1. Collin Broholm Johns Hopkins University and NIST Center for Neutron Research Quantum Phase Transition in a 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. FSU 12/14/01 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) See also paper on CuHpCl M. Stone et al., Cond-Mat/0103023

3. FSU 12/14/01 Spin Hamiltonian of magnetic dielectric  Chemistry determines dimensionality, connectivity  Vary H with pressure, magnetic field  H is affected by any lattice distortions Exchange interaction Dipole in magnetic field

4. H = Singlet Ground State in Cu-Nitrate

5. FSU 12/14/01  A spin-1/2 pair with AFM exchange has a singlet - triplet gap: Simple description of alternating spin chain 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

6. FSU 12/14/01 Magnetic Neutron Scattering The scattering cross section is proportional to the Fourier transformed dynamic spin correlation function

7. FSU 12/14/01 Triplet waves in copper nitrate Xu et al PRL (2000)

8. FSU 12/14/01 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

9. FSU 12/14/01 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

10. FSU 12/14/01 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)

11. 2D dispersion relation   (meV) 0 1 0 1 h

12. FSU 12/14/01 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

13. FSU 12/14/01 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 Cooperative Singlet? Frustration can produce local soft modes that destabilize Neel order Frustration can produce local soft modes that destabilize Neel order

14. FSU 12/14/01 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

15. FSU 12/14/01 Measuring Bond Energies

16. FSU 12/14/01 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

17. 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.

18. FSU 12/14/01 Spin Pair in Magnetic Field J 0 1 H H

19. FSU 12/14/01 Zeeman splitting of cooperative triplet PHCC T=60 mK GS-level crossing for H  8 T Quantum phase transition

20. FSU 12/14/01 Non-linear Magnetization Curve

21. FSU 12/14/01 H-T Phase Diagram from Magnetization

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

23. FSU 12/14/01 Frustrated bonds parallel spins

24. FSU 12/14/01 Gapless paramagnetic phase Gap closes Onset of 3D LRO Gapless paramagnet?

25. FSU 12/14/01 H-T phase diagram PHCC 2D Gapped FM

26. FSU 12/14/01 Temperature Driven Criticality  T =0.4 (1) Bragg Intensity  M 2 Compare to  =0.355 for 3D X-Y model

27. FSU 12/14/01 H-T phase diagram PHCC

28. FSU 12/14/01 Reentrant low T transition?

29. FSU 12/14/01 Extracting the critical field Fit range

30. FSU 12/14/01 Reentrant behavior close to critical point 3 D long range order Spin gap gapless

31. FSU 12/14/01 Reentrant behavior in other frustrated magnet P. Schiffer et al., PRL (1994). Y. K. Tsui et al., PRL (1999).

32. FSU 12/14/01 Magneto-elastic effects in frustrated magnets? Lee et al., PRL (2000). ZnCr 2 O 4 frustrated spinel AFM

33. Conclusions  Quasi-2D singlet ground state in 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 gapless paramagnetic phase  Anomalous low T reentrant behavior may result from magnetoelastic effects close to QC point