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
M. Kenzelmann
Ying Chen
LANL
K. Oka
Guangyong Xu
BNL
T. G. Perring
G. Aeppli
UCL
H. Takagi
J. F. DiTusa
LSU
M. E. Bisher
I. A. Zaliznyak
BNL
M. M. J. Treacy
C. D. Frost
ISIS
R. Paul
T. Ito
Tsukuba
Xu et al., Science 289, 419 (2000)
Kenzelmann et al., PRL 90, 087202 (2003)
* Supported by the National Science Foundation
JHU
Tsuk
ISIS
ISSP
NEC
NEC
NIST
Outline
1. Introduction to pure Y2BaNiO5
2. Site impurities (Mg2+↔ Ni2+)
3. Bond impurities (Ca2+↔ Y3+)
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 '
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MAPS Spectrometer at ISIS in UK
Sendai 11/8/03
Haldane gap in Y2BaNiO5
O2MAPS (ISIS)
60
Y
h (meV)
Ni
40
Ba
1-cosq
S(q)~
d(-e(q))
e(q)
20
0
T. Ito, K. Oka and H. Takagi
Sendai 11/8/03
0
0.5
1
q ()
1.5
2
I(q,w) (1/meV) I(q,w) (1/meV)
Sendai 11/8/03
Da Db Dc
min.)(cts per 15 min.)
Dintensity (coutns per 15Dint.
Inter-chain coupling and anisotropy
Chain
f
Q
Facts on Y2BaNiO5
Intra-chain exchange
H   J  nm S n ,m  S n 1,m

 D nm Snz,m

2

 E  nm Snx,m
 
2
 Sny,m
  nmm ' J 'mm ' S n ,m  S n ,m '
Chemical Formula
Common name
AgVP2S6
Y2BaNiO5
Ni(C3H10N2)2N3(ClO4)
Ni(C3H10N2)2NO2(ClO4)
Ni(C2H8N2)2NO2(ClO4)
Ni(C5D14N2)2N3(PF6)
CsNiCl3
D/J
-3
NINAZ
10
NINO
NENP
-39
J
meV
21
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NDMAP

Anisotropy
2
Inter-chain exchange
J
meV
58(4)
21
-3
10.7
4.5
4.1(3)
2.85
2.275
E/J
10
12
D/J
10-3
5.8
-39
170
250
180
250
-1.9
E/J
10-3
J’/J12
-3
10
< 0.5
gBH/J
0.020
0.055
0.11
0.21
0.28
0.41
0.45
J’/J
10-3
0.01
N < 0.5
<0.7
T
K
0.8
< 0.05
0.6
17
TN
K
<2
< 0.05
<0.06
<1.2
<0.0003
<0.25
4.9
Outline
1. Introduction to pure Y2BaNiO5
2. Site impurities (Mg2+↔ Ni2+)
3. Bond impurities (Ca2+↔ Y3+)
4. Conclusions and outlook
Sendai 11/8/03
Cutting chains in Y2BaNi1-xMgxO5
• Mg2+on Ni2+ sites
finite length chains
Ni2+
3
O2Y3+
Mg2+
Pure
Sendai 11/8/03
Mg2+
Kojima et al. (1995)
Haldane gap with impurities
Kenzelmann
Sendai 11/8/03 et al. PRL (2003)
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 isolated segment of length L
2
2

S  q    L P  L  SD L  q 
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4%
D
Chain length L
2
8%
Gap from chain of length L
Ensemble averaged scattering
Haldane gap with impurities
Kenzelmann
Sendai 11/8/03 et al. PRL (2003)
ESR with neutrons
Sendai 11/8/03
Kenzelmann et al. PRL (2003)
spins
Affleck, Kennedy, Lieb, and Tasaki PRL (1987)
L is odd
L is even
g B H
 
C. D. Batista et al., PRB (1999)


HL  EL0   J L  D L  0 0   L DS z2  E S x2  S y2
Singlet-triplet
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g B H
J  L    1 exp  L
L
g B H
g B H
Single ion anisotropy
  g 
z
B
HS z
Zeeman
Chain-end composite spin
Kenzelmann
et al. PRL (2003)
Sendai
11/8/03
Form factor for chain-end spin
Kenzelmann
Sendai 11/8/03et al. PRL (2003)
Outline
1. Introduction to pure Y2BaNiO5
2. Site impurities (Mg2+↔ Ni2+)
3. Bond impurities (Ca2+↔ Y3+)
4. Conclusions and outlook
Sendai 11/8/03
Hole doping Y2-xCaxBaNiO5
•Ca2+ on Y3+ sites
mobile bond defects
Ni
Ca2+
FM
Ca2+
O2-
Pure
Y3+
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Kojima et al. (1995)
Transport in Ca doped Y2BaNiO5
1D conductivity, no Charge ordering
T. Ito et al. PRL (2002)
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Gap modes in 4% Ca-doped Y2BaNiO5
dq
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Does d q vary with calcium concentration?
dq not strongly
dependent on x
single impurity effect
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Xu et al., Science 289, 419 (2000)
Bond Impurities in a spin-1 chain: Y2-xCaxBaNiO5
Ni
FM
Ca2+
Y3+
O
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Form-factor for FM-coupled chain-end spins
A symmetric AFM droplet

S (q)  2Re M  (q)e
iq / 2

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
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Minimal model of spin polaron
J
J'
SL
SO
SLOR  12
J'
SR
H   JS L  S R  J ' SO   S L  S R 

J ' S
  12 J S 2LR  S 2L  S 2R

1
2
2
LOR
J J'

S S
2
O
SLR  0
2
LR

SLOR  12
SLR  1
SLOR  32
SLR  1
ESLR SLOR   12  J  J ' S LR  S LR  1
 J ' S LOR  S LOR  1  cst
1
2
1
1
S

0,1
S


S

S

LR 11/8/03
LR
LOR
LR
2
2
Sendai
3
2
J'
Intra polaron dynamics in Ca-doped
Y2BaNiO5
Normalized Intensity (Arb)
Pure
Clean gap
Intra quartet
3
2
4% Ca
J J'
J'
?
0
0
Sendai 11/8/03
5
10

15
 meV
20
25
Conclusions:
 Experimental observation of increase in Haldane
gap with decreasing chain length
 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.
 Holes in Y2-xCaxBaNiO5 are surrounded by AFM
spin polaron with central phase shift of 
 Low energy spin polaron excitations could be
―oxygen spin flip between aligned chain-end spins
―Or anisotropy-split quartet
Sendai Viewgraphs
11/8/03
and publications at http://www.pha.jhu.edu/~broholm/homepage
Outlook
1. Determine spin polaron 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 spin polarons
Sendai 11/8/03
Design by T. D. Pike
http://www.pha.jhu.edu/~broholm/MACS