Holes in a Quantum Spin Liquid

1. Holes in a Quantum Spin Liquid Collin Broholm* Johns Hopkins University and NIST Center for Neutron Research Y2-xCaxBaNiO5 Strongly Fluctuating Condensed Matter Magnetism in one dimension Pure systems versus T alternating spin-1/2 chain Uniform spin-1 chain Doped systems Edge states in Mg-doped Y2BaNiO5 Spin polarons in Ca-doped Y2BaNiO5 Conclusions *supported by NSF DMR-0074571

2. Uniform spin-1 chain 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 and CREST-JST M. E. Bisher NEC M. M. J. Treacy NEC R. Paul NIST Center for Neutron Research Science 289, 419 (2000) Alternating spin-1/2 chain 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

3. Dynamic condensed matter: Phonons ZrW2O8 Al2O3 Weak connectivity Low energy “twist” modes Strong connectivity “Hard” spectrum Ernst el al (1998)

4. Dynamic Condensed matter: Magnetic Frustration ZnCr2O4 S.-H. Lee et al Weak connectivity triangular motif Interactions specify local order, not a critical Q vector

5. Dynamic condensed matter: 1D antiferromag. KCuF3 Chain direction NDMAP I.R. divergence destabilizes Neel order Cooperative singlet ground state

6. 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)

7. Nuclear scattering Magnetic scattering Inelastic Neutron Scattering

8. NIST Center for Neutron Research

9. SPINS Cold neutron triple axis spectrometer at NCNR

10. Focusing analyzer system on SPINS

11. MAPS Spectrometer at ISIS in UK

12. Y2BaNiO5 Ito, Oka, and Takagi Cu(NO3)2.2.5 D2O Guangyong Xu

13. Simple example of “Quantum” magnet Cu(NO3)2.2.5D2O : dimerized spin-1/2 system Only Inelastic magnetic scattering

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

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

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

17. Heating coupled dimers

18. SMA fit to scattering data T-Parameters extracted from fit More than 1000 data points per parameter!

19. T-dependence of singlet-triplet mode

20. 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

21. One dimensional spin-1 antiferromagnet Y2BaNiO5 Y2BaNiO5 Ni 2+ Impure Nuclear Elastic Scattering Pure

22. 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

23. Single mode approximation for spin-1 chain Dispersion relation Equal time correlation function

24. Two length scales in a quantum magnet Equal time correlation length Y2BaNiO5 Nuclear Elastic Scattering Triplet Coherence length : length of coherent triplet wave packet

25. Coherence in a fluctuating system w ³ D h w = D h Short range G.S. spin correlations Coherent triplet propagation

26. Mix in thermally excited triplets Coherence length approaches Correlation length for

27. Coherence and correlation lengths versus T Damle and Sachdev semi-classical theory of triplet scattering Jolicoeur and Golinelly Quantum non-linear s model

28. q=p Triplet creation spectrum versus T Anisotropyfinestructure Triplet relaxes due to interaction with thermal triplet ensemble There is slight “blue shift” with increasing T

29. Resonance energy and relaxation rate versus T Damle and Sachdev Jolicoeur and Golinelli Quantum non-linear s model

30. Pure quantum spin chains- at zero and finite T • Gap is possible whenn(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/e(q) • Thermally activated relaxation due to triplet interactions • Thermally activated increase in resonance energy • Coherence length exceeds correlation length for T< D/kB

31. Impurities in Y2BaNiO5 Mg Pure • Mg2+on Ni2+ sites finite length chains • Ca2+ on Y3+ sites mobile bond defects Mg Ca2+ Ni Y3+ Kojima et al. (1995)

32. 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

33. 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

34. 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)

35. Transport in Ca doped Y2BaNiO5 Charge Transfer excitation Charge polaron 1D conductivity, no Charge ordering T. Ito et al. Submitted to PRL (2001)

36. Gap modes in Ca-doped Y2BaNiO5 10% Ca 4% Ca Pure Energy (meV) q (2p) q (2p) q (2p)

37. x q d µ Why is Y2-xCaxBaNiO5 incommensurate? • Charge ordering yields incommensurate spin order • Quasi-particle Quasi-hole pair excitations in Luttinger liquid • Single impurity effect dqindep. ofx

38. Does d q vary with calcium concentration? dq not strongly dependent on x single impurity effect G. Xu et al. Science (2000)

39. Bond Impurities in a spin-1 chain: Y2-xCaxBaNiO5 FM AFM Ni Ca2+ Y3+ O

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

41. Measuring Magnetic DOS for Gap modes 10% Ca 4% Ca Pure Energy (meV) q (2p) q (2p) q (2p)

42. Spin polaron in Ca-doped Y2BaNiO5 Clean gap in pure sample Anisotropy split triplet? Triplet-singlet transition? Impurity interactions sub gap continuum 0 5 10

43. 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. • Ca doping yields charge polarons with 1 eV binding energy • Holes in Y2-xCaxBaNiO5 are surrounded by AFM spin polaron with central phase shift of p • Spin polaron has fine structure possibly from spin space anisotropy • 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.