1. Structure and dynamics of spin polarons induced by doping a Haldane spin-1 chain Collin Broholm * Johns Hopkins University and NIST Center for Neutron Research * Supported by the National Science Foundation Ying Chen LANL Guangyong XuBNL G. AeppliUCL J. F. DiTusaLSU I. A. ZaliznyakBNL C. D. FrostISIS T. ItoTsukuba M. KenzelmannJHU K. Oka Tsukuba H. TakagiISSP M. E. Bisher NEC M. M. J. TreacyNEC R. PaulNIST Xu et al., Science 289, 419 (2000) Kenzelmann et al., PRL 90, 087202 (2003)

2. Outline  Introduction to neutrons and Y 2 BaNiO 5  On-chain non-magnetic doping  Off chain hole doping  Conclusions and outlook

3. APS 3/5/03 SPINS cold neutron spectrometer at NCNR kiki kfkf Q

4. APS 3/5/03 MAPS Spectrometer at ISIS in UK

5. APS 3/5/03 Haldane gap in Y 2 BaNiO 5 Ni 2+ Impure Pure Y 2 BaNiO 5 Nuclear Elastic Scattering

6. APS 3/5/03 Single mode approximation for spin-1 chain Dispersion relation Equal time correlation function Ma et al., PRL 69, 3571 (1992).

7. APS 3/5/03 Anisotropy and inter-chain coupling  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

8. APS 3/5/03 Facts on Y 2 BaNiO 5 Intra-chain exchange Anisotropy Dipole in field Inter-chain exchange

9. APS 3/5/03 Outline  Introduction to neutrons and Y 2 BaNiO 5  On-chain non-magnetic doping  Off chain hole doping  Conclusions and outlook

10. APS 3/5/03 Impurities in Y 2 BaNiO 5 Ca 2+ Y 3+ Mg 2+ on Ni 2+ sites Site centered defects Ca 2+ on Y 3+ sites bond centered defects Mg Ni Kojima et al. (1995) Mg Pure

11. APS 3/5/03 An ensemble of finite length chains Chain length L P(L) 2% 4% 8% P(  )/ max (P(  )) 2% 4% 8% Probability spin in segment of length L Gap from chain of length L Ensemble averaged scattering

12. APS 3/5/03 Haldane gap with impurities Kenzelmann et al. PRL (2003)

13. APS 3/5/03 How about chain ends? L is even L is odd Singlet-triplet Single ion anisotropy Zeeman

14. APS 3/5/03 Chain-end composite spin

15. APS 3/5/03 Form factor for chain-end spin Kenzelmann et al. PRL (2003)

16. APS 3/5/03 Outline  Introduction to neutrons and Y 2 BaNiO 5  On-chain non-magnetic doping  Off chain hole doping  Conclusions and outlook

17. APS 3/5/03 Transport in Ca doped Y 2 BaNiO 5 T. Ito et al. Submitted to PRL (2001) Charge Transfer excitation Charge polaron 1D conductivity, no Charge ordering

18. APS 3/5/03 Impurities in Y 2 BaNiO 5 Ca 2+ Y 3+ Mg Ni Kojima et al. (1995) Mg Ca 2+ Pure Mg 2+ on Ni 2+ sites Site centered defects Ca 2+ on Y 3+ sites bond centered defects

19. APS 3/5/03 Gap modes in 4% Ca-doped Y 2 BaNiO 5

20. APS 3/5/03 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

21. APS 3/5/03 Does  q vary with calcium concentration?  q not strongly dependent on x single impurity effect Xu et al., Science 289, 419 (2000)

22. APS 3/5/03 Bond Impurities in a spin-1 chain: Y 2-x Ca x BaNiO 5 Y3+Y3+ Ni O AFMFM Ca 2+

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

24. APS 3/5/03 Gap modes in 4% Ca-doped Y 2 BaNiO 5 Excited state Quasi-elastic From deg. GS Quasi-elastic From deg. GS

25. APS 3/5/03 Dynamic model of spin polaron

26. APS 3/5/03 Intra polaron dynamics in Ca-doped Y 2 BaNiO 5 0 5 10 15 20 25 0 Normalized Intensity (Arb) Pure 4% Ca Intra quartet Clean gap ?

27. APS 3/5/03 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 Y 2-x Ca x BaNiO 5 are surrounded by AFM spin polaron with central phase shift of   Spin polaron spectrum described as three interacting spins-1/2 with J FM = 9 meV Viewgraphs and publications at http://www.pha.jhu.edu/~broholm/homepage

28. APS 3/5/03 Outlook  Confirm level assignment in field  What is localization length for spin polaron?  Spin polaron structure in frustrated magnets  Spin polarons in high T C superconductors?  Magnetism of interacting spin polarons Design by T. D. Pike http://www.pha.jhu.edu/~broholm/MACS