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Geometric Magnetic Frustration in Double Perovskite Oxides A 2 BB’O 6

Geometric Magnetic Frustration in Double Perovskite Oxides A 2 BB’O 6. Jeremy P. Carlo Department of Physics Villanova University June 2014 Oxides for Energy Meeting, Philadelphia, PA. Outline. Magnetism in Materials Geometric Frustration The Tools: Neutron Scattering

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Geometric Magnetic Frustration in Double Perovskite Oxides A 2 BB’O 6

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  1. Geometric Magnetic Frustration in Double Perovskite OxidesA2BB’O6 Jeremy P. Carlo Department of Physics Villanova University June 2014 Oxides for Energy Meeting, Philadelphia, PA

  2. Outline • Magnetism in Materials • Geometric Frustration • The Tools: • Neutron Scattering • Muon Spin Relaxation • Frustration in Double Perovskites • Results and Conclusions

  3. Outline • Magnetism in Materials • Geometric Frustration • The Tools: • Neutron Scattering • Muon Spin Relaxation • Frustration in Double Perovskites • Results and Conclusions

  4. Magnetism in materials • Why transition metals / lanthanides / actinides? • Need unpaired electrons in valence shell s: 1 orbital p: 3 orbitals d: 5 orbitals f: 7 orbitals

  5. Magnetism in materials • Simplest model: assume moments don’t interact with each other. • High temps: spins fluctuate rapidly and randomly, but can be influenced by an applied magnetic field H: U = -mH M= H = susceptibility • Paramagnetism( > 0) • Diamagnetism ( < 0) • Temp dependence: (T) = C / T Curie Paramagnetism • Real materials: moments do interact Exchange Interaction: U = ̵ J S1  S2 • Then,(T) = C / (T - CW)Curie-Weiss behavior

  6. Magnetism in materials U = ̵ J S1  S2 • kBT > J: thermal fluctuations dominate • kBT < J: interaction energy dominates • Expect: Torder |CW| • Spins may collectively align, leading to a spontaneous nonzero magnetization • Ferromagnetism (FM) (J, CW > 0) • Or they can anti-align: large localmagnetic fields in the material, but zero overall magnetic moment • Antiferromagnetism (AF) (J, CW< 0) (T) = C / (T - CW)

  7. Outline http://leadershipfreak.files.wordpress.com/2009/12/frustration.jpg • Magnetism in Materials • Geometric Frustration • The Tools: • Neutron Scattering • Muon Spin Relaxation • Frustration in Double Perovskites • Results and Conclusions

  8. Geometric Frustration Frustration: Geometric arrangement of magnetic ions prevents all Interactions from being simultaneously satisfied. If all interactions cannot be simultaneously satisfied… the onset of magnetic order is inhibited. f= |QCW| / Torder “frustration index” CW~ Weiss temperature Torder~ actual magnetic ordering tempMFT: f should be  1

  9. Geometric Frustration http://en.wikipedia.org/wiki/File:Herbertsmithite-163165.jpg Herbertsmithite ZnCu3(OH6)Cl2 • In 2-D, associated with AF coupling on triangular lattices • edge-sharing triangles: triangular lattice • corner-sharing triangles: Kagome lattice • Usually quasi-2D systems composedof weakly-interacting layers

  10. Geometric Frustration • In 3-D, associated with AF couplingon tetrahedral architectures corner-sharing tetrahedra:pyrochlorelattice A2B2O7 edge-sharing tetrahedra: FCC lattice

  11. Geometric Frustration • What happens in frustrated systems? • Huge degeneracy of ground states! Sometimes magnetic LRO at sufficiently low T << |Qw| Sometimes a compromise magnetic state: e.g. spin-ice, helimagnetism, spin glass Sometimes exquisite balancing between interactions prevents magnetic order to the lowest achievable temperatures: e.g. spin-liquid Extreme sensitivity to parameters!  Rich phase diagrams Moment size, doping, ionic size / spacing, structural distortion, spin-orbit coupling… • Normally dominant terms in Hamiltonian may cancel, so much more subtle physics can contribute significantly!

  12. Outline • Magnetism in Materials • Geometric Frustration • The Tools: • Neutron Scattering • Muon Spin Relaxation • Frustration in Double Perovskites • Results and Conclusions

  13. Tools to measure magnetism A • Bulk probes • Susceptibility, Magnetization • Local probes • NMR, ESR, Mossbauer , muon spin relaxation • Reciprocal-space (momentum) probes • X-ray, neutron diffraction • Spectroscopic (energy) probes • Inelastic x-ray/neutron scattering

  14. X-Ray / Neutron Scattering Scattered beam Momentum k’ Energy E’ Incoming beam Momentum: k Energy: E Sample Compare incoming and outgoing beams: Q = k – k’ “scattering vector” E = E – E’ “energy transfer” Represent momentum or energy Transferred to the sample

  15. Scattering probes Structure and Dynamics • Q-dependence: structure / spatial information • Neutrons can also give magnetic structure • E-dependence: excitations • Typically phonons, magnons

  16. Latest Generation Instruments! ORNL Spallation Neutron Source SEQUOIA spectrometer TOF-resolved 2D detector array gives simultaneous wide views in Q, E

  17. Muon Spin Relaxation (SR): Probing Local Magnetic Fields Positive muons: ~ light protons 100% spin-polarized muon beam MuonsundergoLarmor precession in a local B field Polarized muon sources: TRIUMF, Vancouver BC PSI, Switzerland ISIS, UK (pulsed) KEK, Japan (pulsed)

  18. Decay Asymmetry Muon spin at decay Detection: +→ e++ + e e = E / Emax normalized e+ energy

  19. e+ detector U incoming muon counter sample e+ m+ detector time D 2.5 e+ detector D

  20. e+ detector U incoming muon counter sample e+ m+ detector time D 2.5 e+ detector D U 1.7

  21. e+ detector U incoming muon counter sample e+ m+ detector time D 2.5 e+ detector D U 1.7 D 1.2

  22. e+ detector U incoming muon counter sample e+ m+ detector time D 2.5 e+ detector D U 1.7 D 1.2 D 9.0 + 106-107 more…

  23. Histograms for opposing counters asy(t) = A0Gz(t) (+ baseline) 135.5 MHz/T Represents muons in a uniform field

  24. Outline • Magnetism in Materials • Geometric Frustration • The Tools: • Neutron Scattering • Muon Spin Relaxation • Frustration in Double Perovskites • Results and Conclusions

  25. Face-Centered Systems • Very common crystal structure“rock salt order” ~ NaCl • Tetrahedral Coordination + AF Correlations = Geometric Frustration

  26. Example: Double perovskite lattice: • A2BB’O6 e.g. Ba2YMoO6 A: divalent cation e.g. Ba2+ B: nonmagnetic cation e.g. Y3+ B’: magnetic (s=½) cation e.g. Mo5+ (4d1) Magnetic ions: edge-sharing tetrahedral network

  27. Nice thing about perovskites: can make them with almost any element in the periodic table! • Variety of phenomena / applications: CMR, multiferroics, photovoltaics, superconductivity, catalysis, frustration… (Courtesy of J. Rondinelli)

  28. Our survey • Goal: systematic survey of face-centered frustrated systems using mSR and neutron scattering.

  29. Our double perovskite survey • We have been systematically surveying double perovskites in the context of GF, studying effects such as: • structural distortion (ideal cubic vs. distorted monoclinic/tetragonal) • Effects of ionic size / lattice parameter • Effects of moment size: s=3/2 s=1 s=1/2 • Effects of spin-orbit coupling: Larger moments More “classical” More amenable to bulk probes + neutrons Smaller moments More “quantum” More difficult to measure L-S J-J nd1 s=1/2 j=3/2 nd2 s=1 j=2 nd3 s=3/2 = j=3/2 Chen et al. PRB 82, 174440 (2010). Chen et al. PRB 84, 194420 (2011).

  30. Comparison of Double Perovskite Systems: A “Family Portrait” • 4d3: (s=3/2 or jeff=3/2: L-S vs. J-J pictures) • Ba2YRuO6: cubic, AF LRO @ 36 K (f ~ 15) • La2LiRuO6: monoclinic, AF LRO @ 24 K (f ~ 8) • 5d2: (s=1 or jeff=2) • Ba2YReO6: cubic, spin freezing TG ~ 50 K (f ~ 12) • La2LiReO6: monoclinic, singlet ~ 50 K (f ~ 5) • Ba2CaOsO6: cubic, AF LRO @ 50 K (f ~ 2.5) • 4d1, 5d1: (s=1/2 or jeff=3/2) • Sr2MgReO6: tetragonal, spin freezing TG ~ 50 K (f ~ 8) • Sr2CaReO6: monoclinic, spin freezing TG ~ 14 K (f ~ 32) • La2LiMoO6: monoclinic, SR correlations < 20 K (f ~ 1) • Ba2YMoO6: cubic, singlet ~ 125K (f > 100)

  31. Neutron Scattering Studies of Ba2YMoO6 Neutron diffraction • Ba2YMoO6: Mo5+ 4d1 • Maintains ideal cubic structure; CW = -219K but no order found down to 2K: f > 100! XRD T = 297K l = 1.33 A Susceptibility T. Aharen et al. PRB 2010

  32. Neutron Scattering Studies of Ba2YMoO6 • Heat capacity shows a broad peak • And NMR shows two signals,one showing the developmentof a gap at low temperatures • But mSR shows nothing…. T. Aharen et al. PRB 2010

  33. Neutron Scattering Studies of Ba2YMoO6 • Resolution comes from inelastic neutron scattering. • What’s happening? At low temps, neighboring moments pair up, to form “singlets.” • But no long range order! J. P. Carlo et al, PRB 2011 SEQUOIA Beamline Spallation Neutron Source Oak Ridge National Laboratory

  34. Neutron Scattering Studies of Ba2YRuO6 Heat capacity • Ba2YRuO6: Ru5+ 4d3 • Much more “conventional” behavior…? qW = -571K T. Aharen et al. PRB 2009

  35. Neutron Scattering Studies of Ba2YRuO6 • Clear signs of antiferromagnetic order, but with f ~ 11-15. [100] magnetic Bragg peak J. P. Carlo et al. PRB 2013.

  36. Neutron Scattering Studies of Ba2YRuO6 • But the inelastic scattering dependence is much more exotic! J. P. Carlo et al. PRB 2013.

  37. Neutron Scattering Studies of Ba2YRuO6 • The ordered state is associated with a gap. • Interesting: Egap kBTorder • But why should such a gap exist? • Suggestive of exotic physics: relativistic spin-orbit coupling! J. P. Carlo et al. PRB 2013.

  38. MuonSpin Relaxation studies of Ba2CaOsO6 + Ba2YReO6 • Ba2YReO6 ~ Re5+, 5d2 ~spin glass ~ 50K • Ba2CaOsO6 ~Os6+, 5d2transition @50K, but is it similar to Ba2YReO6? • Isoelectronic, isostructural, similar S-O coupling? C. M. Thompson et al. Accepted To JPCM(2014).

  39. mSR measurements of Ba2CaOsO6 • mSR, TRIUMF (Vancouver, BC) • Muon spin precession <50K  indicative of LRO. arXiV:1312.6553

  40. mSR measurements of Ba2CaOsO6 • 3 component fit: • Relaxing precession • Fast relaxation • Slow relaxation • f ~ 0.81 MHz @ base TBint = 60 G • Fast front end ~ 7 ms-1 • Order parameter-like evolution = 0.362Torder 50K

  41. mSR Comparison of Related Samples • Ba2CaOsO6: 5d2 (Os6+), LRO • Ba2YReO6: 5d2 (Re5+), spin-frozen • Ba2YRuO6: 4d3 (Ru5+), Type I fcc AF LRO f1, f2 25-45 MHz • Ba2YRuO6 known ordered moment size = 2.2 mB • Comparison of frq / rlx rates yields estimate of Ba2CaOsO6 ordered moment size: ~0.2 mB.

  42. Comparison to theory • Chen et al. – MF theory for d2 DP’s with SOC • J: NN AF • J’: NNN correlation • V: quadrupolar int. • Ba2CaOsO6 in smallJ/J’ regime • Ground state: AFM100, (or ?) Chen et al. (2010) J’/J vs. V/J

  43. Conclusions • Ba2YMoO6: gapped singlet ground state PRB 84, 100404R (2011). • Perfect cancellation of magnetic interactions to T=0? • Anderson’s RVB realized? • Ba2YRuO6: conventional LRO with a “twist” PRB 88, 014412 (2013). • Gap due to SOC? • Ba2YReO6: spin-frozen ground state PRB 81, 064436 (2010). • Why glassy in the absence of structural disorder? • How to comport with theory? • Ba2CaOsO6: long range order revealed by mSR arXiV:1312.6553. • Why so different from Ba2YReO6? • What is the spatial nature of the ordered state? • Geometric frustration provides a rich playground for exotic physics + diverse ground states. • Double perovskites are a versatile laboratory for studies of frustration! • Neutron scattering + mSR provide unique and complementary information regarding magnetism.

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