Solving Impurity Structures Using Inelastic Neutron Scattering Quantum Magnetism - Pure systems - vacancies - bond impurities 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

ACA 7/24/00 Collaborators G. AeppliM. E. Bisher J. F. DiTusaC. D. Frost T. ItoT. H. Kim K. OkaR. Paul D. H. ReichH. Takagi M. M. J. TreacyG. Xu I. A. Zaliznyak

ACA 7/24/00 Inelastic Neutron Scattering Nuclear scattering Magnetic scattering

ACA 7/24/00 SPINS Cold neutron triple axis spectrometer at NCNR

ACA 7/24/00 Simple example of “Quantum” magnet Cu(NO 3 ) D 2 O : dimerized spin-1/2 system Only Inelastic magnetic scattering Only Inelastic magnetic scattering

ACA 7/24/00  A spin-1/2 pair has a singlet - triplet gap:  inter-dimer coupling yields dispersive mode Why dimerized chain is a spin liquid J

ACA 7/24/00 Types of Quantum magnets  Definition: small or vanishing frozen moment at low T:  Conditions that yield quantum magnetism  Low effective dimensionality  Low spin quantum number  geometrical frustration  dimerization  low connectivity  interactions with fermions  Quantum magnets can display novel coherent states

ACA 7/24/00 Why study Quantum magnets ?  Coherent many body states are fascinating and useful  Superconductivity  Fractional Quantum Hall effect  Bose Condensation  Quantum magnets without static order at T=0  Each phenomenon provides different experimental info about macroscopic quantum coherence  Only in quantum magnets are dynamic correlations directly accessible (through neutron scattering)

ACA 7/24/00 Why study impurities in quantum magnets ?  Impurities are inevitable or even necessary to produce coherence  Probing the response to impurities reveals the building blocks of a macroscopic quantum state.  Impurities in quantum magnets can be explored at the microscopic level. Ca 2+ Y 3+

ACA 7/24/00 Dynamic condensed matter: 1D antiferromag. 2 Ni 2+ Y 2 BaNiO 5 : spin 1 AFM Impure Pure

ACA 7/24/00 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

ACA 7/24/00 Coherence in a fluctuating system   Probing spatial coherence of Haldane mode   Probing equal time correlation length

ACA 7/24/00 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

ACA 7/24/00 Zeeman resonance of chain-end spins I(H=9 T)-I(H=0 T) (cts. per min.) h  (meV) H (Tesla) g=

ACA 7/24/00 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%

ACA 7/24/00 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)

ACA 7/24/00 Incommensurate modulations in high T C superconductors Hayden et al. (1998) YBa 2 Cu 3 O 6.6 T=13 K E=25 meV h (rlu) k (rlu) Yamada et al. (1998) La 2-x Sr x CuO 4

ACA 7/24/00 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

ACA 7/24/00 Does  q vary with calcium concentration?  q not strongly dependent on x single impurity effect G. Xu et al. Science (2000)

ACA 7/24/00 (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

ACA 7/24/00 Conclusions  Quantum Magnets  low dimensional frustrated and/or weakly connected  Coherent low T states rather than magnetic order  Challenging to describe because fluctuations are essential  Probing impurities with neutrons  Spectroscopic separation yields unique sensitivity to impurity structures (in quantum magnets) through coherent diffuse inelastic neutron scattering  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 