Holes in a Quantum Spin Liquid

Report
Spinons,
Solitons, &
and
Breathers
Frustrated
Magnetism
Heavy
Fermions
in Quasi-one-dimensional Magnets
Collin Broholm
Johns Hopkins University &
NIST Center for Neutron Research
10/24/01
SCES 2004 Karlsruhe, Germany 7/29/2004
PPHMF-IV
1
Overview
 Introduction
 Frustrated magnetism in insulators
– Order from competing interactions
– Near critical systems
– Quantum liquids
 Metals with frustrated magnetism
– Spinel vanadates
– Spinels with rare earth ions
– Frustration in heavy fermions?
 Conclusions
SCES04 7/29/04
Acknowledgements
Ni3V2O8
G. Lawes, M. Kenzelmann, N. Rogado, K. H. Kim, G. A.
Jorge, R. J. Cava, A. Aharony, O. Entin-Wohlman, A. B.
Harris, T. Yildirim, Q. Z. Huang, S. Park, and A. P.
Ramirez
ZnCr2O4
S.-H. Lee, W. Ratcliff II, S.-W. Cheong, T. H. Kim, Q.
Huang, and G. Gasparovic
PHCC
M. B. Stone, I. A. Zaliznyak, Daniel H. Reich
PrxBi2-xRu2O7
J. van Duijn, K.H. Kim, N. Hur, D. T. Adroja, M. Adams,
Q. Z. Huang, S.-W. Cheong, and T.G. Perring
V2O3
Wei Bao, G. Aeppli, C.D. Frost, T. G. Pering, P. Metcalf,
J. M. Honig
SCES04 7/29/04
Destabilizing Static LRO
Frustration: All spin pairs cannot simultaneously
be in their lowest energy configuration
Frustrated
Weak connectivity: Order in one part of lattice does not
constrain surroundings
SCES04 7/29/04
Effective low dimensionality from frustration
1. Assume Neel order, derive spin wave dispersion relation
2. Calculate the reduction  S in staggered magnetization
due to quantum fluctuations
3. If  S  S then Neel order is an inconsistent assumption
1 1
1 d Q g Q
 
S 
S
S


R
R

R
2S N
2S vBZ  Q
3

 S diverges if  Q  0 on planes in Q-space
SCES04 7/29/04
Frustration + weak connectivity can produce
local soft modes that destabilize Neel order
Si  0
Renormalized Classical
T/J
Si  0
H, P, x, 1/S…
Magnetism on a kagome’ Staircase
Ni3V2O8
c
— S=½ spinons above small gap
— S=∞ No order or spin glass
— Ising no phase transition
— XY Critical at T=0
SCES04 7/29/04
a
b
Order from kagome’ critical state
8 H║a
6
4
C’
2
0
8
H(T)
(a)
LTI
HTI
P
C
(b)
H║b
6
4
C
2
LTI
HTI
P
C’
0
8
(c)
H║c
6
4
C
2
0
SCES04 7/29/04
C’
0
HTI
P
LTI
TCC’
TLC
6 THL
Temperature (K)
TPH
12
Non-collinear order from competition
Anisotropy overpowers
NNN interaction
T<2.1 K
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Spiral reduces
Amplitude modulation
T<6.5K
Spine ANNNI model
T<9 K
Kenzelmann et al. (2004)
From quasi-elastic to local resonance
T=30 K
T=1.5
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Si  0
Near Quantum Critical
Renormalized Classical
T/J
?
Si  0
H, P, x, 1/S…
Frustration and short range correlations
CW
Compound Spin CW (K) Order
1
MgTi2O4
Singlet?
2
MgV2O4
ZnV2O4
CdCr2O4
1
1
TC (K)
260
3
2
-750
-600
-83
Orbital/AFM -/45
Orbital/AFM -/40
AFM
9
MgCr2O4
3
2
-350
AFM
15
ZnCr2O4
3
2
-392
AFM
12.5
TN<T<|CW| : Short range correlations
SCES04 7/29/04
TN<T<|CW| : Dynamic Short Range Order
Points of interest:
• 2p/Qr0=1.4
⇒ nn. AFM correlations
• No scattering at low Q
⇒ satisfied tetrahedra
SCES04 7/29/04
S.-H. Lee et al. PRL (2000)
T<TN : Resonant mode and spin waves
Points of interest:
• 2p/Qr0=1.4
⇒ nn. AFM correlations
• No scattering at low Q
⇒ satisfied tetrahedra
• Resonance for ħ ≈ J
• Low energy spin waves
SCES04 7/29/04
S.-H. Lee et al. PRL (2000)
Average form factor for AFM hexagons
+
▬
nˆ
▬
+
▬
+
I Q  
 Fnˆ Q
2
nˆ  111
 p 
p
p 
 sin h  cos k  cos l  
2
2 
 2 
SCES04 7/29/04
S.-H. Lee et al. Nature (2002)
2
 p 
p
p 
 sin k  cos l  cos h  
2
2 
 2 
2
 p 
p
p 
 sin l  cos h  cos k  
2
2 
 2 
2
Tchernyshyov et al. PRL (2001)
Sensitivity to impurities near quantum criticality
TN
Tf
Ratcliff et7/29/04
al. PRB (2002)
SCES04
Low T spectrum sensitive to bond disorder
5% Cd
0
SCES04 7/29/04
0.5
1.0
1.5
Q (Å-1)
2.0
2.5
Si  0
Si  0
?
Quantum Paramagnet
Near Quantum Critical
T/J
Si  0
H, P, x, 1/S…
c/cmax
Singlet Ground state in PHCC
J1=12.5 K
a=0.6
T J1
SCES04 7/29/04
Daoud et al., PRB (1986).
 (meV)
2D dispersion relation
1
0
h
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1
0
l
Neutrons can reveal frustration
The first  -moment of scattering cross section equals
“Fourier transform of bond energies”
2
1 1
  d  S (Q, )   3 N
H  12  J dSr  Sr d
J
d
 Sr  Sr d  1  cos Q  d 
rd
d4
d3
rd
d1
d2
bond energies are small if J d and/or  S r  S r d  small
Positive terms correspond to “frustrated bonds”
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Frustrated bonds in PHCC
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.
di
Jd<S0 Sd>
1
2
3
4
5
6
7
8
-1.4(3)
0.6(3)
-0.4(1)
-0.2(3)
0.1(3)
-0.95(5)
0.1(2)
0.6(2)
Green colored bonds increase ground state energy
The corresponding interactions are frustrated
Si  0
Near Quantum Critical
T/J
?
Si  0
H, P, x, 1/S…
Colossal T-linear C(T) in PrxBi2-xRu2O7
0.8
2.0
PrxBi2-xRu2O7
10
5
3
10
4
2
10
3
10
2
10
1
10
0
K
Pr1.03Bi
Ru2O7
1.0
4
C (J/mol K)
x=2.0
4K
1
 ( cm)
2
1.6
0.6
1.4
0.5
1.2
6
1.5
0
0.0
0.4
1.0
1.0
1.2
0.8
0.3
0.6
0.2
0.4
0.0
20
20
40
40
1.5
2.0
0T
Y2Ru2O
37T
6T
12 T
18 T
0.4
0.0
0.0
0.8 00
1.0
Pr (x)H=
0.9
0.1
0.2
0.5
22
60
60
80
80
100
100
2
T (K
(K))Pr1.0Bi1.0Ru2O7
T
0.7
y=2.0
NH182
10
-1
10
-2
10
-3
10
-4
2.0x10
PryBi2-yRu2O7
1.6
NH192
0
1.6x10
2
C/T (J/mol K )
0.6
 ( cm)
0.5
0.4
H= 0 T
3T
6T
12 T
18 T
0.2
0.1
0.0
0
20
40
60
2
SCES04 7/29/04
80
150
T (K)
100
1.4x10
-3
1.2x10
-3
1.0x10
-3
8.0x10
-4
6.0x10
-4
4.0x10
-4
2.0x10
-4
0.0
200
250
300
NH181a
KHKim
NH81
y=1.2
-3
NH167
1.0
1.1
NH180a
0.9
JA5a
1.0
NH201
NH202
NH193
1.0
0.95
0.5
0
2
T (K )
100
04/15/02
-3
1.8x10
0.3
50
-3
PryBi2-yRu2O1.0
7
K. H. Kim et al.
2
C/T
(J/molKK
C/T (J/mol
))
1.8
0.7
10
5
04/15/02
50
100
150
T (K)
200
250
300
KHKim
“Resilient” non-dispersive spectrum
T=90 K
J. Van Duijn et al. (2004)
ħ meV
T=30 K
T=1.5 K
SCES04 7/29/04
Q (Å-1)
Properties of disordered two-level system
Generalized susceptibility for two level system, :
c  ( )  pa 2 tanh

2
 (  )   (  )
Generalized susceptibility with distributed splitting,    :


2

c ( )    ( )c  "   d   pa  (|  |) tanh
2
0
How to derive the distribution function from “scattering law”
     a1 1  e    S  
2
How to derive specific heat from distribution function:

eu
2
c p  k B (k B T )   (ukB T )u
du
u
2
(1  e )
0
SCES04 7/29/04
Identify Scaling form for S()
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Colossal “g” from inhomogeneously split doublet
What is the role of frustration?
— It allows high DOS without
order far above percolation
What do we learn from this?
— Be aware of non-kramers
doublets in alloys
— There may be interesting
magneto-elastic effects
associated with frustrated
non-kramers systems
SCES04 7/29/04
Metal Insulator transition in V2O3
Hole doping
Increase U/W
Short Range order in Paramagnetic Insulator
B.Z.
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Spin wave dispersion
Exchange constants
0.6 meV
Bao et al. Unpublished
SCES04 7/29/04
Orbital fluctuations
Orbital occupancy order
Magnetic SRO
Magnetic order
T>TC
T<TC
Orbital frustration in V2O3?
An interesting possibility:
•Bonds occupy kagome’ lattice
•Ising model on kagome’ lattice
has no phase transition whence
the low TC
•Orbital occupational order
eventually occurs because it
enables lower energy spin state
SCES04 7/29/04
Wiebe et al. (2004)
T=22 K
SCES04 7/29/04
Competing Interactions in URu2Si2?
Broholm et al. (1991)
Effective low dimensionality of CeCu6
H.v. Lohneysen et al. (2000)
SCES04 7/29/04
Conclusions
 Frustration is a central aspect of SCES
 Frustrated insulators display
–
–
–
–
–
Reduced TN with complex phase diagrams
Composite spin degrees of freedom
Magneto-elastic effects close to criticality
Hypersensitivity to quenched disorder
Singlet ground state phases are common when symmetry low
 Metals with Frustrated magnetism
– Large “g” from quenched disorder in frustrated non-kramers
doublet systems
– Orbital frustration may help to expose MIT in V2O3
– A possible role of frustration in U and Ce based HF systems
SCES04 7/29/04

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