Transcript Probing magnetism in the geometrically frustrated

Probing magnetism in the geometrically
frustrated antiferromagnet Ba2YMoO6
using inelastic neutron scattering
Jeremy P. Carlo
Villanova University
PRB 84, 100404R (2011)
In conjunction with
B. D. Gaulin, J. P. Clancy , J. J. Wagman, H. A. Dabkowska,
H. M. L. Noad, T. Aharen and J. E. Greedan, McMaster University
Z. Yamani, National Research Council Canada
G. E. Granroth, Oak Ridge National Laboratory
UT condensed matter seminar, Knoxville, TN 4/24/2012
Outline
• Magnetism in Materials
– Frustration, Singlet states
• The Double Perovskite structure
• Magnetism in double perovskites
• Ba2YMoO6 characterization
• INS results on Ba2YMoO6
• Conclusions
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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:
(nearest-neighbor couplings)
Ferromagnetism
Antiferromagnetism
• Frustration: structural arrangement of magnetic ions prevents all
interactions from being simultaneously satisfied; this inhibits
development of magnetic order to lower temps:
f = |Qw| / Torder
“frustration index”
QW ~ Weiss temperature
Torder ~ actual magnetic ordering temp
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Geometric Frustration
• In 2-D systems, associated with triangular
architectures:
edge-sharing triangles:
triangular lattice
e.g. NaCrO2, CsMnBr3
corner-sharing triangles:
Kagome lattice
e.g. herbertsmithite, volborthite
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Geometric Frustration
• In 3-D systems, associated with tetrahedrally
coordinated lattices:
corner-sharing tetrahedra:
e.g. pyrochlore lattice
edge-sharing tetrahedra:
FCC lattice
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Geometric Frustration
• What happens in frustrated systems?
– Sometimes magnetic LRO at sufficiently low T << |Qw|
– Sometimes a “compromise” static state:
e.g. spin-ice, helimagnetism, spin glass
– Sometimes 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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Competing Interactions
• Similar physics is sometimes seen in systems with competing
interactions, e.g.
“J1-J2” square-lattice systems
“tuned” by the relative
strengths of J1 and J2
Shastry-Sutherland system
moments form orthogonal sets
of dimers with spin=0
“spin-singlet state”
Spin-singlet state:
QM of two coupled spin-1/2 moments:
|S Sz> |sz1 sz2>
|1 1 > = |+ +>
|1 0 > = 1/√2( |+ –> +|– +> )
triplet
|1 -1> = |– –>
|0 0 > = 1/√2( |+ –> - |– +> )
singlet
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•
•
•
•
Singlet state in SrCu2(BO3)2
Expt’l realization of Shastry-Sutherland model:
Singlet ground state below ~10 K
Formation of orthogonal dimers in 2-D plane
Triplet, 2-Triplet @ E = 3, 4.85 meV
Kageyama et al. PRL 82, 3168 (1999)
• SrCu2-xMgx(BO3)2, x ~ 0.05
Haravifard et al. PRL 97,
247206 (2006)
• disorder: in-gap spin-polaron states
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Gaulin et al. PRL 93, 267202 (2004)
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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Work on other Double Perovskites
• Spin-3/2 systems
Aharen et al. PRB 80, 134423 (2009)
– Ba2YRuO6 Ru5+: 4d3
• Qw = -522 K (AF coupling)
• LR AFO @ 36 K (f  15)
• SR AFO @ higher temps
(peak in  @ 47 K)
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Work on other Double Perovskites
• Similar results in La2LiRuO6
– s = 3/2
– Monoclinic P21/n: weakens superexchange
– Qw = -184 K
– LR AFO below 24 K (f  8)
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Work on other Double Perovskites
• Spin-1 systems
(T. Aharen et al. PRB 81, 064436 (2010))
– Ba2YReO6 Re5+: 5d2
• Qw = -616 K
• Heat capacity, lack of magnetic Bragg peaks: no LRO
• But SR: fast relaxation <~50K: spin freezing
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Work on other Double Perovskites
• Compare to La2LiReO6:
–
–
–
–
s=1
Monoclinic P21/n, Qw = -204 K
No evidence for LRO in Cp or neutron diff.
SR: collective spin-singlet state, T < ~40 K
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Work on other Double Perovskites
• Going to the extreme spin-1/2 limit:
– Sr2CaReO6 (Wiebe et al.
PRB 65, 14413 (2002)
• Re6+: 5d1,
Qw = -443 K
• P21/n monoclinic structure
• spin-glass state below TG ~ 14 K
– Sr2MgReO6 (Wiebe et al.
PRB 68, 134410 (2003)
– La2LiMoO6 (Aharen et al.
PRB 81, 224409 (2010)
• I4/m tetragonal structure, Qw = -426 K
• Glassy state below TG ~ 50 K
•
•
•
Mo5+: 4d1
P21/n monoclinic structure
SR: oscillations below 20K indicate
short-range correlations
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Comparison of Double Perovskite
Systems
– Spin-3/2:
• Ba2YRuO6: cubic, AF LRO @ 36 K (f ~ 15)
• La2LiRuO6: monoclinic, AF LRO @ 24 K (f ~ 8)
– Spin-1:
• Ba2YReO6: cubic,
spin freezing ~ 50 K (f ~ 12)
• La2LiReO6: monoclinic, spin singlet ~ 50 K (f ~ 5)
– Spin-1/2:
• La2LiMoO6: monoclinic, SR correlations < 20 K (f ~ 1)
• Sr2MgReO6: tetragonal, spin freezing TG ~ 50 K (f ~ 8)
• Sr2CaReO6: monoclinic, spin freezing TG ~ 14 K (f ~ 32)
• Ba2YMoO6: s=1/2, retains cubic symmetry, f > 100!…
Ba2YMoO6: previous structural work
• Aharen et al.
PRB 81 224409 (2010)
T = 297K
l = 1.33 A
• Neutron diffraction
– Cubic Fm3m, a = 8.3827 A
– no evidence for J-T or other
lattice distortion
•
89Y
MAS NMR
– ~3% disorder between B (Y) and
B’ (Mo) sites
T = 288K
sim
data
=> well ordered double perovskite!
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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)
• Qw = -219(1) K (strong AF correlations)
• Frustration index f = |Qw|/TN > 100
• Neutron diffraction
– No magnetic Bragg peaks down to 2.8K
• Heat Capacity
– No l-peak:
evidence against LRO
– Very broad peak in mag.
heat capacity near 50K
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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: SNS
• 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,ħw), then subtract HT data
sets from those at low temperatures.
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SNS magnetic scattering ”(Q, ħw)
28 meV: triplet excitation?
T=175K subtracted
from all data sets
significant in-gap scattering
xfer of spectral weight with T
magnetic scattering subsides
by T = 125K
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Q- and E- dependence vs. T
26-31 meV (“triplet”) band:
At low Q, ” highest at low T
=> magnetic behavior
At high Q, ” slightly increases w/ T
=> phonon-like behavior
1.5-1.8 A-1 (“low Q”) band:
@~28 meV, intensity highest at low T
Is the same true around 15-20 meV?
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Follow-up Measurements: Chalk River
• INS at C5
– ~7g loose packed powder
– C5 triple-axis spectrometer
• 3K-300K @ l = 1.638 Å
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C5 temperature dependence
~28 meV (“triplet”) scans:
Intensity highest at low T
T > ~125K intensity scales
with Bose factor
“In-gap” energy scans:
Intensity scales roughly
as Bose factor
But still some low-T excess!
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Conclusions: Ba2YMoO6
• Ba2YMoO6: well-ordered double perovskite, maintains cubic
structure, extreme s = ½ limit
• Our INS data supports the existence of a gapped singlet
ground state:
• Apparent magnetic scattering at 28 meV
– Bandwidth ~ 4 meV
– Likely triplet excitation from singlet ground state
– Magnetic scattering subsides by T ~ 125K
SCBO:
• Possible analogy to SrCu2(BO3)2, with
T ~ 10 K
E ~ 3 meV
E, T scales ~10x larger?
• In-gap scattering reminiscent of disorder-induced spinpolaron states in Mg-doped SrCu2(BO3)2
– Due to ~3% B-site disorder?
– Or intrinsic to FCC with spin-orbit coupling?
• Mix of “old” and “new” – TOF & TAS
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