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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.