Transcript High Sensitivity Spectroscopy at Reactor Neutron Sources

Neutron Scattering of Frustrated
Antiferromagnets
Collin Broholm
Johns Hopkins University and NIST Center for Neutron Research
Satisfaction without LRO
 Paramagnetic phase
 Low Temperature phase

Spin glass phase
 Long range order
 Spin Peierls like phase


SrCr9pGa12-9pO19
KCr3(OD)6(SO4)2
ZnCr2O4
Conclusions
Supported by the NSF through DMR-9453362 and DMR-0074571
Collaborators
S.-H. Lee
M. Adams
G. Aeppli
E. Bucher
C. J. Carlile
S.-W. Cheong
M. F. Collins
R. W. Erwin
L. Heller
B. Hessen
T. J. L. Jones
T. H. Kim
C. Kloc
N. Lacevic
T. G. Perring
A. P. Ramirez
W. Ratcliff III
NIST and University of MD
ISIS Facility, RAL
NEC Research Institute
University of Konstanz
ISIS Facility, RAL
Bell Labs and Rutgers Univ.
McMaster University
NIST
McMaster University
Bell Labs/Shell
ISIS Facility, RAL
Rutgers University
Bell Labs
Johns Hopkins University
ISIS Facility, RAL
Bell Labs
Rutgers University
A. Taylor
ISIS Facility, RAL
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A simple frustrated magnet:
La4Cu3MoO12
Masaki Azuma et al. (2000)
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Magnetization and order of composite trimer spins
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Theory of spins with AFM interactions on
corner-sharing tetrahedra
What is special about this lattice and this spin system?
• Low coordination number
• Triangular motif
• Infinite set of mean field ground states with zero
net spin on all tetrahedra
• No barriers between mean field ground states
• Q-space degeneracy for spin waves
SPIN TYPE SPIN
VALUE
Isotropic
S= 1/2
Isotropic
S= 
Anisotropic S=
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
LOW T
PHASE
Spin Liquid
METHOD
REFERENCE
Exact Diag.
Spin Liquid
MC sim.
Neel order
MC sim.
Canals and Lacroix
PRL'98
Reimers PRB'92
Moessner, Chalker
PRL'98
Bramwell, Gingras,
Reimers
J. Appl. Phys. '94
9p
12-9p
19
sandwich
Isolated spin dimer
Kagome’-Triangular-Kagome’ sandwich
(111) slab of pyrochlore/spinel AFM
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A. P. Ramirez et al. PRL (1990)
Fe & Cr Jarosite: coupled Kagome’
layers
AM3(OH)6(SO4)2
Material
(D3O)Fe3(SO4)2(OD)6
NaFe3(SO4)2(OD)6
(ND4)Fe3(SO4)2(OD)6
AgFe3(SO4)2(OD)6
RbFe3(SO4)2(OD)6
(D3O)Fe3-xAly(SO4)2(OD)6
KFe3(SO4)2(OD)6
KFe3(CrO4)2(OD)6
KCr3(SO4)2(OD)6
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KCr3(SO
4)2(OD)6
Cr/Fe concentr.
0.97
0.95
0.91
0.89
0.87
0.89
?
?
>0.9
0.8(1)
KCr3(OH)6(CrO4)2
CW (K)
-700(5)
-667(5)
-640(5)
-677(4)
-688(5)
-720(5)
-600
-600
-70(5)
-54(2)
Tf (K)
13.8
42, 62
46,62
51
47
25.5
46
65
1.8
1.55
CW/Tf
51
16, 11
14, 10
13
15
28
13
9
39
34
A. S. Wills et al. (2000)
Townsend et al (1986)
Lee et al. (1997)
ZnCr2O4 : Corner sharing tetrahedra
Material
MgV2O4
ZnV2O4
CdCr2O4
MgCr2O4
ZnCr2O
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4
CW
-750
-600
-83
-350
-392
TN
45
40
9
15
12.5
CW/TN
17
15
9
23
31
Magnetic Neutron Scattering

ki
2

kf
  
Q  ki  k f
  Ei  E f

Q
The scattering cross section is proportional to the
Fourier transformed dynamic spin correlation function

1

it 1
S (Q,  ) 
dt e

2
N
e


 SR (t ) S R ' (0) 
RR '
Fluctuation dissipation theorem:
"Q,   g B   1  e   SQ, 
2
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  
iQ( R  R ')
NIST Center for Neutron
Research
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Detection system on SPINS neutron spectrometer
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Spatial correlation length saturates for T 0
SrCr9pGa12-9pO19
 a
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for
T<CW
Relaxation Rate decreases for T 0
SrCr9pGa12-9pO19
dimer
Kagome’
sandwich
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SrCr9pGa12-9pO19
Paramagnetic state:
Fluctuating AFM spin
clusters that largely satisfy
exchange interactions
Spin glass in concentrated frustrated AFM
Does quenched disorder play a role?
What is structure of SG phases?
What are excitations in SG phases?
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Spin glass transition in SCGO(p=0.92)
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The role of disorder at SG transition
Martinez et al. (1992)
Higher Tf
Higher Cr concentration
Sharper features in S(Q)
Two scenarios remain viable :
A) Strong sensitivity to low levels of disorder
B) Intrinsic disordered frozen phase
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Structure of frozen phase
Short range in plane
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3  3 order
Kagome’ tri-layer correlations
Excitations in a frustrated spin glass
SCGO(p=0.92)
C T   T
T
 "    
    
Gapless 2D Halperin-Saslow
“Spin Waves”
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Long range order in frustrated AFM
Clarify role of symmetry breaking
interactions, quenched disorder and “order
by disorder” effects in stabilizing LRO.
Are there anomalous critical properties at
phase transitions to LRO?
What are the excitations in the ordered
phase of a highly frustrated magnet?
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Phase transition to LRO in Cr-Jarosite
Q0
>90% Cr
75-90% Cr
CW
 40
TN
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3 3
Weak order / strong fluctuations
M q  1.1(3)  B
1
 g B S
3
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Impurity enhanced LRO in (DO3)Fe3-xAly(SO4)2(OD)
Wills et al (1998)
100% Fe
DIntensity (arb)
Only reported
Jarosite w/o
LRO
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Wills et al. (2000)
89% Fe
Diamagnetic
impurities
yield LRO
Magneto-elastic effects in frustrated AFM
Can magneto-elastic coupling relieve
frustration?
What is magnetic and lattice strain
configuration in ordered phase?
Determine energetics of a spin-Peierls like
transition for frustrated magnets.
What are excitations from the ordered
phase?
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First order phase transition in
ZnCr2O4
Dynamics:
• Low energy paramag.
Fluctuations form a
resonance at 4.5 meV
Statics:
• Staggered magnetization
• tetragonal lattice distortion
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Local spin resonance in ordered phase
Paramagnetic
fluctuations in
frustrated AFM
Local spin resonance
in magneto-elastic
LRO phase
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Low T excitations in ZnCr2O4:
Magnetic DOS
Q-dep. of E-integ. intensity
C
C
A: Bragg peaks
B: Spin waves
C: Resonance
D: Upper band
D
B
A
B
A
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Spectra at specific Q
Resonance
Spin waves
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Dispersion relation for resonance
ZnCr2O4 single crystals T=1.5 K
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Structure factor for resonance
ZnCr2O4 T=1.4 K 3 meV    6 meV
Extended sharp
structures in
reciprocal space
Fluctuations satisfy
local constraints
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Comparing resonance to PM fluctuations
  0.7 meV
3 meV    6 meV
1.4 K
15 K
• Paramagnetic fluctuations and resonance satisfy
same local constraints.
• Transition pushes low energy fluctuations into a resonance
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changing spatial correlations
Why does tetragonal strain
encourage Neel order?
Edge sharing n-n exchange in ZnCr2O4 depends strongly on Cr-Cr distance, r
Cr3+
O2-
r

dJ
 40 meV/ A
From series of Cr-compounds:
dr
 a   c dJ
DJ ||

DJ 

2
r0
dr
dJ
 a r0
dr
 0.04 meV
 0.06 meV
The effect for a single tetrahedron is to make 4 bonds more AFM and two bond
are less AFM. This relieves frustration!
Tetragonal dist.
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Magnetic order in ZnCr2O4
-Viewed along tetragonal c-axis
•tetrahedra have zero net moment
=> this is a mean field ground
state for cubic ZnCr2O4
•Tetragonal distortion lowers energy
of this state compared to other
mean field ground states:
D HS
MF
1
 5DJ ||  DJ    0.07 meV
2
•In a strongly correlated magnet
this shift may yield
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k BTN t  D H S
MF
Ftet, Fcub
Analysis of magneto-elastic
transition in ZnCr2O4
Cubic paramagnet
Tetrag. AFM
TC
T
Free energy of the two phases are identical at TC
DF  D H s  D H TcDS  0 
l
D H s  TcDS  D H
l
From this we derive reduction of internal energy of spin system
TcDS
  0.17 meV/Cr
3


a
D H  C  c2  2 a2   0.04 meV/Cr

l 16 11

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D Hs
  0.21meV/Cr
Direct measurement of D H s
confirms validity of analysis
From first moment sum-rule for the dynamic spin correlation function we find

D Hs
3

2


 2   1  e    DS Q,  
0
1
sin Qr0
Qr0
When a single Heisenberg exchange interaction dominates. Inserting magnetic
scattering data acquired at 15 K and 1.7 K we get
D H s  0.35(5) meV
D HS
 k B Tc
D HS

D HS
  where S(Q,) changes
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J
LRO develops from
a strongly
correlated state
Analogies with Spin Peirls transition?
SpinZnCr2 O4
Peirls
Quantum critical above TC
yes
yes
Order suppressed to | T/ CW| < < 1 due to low D frustration
Change of lattice symmetry at TC enables
yes
yes
lower energy spin state
Low energy magnetic spectral weight is
yes
yes
pushed into resonance
Order of phase transition
second
first
Low T phase
isolated
Neel
singlet
LRO
no
yes
TC DS is significant energy scale
There are similarities as well as important distinctions!
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Conclusions
 Low connectivity and triangular motif yields
cooperative paramagnet for|T/CW|<<1.
 The paramagnet consists of small spin clusters with
no net moment, which fluctuate at a rate of order
kBT/ h.
 Spinels can have entropy driven magneto-elastic
transition to Neel order with spin-Peirls analogies.
 The ordered phase has a spin-resonance, as
expected for under-constrained and weakly
connected systems.
 Pyrochlore’s can have a soft mode transition to a
spin-glass even when there is little or no quenched
disorder.
 Variations of sub-leading interactions in pyrochlore’s
give different types of SRO in different compounds.

Lattice
distortions may be a common route to
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ZnCr2O4
Y2Mo2O7
Tetragonal