Transcript Holes in a Quantum Spin Liquid

Structure and dynamics of spin polarons
induced by doping a Haldane spin-1 chain
Collin Broholm*
Johns Hopkins University and NIST Center for Neutron Research
T. Ito
M. Kenzelmann
K. Oka
H. Takagi
M. E. Bisher
M. M. J. Treacy
R. Paul
Xu et al., Science 289, 419 (2000)
Kenzelmann et al., PRL 90, 087202 (2003)
Ying Chen
Guangyong Xu
G. Aeppli
J. F. DiTusa
I. A. Zaliznyak
C. D. Frost
LANL
BNL
UCL
LSU
BNL
ISIS
* Supported by the National Science Foundation
Tsukuba
JHU
Tsuk
ISSP
NEC
NEC
NIST
Outline
1. Introduction to neutrons and Y2BaNiO5
2. On-chain non-magnetic doping
3. Off chain hole doping
4. Conclusions and outlook
kf
ki
Q
  

1
1
it
iQ( R  R ')


S (Q,  ) 
dt
e
e

S
(
t
)
S
(
0
)


R
R
'

at
 NCNR
SPINS cold neutron
spectrometer
2


N
RR '
APS 3/5/03
MAPS Spectrometer at ISIS in UK
APS 3/5/03
Haldane gap in Y2BaNiO5
Ni
2+
Y2BaNiO5
Impure
Nuclear Elastic Scattering
Pure
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Single mode approximation for spin-1 chain
Dispersion relation
Equal time
correlation function
Ma et al., PRL 69, 3571 (1992).
APS 3/5/03
Anisotropy and inter-chain
coupling
Maintaining Q|| 
Dintensity (coutns per 15 min.)
I(q,w) (1/meV)
Da Db Dc

a
, we
•Derive polarization by
rotating Q about chain
•Look for inter-chain
coupling by varying Q 
Weak anisotropy:
 D/D  10%
Highly one dimensional
APS 3/5/03
J '  5  104
J
Facts on Y2BaNiO5
H   J  nm S n,m  S n 1,m
 D nm  S
z
n,m

2
Intra-chain exchange

 E  nm  S
x
n,m
  S  
2
y
n,m
2
 g  B H   nm S n,m
Dipole in field
  nmm ' J 'mm ' S n,m  Sn,m '
Chemical Formula
Common name
AgVP2S6
Y2BaNiO5
-3
Ni(C3H10N2)2N3(ClO4)
Ni(C3H10N2)2NO2(ClO4)
Ni(C2H8N2)2NO2(ClO4)
Ni(C5D14N2)2N3(PF6)
CsNiCl3
E/J
NINAZ
10-3
NINO
NENP
12
J
meV
21
APS 3/5/03
D/J
10
-39
NDMAP
Anisotropy
Inter-chain exchange
J
meV
58(4)
21 B
10.7
4.5
4.1(3)
2.85
2.275
D/J
10-3
5.8
-39
170
250
180
250
-1.9
g H/J
0.055
E/J
10-3
gBH/J
0.020
J’/J
12
0.055
-30.11
10
0.21
0.28
< 0.5
0.41
0.45
J’/J
10-3
0.01
< 0.5 N
<0.7
TN
K
<2
< 0.05
<0.06
<1.2
<0.0003
<0.25
4.9
T
K
0.8< 0.05
0.6
17
Outline
1. Introduction to neutrons and Y2BaNiO5
2. On-chain non-magnetic doping
3. Off chain hole doping
4. Conclusions and outlook
APS 3/5/03
Impurities in Y2BaNiO5
• Mg2+on Ni2+ sites
• Ca2+ on Y3+ sites
Site centered defects
bond centered defects
Mg
Ca2+
Ni
Mg
Y3+
Pure
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Kojima et al. (1995)
P(D)/max(P(D))
An ensemble of finite length chains
P(L)
8%
4%
2%
P  L   Lc 1  c 
L
 
D  L  D   v 
 L
2%
D
Probability spin in segment of length L
2
2

S  q    L P  L  SD L  q 
APS 3/5/03
4%
D
Chain length L
2
8%
Gap from chain of length L
Ensemble averaged scattering
Haldane gap with impurities
Kenzelmann
et al. PRL (2003)
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How about chain ends?
L is even
L is odd
g B H
 
J  L    1 exp  L
L
g B H
g B H
g B H


HL  EL0   J L  D L  0 0   L DS z2  E S x2  S y2
Singlet-triplet
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Single ion anisotropy
  g 
z
B
HS z
Zeeman
Chain-end composite spin
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Form factor for chain-end spin
Kenzelmann
APS 3/5/03 et al. PRL (2003)
Outline
1. Introduction to neutrons and Y2BaNiO5
2. On-chain non-magnetic doping
3. Off chain hole doping
4. Conclusions and outlook
APS 3/5/03
Transport in Ca doped Y2BaNiO5
1D conductivity, no Charge ordering
Charge Transfer excitation
Charge polaron
T. Ito et al. Submitted to PRL (2001)
APS 3/5/03
Impurities in Y2BaNiO5
• Mg2+on Ni2+ sites
• Ca2+ on Y3+ sites
Site centered defects
bond centered defects
Mg
Ca2+
Ca2+
Ni
Mg
Y3+
Pure
APS 3/5/03
Kojima et al. (1995)
Gap modes in 4% Ca-doped Y2BaNiO5
APS 3/5/03
Why is Y2-xCaxBaNiO5 incommensurate?
q  x
q indep. of x
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Charge ordering yields incommensurate spin
order
Quasi-particle Quasi-hole pair excitations in
Luttinger liquid
Single impurity effect
Does  q vary with calcium concentration?
q not strongly
dependent on x
single impurity effect
APS 3/5/03
Xu et al., Science 289, 419 (2000)
Bond Impurities in a spin-1 chain: Y2-xCaxBaNiO5
Ni
AFM
FM
Ca2+
Y3+
O
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Form-factor for FM-coupled chain-end spins
A symmetric AFM droplet

S (q)  2 Re M  (q)eiq / 2

Ensemble of independent
randomly truncated AFM droplets
S (q)   Pll  M l (q )e
ll 
iq / 2
 M ( q )e
*
l
iq / 2 2
Gap modes in 4% Ca-doped Y2BaNiO5
Excited state
Quasi-elastic
From deg. GS
APS 3/5/03
polaron
J
J
H   J SO   S L  S R 

  12 J S2LOR  SO2  S2LR
SLR  1
SLOR  12
SLR  0
SLOR  32
SLR  1
J

1
2
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SLOR  12
J
Intra polaron dynamics in Ca-doped
Y2BaNiO5
Normalized Intensity (Arb)
Pure
Clean gap
4% Ca
Intra quartet
3
2
1
2
J FM
J FM  9 meV
J FM
?
0
0
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5
10

15
 meV
20
25
Conclusions:
 Dilute impurities in the Haldane spin chain create
sub-gap composite spin degrees of freedom.
 Edge states have an AFM wave function that
extends into the bulk over distances of order the
Haldane length.
 Ca doping yields charge polarons with 1 eV binding
energy
 Holes in Y2-xCaxBaNiO5 are surrounded by AFM
spin polaron with central phase shift of 
 Spin polaron spectrum described as three
interacting spins-1/2 with JFM = 9 meV
Viewgraphs
APS 3/5/03
and publications at http://www.pha.jhu.edu/~broholm/homepage
Outlook
1. Confirm level assignment in field
2. What is localization length for spin
polaron?
3. Spin polaron structure in frustrated
magnets
4. Spin polarons in high TC superconductors?
5. Magnetism of interacting
Design by T. D.spin
Pike polarons
APS 3/5/03
http://www.pha.jhu.edu/~broholm/MACS