Holes in a Quantum Spin Liquid Collaborators Collaborators Dynamic condensed matter: Phonons
Kushell, Jennifer, Contributing Editor has reference to this Academic Journal, PHwiki organized this Journal Holes in a Quantum Spin Liquid Strong Fluctuations in Condensed Matter Magnetism in one dimension Pure systems Doped systems Conclusions Collin Broholm Johns Hopkins University in addition to NIST Center as long as Neutron Research Y2-xCaxBaNiO5 supported by the NSF through DMR-0074571 Y2BaNiO5 Ying Chen JHU Guangyong Xu JHU -> University of Chicago G. Aeppli NEC J. F. DiTusa LSU I. A. Zaliznyak JHU -> BNL C. D. Frost ISIS T. Ito Electro-Technical Lab Japan K. Oka Electro-Technical Lab Japan H. Takagi ISSP in addition to CREST-JST M. E. Bisher NEC M. M. J. Treacy NEC R. Paul NIST Center as long as Neutron Research Science 289, 419 (2000) Copper Nitrate [Cu(NO3)2.2.5D2O] Guangyong Xu JHU -> University of Chicago Daniel Reich JHU M. A. Adams ISIS facility PRL 84, 4465 (2000) Collaborators Collaborators Dynamic condensed matter: Phonons Weak connectivity Low energy twist modes Strong connectivity Hard spectrum Ernst el al (1998)
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Dynamic condensed matter: 1D antiferromag. Chain direction KCuF3 NDMAP I.R. divergence destabilizes Neel order Cooperative singlet ground state Dynamic Condensed matter: Magnetic Frustration Weak connectivity triangular motif Interactions specify local order, not a critical Q vector ZnCr2O4 S.-H. Lee et al Consequences of strong fluctuations 0 0 200 400 600 800 1000 Phonons : Thermal contraction Frustration : cooperative paramagnet 1D magnons : macroscopic singlet T (K) c-1 Ajiro et al. (1989) Ernst et al (1998)
NIST Center as long as Neutron Research SPINS Cold neutron triple axis spectrometer at NCNR Focusing analyzer system on SPINS
MAPS Spectrometer at ISIS in UK Y2BaNiO5 Ito, Oka, in addition to Takagi Cu(NO3)2.2.5 D2O Guangyong Xu Simple example of Quantum magnet Cu(NO3)2.2.5D2O : dimerized spin-1/2 system Only Inelastic magnetic scattering
Dispersion relation as long as triplet waves Dimerized spin-1/2 system: copper nitrate Xu et al PRL May 2000 A spin-1/2 pair with AFM exchange has a singlet – triplet gap: Qualitative description of excited states Inter-dimer coupling allows coherent triplet propagation in addition to produces well defined dispersion relation Triplets can also be produced in pairs with total Stot=1 Creating two triplets with one neutron One magnon Two magnon Tennant et al (2000)
Heating coupled dimers SMA fit to scattering data T-Parameters extracted from fit More than 1000 data points per parameter! T-dependence of singlet-triplet mode
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 weak connectivity interactions with fermions Novel coherent states One dimensional spin-1 antiferromagnet Y2BaNiO5 Macroscopic singlet ground state of S=1 chain This is exact ground state as long as 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, in addition to Tasaki PRL 1987
Single mode approximation as long as spin-1 chain Dispersion relation Equal time correlation function Two length scales in a quantum magnet Triplet Coherence length : length of coherent triplet wave packet Coherence in a fluctuating system Coherent triplet propagation Short range G.S. spin correlations
Mix in thermally excited triplets Coherence length approaches Correlation length as long as Coherence in addition to correlation lengths versus T q=p Triplet creation spectrum versus T Triplet relaxes due to interaction with thermal triplet ensemble There is slight blue shift with increasing T Anisotropy fine structure
Resonance energy in addition to relaxation rate versus T Jolicoeur in addition to Golinelli Quantum non-linear s model Pure quantum spin chains – at zero in addition to finite T Gap is possible when n(S-m) is integer gapped systems: alternating spin-1/2 chain, integer chain, gapless systems: uni as long as m spin-1/2 chain gapped spin systems have coherent collective mode For appreciable gap SMA applies: S(q) ~ 1/e(q) Thermally activated relaxation due to triplet interactions Thermally activated increase in resonance energy Coherence length exceeds correlation length as long as T< D/kB Impurities in Y2BaNiO5 Ca2+ Y3+ Mg2+on Ni2+ sites finite length chains Ca2+ on Y3+ sites mobile bond defects Mg Ni Kojima et al. (1995) Gap modes in Ca-doped Y2BaNiO5 Magnetic DOS as long as Ca-doped Y2BaNiO5 Conclusions: Dilute impurities in the Haldane spin chain create sub-gap composite spin degrees of freedom. Edge states have an AFM wave function that extends into the bulk over distances of order the Haldane length. Holes in Y2-xCaxBaNiO5 are surrounded by AFM spin polaron with central phase shift of p Neutron scattering can detect the structure of composite impurity spins in gapped quantum magnets. The technique may be applicable to probe impurities in other gapped systems eg. high TC superconductors. Microscopic details of gapped spin systems may help underst in addition to related systems where there is no direct info.
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