Holes in a Quantum Spin Liquid

1. Holes in a Quantum Spin Liquid Collin Broholm Johns Hopkins University and NIST Center for Neutron Research Y3+ Gapped phases in condensed matter Gapped spin chains Pure systems Doped systems Conclusions Ca2+ Y2-xCaxBaNiO5 Viewgraphs posted at http://www.pha.jhu.edu/~broholm/jhuseminar/index.htm

2. Collaborators Y2BaNiO5 Guangyong Xu JHU -> University of Chicago G. Aeppli NEC J. F. DiTusa Louisiana State University 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 “Holes in a Quantum Spin Liquid” to appear in Science (2000) Copper Nitrate [Cu(NO3)2.2.5D2O] Guangyong Xu JHU -> University of Chicago Daniel Reich JHU M. A. Adams ISIS facility “Triplet Waves in a Quantum Spin Liquid” to appear in PRL May 1 (2000)

3. Quantum effects in atoms and in solids Atom (He) Line spectrum G. Dieke et al. (1968) Solid (Mo) continuous spectrum if Q not specified Christensen (1980)

4. Quantum effects from a gap Empty Band gap only possible for even number of electrons per cell Filled Gap Insulator No gap Metal

5. Impurities create states in the gap 10 3 1011 10 10 9 10-1 10 7 10-3 10 5 Cleaner sample Insulator Resistivity (ohm-cm) Metal “Dirty” sample 0 0.2 0.4 0.6 0.8 1/T (K-1) From Aschroft & Mermin

6. Other gapped phases in condensed matter • High energy physics yields low energy gap • Band insulator • Band semiconductor • Dimerized spin systems • Phase transition to gapped phase • Superconductor • Rotons in superfluid 4He • Mott Metal-Insulator transition • Spin Peierls transition • Cross over to gapped phase for T<<D • Quantum Hall effects • Uniform integer spin chains

7. The beauty of magnetic dielectrics • Well defined low energy Hamiltonian • Chemistry provides qualitatively different H • Vary H with pressure, magnetic field • Efficient experimental techniques Exchange interaction Single ion anisotropy Dipole in magnetic field (Zeeman)

8. Spin systems of recent interest

9. Varying the dimensionality of spin systems • The crystals are actually three dimensional • Exchange links spins on low-D network only Chain direction Non-magnetic “spacer” molecules in NDMAP Anisotropic bonding in cubic KCuF3

10. Susceptibility of gapped spin system Measure magnetization versus T in infinitesimal field: Renard et al (1988) Tatsuo et al. (1995)

11. Magnetization of gapped spin system Ajiro et al. (1989)

12. Specific heat of gapped spin chain A way to probe the low energy density of states NENC Orendac et al. (1995) NENP Tatsuo et al. (1995)

13. Magnetic Neutron Scattering The scattering cross section is proportional to the Fourier transformed dynamic spin correlation function

14. NIST Center for Neutron Research

16. Detection system on SPINS neutron spectrometer

17. Neutron scattering from gapped spin chain Copper nitrate T=0.3 K gap Xu et al. IRIS, ISIS Triplet creation peak Nuclear incoherent scattering Proton extraction pulse

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

19. Why a gap in spectrum of dimerized spin system J • A spin-1/2 pair has a singlet - triplet gap: • Weak inter-dimer coupling cannot close gap • Bond alternation is relevant operator for quantum critical uniform spin chain infinitesimal bond alternation yields gap

20. Gapped phases in isotropic spin systems? n = number of spins per primitive unit cell S = the spin quantum number m = the magnetization per spin n(S-m)= Oshikawa, Yamanaka, and Affleck (1997) and Oshikawa (2000) • gaps in non-magnetized spin chains? • Alternating spin-1/2 chain 2.1/2=1 perhaps • Uniform spin-1/2 chain 1.1/2 =1/2 no • Uniform spin-1 chain 1.1 =1 perhaps Integer: gap possible Non-Integer: gap impossible

21. Low T excitations in spin-1 AFM chain Y2BaNiO5 T=10 K MARI chain ki pure • Haldane gap D=8 meV • Coherent mode • S(q,w)->0 for Q->2np

22. AKLT state for spin-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. Haldane mode in Y2BaNiO5 at finite T • Relaxation rate increases • with T due to • triplet interactions • Resonance energy increases • with T due to • decreasing correlation length Low T fine structure from spin anisotropy

24. 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

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

26. 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

27. 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

28. New 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

29. Why a double ridge below the gap in Y2-xCaxBaNiO5 ? d q is single impurity prop. Indep. of • Charge ordering yields incommensurate spin order • Quasi-particle Quasi-hole pair excitations in Luttinger liquid • Anomalous form factor for independent spin degrees of freedom associated with each donated hole x q d µ x

30. Does dq vary with calcium concentration? dq not strongly dependent on x Double peak is single impurity effect

31. Bond Impurities in a spin-1 chain: Y2-xCaxBaNiO5 (b) Ca (c) (d) (e) (f) Y Ba (a) O Ni

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

33. Calcium doping Y2BaNiO5 Experimental facts: • Ca doping creates sub-gap excitations with doubly peaked structure factor and bandwidth • The structure factor is insensitive to concentration and temperature for 0.04<x<0.14 (and T<100 K) Analysis: • Ca2+ creates FM impurity bonds which nucleate AFM droplets with doubly peaked structure factor • AFM droplets interact through intervening chain forming disordered random bond 1D magnet

34. Incommensurate modulations in high TC superconductors YBa2Cu3O6.6 T=13 K E=25 meV k (rlu) h (rlu) Hayden et al. 1998

35. What sets energy scale for sub gap scattering ? hw (meV) • Possibilities: • Residual spin interactions through • Haldane state. A Random bond AFM. • Hole motion induces additional • interaction between static AFM droplets • AFM droplets move with holes: • scattering from a Luttinger liquid of • holes. 10 5 ? • How to distinguish: • Neutron scattering in an applied field • Transport measurements • Theory 0

36. 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. Viewgraphs posted at http://www.pha.jhu.edu/~broholm/jhuseminar/index.htm