COMPETITION BETWEEN FILLED AND HALF-FILLED STRIPES IN CUPRATES AND NICKELATES

Transcription

1 COMPETITION BETWEEN FILLED AND HALF-FILLED STRIPES IN CUPRATES AND NICKELATES Raymond Frésard Andrzej M. Oleś and Marcin Raczkowski Laboratoire Crismat UMR CNRS-ENSICAEN (ISMRA) 6508 Caen France Marian Smoluchowski Institute of Physics Jagellonian University Cracovie Pologne UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN JANUARY 2006

2 OUTLINE Types of stripes Eperimental evidences Description of the cuprates Competition between stripes Modeling of the nickelates Competition between stripes Summary UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN JANUARY 2006

3 STRIPE PHASES 1D domain walls of holes which separate AF domains of opposite phases. they might be: site-centered centered on rows of metal atoms bond-centered centered on rows of oygen atoms bridging two metal sites their shape and properties are material dependent

4 !! # TYPICAL MATERIALS La Nd Sr CuO La superconducting above with for Sr CuO half filled vertical/horizontal stripes ( hole per Cu atom in a domain wall) for with filled diagonal stripes (one hole per Cu atom in a domain wall) : Cu ( ) Cu ( "orbital degeneracy is absent quantum fluctuations important ) proper treatment of strong electron correlations required %$ La Sr NiO La insulator up to with for NiO filled diagonal stripes (one hole/ni ion in a domain wall) : Ni ( ) Ni "orbital degeneracy more classical Hartree approach should capture the physics of the nickelates ( )

5 EXPERIMENTAL SIGNATURES OF STRIPES: CUPRATES Sr Sr Zn La Sr (Nd-LSCO) La Nd CuO (LSCO) La CuO La Cu O (Zn-LSCO) YBa Cu!O CuO # (LCO) # (YBCO) Summary of eperimental data illustrating the doping dependence of incommensurability in the cuprates. In LSCO has been defined as a distance from the IC peak position to the AF wave vector ( ( ) or tetragonal ( ) notation whereas at diagonal and parallel to the Cu-O bonds spin modulations. ) either in the orthorhombic both definitions are used due to the coeistence of

6 EXPERIMENTAL SIGNATURES OF STRIPES: NICKELATES Summary of the results for La Sr NiO (filled circles) Nd circles) for different net dopant induced hole concentration a checkerboard-type charge order ( ) as well as a stripe-type charge ( ) order and (b) incommensurability after Kajimoto et al. Phys. Rev. B (2003). Sr NiO (diamonds) and La Sr NiO dependence of: (a) transition temperature for ) and spin ( (empty

7 FINGERPRINT OF STRIPES? Temperature dependence of: (a) incommensurability Kajimoto et al. Phys. Rev. B (2001); (b) phonon thermal conductivity Hess et al. Phys. Rev. B 59 R10397 (1999); (c) specific heat Ramirez et al. Phys. Rev. Lett (1996); Cheong et al. Phys. Rev. B (1994); inset: optical conductivity (d) logarithmic resistivity Katsufuji et al. Phys. Rev. B 54 R14230 (1996).

8 q ) / % & %. $# " p SLAVE-BOSON APPROACH single-band Hubbard model with the net-nearest-neighbor hopping in terms of the SB operators SB operators have to fulfill a set of constraints at each site p p p The corresponding action is handled on the saddle-point level. ('p * + -q!

9 1 1 g For large systems one need a proper unit cell (a) (b) R g g g for each (a) Vertical stripe phase its unit cell and two periodicity vectors g SC stripe phase its unit cell and two periodicity vectors g and g and g.. (b) Diagonal in the reciprocal space representation the large original fermionic matri is decoupled into ( ) blocks.

10 % Simple approach to stripe stabilization Characteristics of simple bond-centered and site-centered stripes ( ) The interaction energy is reduced when: The (local) density is reduced A local magnetic moment is formed (δf/t) 10 2 m i - - SCd2-1.5 SCd3 BCd3 (a) (c) δn i 10 2 δd i (b) (d)

11 % Finite size effects ( ) (half-filled domain walls) vertical (half-filled domain walls) diagonal F/t N -1/2 F/t N -1/2 The behavior is stripe dependent

12 Influence of electron correlations on SC stripe profiles ( ) (filled domain walls) (half-filled domain walls) 0.4 vertical 0.4 diagonal vertical diagonal n h n h S π HA SBA S π D 7 7 D l 5 l 4 l 4 l

13 % Influence of the net-neighbor hopping (SBA: ) SB free energy of various phases at temperature on a cluster SB band structure of the HVSC stripe phase phase PM040 HDSC 339 AF393 HVSC 689 VSC 751 DSC 821 VSC PM AF341 HDSC 534 DSC 655 HVSC 749 (ω µ)/t t /t= π/2 π 3π/4 2π ky t /t= π/2 π 3π/4 2π ky

14 Doping dependence of the vertical stripe ground state (SBA: (site-centered domain walls) (bond-centered domain walls) ) δf AF /t δf AF /t δf AF /t d=4 t /t=-0.15 (b) d=5 d= d=2 d=7 d=6 d=8 d=9 d=10 d=11 d=8 d=9 d=10 d=11 d=10 d=11 d=7 d=6 d=9 d=8 d=7 d=6 d=5 d=5 d=4 t /t=0 t /t=-0 d=3 d=3 d=3 d=2 (a) d=2 (c) δf AF /t δf AF /t δf AF /t d=5-1 d=6 d=7 d=8 d=9 d=3-2 d=10 d=11 d=4-3 t /t=-0.15 (b) d=9 d=8 d=7 d=6 d=5 d=10-1 d=11 d=4 d= d=6 d=7 d=8 d=9 d=10 d=11 d=5 d=4 t /t=0 t /t=-0 d=3 (a) (c)

15 Doping dependence of the vertical stripe ground state (SBA: ) SB ground state free energy of the VSC and VBC stripes ( ) VSC VBC ε ν (a) (c) VSC VBC (b) (d) a road to low energy modes? µ/t (e) t /t=0 t /t=-0.15 t /t=-0 (f)

16 'S + + / / Systems with orbital degeneracy Hamiltonian for electrons: and kinetic energy electron-electron interactions S crystal-field splitting between and orbitals along the ais + /

17 Mean-field phase diagram for electrons J H =0.15U J H =5U (U+J H )/t FMz FM CAF CAFz AF AFz PM (U+J H )/t FMz CAFz CAF AFz AF FM PM FM CAF Intricate interplay between ferromagnetic and antiferromagnetic phases

18 Doping dependence of the BC stripe ground state (HA: ( model) ) (equivalent band model) ε ε ν vertical (a) (c) (e) (b) (d) diagonal (f) ν vertical (a) (c) (b) diagonal (d) µ/t E z /t=0 E z /t= µ/t (e) (f)

19 Diagonal bond-centered stripes ( ) filled half-filled D intraorbital double occupancy 1 1 σ σ D z interorbital double occupancies σσ D z l l

20 Filled diagonal BC stripes ( ) Density of states N (ω)/(1/t) 1.5 (a) partial N z (ω)/(1/t) N(ω)/(1/t) N(ω)/(1/t) (b) (c) (d) partial total degenerate Two 1-d bands The lowest one hybridizes with the 2-d background Metallic state Needs to go beyond mean-field (ω µ)/t

21 SUMMARY we have developed a simple but powerful approach which allows one to investigate stripe phases with a large unit cell and carry out the calculation on large ( ) clusters eliminating the role of finite size effects the stripe phases allow for a description of the Hubbard model that involves lower and upper Hubbard bands and a quasiparticle band on mean-field level the description of half-filled vertical stripes in the cuprates involves a proper treatment of strong electron correlations in the - model - filled diagonal stripe phases observed in the nickelates are a generic feature of the model with two electrons there is a need to go beyond mean-field to describe the nickelates UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN JANUARY 2006