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 the NSF through DMR

CURREAC 8/20/99 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 Experiments performed at NIST and ISIS

CURREAC 8/20/99 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

CURREAC 8/20/99 Magnetic Neutron Scattering The scattering cross section is proportional to the Fourier transformed dynamic spin correlation function

Y 2 BaNiO 5 on SPINS E<10 meV NIST cold neutron guide hall

ISIS Experimental hall Y 2 BaNiO 5 on MARI 5 meV<E<100 meV

CURREAC 8/20/99 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 

CURREAC 8/20/99 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

CURREAC 8/20/99 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:

CURREAC 8/20/99 Propagating triplet in alternating spin-1/2 chain Cu(NO 3 ) D 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 h  (meV) Q/ 

CURREAC 8/20/99 Two magnon excitations in an alternating spin chain Tennant, Nagler, Xu, Broholm, and Reich.

CURREAC 8/20/99 Haldane mode in Y 2 BaNiO 5 at finite T Effects of heating: Line-width increases Effective  increases

CURREAC 8/20/99 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  Derived from  T c T  0 )(   Neglecting T-dependence of spin wave velocity c 0

CURREAC 8/20/99 Q-scans versus T: energy resolved and energy integrated   Probing spatial coherence of Haldane mode   Probing equal time correlation length

CURREAC 8/20/99 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)

CURREAC 8/20/99 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|<  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

CURREAC 8/20/99 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

CURREAC 8/20/99 Zeeman resonance of chain-end spins I(H=9 T)-I(H=0 T) (cts. per min.) h  (meV) H (Tesla) g=

CURREAC 8/20/99 Structure factor of chain-end spins Q-dependence reveals that resonating object is AFM. The structure factor is indistinguishable from S(Q) for pure system. Chain end spin carry AFM spin polarization of length  back into chain

CURREAC 8/20/99 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.

CURREAC 8/20/99 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 :

CURREAC 8/20/99 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

CURREAC 8/20/99 Does  q vary with calcium concentration?  q is independent of Double peak is predominantly a single impurity effect 9.5% Ca 14% Ca qq  14.0;095.0  x

CURREAC 8/20/99 (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)

CURREAC 8/20/99 Form-factor for FM-coupled chain-end spins - AFM droplets 9.5% Ca 14% Ca A symmetric AFM droplet Ensemble of independent randomly truncated AFM droplets

CURREAC 8/20/99 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 Current interpretation:  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

CURREAC 8/20/99 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.