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

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

4. Yale 11/29/01 SPINS cold neutron triple axis spectrometer at NCNR

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. Yale 11/29/01 Singlet Ground State in Cu-Nitrate

7. Yale 11/29/01 Simple example of magnet with gapped spectrum Cu(NO 3 ) 2. 2.5D 2 O : dimerized spin-1/2 system Only Inelastic magnetic scattering Only Inelastic magnetic scattering

8. 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

9. Yale 11/29/01 Triplet waves in dimerized copper nitrate Xu et al PRL May 2000

10. Creating two triplets with one neutron One magnon Two magnon Tennant et al (2001)

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

12. Yale 11/29/01 Unconventional magnetism in PHCC

13. 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

14. 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)

15. 2D dispersion relation h   (meV) 0 1 0 1

16. 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

17. 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

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

19. Yale 11/29/01 Measuring Bond Energies

20. Yale 11/29/01 Frustrated bonds in PHCC

21. Significance of findings so far  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.

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

23. Field-induced AFM Order H=14.5 T 1.77 K 10 K Intensity

24. Yale 11/29/01 Frustrated bonds remain frustrated ^ a ^ c 1 8 6 2 3

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

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

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

28. Yale 11/29/01 Reentrant low T transition

29. Yale 11/29/01 Field driven criticality HH

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

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

32. Yale 11/29/01 Magneto-elastic effects in frustrated magnets? Lee et al., PRL (2000).

33. Conclusions  Spin systems with a gap can be mistaken for being quasi-one-dimensional  Two and three dimensional moment free magnetism found in PHCC and CuHpCl  Neutron scattering reveals frustrated bonds in the corner-sharing triangular clusters of these materials  Hypothesis: Moment free magnetism may be a common state of interacting spin systems with triangular motif and weak connectivity  Idea: Novel strongly correlated transport may occur if the materials can be doped