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##### One Dimensional Magnetic Systems

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**Y2-xCaxBaNiO5**One Dimensional Magnetic Systems Collin Broholm* Johns Hopkins University and NIST Center for Neutron Research Y3+ Strong Fluctuations in Condensed Matter Magnetism in one dimension Pure systems Doped systems Magnetized states Conclusions Ca2+ *supported by the NSF through DMR-0074571**Collaborators**G. Aeppli M. E. Bisher S.-W. Cheong J. F. DiTusa D. C. Dender C. D. Frost T. ItoP. R. Hammar T. H. KimS.-H. Lee K. Oka R. Paul W. Ratcliff III D. H. Reich H. Takagi M. M. J. Treacy G. XuI. A. Zaliznyak**Inelastic Neutron Scattering**Nuclear scattering Magnetic scattering**Dynamic condensed matter: Phonons**ZrW2O8 Al2O3 Weak connectivity Low energy “twist” modes Strong connectivity “Hard” spectrum Ernst el al (1998)**Dynamic condensed matter: 1D antiferromag.**Y2BaNiO5 : spin 1 AFM Ni 2+ Infrared divergence destabilizes Neel phase 2 Cooperative singlet ground state**Dynamic Condensed matter: Magnetic Frustration**ZnCr2O4 S.-H. Lee et al Weak connectivity triangular motif Interactions specify local order, not a critical Q vector**Consequences of strong fluctuations**Phonons : Thermal contraction Frustration : cooperative paramagnet c-1 Ernst et al (1998) 0 0 200 400 600 800 1000 T (K) 1D magnons : macroscopic singlet Ajiro et al. (1989)**Macroscopic 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**Impurities in Y2BaNiO5**Ca2+ Mg Pure • Mg2+on Ni2+ sites finite length chains • Ca2+ on Y3+ sites mobile bond defects Mg Ca2+ Ni Y3+ Kojima et al. (1995)**Zeeman resonance of chain-end spins**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**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 length x back into chain**Sub gap excitations in Ca-doped Y2BaNiO5**Pure 9.5% Ca Y2-xCaxBaNiO5: • Ca-doping • creates states • below the gap • sub-gap states • have doubly • peaked structure • factor G. Xu et al. Science (2000)**Incommensurate modulations in high TC superconductors**YBa2Cu3O6.6 T=13 K E=25 meV k (rlu) h (rlu) La2-xSrxCuO4 Hayden et al. 1998 Yamada et al. 1998**Why is Y2-xCaxBaNiO5 incommensurate?**x q d µ • Charge ordering yields incommensurate spin order • Quasi-particle Quasi-hole pair excitations in Luttinger liquid • Single impurity effect dqindep. ofx**Does d q vary with calcium concentration?**dq not strongly dependent on x single impurity effect G. Xu et al. Science (2000)**Bond Impurities in a spin-1 chain: Y2-xCaxBaNiO5**(b) Ca (c) (d) (e) (f) Y Ba (a) O Ni**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 0 0.4 0.8 S=1/2 S=1**Field induced incommensurate soliton lattice**Dender et al. (1997) 0 2 4 6 8 H (T) Copper Benzoate T=0.3 K H=0 T H=7 T**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 • 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 p • 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.