1. Quantum effects in Magnetic Salts Part II G. Aeppli London Centre for Nanotechnology

2. Talk 1 TF Ising model in 3d shows interesting QM effects in real experiments ‘slaved’ degrees of freedom which are classically irrelevant can have qualitative quantum impact

3. outline Introduction – salts  quantum mechanics  classical magnetism RE fluoride magnet LiHoF4 – model quantum phase transition 1d model magnets 2d model magnets – Heisenberg & Hubbard models

4. collaborators G-Y Xu (BNL) C.Broholm (Hopkins) J.F.diTusa(LSU) H. Takagi (Tokyo) Y. Itoh(Tsukuba) Y-A Soh (Dartmouth) M. Treacy (Arizona) D. Reich (Hopkins) D. Dender (NIST)

5. Example #2 - Heisenberg antiferromagnet H=  JS i S j with J>0 classical ground state

6. Consider commutator again M fm =  S z l (ferromagnet) M af =  (-1) l S z l (antiferromagnet) [M,H]=... (-1) l ([S z l,S l ](S l-1 +S l+1 ) -([S z l-1,S l-1 ]+[S z l-1,S l-1 ])S l ) for FM, [M,H]=0 while not so for AFM

7. Antiferromagnets can self-destruct

8. does the classical picture ever go wrong- look at spin wave amplitudes | | 2 Diverge as 1/Q when Q  magnetic zone center for AFM ~ constant for FM

9. Break-down of S-W theory =S(S+1)=static piece + fluctuating piece = M o 2 +  (E-Eo(Q))| | 2 dEd d Q =M o 2 +  (1/Q)d d Q(AFM) (M o =ordered moment) clearly a problem for AFM in d=1

10. >, < > -> > +> J

11. Consequence- antiferromagnetism can be unstable, especially for low d What do experiments say?

12. S=1/2 chain AFM (CuGeO 3 )

13. S=1/2 for zero field No magnetic order pairs of fermionic excitations rather than harmonic spin waves but at first sight, difficult to distinguish from multimagnon series expansion... Want something qualitatively different…

14. For a conventional antiferromagnet in a field, only rounding effects, both types of modes have peak intensity at  -0.500.51 1 ||B BB

15. Dender et al., Phys. Rev. Lett. 79(9), pp. 1750-1753, (1997)

16. E=0.21meV Dender et al., Phys. Rev. Lett. 79(9), pp. 1750-1753, (1997)

17. Zeeman-split spinon Fermi surface Dender et al., Phys. Rev. Lett. 79(9), pp. 1750-1753, (1997)

18. Consider S=1 AFM chain compound YBaNiO 5

19. S(Q)=S expi|l-m|Q equal-time correlation function = liquid structure factor no AFM order, only fluctuations width =1/x o where x o ~7a

20. An unstable antiferromagnet

21. 0 20 40 60 0 0.511.5 2 h  (meV) Xu et al, unpublished

22. a gapped ‘spin liquid’(Haldane) Why? rationalization #1 S z =-1,0,+1 -+-+-+0-+-+-+0-0+-+-+ (‘floating zeroes) rationalization #2(‘valence bond solid’)- consider J Hund <J Ni-Ni Ni +2

24. Just a simple liquid? secret order(quantum coherence) in explanations, but apparently not visible in the equal-time two-spin correlation function =  S(q,  can we measure coherence length for this new state?

25. 0 20 40 60 0 0.511.5 2 h  (meV)

26.  S(q,  S(q,  meV) Xu et al, unpublished

27. Theory by Sachdev et al Xu et al, unpublished

28. Mesoscopic phase(>15nm) phase coherence in quantum spin fluid as T  0, | | 2  q  even while the 2-spin correlations in ground state are short-ranged: =exp-|i-j|/  where  ~7 T=0 quantum coherence limited only by inter-impurity spacing dephasing at finite T observed

29. What happens when we insert incorrect bonds? via Ca substitution for Y which adds holes mainly to oxygens on chains(DiTusa et al ‘94) …Ni 2+ -O 2- -Ni 2+ - O 2- -Ni 2+ -O - -Ni 2+ -O 2- -Ni 2+...

30. Subgap bound states in Ca-doped YBaNiO 5 Xu et al, unpublished

31. G. Xu et al., Science, 289(5478), pp. 419-422, (2000)

32. Ca-doping induces subgap resonance incommensurability which does not seem to depend on x sharper at low x net spectral weight well in excess(~4 times larger) of spectral Weight for S=1/2 one might associate with added hole

33. S=1/2 X S=1/2 X S=1/2 O-O- Strong coupling J O-Ni between oxygen & nickel spins  net ferromagnetic(no matter what is sign of J O-Ni ) bond of strength J O-Ni 2

34. S(Q)=cos 2 (Q) peaks at 2n , nodes at (2n+1) 

35. but really J Hund >>J Ni-Ni J hund <<J Ni-Ni dispersionless VB state real S=1 chain

36. antiferromagnetism survives on a length scale >lattice spacing edge states are more extended than single lattice spacing Therefore- 1/ 

37. 12345 0 5 10 15 20 2  … interference between left and right hand side of bound state wavefunction produces two incommensurate peaks centered around 

38. for finite(rather than infinitesimal) impurity density, interference effect no longer perfect, and node at  partially relieved

39. Test: No interference effect when chain is cut rather than FM bond inserted - Direct observation of effective S=1/2 edge state for chain cut by substitution of nonmagnetic Mg for magnetic Ni M. Kenzelmann et al. Physical Review Letters, 90, 087202/1-4, (2003)

40. Immobile holes in 1-d quantum spin liquid nucleate subgap edge states Incommensurate structure factor - not from charge ordering Fermi surface etc. - but from delocalized quantum spin degree of freedom which extends over several Ni-Ni spacings into QSF and accounts for large spectral weight

41. summary Antiferromagnets in 1d avoid classical order & display mesoscopic quantum effects 1d magnets a good experimental laboratory for edge states in quantum systems