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

* Supported by the National Science Foundation

Ying Chen LANLGuangyong Xu BNLG. Aeppli UCLJ. F. DiTusa LSU I. A. Zaliznyak BNLC. D. Frost ISIST. Ito Tsukuba

M. Kenzelmann JHUK. Oka TsukubaT. G. Perring ISISH. Takagi ISSP M. E. Bisher NECM. M. J. Treacy NECR. Paul NIST

Xu et al., Science 289, 419 (2000)Kenzelmann et al., PRL 90, 087202 (2003)

Outline

1. Introduction to pure Y2BaNiO5

2. Site impurities (Mg2+↔ Ni2+)

3. Bond impurities (Ca2+↔ Y3+)

4. Conclusions and outlook

Sendai 11/8/03SPINS cold neutron spectrometer at NCNR

kikf Q

''R

)'( )0(S)(S1

2

1),(

RRR

RRQiti teN

edtQ

S

''R

)'( )0(S)(S1

2

1),(

RRR

RRQiti teN

edtQ

S

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MAPS Spectrometer at ISIS in UK

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Haldane gap in Y2BaNiO5

40

20

60

00 0.5 1 1.5 2

q ()

h

(m

eV

)S(q)~ (-(q))1-cosq(q)

Ba

Y

O2-

Ni

T. Ito, K. Oka and H. Takagi

MAPS (ISIS)

Sendai 11/8/03

in

ten

sity

(co

utn

s p

er

15

min

.)

I(q

,w)

(1/m

eV

)

a b c

Inter-chain coupling and anisotropy

I(q

,w)

(1/m

eV

)

in

t. (

cts

per

15

min

.)

Chain

Q

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Facts on Y2BaNiO5

, 1,

2 2 2

, , ,

' , , '''

n m n mnm

z x yn m n m n mnm nm

mm n m n mnmm

J

D S E S S

J

S S

S S

HIntra-chain exchangeIntra-chain exchange

AnisotropyAnisotropy

Inter-chain exchangeInter-chain exchange

Chemical Formula Common name J meV

D/J 10-3

E/J 10-3

gBH/J J’/J 10-3

TN K

AgVP2S6 58(4) 5.8 0.020 0.01 < 2 Y2BaNiO5 21 -39 12 0.055 < 0.5 < 0.05 Ni(C3H10N2)2N3(ClO4) NINAZ 10.7 170 0.11 <0.7 <0.06 Ni(C3H10N2)2NO2(ClO4) NINO 4.5 250 0.21 <1.2 Ni(C2H8N2)2NO2(ClO4) NENP 4.1(3) 180 0.28 0.8 <0.0003 Ni(C5D14N2)2N3(PF6) NDMAP 2.85 250 0.41 0.6 <0.25 CsNiCl3 2.275 -1.9 0.45 17 4.9

J meV

D/J 10-3

E/J 10-3

J’/J 10-3

TN K

21 -39 12 < 0.5 < 0.05

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Outline

1. Introduction to pure Y2BaNiO5

2. Site impurities (Mg2+↔ Ni2+)

3. Bond impurities (Ca2+↔ Y3+)

4. Conclusions and outlook

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Cutting chains in Y2BaNi1-xMgxO5

• Mg2+on Ni2+ sites finite length chains

Kojima et al. (1995)

Pure

Ni2+Ni2+

Mg2+Mg2+

3

Mg2+ Y3+

O2-

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Haldane gap with impurities

Kenzelmann et al. PRL (2003)

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An ensemble of finite length chains

Chain length L

P(L

)

2%

4%

8%

P(

)/m

ax(

P(

))

2%

4%

8%

2 1L

P L Lc c Probability spin in isolated segment of length L

Gap from chain of length L 2

2L vL

Ensemble averaged scattering LLS q P L S q

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Haldane gap with impurities

Kenzelmann et al. PRL (2003)

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ESR with neutrons

Kenzelmann et al. PRL (2003)

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Minimal model for chain end spins

Bg H

Bg H

1 expL LJ L

L is odd

Bg H

Bg HL is even

0 2 2 20 0L L L L L z x y z B zE J D DS E S S g HS HSinglet-triplet Single ion anisotropy Zeeman

C. D. Batista et al., PRB (1999)

Affleck, Kennedy, Lieb, and Tasaki PRL (1987)

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Chain-end composite spin

Kenzelmann et al. PRL (2003)

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Form factor for chain-end spin

Kenzelmann et al. PRL (2003)

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Outline

1. Introduction to pure Y2BaNiO5

2. Site impurities (Mg2+↔ Ni2+)

3. Bond impurities (Ca2+↔ Y3+)

4. Conclusions and outlook

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Hole doping Y2-xCaxBaNiO5

•Ca2+ on Y3+ sites mobile bond defects

Kojima et al. (1995)

Pure

Ca2+Ca2+

Y3+Y3+

FMCa2+

Ni

O2-

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Transport in Ca doped Y2BaNiO5

T. Ito et al. PRL (2002)

1D conductivity, no Charge ordering1D conductivity, no Charge ordering

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Gap modes in 4% Ca-doped Y2BaNiO5

q

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Does q vary with calcium concentration?

q not strongly dependent on x

q not strongly dependent on x

single impurity effectsingle impurity effect

Xu et al., Science 289, 419 (2000)

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Bond Impurities in a spin-1 chain: Y2-

xCaxBaNiO5

Y3+

Ni

O

FM

Ca2+

Form-factor for FM-coupled chain-end spins

2/ 2( ) 2Re ( ) iqS q M q e

A symmetric AFM droplet

22/*2/ )()()(

ll

iql

iqlll eqMeqMPqS

Ensemble of independent randomly truncated AFM droplets

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Gap modes in 4% Ca-doped Y2BaNiO5

Excited state ?Excited state ?

Quasi-elasticFrom deg. GSQuasi-elasticFrom deg. GS

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Minimal model of spin polaron

'J'J

2 2 212

2 2 212

12

12

'

'

' 1

' 1LR LOR

L R O L R

LR L R

LOR O LR

S S LR LR

LOR LOR

J J

J

J

E J J S S

J S S cst

S S S S S

S S S

S S S

H

32 'J

'J J

32 1LOR LRS S

12 1LOR LRS S

12 0LOR LRS S

1 12 20,1LR LR LOR LRS S S S

J

LS RS

OS

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Intra polaron dynamics in Ca-doped Y2BaNiO5

0 5 10 15 20 250

meV

Norm

ali

zed

In

ten

sity

(A

rb)

Pure

4% Ca

Clean gapClean gap

32 'J

?

'J JIntra quartetIntra quartet

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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

Viewgraphs and publications at http://www.pha.jhu.edu/~broholm/homepage

Sendai 11/8/03

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

Design by T. D. Pikehttp://www.pha.jhu.edu/~broholm/MACS