Yoshida Laboratory Mino Yoshitaka

1. Electronic structure of La2-xSrxCuO4 calculated by the self-interaction correction method Yoshida Laboratory Mino Yoshitaka

2. 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

3. Introduction Warren E. Pickett ; Rev. Mod. Phys. 61, 433 (1989) La2CuO4 AFM ：anti-ferromagnetism, PM : paramagnetic, SG : spin glass, I : insulator,M : metal, N : normal conductivity, SC : superconductivity, T : tetragonal, O : orthorhombic La Oz Oxy Cu

4. Introduction Warren E. Pickett ; Rev. Mod. Phys. 61, 433 (1989) La2CuO4 La2-xSrxCuO4 AFM ：anti-ferromagnetism, PM : paramagnetic, SG : spin glass, I : insulator,M : metal, N : normal conductivity, SC : superconductivity, T : tetragonal, O : orthorhombic TN:200～300 K La x=0.02 • 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. Oz Oxy Cu

5. Kohn-Sham theory We map a many body problem on one electron problem with effective potential. Schrodinger equation Kohn-Sham equation veff(r) : effective potential ψi(r) : wave function ψi(r) veff(r) W. Kohn, L. J. Sham ; Phys. Rev. 140, A1133 (1965)

6. Local Density Approximation (LDA) • We do not know the μxcand we need approximate expressions of them to perform electronic structure calculations. • For a realistic approximation, we refer homogeneous electron gas. Local Density Approximation (LDA) When the electron density changes in the space, we assume that the change is moderate and the electron density is locally homogeneous. External potential Coulomb potential from electron density effective potential We call this “exchange correlation potential”.

7. Systematic error of LDA LDA 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. • ...

8. Self-interaction correction(SIC) External potential Coulomb interaction between electrons exchange correlation potential effective potential LDA Self Coulomb interaction and self exchange correlation interaction don’t cancel each other perfectly. We need self-interaction correction (SIC) . J. P. Perdew, Alex Zunger; Phys. Rev. B23, 5048 (1981) Alessio Filippetti and Nicola A. Spaldin; Phys. Rev. B67, 125109 (2003)

9. DOS of La2CuO4 by LDA and by SIC-LDA LDA 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 Cu 3d O 2p Cu 3d anti-ferromagnetism with SIC-LDA Cu 3d O 2p Cu 3d Cu 3d T. Takahashi et al ; Phys. Rev. B 37, 9788 (1988)

10. Type of the insulatorof transition metal oxide Ud charge transfer insulator: Ud > Δ (La2CuO4) Δ LH d state p state UH dstate E Ud Mott-Hubbard insulator: Ud < Δ LH d state p state UH d state E Δ

11. LDA vs. SIC

12. The magnetic phase diagram The stability of anti-ferromagnetic state The energy difference between paramagnetic and anti-ferromagnetic state. La2-xSrxCuO4 :Cu The random system is calculated by Coherent Potential Approximation (CPA) AFM ：anti-ferromagnetism, PM : paramagnetic, SG : spin glass, I : insulator,M : metal, N : normal conductivity, SC : superconductivity, T : tetragonal, O : orthorhombic x=0.02 Warren E. Pickett ; Rev. Mod. Phys. 61, 433 (1989)

13. Stability of anti-ferromagnetic state La2-xSrxCuO4 Experimental result of x The anti-ferromagnetism becomes unstable by hole doping.

14. The doping dependence with Sr anti-ferromagnetism (x=0) anti-ferromagnetism (x=0.16) Cu 3d O 2p Sr 5p Cu 3d O 2p La2-xSrxCuO4 anti-ferromagnetism (x=0.06) • 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. Sr 5p Cu 3d O 2p

15. Super exchange interaction EF dstate A E A site dstate anti-ferromagnetic A B dstate B site E B dstate

16. p-d exchange interaction EF A B dstate pstate E pstate dstate ferromagnetic. The p-hole with up spin runs around in the crystal. EF dstate E A B pstate dstate pstate

17. 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. future work • I will estimate the Neel temperature with the Monte Carlo simulation.

18. Thank you for your attention.