LDA: non-magnetic and metallic.

SIC: anti-ferromagnetic and insulating: local magnetic moment on Cu: 0.53 μB

band gap: about 0.8 eV

Exp: anti-ferromagnetic and insulating: Cu local magnetic moment: 0.3 ～ 0.5 μB

band gap: about 0.9 eV

T. Takahashi et al ; Phys. Rev. B 37, 9788 (1988)

DOS of La2CuO4 by LDA and by SIC-LDA

Cu 3d

LDA

anti-ferromagnetism with SIC-LDA

LH d state UH d state

LH d state

UH d statep state

E

E

Ud

Ud

Δ

Δ

charge transfer insulator:Ud > Δ

(La2CuO4)

Mott-Hubbard insulator:Ud < Δ

p state

Type of the insulator of transition metal oxide

LDA vs. SIC

For the La2CuO4 The experimental result Calculated by the LDA Calculated by the SIC-LDA

Magnetism Anti-ferromagnetic Nonmagnetic(×)

Anti-ferromagnetic(○)

Metal or insulator Insulator Metal(×)

Insulator(○)

Local magnetic moment on Cu 0.3 ～ 0.5 μB

0(×)

0.53 μB

(○)

position of Cu d state About -8.0 eV About -3.0 eV

(×)About -7.0 eV

(○)

Band gap energy About 0.9 eV 0(×)

About 0.8 eV(○)

The magnetic phase diagram

AFM ： anti-ferromagnetism, PM : paramagnetic, SG : spin glass, I : insulator, M : metal, N : normal conductivity, SC : superconductivity, T : tetragonal, O : orthorhombic

Warren E. Pickett ; Rev. Mod. Phys. 61, 433 (1989)x=0.02

The energy difference between paramagnetic and anti-ferromagnetic state.

The stability of anti-ferromagnetic stateLa2-xSrxCuO4

:Cu The random system is calculated by Coherent Potential Approximation (CPA)

0

0.02

0.04

0.06

0.08

0.1

0.12

para...

Concentration x

ΔE [

Ry]

The anti-ferromagnetism becomes unstable by hole doping.

Stability of anti-ferromagnetic state

La2-xSrxCuO4

Experimental result of x

Cu 3d

Cu 3d

Cu 3dO 2p

O 2p

O 2p

Sr 5p

Sr 5p

Holes are doped in O 2p state → Fermi level comes close to the

valence band.

At x=0.16, the Fermi level comes into the valence band.

The doping dependence with Sr

La2-xSrxCuO4

anti-ferromagnetism (x=0) anti-ferromagnetism (x=0.16)

anti-ferromagnetism (x=0.06)

A site

B site

E

E

A

B

A B

EF

anti-ferromagnetic

Super exchange interaction

d state

d state

d state

d state

E

E A B

A B

EF

ferromagnetic. EF

The p-hole with up spin runs around in the crystal.

p-d exchange interaction

d state

d state

d state

d state

p state

p state

p state

p state

Summary• The electronic structure is not reproduced by the

LDA.• The anti-ferromagnetic state of La2CuO4 is well

reproduced by the SIC method.• The trend of the stability of the anti-ferromagnetism

has been reproduced by using the SIC method.

I will estimate the Neel temperature with the Monte Carlo simulation.

future work

Thank you for your attention.