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Theory of giant spin gaps in ¼-filled ladders

Theory of giant spin gaps in ¼-filled ladders. R.Torsten Clay Department of Physics & Astronomy ERC Center for Computational Sciences Mississippi State University Support: Petroleum Research Fund, ORAU Paper: RTC, S. Mazumdar PRL 94 , 207206 (2005)

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Theory of giant spin gaps in ¼-filled ladders

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  1. Theory of giant spin gaps in ¼-filled ladders R.Torsten Clay Department of Physics & Astronomy ERC Center for Computational Sciences Mississippi State University Support: Petroleum Research Fund, ORAU Paper: RTC, S. Mazumdar PRL 94, 207206 (2005) Collaborator: S. Mazumdar, Y. Yan, University of Arizona ISCOM2005 09/16/05

  2. Outline of talk • Ladder materials: ½-filled, ¼-filled • Does well-known theory of ½-filled ladders carry over to ¼-filled organics? • Ladder models: can we get a spin gap? • rectangular lattice • zigzag lattice: new model for organic ladders • Conclusion ISCOM2005 09/16/05

  3. Spin Ladders (½-filled) Spin gap: SG = E(S=1) – E(S=0) • Ladder materials are peculiar: properties unlike 1D or 2D • Spin ½ ladders: even number of legs SG>0; odd number gives SG=0 • Easy to understand in strong coupling: one spin per site, strong rung bonds give singlets • Doped ladder: superconducting correlations ISCOM2005 09/16/05

  4. Organic ladders (¼-filled) Organic ladders have now been synthesized. Two examples: (BDTFP)2X[PhCl]0.5: T. Ise et al, J. Mater. Chem. 11, 264 (2001) (DT-TTF)2M(mnt)2: C. Rovira et al, Chem. Eur. J 5, 2025 (1999) ISCOM2005 09/16/05

  5. Organic ladders • Summary of experiments: • High-temperature metal-insulator transition (T~300K or above). Dimerization along stacks • Low temperature spin-gap transition at TSG~50-100K. Compare to 1D ¼-filled organics eg (TMTTF)2X, MEM(TCNQ)2 typical Spin-Peierls gap transition temperature TSG~15K why is the spin gap larger in the ladders? ISCOM2005 09/16/05

  6. ¼-filled Spin-Peierls See PRB 67, 115121 (2003): • for V<Vc, 2kF (period 4) Charge order (CO), bond tetramerization • “dimerization of dimer lattice”, spin gap due to local singlets • Bond pattern measured explicitly via neutrons for MEM(TCNQ)2 and 1:2 TCNQ’s: Visser et al, PRB 28, 2074 (1983). ISCOM2005 09/16/05

  7. Rectangular Ladder Model One possible model: dimerization along stacks gives effectively ½-filled band. Does dimerized rectangular ladder have spin gap? DMRG calculations: Y. Yan, S. Mazumdar, S. Ramasesha: only realistic SG for t>0.7t Not clear how to map this model to crystal structure; All site charges remain equal. ISCOM2005 09/16/05

  8. Results of Y. Yan, S. Mazumdar, S. Ramasesha (DMRG) Questions: (i) Is SG> 0 for arbitrary small ? (ii) Is SG> 0 for arbitrarily small t? (iii) Effect of U, V? (iv) Can we fit experiment? t1 = t(1-), t2 = t(1+) Sample results SG 0 for  = 0+ at t = 1 t dependence of s with different U

  9. Zigzag ladder model • Hopping integrals: ts stack, td zigzag • Can view as 1D chain with next-nearest neighbor hopping ts. In materials, ts>td • noninteracting electrons: 2kF Peierls distortion along zigzag direction for td > 0.5858 ts (simple nesting criterion) • As in 1D, this is unconditional for 0+ electron-phonon coupling, and involves both charge and bonds ISCOM2005 09/16/05

  10. Zigzag ladder model Bond-Charge-Density-Wave (BCDW) state: • tetramerization of zigzag bonds and charges, bond pattern strong-intermediate-weak-intermediate • dimerization of stack bonds and charges What is effect of Coulomb interactions? spin gap? ISCOM2005 09/16/05

  11. Extended HubbardModel Appropriate model: Extended Hubbard model U=onsite Coulomb interaction V=inter-site Coulomb interaction; include Vs (stack), Vd (interstack) • Electron-phonon interactions: • Inter-site (SSH type) dimensionless couplings s,d • onsite (Holstein type) dimensionless couplings  ISCOM2005 09/16/05

  12. 16 site exact diagonalization (td=.7ts) Order parameters: f(B): strength of BOW n: strength of CO All increase with e-ph coupling Effect of U: squares: zigzag ladder circles: 1D chain BCDW does not weaken with U ISCOM2005 09/16/05

  13. Spin Gap To quantify spin gap SG, must perform finite-size scaling Compare SG of zigzag ladder with that of 1D chain, for same amount of CO Used Constrained Path Monte Carlo for zigzag ladder, exact QMC method for 1D chain  SG several times larger for zigzag ladder SG vs charge disproportiation. Filled: zigzag ladder; open: 1D chain (1100) Inset: typical finite-size scaling of gap ISCOM2005 09/16/05

  14. Why giant spin gap? • 1D ¼-filled band: • 2kF distortions (period 4) suppressed by Coulomb interactions • 4kF distortions (period 2) enhanced by Coulomb interactions • In zigzag ladder, these effects cancel out: period-2 along stack, period-4 along zigzag. BCDW remains strong with U,V • Interchain bond order always strongest  spin gap again due to local singlet formation ISCOM2005 09/16/05

  15. Spin Gap: -(ET)? Does the zigzag ladder tell us anything about the CO and spin gap found in -(ET)? See JPSJ 71, 1816 (2002). Zigzag BCDW appears very similar to horizontal stripe: = + + … ISCOM2005 09/16/05

  16. ¼-filled zigzag ladder: can explain large spin gaps in ¼-filled organic ladders • Experiments: distinguish between rectangular and zigzag models by presence of charge order and bond distortions. • (“checkerboard” charge order and spin gap only coexist in small region in rectangular model) • Advantages of zigzag model: • Better representation of the actual crystal structure • Gives explanation why spin gap is larger than in 1D • Related to horizontal stripe and spin gap in -(ET)? • More details: PRL 94, 207206 (2005) Conclusions ISCOM2005 09/16/05

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