Impurities and finite temperature effects in a one-dimensional spin-1 antiferromagnet

1
Impurities and finite temperature effects in a
one-dimensional spin-1 antiferromagnet
Collin Broholm Johns Hopkins University and NIST
Center for Neutron Research

• Coherent excitations in Y2BaNiO5
• Loss of coherence for Tgt0
• Chain-end spins in Y2BaNi1-xMgxO5
• AFM droplets in Y2-xCaxBaNiO5
• Conclusion

Supported by the NSF through DMR-9453362
2
Collaborators
Guangyong Xu JHU -gt University of Chicago G.
Aeppli NEC J. F. DiTusa Louisiana State
University I. A. Zaliznyak JHU -gt BNL C. D.
Frost ISIS T. Ito Electro-technical Lab
Japan K. Oka Electro-technical Lab Japan H.
Takagi ISSP and CREST-JST M. E. Bisher NEC M.
M. J. Treacy NEC Experiments performed at NIST
and ISIS
3
Why does spin-1 AFM have a spin gap?
Haldane PRL 1983 Affleck, Kennedy, Lieb, and
Tasaki PRL 1987
4
Magnetic Neutron Scattering
The scattering cross section is proportional to
the Fourier transformed dynamic spin correlation
function
5
Y2BaNiO5 on SPINS Elt10 meV
NIST cold neutron guide hall
6
ISIS Experimental hall
Y2BaNiO5 on MARI 5 meVltElt100 meV
7
Low T excitations in spin-1 AFM chain
Y2BaNiO5 T10 K MARI chain ki

• Points of interest
• Haldane gap D8 meV
• Coherent mode
• S(q,w)-gt0 for Q-gt2np

8
Probing anisotropy and inter-chain coupling in
Y2BaNiO5
Da Db Dc

• Maintaining , we
• Derive polarization by
• rotating about chain
• Look for inter-chain
• coupling by varying

Dintensity (coutns per 15 min.)
I(q,w) (1/meV)
Weak anisotropy
Highly one dimensional
9
Sum rules and the single mode approximation
The dynamic spin correlation function obeys
sum-rules
When a coherent mode dominates the spectrum
Then sum-rules link S(q) and e(q)
10
Propagating triplet in alternating spin-1/2
chain Cu(NO3)2.2.5D2O
The incommensurate size of spin dimers yields
different periods for dispersion relation and
structure factor. An effect captured by the SMA.
11
Two magnon excitations in an alternating spin
chain
Tennant, Nagler, Xu, Broholm, and Reich.
12
Haldane mode in Y2BaNiO5 at finite T

• Effects of heating
• Line-width increases
• Effective D increases

13
T-dependence of relaxation rate and resonance
energy

• Parameter free comparison
• Semi-classical theory of triplet
• scattering by Damle and Sachdev

ö
æ
D
T
k
3
(
)

ç
-

G
B
0
T
exp

ç
T
k
p
ø
è
B

• Quantum non linear s model

ö
æ
D
(
)

ç
-
D

D

D
p
T
0
T
k
exp
2

ç
B
0
0
T
k
ø
è
B
Derived from
c

0
T
)
(
D
(
)
x
T
Neglecting T-dependence of spin wave velocity c0
14
Q-scans versus T energy resolved and energy
integrated
D
³
w
h
Probing equal time correlation length
D

w
h
Probing spatial coherence of Haldane mode
15
Coherence and correlation lengths versus T
Equal-time correlation length saturates at x8.

(Solid line from Quantum non linear s model)
16
Properties of pure Y2BaNiO5

• Anisotropy split Haldane gap
• Da7.5 meV, Db8.6 meV, Dc9.5 meV
• No inter-chain coupling detected J/Jlt5.10-4
• Coherent mode described by SMA for TltltD/kB
• Activated relaxation rate of qp mode is
  described by semi-classical theory of interacting
  triplet wave packets.
• Activated increase in resonance energy is
  significantly less than predicted by Qnls-model
• Coherence length exceeds correlation length for
• Tlt D/kB and exceeds 40 lattice spacings for
  kBT/D0.1

17
Effects of finite chain length on Haldane mode
qp T10 K

• Mode shifts towards
• J as in numerical
• work on finite length
• chains
• Peak Broadens
• because of chain
• length distribution

Pure
4 Mg
18
Zeeman resonance of chain-end spins
g2.16
20
hw (meV)
15
0 2 4 6 8
H (Tesla)
10
I(H9 T)-I(H0 T) (cts. per min.)
0
-5
0 0.5 1 1.5 2
hw (meV)
19
Structure factor of chain-end spins
Q-dependence reveals that resonating object is
AFM. The structure factor is indistinguishable fr
om S(Q) for pure system.
Chain end spin carry AFM spin polarization of
length x back into chain
20
Vacancy doping a Haldane spin chain

• qp mode shifts towards J
• qp mode broadens due to random chain length
  distribution
• Applied field induces Zeeman resonance below
  Haldane gap
• Resonating chain end spins have AFM form factor
  resembling S(q) for pure system.

21
New excitations in Ca-doped Y2BaNiO5
Pure
9.5 Ca
Y2-xCaxBaNiO5

• Ca-doping
• creates states
• below the gap
• sub-gap states
• have doubly
• peaked structure
• factor

22
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

x
q
µ
d
x
23
Does dq vary with calcium concentration?
dq is independent of


Î
14
.
0

095
.
0
x
Double peak is predominantly a single impurity
effect
24
Bond Impurities in a spin-1 chain Y2-xCaxBaNiO5
Y
Ba
(a)
O
Ni
25
Form-factor for FM-coupled chain-end spins- AFM
droplets
26
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 0.095ltxlt0.14
  and Tlt100 K
• Current interpretation
• Ca2 creates FM impurity bonds which nucleate
• AFM droplets with doubly peaked structure
  factor
• AFM droplets interact through intervening chain
  forming disordered random bond 1D magnet

27
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.