1. 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

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

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

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 4

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 / TCurie Paramagnetism Real materials: moments do interact Exchange Interaction: U = ̵ J S 1  S 2 Then,  (T) = C / (T -  CW ) Curie-Weiss behavior 5

6. Magnetism in materials k B T > J: thermal fluctuations dominate k B T < J: interaction energy dominates Expect: T order  |  CW | Spins may collectively align, leading to a spontaneous nonzero magnetization – Ferromagnetism (FM)(J,  CW > 0) Or they can anti-align: large local magnetic fields in the material, but zero overall magnetic moment – Antiferromagnetism (AF)(J,  CW < 0)  (T) = C / (T -  CW ) U = ̵ J S 1  S 2 6

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

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 = |  CW | / T order “frustration index”  CW ~ Weiss temperature T order ~ actual magnetic ordering temp MFT: f should be  1 8

9. Geometric Frustration In 2-D, associated with AF coupling on triangular lattices edge-sharing triangles: triangular lattice corner-sharing triangles: Kagome lattice Usually quasi-2D systems composed of weakly-interacting layers http://en.wikipedia.org/wiki/File:Herbertsmithite-163165.jpg Herbertsmithite ZnCu 3 (OH 6 )Cl 2 9

10. Geometric Frustration In 3-D, associated with AF coupling on tetrahedral architectures corner-sharing tetrahedra: pyrochlore lattice A 2 B 2 O 7 edge-sharing tetrahedra: FCC lattice 10

11. Geometric Frustration What happens in frustrated systems? – Huge degeneracy of ground states! Sometimes magnetic LRO at sufficiently low T << |  w | 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! 11

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

13. Tools to measure magnetism 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 A 13

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

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

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

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

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19. Decay Asymmetry Muon spin at decay  = E / E max normalized e + energy Detection:  + → e + +   + e 19

20. e+e+ e+ detector U sample  e+ detector D detectortime D 2.5 incoming muon counter 20

21. e+e+ e+ detector U sample  e+ detector D detectortime D 2.5 U 1.7 incoming muon counter 21

22. e+e+ e+ detector U sample  e+ detector D detectortime D 2.5 U 1.7 D 1.2 incoming muon counter 22

23. e+e+ e+ detector U sample  e+ detector D detectortime D 2.5 U 1.7 D 1.2 D 9.0 incoming muon counter + 10 6 -10 7 more… 23

24. Represents muons in a uniform field 135.5 MHz/T Histograms for opposing counters asy(t) = A 0 G z (t) (+ baseline) 24

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26. Outline Magnetism in Materials Geometric Frustration The Tools: – Neutron Scattering – Muon Spin Relaxation Frustration in Double Perovskites Results and Conclusions 26

27. Face-Centered Systems Very common crystal structure “rock salt order” ~ NaCl Tetrahedral Coordination + AF Correlations = Geometric Frustration 27

28. Example: Double perovskite lattice: – A 2 BB’O 6 e.g. Ba 2 YMoO 6 A: divalent cation e.g. Ba 2+ B: nonmagnetic cation e.g. Y 3+ B’: magnetic (s=½) cation e.g. Mo 5+ (4d 1 ) Magnetic ions: edge-sharing tetrahedral network 28

29. 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) 29

30. Our survey Goal: systematic survey of face-centered frustrated systems using  SR and neutron scattering. 30

31. 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=3/2s=1s=1/2 – Effects of spin-orbit coupling: Smaller moments More “quantum” More difficult to measure Larger moments More “classical” More amenable to bulk probes + neutrons L-S J-J nd 1 s= 1 / 2 j= 3 / 2 nd 2 s=1 j=2 nd 3 s= 3 / 2 = j= 3 / 2 Chen et al. PRB 82, 174440 (2010). Chen et al. PRB 84, 194420 (2011). 31

32. Comparison of Double Perovskite Systems: A “Family Portrait” – 4d 3 : (s= 3 / 2 or j eff = 3 / 2 : L-S vs. J-J pictures) Ba 2 YRuO 6 : cubic, AF LRO @ 36 K (f ~ 15) La 2 LiRuO 6 : monoclinic, AF LRO @ 24 K (f ~ 8) – 5d 2 : (s=1 or j eff =2) Ba 2 YReO 6 : cubic, spin freezing T G ~ 50 K (f ~ 12) La 2 LiReO 6 : monoclinic, singlet ~ 50 K (f ~ 5) Ba 2 CaOsO 6 : cubic, AF LRO @ 50 K (f ~ 2.5) – 4d 1, 5d 1 : (s= 1 / 2 or j eff = 3 / 2 ) Sr 2 MgReO 6 : tetragonal, spin freezing T G ~ 50 K (f ~ 8) Sr 2 CaReO 6 : monoclinic, spin freezing T G ~ 14 K (f ~ 32) La 2 LiMoO 6 : monoclinic, SR correlations < 20 K (f ~ 1) Ba 2 YMoO 6 : cubic, singlet ~ 125K (f > 100) 32

33. Neutron Scattering Studies of Ba 2 YMoO 6 Ba 2 YMoO 6 : Mo 5+ 4d 1 Maintains ideal cubic structure;  CW = -219K but no order found down to 2K: f > 100! XRD T = 297K  = 1.33 A Susceptibility Neutron diffraction T. Aharen et al. PRB 2010 33

34. Neutron Scattering Studies of Ba 2 YMoO 6 Heat capacity shows a broad peak And NMR shows two signals, one showing the development of a gap at low temperatures But  SR shows nothing…. T. Aharen et al. PRB 2010 34

35. Neutron Scattering Studies of Ba 2 YMoO 6 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 35

36. Neutron Scattering Studies of Ba 2 YRuO 6 Ba 2 YRuO 6 :Ru 5+ 4d 3 Much more “conventional” behavior…? Heat capacity  W = -571K T. Aharen et al. PRB 2009 36

37. Neutron Scattering Studies of Ba 2 YRuO 6 Clear signs of antiferromagnetic order, but with f ~ 11-15. [100] magnetic Bragg peak J. P. Carlo et al. PRB 2013. 37

38. Neutron Scattering Studies of Ba 2 YRuO 6 But the inelastic scattering dependence is much more exotic! J. P. Carlo et al. PRB 2013. 38

39. Neutron Scattering Studies of Ba 2 YRuO 6 The ordered state is associated with a gap. Interesting: E gap  k B T order But why should such a gap exist? Suggestive of exotic physics: relativistic spin-orbit coupling! J. P. Carlo et al. PRB 2013. 39

40. Muon Spin Relaxation studies of Ba 2 CaOsO 6 + Ba 2 YReO 6 Ba 2 YReO 6 ~ Re 5+, 5d 2 ~spin glass ~ 50K Ba 2 CaOsO 6 ~Os 6+, 5d 2 transition @50K, but is it similar to Ba 2 YReO 6 ? Isoelectronic, isostructural, similar S-O coupling? C. M. Thompson et al. Accepted To JPCM (2014). 40

41.  SR measurements of Ba 2 CaOsO 6  SR, TRIUMF (Vancouver, BC) Muon spin precession <50K  indicative of LRO. arXiV:1312.6553 41

42.  SR measurements of Ba 2 CaOsO 6 3 component fit: – Relaxing precession – Fast relaxation – Slow relaxation f ~ 0.81 MHz @ base T B int = 60 G Fast front end ~ 7  s -1 Order parameter-like evolution  = 0.362 T order  50K 42

43.  SR Comparison of Related Samples Ba 2 CaOsO 6 : 5d 2 (Os 6+ ), LRO Ba 2 YReO 6 : 5d 2 (Re 5+ ), spin-frozen Ba 2 YRuO 6 : 4d 3 (Ru 5+ ), Type I fcc AF LRO f 1, f 2  25-45 MHz Ba 2 YRuO 6 known ordered moment size = 2.2  B Comparison of frq / rlx rates yields estimate of Ba 2 CaOsO 6 ordered moment size: ~0.2  B. 43

44. Comparison to theory Chen et al. – MF theory for d 2 DP’s with SOC – J: NN AF – J’: NNN correlation – V: quadrupolar int. Ba 2 CaOsO 6 in small J/J’ regime – Ground state: AFM100,  (or  ?) 44 Chen et al. (2010) J’/J vs. V/J

45. Conclusions Ba 2 YMoO 6 : gapped singlet ground state PRB 84, 100404R (2011). – Perfect cancellation of magnetic interactions to T=0? – Anderson’s RVB realized? Ba 2 YRuO 6 : conventional LRO with a “twist” PRB 88, 014412 (2013). – Gap due to SOC? Ba 2 YReO 6 : spin-frozen ground state PRB 81, 064436 (2010). – Why glassy in the absence of structural disorder? – How to comport with theory? Ba 2 CaOsO 6 : long range order revealed by  SR arXiV:1312.6553. – Why so different from Ba 2 YReO 6 ? – 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 +  SR provide unique and complementary information regarding magnetism. 45