1 / 50

Adventures in Frustrated Magnetism

Adventures in Frustrated Magnetism. Jeremy P. Carlo Villanova University Jan. 22, 2014 St . Joseph’s University Physics Seminar. Feb. 5, 2014. Outline. Magnetism in solids Chemistry for magnet jocks Magnetic frustration Tools to measure magnetism:

dakota-huff
Download Presentation

Adventures in Frustrated Magnetism

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Adventures in Frustrated Magnetism Jeremy P. Carlo Villanova University Jan. 22, 2014 St. Joseph’s University Physics Seminar Feb. 5, 2014

  2. Outline • Magnetism in solids • Chemistry for magnet jocks • Magnetic frustration • Tools to measure magnetism: Neutron scattering, muon spin relaxation • Magnetism in face-centered cubic systems • Results / Conclusions

  3. Outline • Magnetism in solids • Chemistry for magnet jocks • Magnetic frustration • Tools to measure magnetism: Neutron scattering, muon spin relaxation • Magnetism in face-centered cubic systems • Results / Conclusions

  4. Magnetism in materials • Electrons have charge, and also “spin” • “Spin”  magnetic moment • May also have orbital magnetic moment • The key is… unpaired electrons… 3d 4d 5d 4f 5f

  5. Magnetism in materials Fill according to Hund’s rules: • Why transition metals / lanthanides / actinides? • Number of orbitals per subshell s: 1 orbital p: 3 orbitals d: 5 orbitals f: 7 orbitals Example: 3d s p d f

  6. 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: moments tend to align with field ( > 0) • Diamagnetism: moments tend to align against field ( < 0) • Temp dependence of : (T) = C / T “Curie Paramagnetism” • Real materials: moments do “talk” to each other “Exchange Interaction:” U = ̵ J S1  S2 • Then,(T) = C / (T - CW) “Curie-Weiss behavior”

  7. Magnetism in materials • If the moments “talk” to each other with a nearest-neighbor interaction energy J, when kBT < J the interaction energy dominates over thermal fluctuations • Mean field theory: Torder |CW| • Unpaired spins may collectively align, leading to a spontaneous nonzero magnetic moment • 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)

  8. Outline • Magnetism in solids • Chemistry for magnet jocks • Magnetic frustration • Tools to measure magnetism: Neutron scattering, muon spin relaxation • Magnetism in face-centered cubic systems • Results / Conclusions

  9. http://leadershipfreak.files.wordpress.com/2009/12/frustration.jpghttp://leadershipfreak.files.wordpress.com/2009/12/frustration.jpg

  10. Geometric Frustration • Structural arrangement of magnetic ions prevents all interactions from being simultaneously satisfied; this inhibits development of magnetic order. f= |QCW| / Torder “frustration index” • So f >> 1 means that most of the interaction energy is cancelled out through frustration / competition! • Most common with AF correlations (QCW < 0) CW~ Weiss temperature (measure of strength of interactions) Torder~ actual magnetic ordering tempMFT result: f should be  1

  11. 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 • In a 3-D world , this usually means “quasi-2D systems“ composedof weakly-interacting layers:

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

  13. Geometric Frustration • What happens in frustrated systems? • 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,” “spin-singlet” • Extreme sensitivity to parameters! • 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!

  14. Outline • Magnetism in solids • Chemistry for magnet jocks • Magnetic frustration • Tools to measure magnetism: Neutron scattering, muon spin relaxation • Magnetism in face-centered cubic systems • Results / Conclusions

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

  16. X-Ray / Neutron Scattering Detector 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

  17. X-Ray / Neutron Scattering • How many neutrons are scattered at a given (Q,E) tells you the propensity for the sample to “accept” an excitation at that (Q,E). • Q-dependence: structure / spatial information “diffraction” • E-dependence: excitations from ground state “spectroscopy”

  18. Neutron / X-Ray Diffraction Bragg condition: Constructive interference occurs when n = 2d sin Bonus: neutrons have a magnetic moment, so they reveal magnetic structure too! “Magnetic Bragg peaks”

  19. Muon Spin Relaxation (SR): Probing Local Magnetic Fields Muons: “heavy electrons” or “light protons” Parity violation: muon beam is spin-polarized Muons act as local field “detectors”due to Larmor precession Polarized muon sources: TRIUMF, Vancouver BC PSI, Switzerland ISIS, UK (pulsed) KEK, Japan (pulsed)

  20. Continuous-beam SR

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

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

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

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

  25. 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…

  26. Histograms for opposing counters asy(t) = A0Gz(t) (+ baseline) a Total asymmetry ~0.2-0.3 Muon spin polarization function 135.5 MHz/T Represents muons in a uniform field

  27. Outline • Magnetism in solids • Chemistry for magnet jocks • Magnetic frustration • Tools to measure magnetism: Neutron scattering, muon spin relaxation • Magnetism in face-centered systems • Results / Conclusions

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

  29. 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

  30. Nice thing about perovskites: can make them with almost any element in the periodic table! • Can study a variety of phenomena: colossal magnetoresistance, ferroelectrics, multiferroics, superconductivity, frustration… (Courtesy of J. Rondinelli)

  31. Outline • Magnetism in solids • Chemistry for magnet jocks • Magnetic frustration • Tools to measure magnetism: Neutron scattering, muon spin relaxation • Magnetism in face-centered cubic systems • Results / Conclusions

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

  33. 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).

  34. 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)

  35. Project 1: 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

  36. Project 1: Neutron Scattering Studies of Ba2YMoO6 • However, 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

  37. Project 1: 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! SEQUOIA Beamline Spallation Neutron Source Oak Ridge National Laboratory J. P. Carlo et al, PRB 2011

  38. Project 2: Neutron Scattering Studies of Ba2YRuO6 Heat capacity • Ba2YRuO6: Ru5+ 4d3 • Much more “conventional” behavior qW = -571K T. Aharen et al. PRB 2009

  39. Project 2: Neutron Scattering Studies of Ba2YRuO6 • Clear signs of antiferromagnetic order, but with f ~ 11-15. • Much more “conventional” behavior [100] magnetic Bragg peak J. P. Carlo et al. PRB 2013.

  40. Project 2: Neutron Scattering Studies of Ba2YRuO6 • But the inelastic scattering dependence is much more exotic! J. P. Carlo et al. PRB 2013.

  41. Project 2: Neutron Scattering Studies of Ba2YRuO6 • The ordered state is associated with the formation of 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.

  42. Project 3: Muon Spin Relaxation studies of Ba2CaOsO6 • Ba2YReO6 ~ Re5+, 5d2 ~spin glass ~ 50K • Ba2CaOsO6 ~Os6+, 5d2 orders at 50K, but is it similar to Ba2YReO6? • Isoelectronic, isostructural, lattice match, similar S-O coupling? C. M. Thompson et al. Submitted To PRB (2013).

  43. Project 3: Muon Spin Relaxation studies of Ba2CaOsO6 • Long-livedprecession:sure sign ofLRO! C. M. Thompson et al. Submitted To PRB (2013).

  44. Project 3: Muon Spin Relaxation studies of Ba2CaOsO6 • Precession notseenin “doppelganger”Ba2YReO6, but isseen in Ba2YRuO6! C. M. Thompson et al. Submitted To PRB (2013).

  45. Summary • Frustration is widespread, and of great interest! • Very small differences in composition can lead to vastly different properties. Why? • Structural distortions / moment size / spin-orbit coupling • mSRand neutron scattering are “natural allies” • Ba2YMoO6: spin-singlet state; magnetic order is frustrated away! • Ba2YRuO6: conventional AF order, with a twist due to SOC? • Ba2YReO6: spin-glass, “filling the gap” from Ba2YMoO6 to Ba2YRuO6? • Ba2CaOsO6: how does it fit into the double perovskite “family tree?”

  46. Neutron Diffraction (Q dependence) • Location of “Bragg peaks” reveal position of atoms in structure! Clifford G. Shull (1915-2001), Nobel Prize in Physics 1994

  47. What about the energy dependence? • Tells us about excitations / time dependence • Phonons • Magnetism • To do this we need a way to discriminate between neutrons at different energies! • Triple-axis spectrometry (TAS) • Time-of-flight spectrometry (TOF)

More Related