Probing magnetism in geometrically frustrated materials using

neutron scattering

Jeremy P. CarloIn 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 CanadaG. E. Granroth, Oak Ridge National Laboratory

Villanova Physics / Astronomy “debate,” Jan. 27, 2012

PRB 84, 100404R (2011)

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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…

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Magnetism & Geometric Frustration• The ith and kth spins interact through the “exchange term” in Hamiltonian

Hik = -Jik si sk

J > 0 Hik minimized when si and sk are parallel: “ferromagnetic coupling”

J < 0 Hik minimized when si and sk are antiparallel: “antiferromagnetic coupling”

• Simultaneously satisfy for all i,k:(real materials: n ~ 1023)

• Geometric frustration: structural arrangement of magnetic ions prevents all interactions from being simultaneously satisfied; this inhibits development of magnetic order:

f = |w| / Torder “frustration index”

Ferromagnetism Antiferromagnetism

W ~ Weiss temperature (measure of strength of interactions)Torder ~ actual magnetic ordering temp

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Geometric Frustration• In 2-D, associated with

AF coupling on triangular lattices

• In a 3-D world , this usually means “quasi-2Dsystems“ composedof weakly-interactinglayers:

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Geometric Frustration

• edge-sharing triangles: triangular lattice

• corner-sharing triangles: Kagome lattice

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Geometric Frustration• In 3-D, associated with AF coupling

on tetrahedral architectures

corner-sharing tetrahedra:pyrochlore lattice

edge-sharing tetrahedra:FCC lattice

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Geometric Frustration• Similar physics in systems with competing interactions, e.g.

“J1-J2” square-lattice systems“tuned” by the relativestrengths of J1 and J2

Shastry-Sutherland systemmoments form orthogonal sets of dimers with spin=0“spin-singlet state”

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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!

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Spin-singlet state:QM of two coupled spin-1/2 moments:

|S Sz> |sz1 sz2>

|1 1 > = |+ +>

|1 0 > = 1/√2( |+ –> +|– +> )

|1 -1> = |– –>

|0 0 > = 1/√2( |+ –> - |– +> )

triplet

singlet

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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, Ba2YMoO6.

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• Double perovskite lattice:– A2BB’O6

e.g. Ba2YMoO6

A: divalent cation e.g. Ba2+

B: nonmagnetic cation e.g. Y3+

B’: magnetic (spin-1/2) cation e.g. Mo5+ (4d1)

Magnetic ions: network of edge-sharing tetrahedra

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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 energyTransferred to the sample

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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”

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Neutron Diffraction• Analogous to x-ray diffraction

– Location of “Bragg peaks” reveal position of atoms in structure!

Clifford G. Shull (1915-2001), Nobel Prize in Physics 1994

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Neutron / X-Ray DiffractionBragg condition:

Constructive interference occurs whenn = 2d sin

Bonus: neutrons have a magnetic moment, so they reveal magnetic structure too! “Magnetic Bragg peaks”04/18/23 17:59 15

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)

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Triple-axis spectrometryDetector

Analyser

Sample

Mono-chromator

Bertram Brockhouse (1918-2003),Nobel Prize in Physics 1994

E3 Spectrometer,Canadian Neutron Beam Centre,Chalk River, Ontario:

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Ba2YMoO6: previous structural work

• Aharen et al, (2010)

• Neutron diffraction– Undistorted double

perovskite structure

• 89Y MAS NMR– ~3% disorder between B and B’

sites

=> well ordered double perovskite!

T = 297K= 1.33 A

T = 288K

sim

data

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Ba2YMoO6: 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|/TN > 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 50K04/18/23 17:59 19

Ba2YMoO6: previous local magnetic work

• Muon Spin Relaxation– No rapid relaxation

or precession to 2K:evidence against LRO, spin freezing

• 89Y NMR

– 2 peaks of comparable intensity

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Ba2YMoO6: previous local magnetic work

• 89Y NMR

– one peak consistent with paramagnetic state

– other consistent with singlet,gapped state

gap estimate ~ 140K = 12 meV

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Present Measurements: Oak Ridge

• INS at SNS, ORNL– ~6g loose packed powder– SEQUOIA TOF spectrometer

• 6K-290K @ Ei = 60 meV

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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.

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SNS magnetic scattering ”(Q, ħ)

28 meV: triplet excitation?

significant in-gap scattering

xfer of spectral weight with T

magnetic scattering subsidesby T = 125K

T=175K subtracted from all data sets

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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

26-31 meV (“triplet”) band:

@~28 meV, intensity highest at low T

Is the same true around 15-20 meV?

1.5-1.8 A-1 (“low Q”) band:

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• INS at C5– ~7g loose packed powder– C5 triple-axis spectrometer

• 3K-300K @ = 1.638 Å

Follow-up Measurements: Chalk River

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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:

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Conclusions: Ba2YMoO6• 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.

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