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Neutron Scattering of Frustrated Antiferromagnets

Neutron Scattering of Frustrated Antiferromagnets. Collin Broholm Johns Hopkins University and NIST Center for Neutron Research. Satisfaction without LRO Paramagnetic phase Low Temperature phase Spin glass phase Long range order Spin Peierls like phase Conclusions .

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Neutron Scattering of Frustrated Antiferromagnets

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  1. Neutron Scattering of Frustrated Antiferromagnets Collin Broholm Johns Hopkins University and NIST Center for Neutron Research Satisfaction without LRO Paramagnetic phase Low Temperature phase Spin glass phase Long range order Spin Peierls like phase Conclusions SrCr9pGa12-9pO19 KCr3(OD)6(SO4)2 ZnCr2O4 Supported by the NSF through DMR-9453362 and DMR-0074571

  2. Collaborators S.-H. Lee NIST and University of MD M. Adams ISIS Facility, RAL G. Aeppli NEC Research Institute E. Bucher University of Konstanz C. J. Carlile ISIS Facility, RAL S.-W. Cheong Bell Labs and Rutgers Univ. M. F. Collins McMaster University R. W. Erwin NIST L. Heller McMaster University B. Hessen Bell Labs/Shell T. J. L. Jones ISIS Facility, RAL T. H. Kim Rutgers University C. Kloc Bell Labs N. Lacevic Johns Hopkins University T. G. Perring ISIS Facility, RAL A. P. Ramirez Bell Labs W. Ratcliff III Rutgers University A. Taylor ISIS Facility, RAL

  3. A simple frustrated magnet: La4Cu3MoO12 Masaki Azuma et al. (2000)

  4. Magnetization and order of composite trimer spins

  5. Theory of spins with AFM interactions on corner-sharing tetrahedra • What is special about this lattice and this spin system? • 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

  6. SrCr9pGa12-9pO19 : Kagome’ sandwich Isolated spin dimer Kagome’-Triangular-Kagome’ sandwich (111) slab of pyrochlore/spinel AFM A. P. Ramirez et al. PRL (1990)

  7. Fe & Cr Jarosite: coupled Kagome’ layers AM3(OH)6(SO4)2 KCr3(OH)6(CrO4)2 A. S. Wills et al. (2000) Townsend et al (1986) Lee et al. (1997)

  8. ZnCr2O4 : Corner sharing tetrahedra

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

  10. NIST Center for Neutron Research

  11. Detection system on SPINS neutron spectrometer

  12. Spatial correlation length saturates for T 0 SrCr9pGa12-9pO19 for T<QCW

  13. Relaxation Rate decreases forT 0 SrCr9pGa12-9pO19 SrCr9pGa12-9pO19 Paramagnetic state: Fluctuating AFM spin clusters that largely satisfy exchange interactions dimer Kagome’ sandwich

  14. Spin glass in concentrated frustrated AFM • Does quenched disorder play a role? • What is structure of SG phases? • What are excitations in SG phases?

  15. Spin glass transition in SCGO(p=0.92)

  16. The role of disorder at SG transition Martinez et al. (1992) Higher Tf Sharper features in S(Q) Higher Cr concentration • Two scenarios remain viable : • A) Strong sensitivity to low levels of disorder • B) Intrinsic disordered frozen phase

  17. Structure of frozen phase Short range in plane order Kagome’ tri-layer correlations

  18. Excitations in a frustrated spin glass Gapless 2D Halperin-Saslow “Spin Waves” SCGO(p=0.92)

  19. Long range order in frustrated AFM • Clarify role of symmetry breaking interactions, quenched disorder and “order by disorder” effects in stabilizing LRO. • Are there anomalous critical properties at phase transitions to LRO? • What are the excitations in the ordered phase of a highly frustrated magnet?

  20. Phase transition to LRO in Cr-Jarosite >90% Cr 75-90% Cr

  21. Weak order / strong fluctuations

  22. Impurity enhanced LRO in (DO3)Fe3-xAly(SO4)2(OD)6 100% Fe Wills et al (1998) Only reported Jarosite w/o LRO 89% Fe Wills et al. (2000) Diamagnetic impurities yield LRO DIntensity (arb)

  23. Magneto-elastic effects in frustrated AFM • Can magneto-elastic coupling relieve frustration? • What is magnetic and lattice strain configuration in ordered phase? • Determine energetics of a spin-Peierls like transition for frustrated magnets. • What are excitations from the ordered phase?

  24. First order phase transition in ZnCr2O4 • Dynamics: • Low energy paramag. • Fluctuations form a • resonance at 4.5 meV • Statics: • Staggered magnetization • tetragonal lattice distortion

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

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

  27. Spectra at specific Q Resonance Spin waves

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

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

  30. Comparing resonance to PM fluctuations 1.4 K 15 K • Paramagnetic fluctuations and resonance satisfy • same local constraints. • Transition pushes low energy fluctuations into a resonance • w/o changing spatial correlations

  31. Why does tetragonal strain encourage Neel order? Cr3+ O2- Tetragonal dist. Edge sharing n-n exchange in ZnCr2O4 depends strongly on Cr-Cr distance,r: From series of Cr-compounds: r The effect for a single tetrahedron is to make 4 bonds more AFM and two bonds are less AFM.This relieves frustration!

  32. Magnetic order in ZnCr2O4-Viewed along tetragonal c-axis • 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

  33. Analysis of magneto-elastic transition in ZnCr2O4 Ftet, Fcub TC T Cubic paramagnet Tetrag. AFM Free energy of the two phases are identical at TC From this we derive reduction of internal energy of spin system

  34. Direct measurement of confirms validity of analysis where S(Q,w) changes From first moment sum-rule for the dynamic spin correlation function we find When a single Heisenberg exchange interaction dominates. Inserting magnetic scattering data acquired at 15 K and 1.7 K we get LRO develops from a strongly correlated state

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

  36. Conclusions ZnCr2O4 • Low connectivity and triangular motif yields cooperative paramagnet for|T/QCW|<<1. • The paramagnet consists of small spin clusters with no net moment, which fluctuate at a rate of order kBT/ h. • Spinels can have entropy driven magneto-elastic transition to Neel order with spin-Peirls analogies. • The ordered phase has a spin-resonance, as expected for under-constrained and weakly connected systems. • Pyrochlore’s can have a soft mode transition to a spin-glass even when there is little or no quenched disorder. • Variations of sub-leading interactions in pyrochlore’s give different types of SRO in different compounds. • Lattice distortions may be a common route to relieving frustration and lowering the free energy of geometrically frustrated magnets. Y2Mo2O7 Tetragonal

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