1. Impurities and finite temperature effects in a one-dimensional spin-1 antiferromagnet Coherent excitations in Y 2 BaNiO 5 Loss of coherence for T>0 Chain-end spins in Y 2 BaNi 1-x Mg x O 5 AFM droplets in Y 2-x Ca x BaNiO 5 Conclusion Collin Broholm Johns Hopkins University and NIST Center for Neutron Research Supported by NSF DMR-9453362 Talk at http://www.pha.jhu.edu/~broholm/nhmfl/index.htm

2. NHMFL 11/19/99 Collaborators Guangyong XuJHU -> University of Chicago G. AeppliNEC J. F. DiTusaLouisiana State University I. A. ZaliznyakJHU -> BNL C. D. FrostISIS T. ItoElectro-technical Lab Japan K. OkaElectro-technical Lab Japan H. TakagiISSP and CREST-JST M. E. BisherNEC M. M. J. TreacyNEC

3. NHMFL 11/19/99 Why study quantum magnets ?  Coherent many body wave functions are fascinating and useful  Laser beams  Superconductivity  Fractional Quantum Hall effect  Bose Condensation  Quantum magnets without static order at T=0  Each phenomenon provides different experimental info about macroscopic quantum coherence  Only in quantum magnets are dynamic correlations directly accessible (through neutron scattering)

4. NHMFL 11/19/99 Why study impurities in quantum magnets ?  Impurities are inevitable or even necessary to produce coherence  Probing the response to impurities reveals the building blocks of a macroscopic quantum state.  Impurities in quantum magnets can be explored at the microscopic level. Ca 2+ Y 3+

5. NHMFL 11/19/99 NIST Center for Neutron Research

6. NHMFL 11/19/99

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

9. NHMFL 11/19/99 Low T excitations in spin-1 AFM chain Y 2 BaNiO 5 T=10 K MARI chain k i Points of interest: Haldane gap  =8 meV Coherent mode S(q,  )->0 for Q->2n  pure

10. NHMFL 11/19/99 Why does spin-1 AFM have a spin gap? For integer spin chains (S=n, z=2) this state is “close to” the ground state Magnets with 2S=nz have a nearest neighbor singlet covering. 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

11. NHMFL 11/19/99 Probing anisotropy and inter-chain coupling in Y 2 BaNiO 5  intensity (coutns per 15 min.) I(q,w) (1/meV)  a  b  c Maintaining, we Derive polarization by rotating about chain Look for inter-chain coupling by varying Weak anisotropy: Highly one dimensional

12. NHMFL 11/19/99 Sum rules and the single mode approximation When a coherent mode dominates the spectrum : Then sum-rules link S(q) and  (q) The dynamic spin correlation function obeys sum-rules:

13. NHMFL 11/19/99 Propagating triplet in alternating spin-1/2 chain Cu(NO 3 ) 2. 2.5D 2 O The “incommensurate” size of spin dimers yields different periods for dispersion relation and structure factor. An effect captured by the SMA. IRIS dataSMA model 0 2 4 0 2 4 6 h  (meV) 0.4 0.5 Q/ 

14. NHMFL 11/19/99 Two magnon excitations in an alternating spin chain Tennant, Nagler, Xu, Broholm, and Reich.

15. NHMFL 11/19/99 Haldane mode in Y 2 BaNiO 5 at finite T Effects of heating: Line-width increases Effective  increases

16. NHMFL 11/19/99 T-dependence of relaxation rate and “resonance” energy Parameter free comparison: Semi-classical theory of triplet scattering by Damle and Sachdev Quantum non linear  model            Tk Tk T B B 0 exp 3             Tk Tk T B B 0 00 2  Derived from  T c T  0 )(   Neglecting T-dependence of spin wave velocity c 0

17. NHMFL 11/19/99 Q-scans versus T: energy resolved and energy integrated   Probing spatial coherence of Haldane mode   Probing equal time correlation length

18. NHMFL 11/19/99 Coherence and correlation lengths versus T Equal-time correlation length saturates at  =8. Coherence length exceeds correlation length for k B T<  becoming very long as T 0 (Solid line from Quantum non linear  model)

19. NHMFL 11/19/99 Properties of pure Y 2 BaNiO 5  Anisotropy split Haldane gap:  a =7.5 meV,  b =8.6 meV,  c =9.5 meV  No inter-chain coupling detected: |J’/J|<5. 10 -4  Coherent mode described by SMA for T<<  /k B  Activated relaxation rate of q=  mode is described by semi-classical theory of interacting triplet wave packets.  Activated increase in resonance energy is significantly less than predicted by Qnl  -model  Coherence length exceeds correlation length for T<  /k B and exceeds 40 lattice spacings for k B T/  =0.1

20. NHMFL 11/19/99 Effects of finite chain length on Haldane mode Mode shifts towards J as in numerical work on finite length chains Peak Broadens because of chain length distribution 4% Mg Pure q=  T=10 K

21. NHMFL 11/19/99 Zeeman resonance of chain-end spins I(H=9 T)-I(H=0 T) (cts. per min.) h  (meV) H (Tesla) 0 2 4 6 8 g=2.16 0 0.5 1 1.5 2 -5 0 10 15 20

22. NHMFL 11/19/99 Form factor of chain-end spins 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 Y 2 BaNi 1-x Mg x O 5 x=4%

23. NHMFL 11/19/99 Vacancy doping a Haldane spin chain  q=  mode shifts towards J  q=  mode broadens due to random chain length distribution  Applied field induces Zeeman resonance below Haldane gap  Resonating chain end spins have AFM form factor resembling S(q) for pure system.

24. NHMFL 11/19/99 New excitations in Ca-doped Y 2 BaNiO 5 Pure 9.5% Ca Ca-doping creates states below the gap sub-gap states have doubly peaked structure factor Y 2-x Ca x BaNiO 5 :

25. NHMFL 11/19/99 Why a double ridge below the gap in Y 2-x Ca x BaNiO 5 ?  Charge ordering yields incommensurate spin order  Quasi-particle Quasi-hole pair excitations in a one dimensional hole liquid  Anomalous form factor for independent spin degrees of freedom associated with each donated hole x q  q  is single impurity prop. Indep. of x

26. NHMFL 11/19/99 Does  q vary with calcium concentration?  q is independent of Double peak is predominantly a single impurity effect 4% Ca 14% Ca qq  14.0;04.0  x 9.5% Ca

27. NHMFL 11/19/99 (b) Ca Ba Ni Y (e) (f) (c) (d) O Bond Impurities in a spin-1 chain: Y 2-x Ca x BaNiO 5 (a)

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

29. NHMFL 11/19/99 Calcium doping Y 2 BaNiO 5 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 0.095<x<0.14 and T<100 K Analysis:  Ca 2+ 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

30. NHMFL 11/19/99 What sets energy scale for sub gap scattering ? 0 5 10 h  (meV) q (  ) 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. How to distinguish: Neutron scattering in an applied field Transport measurements Theory ?

31. NHMFL 11/19/99 Broader Conclusions:  Dilute impurities in the Haldane spin chain create sub-gap composite spin degrees of freedom.  Composite spins have an AFM wave function that extends into the bulk over distances of order the Haldane length.  Neutron scattering can detect the structure of composite impurity spins in quantum magnets when the corresponding states exist at energies where the bulk magnetic density of states vanishes.