1. Collin Broholm Johns Hopkins University and NIST Center for Neutron Research Quantum Phase Transition in Quasi-two-dimensional Frustrated Magnet M. A. AdamsISIS Y. ChenJHU D. V. FerrarisJHU N. HarrisonLANL T. LectkaJHU D. H. ReichJHU J. RittnerJHU M. B. StoneJHU Guangyong XuU. Chicago H. YardimciJHU I. ZaliznyakBNL * Work at JHU Supported by the National Science Foundation

2. Yale 11/29/01 Outline of Seminar  A simple D=1 quantum magnet: Copper Nitrate  A not so simple D=2 quantum magnet: PHCC  Frustration in PHCC  Field induced phase transition in PHCC  Conclusions Some results published in M. Stone et al., PRB 64, 144405 (2001)

3. Yale 11/29/01 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)

4. Yale 11/29/01 Magnetic Neutron Scattering The scattering cross section is proportional to the Fourier transformed dynamic spin correlation function

5. MACS spectrometer now being built at NIST Design by C. Brocker, C. Wrenn, and M. Murbach 10 8 n/cm 2 /s in  E=0.2 meV 21 detection channels 10 8 n/cm 2 /s in  E=0.2 meV 21 detection channels

6. Singlet Ground State in Cu-Nitrate H =

7. Yale 11/29/01  A spin-1/2 pair with AFM exchange has a singlet - triplet gap: Qualitative description of excited states J  Inter-dimer coupling allows coherent triplet propagation and produces well defined dispersion relation  Triplets can also be produced in pairs with total S tot =1

8. Yale 11/29/01 Triplet waves in dimerized copper nitrate Xu et al PRL (2000)

9. Yale 11/29/01 Magnetizing a gapped quantum magnet Copper Nitrate T=0.1 K Field induced order Eckert et al (1980)

10. Yale 11/29/01 Singlet Ground state in PHCC Daoud et al., PRB (1986). J 1 =12.5 K  =0.6 J 1 =12.5 K  =0.6  /  max

11. Yale 11/29/01 b c Structure is “consistent” with spin chains PHCC = C 4 H 12 N 2 Cu 2 Cl 6 a c Cu Cl C N

12. Yale 11/29/01 Dispersion along c axis Could be spin chain No dispersion along b Is PHCC quasi-one-dimensional? PHCC is quasi-two-dimensional Dispersion to “chains” Not chains but planes   (meV)

13. 2D dispersion relation   (meV) 0 1 0 1 h

14. Yale 11/29/01 Other means of destabilizing Neel order Magnetic Frustration: All spin pairs cannot simultaneously be in their lowest energy configuration Frustrated Weak connectivity: Order in one part of lattice does not constrain surrounding spins

15. Yale 11/29/01 1. Assume Neel order, derive spin wave dispersion relation 2. Calculate the reduction in staggered magnetization due to quantum fluctuations 3. If then Neel order is an inconsistent assumption diverges if on planes in Q-space A Frustrated Route to Moment Free Magnetism? Frustration can produce local soft modes that destabilize Neel order Frustration can produce local soft modes that destabilize Neel order

16. Yale 11/29/01 Neutrons can reveal frustration The first  -moment of scattering cross section equals “Fourier transform of bond energies”  bond energies are small if small  Positive terms correspond to “frustrated bonds”   drrd SSand/or J

17. Yale 11/29/01 Measuring Bond Energies

18. Yale 11/29/01 Frustrated bonds in PHCC Green colored bonds increase ground state energy The corresponding interactions are frustrated Green colored bonds increase ground state energy The corresponding interactions are frustrated

19. Results in zero field  Systems thought to be one dimensional may represent a richer class of quantum spin liquids.  Neutron scattering required to classify these.  Experimental realizations of spin liquids were sought, not found, in symmetric frustrated magnets.  Hypothesis: Spin liquids may be more abundant in complex geometrically frustrated lattices.

20. Yale 11/29/01 Zeeman splitting of cooperative triplet PHCC T=60 mK GS-level crossing for H  8 T Quantum phase transition

21. Yale 11/29/01 H-T phase diagram PHCC

22. Field-induced AFM Order H=14.5 T T=1.77 K Intensity  c

23. Yale 11/29/01 Frustrated bonds parallel spins

24. Yale 11/29/01 Temperature Driven Criticality  T =0.44(2) Bragg Intensity  M 2

25. Yale 11/29/01 H-T phase diagram PHCC

26. Yale 11/29/01 Reentrant low T transition?

27. Yale 11/29/01 Extracting the critical field Fit range

28. Yale 11/29/01 Reentrant behavior close to critical point 3 D long range order Spin gap gapless

29. Yale 11/29/01 Reentrant behavior in other frustrated magnet P. Schiffer et al., PRL (1994). Y. K. Tsui et al., PRL (1999).

30. Yale 11/29/01 Magneto-elastic effects in frustrated magnets? Lee et al., PRL (2000). ZnCr 2 O 4 frustrated spinel AFM

31. Yale 11/29/01 Critical exponent  H versus temperature HH T min  No indications of change in critical properties at T *  However, transition could be weakly first order  No indications of change in critical properties at T *  However, transition could be weakly first order

32. Conclusions  Quasi-two dimensional singlet ground state PHCC  Neutron scattering reveals frustrated bonds that may be instrumental in suppressing Neel order  Ordered state consistent with bond energies derived from inelastic scattering at H=0  Phase diagram features a cross-over to quasi-two- dimensional gapless paramagnetic phase  At low fields ordered phase drops below extrapolation of cross over line to gap-less phase  Indications of low T reentrant behavior  Anomalous low T phase boundary may result from magnetoelastic effects close to QC point