Collin Broholm * Johns Hopkins University and NIST Center for Neutron Research Y. ChenJHU, Baltimore, USA M. EnderleILL, Grenoble, France Z. HondaRiken, Japan K. KatsumataRiken, Japan L. P. RegnaultCEA, Grenoble, France D. H. ReichJHU, Baltimore, USA J. RittnerJHU, Baltimore, USA S. M. ShapiroBNL, Upton, USA M. SielingUniv. Frankfurt, Germany I. ZaliznyakBNL, Upton, USA A. ZheludevORNL, Oak Ridge, USA * Work at JHU Supported by the National Science Foundation Spin Correlations in Magnetized Haldane Chains

PPHMF IV 10/24/01 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

PPHMF IV 10/24/01 The beauty of magnetic dielectrics  Well defined low energy Hamiltonian  Chemistry provides qualitatively different H  Vary H with pressure, magnetic field  Efficient experimental techniques Exchange interaction Single ion anisotropy Dipole in magnetic field (Zeeman)

PPHMF IV 10/24/01 Spin-1 chains that can be magnetized NDMAP=Ni(C 5 H 14 N 2 ) 2 N 3 (PF 6 ) [ClO 4 ] - Ni(en) 2 NO 2 NENP=Ni(C 2 H 8 N 2 ) 2 NO 2 ClO 4 Staggered g-tensor b No staggered g-tensor c

PPHMF IV 10/24/01 Thermodynamic indications of spin gap Similar chi data for ndmap NENP NDMAP Katsumata et al., PRL (1999) 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 High T Curie Weiss susceptibility indicates AFM interactions Low T thermal activation indicates spin gap Crystal structure indicates extended one dimensional system

PPHMF IV 10/24/01 Magnetic Neutron Scattering The scattering cross section is proportional to the Fourier transformed dynamic spin correlation function

PPHMF IV 10/24/01 Techniques to enhance sensitivity NDMAP Honda and Katsumata Dispersive Analyzer SPINS cold neutron NIST

PPHMF IV 10/24/01 Spin gap in NENP  ||  S. Ma et al. PRL (1992) Data from NIST Center for neutron research T=0.3 K

PPHMF IV 10/24/01 Spin gap in NDMAP Data from NIST Center for neutron research  ||

PPHMF IV 10/24/01 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) = To be gapped or not to be gapped : gap possible : gap impossible Oshikawa et al., PRL (1997) and (2000) 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 = nperhaps  Uniform spin 1 chain 1. 1 = 1 perhaps

PPHMF IV 10/24/01 singlet ground state of S=1 chain This is exact ground state for spin projection Hamiltonian Magnets with 2S=nz have a nearest neighbor singlet covering with full lattice symmetry. 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)

PPHMF IV 10/24/01 Spin-less impurities induce Curie Tail Tatsuo et al. (1995)

PPHMF IV 10/24/01 Zeeman resonance in Y 2 BaNi 1-x Mg x O 5 I(H=9 T)-I(H=0 T) (cts. per min.) h  (meV) H (Tesla) g= Zaliznyak et al. (2001) Data from NIST Center for neutron research

PPHMF IV 10/24/01 Form factor of chain-end spins Q-dependence reveals that resonating object is AFM. The peak resembles S(Q) for pure system. Q-dependence reveals that resonating object is AFM. The peak resembles S(Q) for pure system. Chain end spin carry AFM spin polarization of length  back into chain Chain end spin carry AFM spin polarization of length  back into chain Y 2 BaNi 1-x Mg x O 5 x=4% Zaliznyak et al. (2001) Data from NIST Center for neutron research

PPHMF IV 10/24/01 “Mixed phase” of quantum spin liquid? Magnetized state of classical antiferromagnet Magnetized state of quantum spin liquid Spin flop transition Staggered magnetization cants along field Gapless spectrum Incommensurate soft modes Chitra and Giamarchi PRB 1997, Affleck et al. PRB 1991

PPHMF IV 10/24/01 Fermions in spin ½ chain Jordan-Wigner transformation Uniform spin-1/2 chain (XY case for simplicity) Diagonalizes H || Non interacting fermionic lattice gas q (  )  /J 

PPHMF IV 10/24/01 Spin ½ chain in a field  -2  m - q (  ) Q (  ) Pytte PR (1974) Ishimura and Shiba, JPSJ (1977) Muller et al., PRB (1981) Karbach and Muller PRB (2000)

PPHMF IV 10/24/01 Field Induced Incommensurate Soft Modes Copper Benzoate Dender et al PRL 97 Data from NIST Center for neutron research

On to new results for bulk spin-1 chains

PPHMF IV 10/24/01 q=  excitations versus H in NENP 0 T 12 T 13 T 14.5 T NENP T=35 mK Enderle et al. Physica B (2000) Data from BENSC, Hahn-Meittner Institute

PPHMF IV 10/24/01 NENP with staggered g-tensor: Statics T (K) Intensity (10 3 cts/min.) (110) B=2 T Applied field breaks translational symmetry when g-tensor is staggered

PPHMF IV 10/24/01 Renormalized spin wave velocity for H>H C Data from BENSC, Hahn-Meittner Institute

PPHMF IV 10/24/01 NDMAP without staggered field: Statics Data from NIST Center for neutron research Chen et al., PRL (2001) 3D LRO H||a H||b Haldane Singlet Quasi 2D

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

PPHMF IV 10/24/01 Analysis of field dependent spectra Data from NIST Center for neutron research H (Tesla) Zheludev et al. cond-mat/

PPHMF IV 10/24/01 Excitations for H>H C Zheludev et al. cond-mat/

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

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

PPHMF IV 10/24/01 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=  condition for low energy excitations in spin-1 chains at H>H C

PPHMF IV 10/24/01 Field induced 2 and 3 dimensional order

PPHMF IV 10/24/01 Frozen short range ordered phase in SrCuO 2 Data from NIST Center for neutron research Zaliznyak et al., PRL (1999)