Spin Correlations in Magnetized Haldane Chains

1. Spin Correlations in Magnetized Haldane Chains Collin Broholm* Johns Hopkins University and NIST Center for Neutron Research Y. Chen JHU, Baltimore, USA M. Enderle ILL, Grenoble, France Z. Honda Riken, Japan K. Katsumata Riken, Japan L. P. Regnault CEA, Grenoble, France D. H. Reich JHU, Baltimore, USA J. Rittner JHU, Baltimore, USA S. M. Shapiro BNL, Upton, USA M. Sieling Univ. Frankfurt, Germany I. Zaliznyak BNL, Upton, USA A. Zheludev ORNL, Oak Ridge, USA * Work at JHU Supported by the National Science Foundation

2. Outline of Talk • Introduction • Properties of NENP and NDMAP • Zero field state of spin-1 chain • Magnetized state of spin-1 chain • Chain end spins • Dynamic correlations • Static correlations • Conclusions

3. The beauty of magnetic dielectrics • Well defined low energy Hamiltonian • Chemistry provides qualitatively differentH • VaryHwith pressure, magnetic field • Efficient experimental techniques Exchange interaction Single ion anisotropy Dipole in magnetic field (Zeeman)

4. Spin-1 chains that can be magnetized b c No staggered g-tensor Staggered g-tensor NENP=Ni(C2H8N2)2NO2ClO4 NDMAP=Ni(C5H14N2)2N3(PF6) [ClO4]- Ni(en)2 NO2

5. Thermodynamic indications of spin gap NDMAP NENP Katsumata et al., PRL (1999) Similar chi data for ndmap Meyer et al. (1982) • High T Curie Weiss susceptibility indicates AFM interactions • Low T thermal activation indicates spin gap • Crystal structure indicates extended one dimensional system

6. Magnetic Neutron Scattering The scattering cross section is proportional to the Fourier transformeddynamic spin correlation function

7. Dispersive Analyzer SPINS cold neutron spectrometer @ NIST Techniques to enhance sensitivity NDMAP Honda and Katsumata

8. Spin gap in NENP ^ || D T=0.3 K S. Ma et al. PRL (1992) Data from NIST Center for neutron research

9. Spin gap in NDMAP ^ || Data from NIST Center for neutron research

10. To be gapped or not to be gapped n = number of spins per primitive unit cell S = the spin quantum number m = the magnetization per spin fluctuating spin per u. c.= n(S-m) = : gap possible : gap impossible gaps in non-magnetized spin chains? • Uniform spin ½ chain 1.½ = ½ no gap • Alternating spin ½ chain 2.½ = 1 perhaps • (2n+1) leg spin ½ ladder (2n+1).½ = n+½ no gap • 2n leg spin ½ ladder 2n.½ = n perhaps • Uniform spin 1 chain 1.1 = 1 perhaps Oshikawa et al., PRL (1997) and (2000)

11. singlet ground state of S=1 chain • Magnets with 2S=nz have a nearest neighbor singlet covering • with full lattice symmetry. • This is exact ground state for spin projection Hamiltonian • Excited states are propagating bond triplets separated from the • ground state by an energy gap Haldane PRL (1983) Affleck, Kennedy, Lieb, and Tasaki PRL (1987)

12. Spin-less impurities induce Curie Tail Tatsuo et al. (1995)

13. Zeeman resonance in Y2BaNi1-xMgxO5 20 g=2.16 hw (meV) 15 0 2 4 6 8 H (Tesla) 10 I(H=9 T)-I(H=0 T) (cts. per min.) 0 -5 0 0.5 1 1.5 2 Zaliznyak et al. (2001) Data from NIST Center for neutron research

14. Form factor of chain-end spins Y2BaNi1-xMgxO5 x=4% Q-dependence reveals that resonating object is AFM. The peak resembles S(Q) for pure system. Chain end spin carry AFM spin polarization of lengthxback into chain Zaliznyak et al. (2001) Data from NIST Center for neutron research

15. “Mixed phase” of quantum spin liquid? Magnetized state of classical antiferromagnet • Spin flop transition • Staggered magnetization cants along field Magnetized state of quantum spin liquid • Gapless spectrum • Incommensurate soft modes Chitra and Giamarchi PRB 1997, Affleck et al. PRB 1991

16. Fermions in spin ½ chain Uniform spin-1/2 chain (XY case for simplicity) Jordan-Wigner transformation Diagonalizes H|| e/J p Non interacting fermionic lattice gas q (p)

17. Spin ½ chain in a field p-2pm - q (p) Q (p) Pytte PR (1974) Ishimura and Shiba, JPSJ (1977) Muller et al., PRB (1981) Karbach and Muller PRB (2000)

18. Field Induced Incommensurate Soft Modes Copper Benzoate Dender et al PRL 97 Data from NIST Center for neutron research

19. On to new results for bulk spin-1 chains

20. q=p excitations versus H in NENP Enderle et al. Physica B (2000) NENP T=35 mK 0 T 12 T 13 T 14.5 T Data from BENSC, Hahn-Meittner Institute

21. NENP with staggered g-tensor: Statics 3 (110) B=2 T 2 Intensity (103 cts/min.) 1 0 0 2 4 6 8 10 T (K) Applied field breaks translational symmetry when g-tensor is staggered

22. Renormalized spin wave velocity for H>HC Data from BENSC, Hahn-Meittner Institute

23. NDMAP without staggered field: Statics H||a Quasi 2D H||b 3D LRO Haldane Singlet Chen et al., PRL (2001) Data from NIST Center for neutron research

24. Gapless spectrum for HHC Zheludev et al. cond-mat/0107416 Data from NIST Center for neutron research

25. Analysis of field dependent spectra H (Tesla) Zheludev et al. cond-mat/0107416 Data from NIST Center for neutron research

26. Excitations for H>HC Zheludev et al. cond-mat/0107416

27. Zheludev et al. cond-mat/0107416 Data from NIST Center for neutron research

28. Zheludev et al. cond-mat/0107416 Data from NIST Center for neutron research

29. Conclusions • Spin-1 chain ends develop staggered magnetization in a field • Field induced staggered magnetization in spin-1 chain with staggered g-tensor • Gap-full spectrum for spin-1 chain with staggered g-tensor • Gapless spectrum for uniform spin-1 chain close to critical field • Field induced second order phase transition in uniform spin-1 chain • Softening of q=p condition for low energy excitations in spin-1 chains at H>HC

30. Field induced 2 and 3 dimensional order

31. Frozen short range ordered phase in SrCuO2 Data from NIST Center for neutron research Zaliznyak et al., PRL (1999)