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Resolving a Magnetic Quandary

Resolving a Magnetic Quandary. Collin Broholm Johns Hopkins University and NIST Center for Neutron Research. Introduction Magneto-elastic transitions Magnetic frustration Order by coupling to lattice or charge Spin Peierls like transition in ZnCr 2 O 4

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Resolving a Magnetic Quandary

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  1. Resolving a Magnetic Quandary Collin Broholm Johns Hopkins University and NIST Center for Neutron Research • Introduction • Magneto-elastic transitions • Magnetic frustration • Order by coupling to lattice or charge • Spin Peierls like transition in ZnCr2O4 • Resolving frustration in Y2Mo2O7 • orbital fluctuations and magnetism in (V1-xCrx)2O3 • Conclusions Supported by the NSF through DMR-0074571

  2. Collaborators S.-H. Lee G. Aeppli W. Bao S. A. Carter S.-W. Cheong P. Dai J. S. Gardner B. D. Gaulin J. E. Greedan J. M. Honig T. H. Kim P. Metcalf N. P. Raju W. Ratcliff III T. F. Rosenbaum

  3. Magnetic Neutron Scattering The scattering cross section is proportional to the Fourier transformed dynamic spin correlation function Fluctuation dissipation theorem:

  4. Jahn-Teller Theorem Any molecule or complex ion in an electronically degenerate state will be unstable relative to a configuration of lower symmetry in which the degeneracy is absent

  5. Is exchange constant ? • Jij is controlled by higher energy physics that we like to consider irrelevant at low energies • atomic spacing • Orbital overlap • Orbital occupancy • localized or itinerant electronic states • These degrees of freedom can become relevant if H produces “degenerate” state • The result can be intricate interplay between spin charge and lattice sectors

  6. D<3 magnets can have extensive soft modes Cu Copper Benzoate Dender et al. (1996)

  7. Spin Peierls Transition M. Arai et al. (1996) Q Q

  8. Spins with AFM interactions on corner-sharing tetrahedra • What is special about this lattice? • Low coordination number • Triangular motif • Infinite set of mean field ground states • with zero net spin on all tetrahedra • No barriers between mean field ground states • Q-space degeneracy for spin waves

  9. spins on corner sharing tetrahedra B-spinel Pyrochlore Subjects of this talk

  10. ZnCr2O4 : Corner sharing tetrahedra

  11. NIST Center for Neutron Research

  12. Signs of frustration: short range order for T<|QCW| 0 0.5 1.0 1.5 2 2.5 Q (A-1) • Points of interest: • 2p/Qr0=1.4 • => nn. AFM correlations • No scattering at low Q • => satisfied tetrahedra • Relaxation rate of order kBT • => quantum critical hw (meV)

  13. Approaching quantum criticality Lorentzian relaxation spectrum: Near Quantum Critical spin system: No indication of finite T cross over or phase transition in cubic phase

  14. First order phase transition in ZnCr2O4 • Dynamics: • Low energy PM. • Fluctuations form • resonance • Statics: • Staggered magnetization • tetragonal distortion

  15. Local spin resonance in ordered phase Paramagnetic fluctuations in frustrated AFM Local spin resonance in magneto-elastic LRO phase

  16. Low T excitations in ZnCr2O4: C C D B A B A Magnetic DOS Q-dep. of E-integ. intensity A: Bragg peaks B: Spin waves C: Resonance D: Upper band

  17. Spectra at specific Q Resonance Spin waves

  18. Dispersion relation for resonance ZnCr2O4 single crystals T=1.5 K

  19. Structure factor for resonance Extended sharp structures in reciprocal space Fluctuations satisfy local constraints ZnCr2O4 T=1.4 K

  20. Comparing resonance and PM fluctuations 1.4 K 15 K • Paramagnetic fluctuations and resonance satisfy • same local constraints. • Transition pushes low energy fluctuations into a resonance

  21. How can this frustrated system order? Cr3+ O2- Tetragonal dist. Edge sharing n-n exchange in ZnCr2O4 depends strongly on Cr-Cr distance,r: (JAFM<0) From series of Cr-compounds: r The effect for a single tetrahedron is to make 4 bonds more AFM and two bonds less AFM.This relieves frustration!

  22. Magnetic order in ZnCr2O4 • tetrahedra have zero net moment • this is a mean field ground • state for cubic ZnCr2O4 • Tetragonal distortion lowers energy • of this state compared to other • mean field ground states: • In a strongly correlated magnet • this shift may yield -View along tetragonal c-axis

  23. Analysis of spin and lattice energies at TC Cubic paramagnet Ftet, Fcub TC T Tetrag. AFM From first moment sum-rule Based on scattering data above and below TC and assuming that nearest neighbor exchange dominates

  24. Change in lattice energy at TC Free energy of the two phases coincide at TC From this we derive increase in lattice energy at transition Compare to tetragonal strain energy Discrepancy calls for additional lattice changes at TC

  25. Analogies with Spin Peirls transition? There are similarities as well as important distinctions!

  26. Short range correlations in Y2Mo2O7

  27. Spin-glass transition in Y2Mo2O7 • Elastic scattering intensity: • Development of spin correlations • static on the 50 ps time-scale • of the experiment. • Inelastic scattering intensity: • Inelastic scattering decreases • as spins cease to fluctuate. • Spin relaxation rate: • G(T) decreases linearly with • T and extrapolates to • Tg=23 K derived from • AC-susceptibility

  28. EXAFS Evidence for disorder in Y2Mo2O7 Booth et al (2000)

  29. Metal Insulator transition in V2O3 Hole doping Increase U/W Mott

  30. The World according to Bill Gates Mott, Sir Nevill Francis Mott (mòt), Sir Nevill Francis Born 1905 British physicist. He shared a 1977 Nobel Prize for developments in computer memory. - from Microsoft Bookshelf Basics circulation >50,000,000? on every Windows 98 based PC with Office

  31. Short Range order in Paramagnetic Insulator B.Z.

  32. Correlations in (V1-xCrx)2O3 and La2CuO4 (V1-xCrx)2O3 Bao et al. TC TC La2CuO4 Keimer et al.

  33. First order phase transition in (V1-xCrx)2O3 Neel order Spin Waves Paramagnetic Short Range Order

  34. Spin wave dispersion Exchange constants 0.6 meV -22 meV -22 meV Bao et al. Unpublished (2000)

  35. Orbital fluctuationsMagnetic SRO Orbital occupancy orderMagnetic order T>TC T<TC

  36. Why orbital fluctuations at low T ? • An interesting possibility: • Bonds occupy kagome’ lattice • Ising model on kagome’ lattice • has no phase transition whence • the low TC • Orbital occupational order • occurs to lower energy of • spin system

  37. Conclusions ZnCr2O4 • Quantum critical fluctuations in PM phase • strain relieves frustration, enables Neel order Y2Mo2O7 • Short range order at all temperatures T<|QCW| • spin freezing due to quenched lattice disorder ? (V1-xCrx)2O3 -2 E (meV) 2 • MIT visible due to orbital occupational frustration ? • Short range order due to orbital fluctuations • Orbital occupational order enables spin order Is there a Jahn-Teller like theorem for quantum critical magnets?

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