Probing magnetism in geometrically frustrated materials using neutron scattering Jeremy P. Carlo In conjunction with B. D. Gaulin, J. J. Wagman, J. P. Clancy, H. A. Dabkowska, T. Aharen and J. E. Greedan, McMaster University Z. Yamani, National Research Council Canada G. E. Granroth, Oak Ridge National Laboratory Villanova Physics / Astronomy “debate,” Jan. 27, 2012 PRB 84, R (2011) 12/3/2015 6:22 AM1

Magnetism in materials Electrons have charge, and also “spin” – Spin  magnetic moment High temps: spins fluctuate rapidly and randomly, but can be influenced by an applied B field – Paramagnetism / Diamagnetism Lower temps: unpaired spins may collectively align, leading to a spontaneous nonzero magnetic moment – Ferromagnetism (FM)e.g. iron, “refrigerator magnets” Or they can anti-align: large local magnetic fields in the material, but zero overall magnetic moment – Antiferromagnetism (AF)e.g. chromium But those are just the simplest cases… 12/3/2015 6:22 AM2

Magnetism & Geometric Frustration The i th and k th spins interact through the “exchange term” in Hamiltonian H ik = -J ik s i  s k J > 0 H ik minimized when s i and s k are parallel: “ferromagnetic coupling” J < 0 H ik minimized when s i and s k are antiparallel: “antiferromagnetic coupling” Simultaneously satisfy for all i,k: (real materials: n ~ ) Geometric frustration: structural arrangement of magnetic ions prevents all interactions from being simultaneously satisfied; this inhibits development of magnetic order: f = |  w | / T order “frustration index” FerromagnetismAntiferromagnetism  W ~ Weiss temperature (measure of strength of interactions) T order ~ actual magnetic ordering temp 12/3/2015 6:22 AM3

Geometric Frustration In 2-D, associated with AF coupling on triangular lattices In a 3-D world, this usually means “quasi-2D systems“ composed of weakly-interacting layers: 12/3/2015 6:22 AM4

Geometric Frustration edge-sharing triangles: triangular lattice corner-sharing triangles: Kagome lattice 12/3/2015 6:22 AM5

Geometric Frustration In 3-D, associated with AF coupling on tetrahedral architectures corner-sharing tetrahedra: pyrochlore lattice edge-sharing tetrahedra: FCC lattice 12/3/2015 6:22 AM6

Geometric Frustration Similar physics in systems with competing interactions, e.g. “J 1 -J 2 ” square-lattice systems “tuned” by the relative strengths of J 1 and J 2 Shastry-Sutherland system moments form orthogonal sets of dimers with spin=0 “spin-singlet state” 12/3/2015 6:22 AM7

Geometric Frustration What happens in frustrated and competing-interaction systems? – 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,” “spin-singlet” – Extreme sensitivity to parameters! – Normally dominant terms in Hamiltonian may cancel, so much more subtle physics can contribute significantly! 12/3/2015 6:22 AM8

Spin-singlet state: QM of two coupled spin- 1 / 2 moments: |S S z > |s z1 s z2 > |1 1 > = |+ +> |1 0 > = 1 / √2 ( |+ –> +|– +> ) |1 -1> = |– –> |0 0 > = 1 / √ 2 ( |+ –> - |– +> ) triplet singlet 12/3/2015 6:22 AM9

Geometric Frustration in Double Perovskite Systems Motivation: While triangular, Kagome, pyrochlore and square-lattice systems have been extensively studied, there have been relatively few studies of frustrated FCC systems. One example: double perovskite lattice with AF-correlated moments. Present study: use inelastic neutron scattering to study one such system, Ba 2 YMoO 6. 12/3/2015 6:22 AM10

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 (spin- 1 / 2 ) cation e.g. Mo 5+ (4d 1 ) Magnetic ions: network of edge-sharing tetrahedra 12/3/2015 6:22 AM11

Neutron Scattering Sample Incoming neutron beam Momentum: k Energy: E Scattered neutron beam Momentum k’ Energy E’ Detector Compare incoming and outgoing beams: Q = k – k’ “scattering vector”  E = E – E’ “energy transfer” Represent momentum or energy Transferred to the sample 12/3/2015 6:22 AM12

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  E-dependence: excitations from ground state If  E = 0, called “neutron diffraction” or “elastic neutron scattering” If  E  0, called “neutron spectroscopy” or “inelastic neutron scattering” 12/3/2015 6:22 AM13

Neutron Diffraction Analogous to x-ray diffraction – Location of “Bragg peaks” reveal position of atoms in structure! Clifford G. Shull ( ), Nobel Prize in Physics /3/2015 6:22 AM14

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” 12/3/2015 6:22 AM15

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) 12/3/2015 6:22 AM16

Triple-axis spectrometry Detector Analyser Sample Mono- chromator Bertram Brockhouse ( ), Nobel Prize in Physics 1994 E3 Spectrometer, Canadian Neutron Beam Centre, Chalk River, Ontario: 12/3/2015 6:22 AM17

Ba 2 YMoO 6 : previous structural work Aharen et al, (2010) Neutron diffraction – Undistorted double perovskite structure 89 Y MAS NMR – ~3% disorder between B and B’ sites => well ordered double perovskite! T = 297K  = 1.33 A T = 288K sim data 12/3/2015 6:22 AM18

Ba 2 YMoO 6 : previous bulk magnetic work Susceptibility – Bulk Paramagnetic (PM) behavior to 2K – Deviation from Curie PM behavior, but no evidence for order – Curie-Weiss:  = 1.73  B (consistent with spin- 1 / 2 )  w = -219(1) K (strong AF correlations) Frustration index f = |  w |/T N > 100 Magnetic neutron diffraction – No magnetic Bragg peaks down to 2.8K Heat Capacity – No -peak: evidence against LRO – Very broad peak in mag. heat capacity near 50K 12/3/2015 6:22 AM19

Ba 2 YMoO 6 : previous local magnetic work Muon Spin Relaxation – No rapid relaxation or precession to 2K: evidence against LRO, spin freezing 89 Y NMR – 2 peaks of comparable intensity 12/3/2015 6:22 AM20

Ba 2 YMoO 6 : previous local magnetic work 89 Y NMR – one peak consistent with paramagnetic state – other consistent with singlet, gapped state gap estimate ~ 140K = 12 meV 12/3/2015 6:22 AM21

Present Measurements: Oak Ridge INS at SNS, ORNL – ~6g loose packed powder – SEQUOIA TOF spectrometer Ei = 60 meV 12/3/2015 6:22 AM22

Present Measurements Analysis: – Assume inelastic signal is coming from three components: 1.Temperature-independent component (“background”) 2.A component which scales with the Bose factor (“phonons”) 3.The magnetic component. – To remove Term 1: subtract empty sample-can data – To remove Term 2: normalize all data by the Bose factor to yield susceptibility  ”(Q,ħ  ), then subtract HT data sets from those at low temperatures. 12/3/2015 6:22 AM23

SNS magnetic scattering  ”(Q, ħ  ) 28 meV: triplet excitation? significant in-gap scattering xfer of spectral weight with T magnetic scattering subsides by T = 125K T=175K subtracted from all data sets 12/3/2015 6:22 AM24

Q- and E- dependence vs. T At low Q,  ” highest at low T => magnetic behavior At high Q,  ” slightly increases w/ T => phonon-like behavior meV (“triplet”) meV, intensity highest at low T Is the same true around meV? A -1 (“low Q”) band: 12/3/2015 6:22 AM25

INS at C5 – ~7g loose packed powder – C5 triple-axis spectrometer = Å Follow-up Measurements: Chalk River 12/3/2015 6:22 AM26

C5 temperature dependence Intensity highest at low T T > ~125K intensity scales with Bose factor ~28 meV (“triplet”) scans: Intensity scales roughly as Bose factor But still some low-T excess! “In-gap” energy scans: 12/3/2015 6:22 AM27

Conclusions: Ba 2 YMoO 6 Our data supports the existence of a spin-singlet ground state – Spectrum dominated by background, phonons Background subtraction, Bose correction, and high-T subtraction to isolate magnetic signal – Apparent magnetic scattering at 28 meV Bandwidth ~ 4 meV Likely triplet excitation from singlet ground state – Some in-gap scattering seen as well – Magnetic scattering subsides at T ~ 125K. 12/3/2015 6:22 AM28