One Dimensional Magnetic Systems Strong Fluctuations in Condensed Matter Magnetism in one dimension Pure systems Doped systems Magnetized states Conclusions Collin Broholm* Johns Hopkins University and NIST Center for Neutron Research *supported by the NSF through DMR Ca 2+ Y 3+ Y 2-x Ca x BaNiO 5

SSSC 6/26/00 Collaborators G. AeppliM. E. Bisher S.-W. CheongJ. F. DiTusa D. C. DenderC. D. Frost T. ItoP. R. Hammar T. H. KimS.-H. Lee K. OkaR. Paul W. Ratcliff IIID. H. Reich H. TakagiM. M. J. Treacy G. XuI. A. Zaliznyak

SSSC 6/26/00 Inelastic Neutron Scattering Nuclear scattering Magnetic scattering

SSSC 6/26/00 SPINS Cold neutron triple axis spectrometer at NCNR

SSSC 6/26/00 Dynamic condensed matter: Phonons Al 2 O 3 ZrW 2 O 8 Weak connectivity Low energy “twist” modes Low energy “twist” modes Strong connectivity “Hard” spectrum Ernst el al (1998)

SSSC 6/26/00 Dynamic condensed matter: 1D antiferromag. 2 Infrared divergence destabilizes Neel phase Infrared divergence destabilizes Neel phase Cooperative singlet ground state Ni 2+ Y 2 BaNiO 5 : spin 1 AFM

SSSC 6/26/00 Dynamic Condensed matter: Magnetic Frustration Weak connectivity triangular motif Weak connectivity triangular motif Interactions specify local order, not a critical Q vector Interactions specify local order, not a critical Q vector ZnCr 2 O 4 S.-H. Lee et al

Consequences of strong fluctuations Phonons : Thermal contraction Frustration : cooperative paramagnet 1D magnons : macroscopic singlet T (K)   Ajiro et al. (1989) Ernst et al (1998)

SSSC 6/26/00 Macroscopic 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

SSSC 6/26/00 Coherence in a fluctuating system   Probing spatial coherence of Haldane mode   Probing equal time correlation length

SSSC 6/26/00 Impurities in Y 2 BaNiO 5 Ca 2+ Y 3+ Mg 2+ on Ni 2+ sites finite length chains Ca 2+ on Y 3+ sites mobile bond defects Mg Ni Kojima et al. (1995) Mg Ca 2+ Pure

SSSC 6/26/00 Zeeman resonance of chain-end spins I(H=9 T)-I(H=0 T) (cts. per min.) h  (meV) H (Tesla) g=

SSSC 6/26/00 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%

SSSC 6/26/00 Sub gap excitations in Ca-doped Y 2 BaNiO 5 Pure 9.5% Ca Ca-doping creates states below the gap sub-gap states have doubly peaked structure factor Y 2-x Ca x BaNiO 5 : G. Xu et al. Science (2000)

SSSC 6/26/00 Incommensurate modulations in high T C superconductors Hayden et al YBa 2 Cu 3 O 6.6 T=13 K E=25 meV h (rlu) k (rlu) Yamada et al La 2-x Sr x CuO 4

SSSC 6/26/00 Why is Y 2-x Ca x BaNiO 5 incommensurate?  Charge ordering yields incommensurate spin order  Quasi-particle Quasi-hole pair excitations in Luttinger liquid  Single impurity effect x q   q indep. of x

SSSC 6/26/00 Does  q vary with calcium concentration?  q not strongly dependent on x single impurity effect G. Xu et al. Science (2000)

SSSC 6/26/00 (b) Ca Ba Ni Y (e) (f) (c) (d) O Bond Impurities in a spin-1 chain: Y 2-x Ca x BaNiO 5 (a)

Form-factor for FM-coupled chain-end spins A symmetric AFM droplet Ensemble of independent randomly truncated AFM droplets

Gap-less continuum in spin-1/2 chain Copper Benzoate T=0.3 K S=1/2 S=1

SSSC 6/26/00 Field induced incommensurate soliton lattice H=0 T H=7 T Copper Benzoate T=0.3 K H (T) Dender et al. (1997)

SSSC 6/26/00 Conclusions  Weakly connected systems  Low energy fluctuations of composite degrees of freedom  Unusual bulk properties and impurity effects  Challenging to describe because fluctuations are essential  Field effects in spin-1/2 chain  Gap-less RVB state, singlet formation on all length scales  Magnetization is carried by soliton defects that form dynamic incommensurate superstructure.  Impurities in spin-1 chain  They create sup-gap composite spin degrees of freedom  Edge states have extended AFM wave function  Holes create AFM spin polaron with phase shift 