Transcript Geometric Magnetic Frustration in Double Perovskite Oxides A2BB’O6 Jeremy P. Carlo Department of Physics Villanova University June 2014 Oxides for Energy Meeting, Philadelphia, PA.

Geometric Magnetic Frustration
in Double Perovskite Oxides
A2BB’O6
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
– Muon Spin Relaxation
• Frustration in Double Perovskites
• Results and Conclusions
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Outline
• Magnetism in Materials
• Geometric Frustration
• The Tools:
– Neutron Scattering
– Muon Spin Relaxation
• Frustration in Double Perovskites
• Results and Conclusions
3
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
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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
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Magnetism in materials
• kBT > J: thermal fluctuations dominate
• kBT < J: interaction energy dominates
U = ̵ J S1  S2
(T) = C / (T - CW)
• Expect: Torder  |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)
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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
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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| / Torder
“frustration index”
CW ~ Weiss temperature
Torder ~ actual magnetic ordering temp
MFT: f should be  1
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Geometric Frustration
http://en.wikipedia.org/wiki/File:Herbertsmithite-163165.jpg
Herbertsmithite
• In 2-D, associated
with
AF coupling on ZnCu3(OH6)Cl2
triangular lattices
• edge-sharing triangles:
triangular lattice
•
corner-sharing triangles:
Kagome lattice
• Usually quasi-2D systems
composed of weakly-interacting layers
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Geometric Frustration
• In 3-D, associated with AF coupling
on tetrahedral architectures
corner-sharing tetrahedra:
pyrochlore lattice A2B2O7
edge-sharing tetrahedra:
FCC lattice
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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!
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Outline
• Magnetism in Materials
• Geometric Frustration
• The Tools:
– Neutron Scattering
– Muon Spin Relaxation
• Frustration in Double Perovskites
• Results and Conclusions
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Tools to measure magnetism
• Bulk probes
A
– 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
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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
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Scattering probes Structure and
Dynamics
• Q-dependence: structure / spatial information
– Neutrons can also give magnetic structure
• E-dependence: excitations
– Typically phonons, magnons
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Latest Generation Instruments!
ORNL Spallation Neutron Source
SEQUOIA spectrometer
TOF-resolved 2D detector array gives simultaneous wide
views in Q, E
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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)
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Decay Asymmetry
Muon spin
at decay
Detection:
+ → e+ + + e
e = E / Emax normalized e+ energy
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e+ detector U
incoming
muon counter
sample
e+
+
detector
e+ detector D
D
time
2.5
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e+ detector U
incoming
muon counter
sample
e+
+
detector
e+ detector D
time
D
2.5
U
1.7
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e+ detector U
incoming
muon counter
sample
e+
+
detector
e+ detector D
time
D
2.5
U
1.7
D
1.2
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e+ detector U
incoming
muon counter
sample
e+
+
detector
e+ detector D
time
D
2.5
U
1.7
D
1.2
D
9.0
+ 106-107 more…
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Histograms for
opposing counters
asy(t) = A0 Gz(t)
(+ baseline)
135.5 MHz/T
Represents
muons in a
uniform field
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Outline
• Magnetism in Materials
• Geometric Frustration
• The Tools:
– Neutron Scattering
– Muon Spin Relaxation
• Frustration in Double Perovskites
• Results and Conclusions
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Face-Centered Systems
• Very common crystal structure
“rock salt order” ~ NaCl
• Tetrahedral Coordination
+
AF Correlations
=
Geometric Frustration
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• 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
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• Nice thing about perovskites: can make them
with almost any element in the periodic table!
(Courtesy of
J. Rondinelli)
• Variety of phenomena / applications: CMR,
multiferroics, photovoltaics, superconductivity, catalysis,
frustration…
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Our survey
• Goal: systematic survey of face-centered
frustrated systems using SR and neutron
scattering.
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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:
– Effects of spin-orbit coupling:
s=3/2
s=1
Larger moments
More “classical”
More amenable to
bulk probes + neutrons
nd1
nd2
nd3
L-S
s=1/2
s=1
s=3/2 =
s=1/2
Smaller moments
More “quantum”
More difficult
to measure
J-J
j=3/2 Chen et al. PRB 82,
174440 (2010).
j=2
j=3/2 Chen et al. PRB 84,
194420 (2011).
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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,
• La2LiReO6: monoclinic,
• Ba2CaOsO6: cubic,
spin freezing TG ~ 50 K (f ~ 12)
singlet ~ 50 K (f ~ 5)
AF LRO @ 50 K (f ~ 2.5)
– 4d1, 5d1: (s=1/2 or jeff=3/2)
•
•
•
•
Sr2MgReO6: tetragonal,
Sr2CaReO6: monoclinic,
La2LiMoO6: monoclinic,
Ba2YMoO6: cubic,
spin freezing TG ~ 50 K (f ~ 8)
spin freezing TG ~ 14 K (f ~ 32)
SR correlations < 20 K (f ~ 1)
singlet ~ 125K (f > 100)
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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
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Neutron Scattering Studies of
Ba2YMoO6
• 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
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Neutron Scattering Studies of
Ba2YMoO6
• Resolution comes from inelastic neutron scattering.
• What’s happening? At low temps, neighboring moments pair
up, to form “singlets.”
J. P. Carlo et al, PRB 2011
• But no long range order!
SEQUOIA Beamline
Spallation Neutron Source
Oak Ridge National Laboratory
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Neutron Scattering Studies of
Heat capacity
Ba2YRuO6
• Ba2YRuO6: Ru5+
4d3
• Much more “conventional” behavior…?
qW = -571K
T. Aharen et al. PRB 2009
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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.
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Neutron Scattering Studies of
Ba2YRuO6
• But the inelastic scattering dependence is much more exotic!
J. P. Carlo et al. PRB 2013.
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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.
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Muon Spin Relaxation studies of
Ba2CaOsO6 + Ba2YReO6
• Ba2YReO6
~ Re5+, 5d2 ~spin glass ~ 50K
• Ba2CaOsO6 ~Os6+, 5d2
transition @50K, but is it similar to Ba2YReO6?
• Isoelectronic, isostructural, similar S-O coupling?
C. M. Thompson
et al. Accepted
To JPCM (2014).
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SR measurements of Ba2CaOsO6
• SR, TRIUMF
(Vancouver, BC)
• Muon spin
precession <50K
 indicative of LRO.
arXiV:1312.6553
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SR measurements of Ba2CaOsO6
• 3 component fit:
– Relaxing precession
– Fast relaxation
– Slow relaxation
• f ~ 0.81 MHz @ base T
Bint = 60 G
• Fast front end ~ 7 s-1
• Order parameter-like
evolution
 = 0.362
Torder  50K
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SR 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 B
• Comparison of frq / rlx rates yields
estimate of Ba2CaOsO6 ordered
moment size: ~0.2 B.
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Comparison to theory
• Chen et al. – MF theory for d2 DP’s with SOC
– J: NN AF
– J’: NNN correlation
– V: quadrupolar int.
Chen et al. (2010)
J’/J vs. V/J
• Ba2CaOsO6 in small
J/J’ regime
– Ground state:
AFM100, (or ?)
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Conclusions
• Ba2YMoO6: gapped singlet ground state
PRB 84, 100404R (2011).
• Ba2YRuO6: conventional LRO with a “twist”
PRB 88, 014412 (2013).
• Ba2YReO6: spin-frozen ground state
PRB 81, 064436 (2010).
• Ba2CaOsO6: long range order revealed by SR
arXiV:1312.6553.
– Perfect cancellation of magnetic interactions to T=0?
– Anderson’s RVB realized?
– Gap due to SOC?
– Why glassy in the absence of structural disorder?
– How to comport with theory?
– 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 + SR provide unique and complementary information
regarding magnetism.
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