Solving Impurity Structures Using Inelastic Neutron Scattering

Quantum Magnetism - Pure systems - vacancies - bond impuritiesConclusions

Collin Broholm*Johns Hopkins University and NIST Center for Neutron Research

*supported by the NSF through DMR-0074571

Ca2+

Y3+

Y2-x Ca

x BaNiO

5

ACA 7/24/00

Collaborators

G. Aeppli M. E. BisherJ. F. DiTusa C. D. FrostT. Ito T. H. Kim

K. Oka R. PaulD. H. Reich H. TakagiM. M. J. Treacy G. Xu

I. A. Zaliznyak

ACA 7/24/00

Inelastic Neutron Scattering

fi kkQ

fi EE

ikfk

Q

2

t

Nedt ti

QQQ

01

2

1),(

S

Nuclear scattering

RR'RR

RRQQ )(S)0(1

2

1),( '

' tSeN

edt iti

S

Magnetic scattering

ACA 7/24/00SPINS Cold neutron triple axis spectrometer at NCNR

ACA 7/24/00

Simple example of “Quantum” magnet

Cu(NO3)2.2.5D2O : dimerized spin-1/2 system

Only Inelastic magnetic scatteringOnly Inelastic magnetic scattering

ACA 7/24/00

A spin-1/2 pair has a singlet - triplet gap:

inter-dimer coupling yields dispersive mode

Why dimerized chain is a spin liquid

J0totS

1totS

ACA 7/24/00

Types of Quantum magnets

Definition: small or vanishing frozen moment at low T:

Conditions that yield quantum magnetism Low effective dimensionality Low spin quantum number geometrical frustration dimerization low connectivity interactions with fermions

Quantum magnets can display novel coherent states

JTkS B S for

ACA 7/24/00

Why study Quantum magnets ?

Coherent many body states are fascinating and useful Superconductivity Fractional Quantum Hall effect Bose Condensation Quantum magnets without static order at T=0

Each phenomenon provides different experimental info about macroscopic quantum coherence

Only in quantum magnets are dynamic correlations directly accessible (through neutron scattering)

ACA 7/24/00

Why study impurities in quantum magnets ?

Impurities are inevitable or even necessary to produce coherence

Probing the response to impurities reveals the building blocks of a macroscopic quantum state.

Impurities in quantum magnets can be explored at the microscopic level.

Ca2+Y3+

ACA 7/24/00

Dynamic condensed matter: 1D antiferromag.

q~2

Ni 2+

Y2BaNiO5 : spin 1 AFM

Impure

Pure

ACA 7/24/00

Macroscopic singlet ground state of S=1 chain

• This is exact ground state for spin projection Hamiltonian

• Magnets with 2S=nz have a nearest neighbor singlet covering with full lattice symmetry.

• 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

i

iii

iiiii

toti SP 12

131

12 SSSSSSH

ACA 7/24/00

Coherence in a fluctuating system

Probing spatialcoherence of Haldane mode

Probing equal time correlation length

ACA 7/24/00

Impurities in Y2BaNiO5

Ca2+

Y3+

• Mg2+on Ni2+ sites finite length chains• Ca2+ on Y3+ sites mobile bond defectsMg

Ni

Kojima et al. (1995)

Mg

Ca2+

Pure

ACA 7/24/00

Zeeman resonance of chain-end spinsI(

H=

9 T

)-I(

H=

0 T

) (

cts.

per

min

.)

Hg B

h (

meV

)

H (Tesla)0 2 4 6 8

g=2.16

0 0.5 1 1.5 2

-5

0

10

15

20

Hg B

meV)(

ACA 7/24/00

Form factor of chain-end spins

Q-dependence revealsthat resonating objectis AFM.

The peak resemblesS(Q) for pure system.

Q-dependence revealsthat resonating objectis AFM.

The peak resemblesS(Q) for pure system.

Chain end spin carryAFM spin polarizationof length back into chain

Chain end spin carryAFM spin polarizationof length back into chain

Y2BaNi1-xMgxO5 x=4% Hg B

ACA 7/24/00

Sub gap 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:

G. Xu et al. Science (2000)

ACA 7/24/00

Incommensurate modulations in high TC superconductors

Hayden et al. (1998)

YBa2Cu3O6.6 T=13 K E=25 meV

h (rlu)

k

(rl

u)

Yamada et al. (1998)

La2-xSrxCuO4

ACA 7/24/00

Why is Y2-xCaxBaNiO5 incommensurate?

Charge ordering yields incommensurate spin order

Quasi-particle Quasi-hole pair excitations in Luttinger liquid

Single impurity effect

xq

q indep. of xq indep. of x

ACA 7/24/00

Does q vary with calcium concentration?

q not strongly dependent on x

q not strongly dependent on x

single impurity effectsingle impurity effect

G. Xu et al. Science (2000)

ACA 7/24/00

(b)

Ca

Ba

Ni

Y

c

b

a

(e)

(f)

(c)

(d)

a

O

Bond Impurities in a spin-1 chain: Y2-

xCaxBaNiO5

(a)

Form-factor for FM-coupled chain-end spins

2/)(Re2)( iqeqMqS

A symmetric AFM droplet

22/*2/ )()()(

ll

iql

iqlll eqMeqMPqS

Ensemble of independent randomly truncated AFM droplets

ACA 7/24/00

ConclusionsQuantum Magnets

low dimensional frustrated and/or weakly connected Coherent low T states rather than magnetic order Challenging to describe because fluctuations are essential

Probing impurities with neutrons Spectroscopic separation yields unique sensitivity to

impurity structures (in quantum magnets) through coherent diffuse inelastic neutron scattering

Impurities in spin-1 chain They create sup-gap composite spin degrees of freedom Edge states have extended AFM wave function Holes create AFM spin polaron with phase shift