Holes in a Quantum Spin Liquid Collin Broholm * Johns Hopkins University and NIST Center for Neutron Research Y 2-x Ca x BaNiO 5 *supported by the NSF through DMR Strong Fluctuations in Condensed Matter Magnetism in one dimension Pure systems Doped systems Conclusions

Y 2 BaNiO 5 Ying Chen JHU Guangyong Xu JHU -> University of Chicago G. AeppliNEC J. F. DiTusaLSU I. A. Zaliznyak JHU -> BNL C. D. FrostISIS T. ItoElectro-Technical Lab Japan K. Oka Electro-Technical Lab Japan H. TakagiISSP and CREST-JST M. E. Bisher NEC M. M. J. Treacy NEC R. Paul NIST Center for Neutron Research Science 289, 419 (2000) Copper Nitrate [Cu(NO 3 ) D 2 O] Guangyong Xu JHU -> University of Chicago Daniel ReichJHU M. A. AdamsISIS facility PRL 84, 4465 (2000) Collaborators

Princeton 3/2/1 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)

Princeton 3/2/1 Chain direction Dynamic condensed matter: 1D antiferromag. KCuF 3 NDMA P I.R. divergence destabilizes Neel order Cooperative singlet ground state

Princeton 3/2/1 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)

Princeton 3/2/1 NIST Center for Neutron Research

Princeton 3/2/1 SPINS Cold neutron triple axis spectrometer at NCNR

Princeton 3/2/1 Focusing analyzer system on SPINS

Princeton 3/2/1 MAPS Spectrometer at ISIS in UK

Y 2 BaNiO 5 Ito, Oka, and Takagi Cu(NO 3 ) D 2 O Guangyong Xu

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

Princeton 3/2/1 Dispersion relation for triplet waves Dimerized spin-1/2 system: copper nitrate Xu et al PRL May 2000

Princeton 3/2/1  A spin-1/2 pair with AFM exchange has a singlet - triplet gap: Qualitative description of excited states J  Inter-dimer coupling allows coherent triplet propagation and produces well defined dispersion relation  Triplets can also be produced in pairs with total S tot =1

Creating two triplets with one neutron One magnon Two magnon Tennant et al (2000)

Princeton 3/2/1 Heating coupled dimers

Princeton 3/2/1 SMA fit to scattering data T-Parameters extracted from fit More than 1000 data points per parameter!

Princeton 3/2/1 T-dependence of singlet-triplet mode

Princeton 3/2/1 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

Princeton 3/2/1 One dimensional spin-1 antiferromagnet Y 2 BaNiO 5 Ni 2+ Impure Pure Y 2 BaNiO 5 Nuclear Elastic Scattering

Princeton 3/2/1 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

Princeton 3/2/1 Single mode approximation for spin-1 chain Dispersion relation Equal time correlation function

Princeton 3/2/1 Two length scales in a quantum magnet Equal time correlation length Y 2 BaNiO 5 Nuclear Elastic Scattering Triplet Coherence length : length of coherent triplet wave packet

Princeton 3/2/1 Coherence in a fluctuating system   Coherent triplet propagation   Short range G.S. spin correlations

Princeton 3/2/1 Mix in thermally excited triplets Coherence length approaches Correlation length for Coherence length approaches Correlation length for

Princeton 3/2/1 Coherence and correlation lengths versus T Damle and Sachdev semi-classical theory of triplet scattering Damle and Sachdev semi-classical theory of triplet scattering Jolicoeur and Golinelly Quantum non-linear  model Jolicoeur and Golinelly Quantum non-linear  model

Princeton 3/2/1 q=  Triplet creation spectrum versus T Triplet relaxes due to interaction with thermal triplet ensemble Triplet relaxes due to interaction with thermal triplet ensemble There is slight “blue shift” with increasing T There is slight “blue shift” with increasing T Anisotropy fine structure

Princeton 3/2/1 Resonance energy and relaxation rate versus T Jolicoeur and Golinelli Quantum non-linear  model Jolicoeur and Golinelli Quantum non-linear  model Damle and Sachdev

Princeton 3/2/1 Pure quantum spin chains - at zero and finite T  Gap is possible when n(S-m) is integer  gapped systems: alternating spin-1/2 chain, integer chain,…  gapless systems: uniform spin-1/2 chain  gapped spin systems have coherent collective mode  For appreciable gap SMA applies: S(q) ~ 1/  (q)  Thermally activated relaxation due to triplet interactions  Thermally activated increase in resonance energy  Coherence length exceeds correlation length for T<  /k B

Princeton 3/2/1 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 Pure

Princeton 3/2/1 Zeeman resonance of chain-end spins I(H=9 T)-I(H=0 T) (cts. per min.) h  (meV) H (Tesla) g=

Princeton 3/2/1 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%

Princeton 3/2/1 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

Princeton 3/2/1 Transport in Ca doped Y 2 BaNiO 5 T. Ito et al. Submitted to PRL (2001)

Princeton 3/2/1 Gap modes in Ca-doped Y 2 BaNiO 5 q (2  ) Energy (meV) Pure 4% Ca 10% Ca

Princeton 3/2/1 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

Princeton 3/2/1 Does  q vary with calcium concentration?  q not strongly dependent on x single impurity effect G. Xu et al. Science (2000)

Princeton 3/2/1 Bond Impurities in a spin-1 chain: Y 2-x Ca x BaNiO 5 Y3+Y3+ Ni O AFMFM Ca 2+

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

Princeton 3/2/1 Gap modes in Ca-doped Y 2 BaNiO 5 q (2  ) Energy (meV) Pure 4% Ca 10% Ca

Princeton 3/2/1 Magnetic DOS for Ca-doped Y 2 BaNiO Triplet-singlet transition? Anisotropy split triplet? Impurity interactions sub gap continuum Impurity interactions sub gap continuum Clean gap in pure sample

Princeton 3/2/1 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 Y 2-x Ca x BaNiO 5 are surrounded by AFM spin polaron with central phase shift of   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 T C superconductors.  Microscopic details of gapped spin systems may help understand related systems where there is no direct info.