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 Strong Fluctuations in Condensed Matter Magnetism in one dimension Pure systems Doped systems Conclusions *supported by the NSF through DMR-0074571

2. 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) 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

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

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

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. NIST Center for Neutron Research

8. SPINS Cold neutron triple axis spectrometer at NCNR

9. Focusing analyzer system on SPINS

10. MAPS Spectrometer at ISIS in UK

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

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

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

14. 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

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

16. Heating coupled dimers

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

18. T-dependence of singlet-triplet mode

19. 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

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

21. 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

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

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

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

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

26. 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

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

28. 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

29. 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)

30. 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

31. 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

32. 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)

33. Transport in Ca doped Y2BaNiO5 T. Ito et al. Submitted to PRL (2001)

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

35. 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

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

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

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

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

40. Magnetic DOS for Ca-doped Y2BaNiO5 Clean gap in pure sample Anisotropy split triplet? Triplet-singlet transition? Impurity interactions sub gap continuum 0 5 10

41. 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 understand related systems where there is no direct info.