impurities and finite temperature effects in a one-dimensional spin-1 antiferromagnet coherent...
TRANSCRIPT
Impurities and finite temperature effects in a one-dimensional spin-1
antiferromagnet
Coherent excitations in Y2BaNiO5
Loss of coherence for T>0 Chain-end spins in Y2BaNi1-xMgxO5
AFM droplets in Y2-xCaxBaNiO5
Conclusion
Collin BroholmJohns Hopkins University and NIST Center for Neutron Research
Supported by the NSF through DMR-9453362
CURREAC 8/20/99
Collaborators
Guangyong Xu JHU -> University of ChicagoG. Aeppli NECJ. F. DiTusa Louisiana State University I. A. Zaliznyak JHU -> BNLC. D. Frost ISIST. Ito Electro-technical Lab JapanK. Oka Electro-technical Lab JapanH. Takagi ISSP and CREST-JST M. E. Bisher NECM. M. J. Treacy NEC
Experiments performed at NIST and ISIS
CURREAC 8/20/99
Why does spin-1 AFM have a spin gap?
• For integer spin chains (S=n, z=2) this state is “close to” the ground state
• Magnets with 2S=nz have a nearest neighbor singlet covering.
• Excited states are propagating bond triplets separated from the ground state by an energy gap .J
Haldane PRL 1983Affleck, Kennedy, Lieb, and Tasaki PRL 1987
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Magnetic Neutron Scattering
fi kkQ
fi EE
The scattering cross section is proportional to the Fourier transformed dynamic spin correlation function
ik fk
Q
2
''R
)'( )0(S)(S1
2
1),(
RRR
RRQiti teN
edtQ
S
Y2 B
aN
iO5
on
SPIN
SE
<1
0 m
eV
NIS
T co
ld n
eu
tron
gu
ide h
all
ISIS Experimental hall
Y2BaNiO5 on MARI5 meV<E<100 meV
CURREAC 8/20/99
Low T excitations in spin-1 AFM chain
Y2BaNiO5 T=10 KMARI chain ki
Points of interest:
•Haldane gap =8 meV
•Coherent mode
•S(q,)->0 for Q->2n
CURREAC 8/20/99
Probing anisotropy and inter-chain coupling in Y2BaNiO5
in
ten
sity
(co
utn
s p
er
15
min
.)
I(q
,w)
(1/m
eV
)
a b c Maintaining , we
•Derive polarization by rotating about chain
•Look for inter-chain coupling by varying
aQ
||
Q
Q
Weak anisotropy:
%10/ Highly one dimensional
4105' JJ
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Sum rules and the single mode approximation
'cos1SS1
3
2),(
)(SS1
),(
'
2
)'(
''
ddqJN
qSd
qSeN
qSd
dddd
dd
ddqi
ddd
d
When a coherent mode dominates the spectrum:
)(
'cos1SS1
3
2
)(
),()(
'2
q
ddqJN
q
qSdqS
dddd
dd
Then sum-rules link S(q) and (q)
)()(),( qqSqS
The dynamic spin correlation function obeys sum-rules:
CURREAC 8/20/99
Propagating triplet in alternating spin-1/2 chain Cu(NO3)2
.2.5D2O
The “incommensurate” size of spin dimers yields different periods fordispersion relation and structure factor. An effect captured by the
SMA.
IRIS data SMA model
0 2 4 0 2 4 6
h
(meV
)
0.4
0.5
Q/
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Two magnon excitations in an alternating spin chain
Tennant, Nagler, Xu, Broholm, and Reich.
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Haldane mode in Y2BaNiO5 at finite T
Effects of heating:
• Line-width increases
• Effective increases
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T-dependence of relaxation rate and “resonance” energy
Parameter free comparison:
•Semi-classical theory of triplet scattering by Damle and Sachdev
•Quantum non linear model
Tk
TkT
B
B 0exp3
Tk
TkTB
B0
00 exp2
Derived from
Tc
T
0)(
Neglecting T-dependence of spin wave velocity c0
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Q-scans versus T: energy resolved and energy
integrated
Probing spatialcoherence of Haldane mode
Probing equal time correlation length
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Coherence and correlation lengths versus T
Equal-time correlation length saturates at =8.
Coherence length exceeds correlationlength for kBT<becoming very longas T 0
(Solid line from Quantum non linear model)
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Properties of pure Y2BaNiO5
Anisotropy split Haldane gap: a=7.5 meV, b=8.6 meV, c=9.5 meVNo inter-chain coupling detected: |J’/J|<5.10-4
Coherent mode described by SMA for T<</kB
Activated relaxation rate of q= mode is described by semi-classical theory of interacting triplet wave packets.
Activated increase in resonance energy is significantly less than predicted by Qnl-model
Coherence length exceeds correlation length for T< /kB and exceeds 40 lattice spacings for kBT/=0.1
CURREAC 8/20/99
Effects of finite chain length on Haldane mode
•Mode shifts towards J as in numerical work on finite length chains
•Peak Broadens because of chain length distribution
4% Mg
Pure
q= T=10 K
CURREAC 8/20/99
Zeeman resonance of chain-end spins
I(H
=9 T
)-I(
H=
0 T
) (
cts.
per
min
.)
h (meV)
Hg B
h
(m
eV
)
H (Tesla)0 2 4 6 8
g=2.16
0 0.5 1 1.5 2
-5
0
10
15
20
Hg B
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Structure factor of chain-end spins
Q-dependence revealsthat resonating objectis AFM.
The structure factoris indistinguishablefrom S(Q) for puresystem.
Chain end spin carryAFM spin polarizationof length back into chain
CURREAC 8/20/99
Vacancy doping a Haldane spin chain
q= mode shifts towards Jq= mode broadens due to random
chain length distributionApplied field induces Zeeman
resonance below Haldane gapResonating chain end spins have
AFM form factor resembling S(q) for pure system.
CURREAC 8/20/99
New excitations in Ca-doped Y2BaNiO5
Pure 9.5% Ca
•Ca-doping creates states below the gap
•sub-gap states have doubly peaked structure factor
Y2-xCaxBaNiO5:
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Why a double ridge below the gap in Y2-xCaxBaNiO5 ?
Charge ordering yields incommensurate spin order
Quasi-particle Quasi-hole pair excitations in a one dimensional hole liquid
Anomalous form factor for independent spin degrees of freedom associated with each donated hole
xq
q is single impurity prop.Indep. of
x
CURREAC 8/20/99
Does q vary with calcium concentration?
q is independent of
Double peak is predominantly asingle impurity effect
9.5% Ca
14% Ca
q
14.0;095.0x
CURREAC 8/20/99
(b)
Ca
Ba
Ni
Y
c
b
a
(e)
(f)
(c)
(d)
a
O
Bond Impurities in a spin-1 chain: Y2-
xCaxBaNiO5
(a)
CURREAC 8/20/99
Form-factor for FM-coupled chain-end spins- AFM droplets
9.5% Ca
14% Ca
2/)(Re2)( iqeqMqS
A symmetric AFM droplet
22/*2/ )()()(
ll
iql
iqlll eqMeqMPqS
Ensemble of independent randomly truncated AFM droplets
CURREAC 8/20/99
Calcium doping Y2BaNiO5
Experimental facts:Ca doping creates sub-gap excitations with
doubly peaked structure factor and bandwidth The structure factor is insensitive to
concentration and temperature for 0.095<x<0.14 and T<100 K
Current interpretation:Ca2+ creates FM impurity bonds which nucleate AFM droplets with doubly peaked structure factorAFM droplets interact through intervening chain
forming disordered random bond 1D magnet
CURREAC 8/20/99
Broader Conclusions:
Dilute impurities in the Haldane spin chain create sub-gap composite spin degrees of freedom.
Composite spins have an AFM wave function that extends into the bulk over distances of order the Haldane length.
Neutron scattering can detect the structure of composite impurity spins in quantum magnets when the corresponding states exist at energies where the bulk magnetic density of states vanishes.