Frustrated magnetism in 2D Collin Broholm Johns Hopkins University & NIST

1. Frustrated magnetism in 2D Collin BroholmJohns Hopkins University & NIST Introduction Two types of antiferromagnets Experimental tools Frustrated dimers in 2D Low T spectrum Field driven critical response H-T Phase diagram Conclusions and plans

2. Spin Versus Dimer Order 3D bi-partite AFM Interacting spin pairs 2×(2S+1) PCCM SCES workshop

3. Conceptual Phase Diagram for Quantum Magnets Chakravarty, Halperin, Nelson Sachdev T/J Heavy Fermion behavior Non-fermi-liquids High TC Superconductivity Quantum Critical 1/S, frustration, 1/z, H, P, x, … PCCM SCES workshop

4. Approach QCP from Neel state 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 untenable • diverges if through a surface • Soft points in D=1 magnets • Soft lines in D=2 magnets • Soft planes in D=3 magnets PCCM SCES workshop

5. Geometrical Interpretation Weak connectivity: Order in one part of lattice does not constrain surroundings This can occur in higher dimensions when there is frustration and/or low coordination number, z. PCCM SCES workshop

6. Why 2D frustration is particularly interesting • More interesting than 1D less complicated than 3D (at least for experimentalist) • Two being the lower critical dimension for Neel order, frustration can have a qualitative impact • High TC demands better understanding of 2D cooperative phenomena • The panoply of ordered states in frustrated systems offers potentials for applications PCCM SCES workshop

7. Inelastic Neutron Scattering • We can measure dispersion relations • We determine structure through transition rate PCCM SCES workshop

8. MACS spectrometer under construction at NIST pi pf ħQ MACS spectrometer under construction at NIST PCCM SCES workshop

9. Renormalized Classical 2D AFM La2CuO4 Sr2CuO2Cl2 Coldea et al. PRL (2001) Greven et al PRL (1994) J. Tranquada PCCM SCES workshop

10. AFM on 2D kagome’ sandwich I. S. Hagemann et al. PRL (2001) TC/QCW << 1 ⇒Near Quantum Critical PCCM SCES workshop

11. Satisfied Simplexes DCS/NIST PCCM SCES workshop Gasparovic et al. (2005)

12. Relieving Frustration in a tetrahedron Available from for $700 PCCM SCES workshop

13. SCGO QS-Ferrite Slowing local spin fluctuations at QCP DCS/NIST PCCM SCES workshop

14. Anomalous Freezing with minimal disorder Order-parameter-like Development of Small “frozen” moment IRIS/ISIS Low T specific heat indicates spin-wave-like normal modes A “simplex glass” PCCM SCES workshop

15. hw(meV) Frustrated Magnet with spin gap PCCM SCES workshop (C4H12N2)Cu2Cl6(PHCC) Stone et al. PRB (2001)

16. hw(meV) 1 0 l h 0 1 2D dispersion and first moment PCCM SCES workshop

17. Frustrated bonds in PHCC Green colored bonds increase ground state energy The corresponding interactions are frustrated PCCM SCES workshop

18. Multi-magnon excitations PCCM SCES workshop

19. Bound state meets continuum PCCM SCES workshop

20. Bound state meets continuum PCCM SCES workshop

21. J H 1 0 H Field driven level Crossing Field driven QCP PCCM SCES workshop

22. Dynamic correlations at the QCP T=8 K • Fix field at HC=7.5 T • Heating at the QCP yields finite ħwmaximum • This indicates triplon repulsion T=3 K T=0.04 K h (r. l. u.)

23. Theory of dynamic correlations at QCP Subir Sachdev, Yale and E. R. Dunkel, Harvard • S from self consistent Hartree Fock • U =5 meV2 • g~w fitted at each T • overall scale fitted at each T PCCM SCES workshop

24. Dynamic correlations at the QCP T=8 K T=8 K T=3 K T=3 K T=0.04 K h (r. l. u.)

25. Non-linear magnetization PCCM SCES workshop Stone et al to (2005)

26. Phase diagram for frustrated 2D magnet PCCM SCES workshop Stone et al to (2005)

27. Cross over to 2D gapless phase w/o LRO Stone et al to (2005) PCCM SCES workshop

28. Phase diagram for frustrated 2D magnet PCCM SCES workshop Stone et al to (2005)

29. Evidence of non-monotonic HC(T) PCCM SCES workshop Stone et al to (2005)

30. Anomalies near QCP • Scenarios: • Cross over between 2 regimes: • 3D ordering of magnetized dimers at low T • 3D ordering of 2D bose condensate at higher T • Additional low T degrees of freedom • Nuclear spin order • Spin Peierls like lattice distortion Neel order BEC Singlet PCCM SCES workshop Stone et al to (2005)

31. Summary • Three regimes for quasi-2D magnets • Renormalized classical (La2CuO4) • Near quantum critical and gapless (QS-ferrite) • Isolated singlet ground state systems (PHCC) • PHCC: Excitation spectrum • Evidence for competing interactions • Complex cooperative singlet • Bound state decay into continuum • PHCC: phase diagram • 3D Neel phase within bose condensed triplon phase • Cross over and/or extra degrees of freedom at QCP PCCM SCES workshop

32. Outlook on 2D frustration • Excitations in gapless 2D phase • More complete clarification of QCP anomalies to distinguish explanations • Cross over between different regimes for interlayer coupling • Novel degrees of freedom, a generalized spin Peierls effect? • Quantum impurities in PHCC • Novel neutron instrumentation • Access to spin dynamics in small samples • Comprehensive surveys of Q-E space • Parametric studies versus H and pressure PCCM SCES workshop

33. Collaborators • PHCC • M. Bouloubasis • N. Harrison • M. Kenzelmann • D. H. Reich • M. B. Stone • H. Tao • P. Vorserwisch • I. Zaliznyak • Pyrochlore slabs • G. Aeppli • R. Cava • G. Gasparovic • I. S. Hagemann • S. H. Lee Theory E. R. Dunkel S. Sachdev PCCM SCES workshop