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

Contents Introduction Calculation method Results Discussion Summary 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 La2CuO4 La Oz Oxy Cu Experiment Neel temperature TN 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 Experiment Neel temperature TN 200～300 K Local 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=0.15 Oz Oxy Cu

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

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)

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. 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”.

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. ...

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)

DOS of La2CuO4 by LDA and by SIC-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)

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

The experimental result Calculated by the SIC-LDA LDA vs. SIC For the La2CuO4 The experimental result Calculated by the LDA Calculated by the SIC-LDA Magnetism Anti-ferromagnetic Nonmagnetic (×) (○) Metal or insulator Insulator Metal Local magnetic moment on Cu 0.3～0.5 μB 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 About 0.8 eV

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)

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

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

Super exchange interaction EF d state A E A site d state anti-ferromagnetic A B d state B site E B d state

p-d exchange interaction EF A B d state p state E p state d state ferromagnetic. The p-hole with up spin runs around in the crystal. EF d state p state E A B p state d 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. future work I will estimate the Neel temperature with the Monte Carlo simulation.

Thank you for your attention.