Quantum effects in Magnetic Salts Part II

G. Aeppli

London Centre for Nanotechnology

London Centre for NanotechnologyLondon Centre for Nanotechnology

Talk 1

• TF Ising model in 3d shows interesting QM effects in real experiments

• ‘slaved’ degrees of freedom which are classically irrelevant can have qualitative quantum impact

outline

Introduction – saltsquantum mechanicsclassical magnetism

RE fluoride magnet LiHoF4 – model quantum phase transition

1d model magnets

2d model magnets – Heisenberg & Hubbard models

collaborators

• G-Y Xu (BNL)• C.Broholm (Hopkins)• J.F.diTusa(LSU)• H. Takagi (Tokyo)• Y. Itoh(Tsukuba)• Y-A Soh (Dartmouth)• M. Treacy (Arizona)• D. Reich (Hopkins)• D. Dender (NIST)

Example #2 - Heisenberg antiferromagnet

• H=JSiSj with J>0

• classical ground state

Consider commutator again

Mfm=Szl (ferromagnet)

Maf=(-1)l Szl (antiferromagnet)

[M,H]=... (-1)l([Szl,Sl](Sl-1+Sl+1)

-([Szl-1,S l-1]+[Sz

l-1,S l-1])Sl)

for FM, [M,H]=0 while not so for AFM

Antiferromagnets can self-destruct

does the classical picture ever go wrong- look at spin wave

amplitudes |<Q|S+|0>|2

• Diverge as 1/Q when Qmagnetic zone center for AFM

• ~ constant for FM

Break-down of S-W theory

• <M2>=S(S+1)=static piece + fluctuating piece

• <M2>= Mo2+ (E-Eo(Q))|<Q|S+|0>|2 dEddQ

=Mo2+ (1/Q)ddQ(AFM) (Mo=ordered moment)

• clearly a problem for AFM in d=1

>,

<> - >

> + >J

Consequence- antiferromagnetism can be

unstable, especially for low d

What do experiments say?

S=1/2 chain AFM (CuGeO3)

S=1/2 for zero field

No magnetic orderpairs of fermionic excitations rather than harmonic spin wavesbut at first sight, difficult to distinguish from multimagnon series

expansion...

Want something qualitatively different…

For a conventional antiferromagnet in a field, only

rounding effects, both types of modes have peak intensity at

-1 -0.5 0 0.5 1

1||B

B

Dender et al., Phys. Rev. Lett. 79(9), pp. 1750-1753, (1997)

E=0.21meV

Dender et al., Phys. Rev. Lett. 79(9), pp. 1750-1753, (1997)

Zeeman-split spinon Fermi surface

Dender et al., Phys. Rev. Lett. 79(9), pp. 1750-1753, (1997)

Consider S=1 AFM chain compound YBaNiO5

S(Q)=S<SlSm>expi|l-m|Q

equal-time correlationfunction = liquid structure factor

no AFM order, only fluctuations

width =1/xo where xo~7a

An unstable antiferromagnet

0

20

40

60

0 0.5 1 1.5 2

q

h (

meV

)

Xu et al, unpublished

a gapped ‘spin liquid’(Haldane)

Why?

rationalization #1 Sz=-1,0,+1 -+-+-+0-+-+-+0-0+-+-+ (‘floating zeroes)

rationalization #2(‘valence bond solid’)- consider JHund<JNi-Ni

Ni +2

Just a simple liquid?

secret order(quantum coherence) in explanations, but apparently not visible in the equal-time two-spin

correlation function <0|S-

-q S+q|0>= S(q,

can we measure coherence length for this new state?

0

20

40

60

0 0.5 1 1.5 2

q

h (

meV

)

S(q

,

S(q

,

m

eV)

Xu et al, unpublished

Theory by Sachdev et alXu et al, unpublished

Mesoscopic phase(>15nm) phase coherence in quantum spin fluid

as T0, |<triplet|S+q|collective singlet ground state>|2q

even while the 2-spin correlations in ground state are short-ranged:

<0|SiSj|0>=exp-|i-j|/ where ~7

T=0 quantum coherence limited only by inter-impurity spacing

dephasing at finite T observed

What happens when we insert incorrect bonds?

via Ca substitution for Y which adds holes mainly to oxygens

on chains(DiTusa et al ‘94)

…Ni2+-O2--Ni2+- O 2--Ni2+-O--Ni2+-O2--Ni2+ ...

Subgap bound statesin Ca-doped YBaNiO5

Xu et al, unpublished

G. Xu et al., Science, 289(5478), pp. 419-422, (2000)

Ca-doping induces subgap resonance

incommensurability which does not seem to depend on x

sharper at low x

net spectral weight well in excess(~4 times larger) of spectral

Weight for S=1/2 one might associate with added hole

S=1/2 X S=1/2 X S=1/2

O-

Strong coupling JO-Ni between oxygen & nickel spins

net ferromagnetic(no matter what is sign of JO-Ni )

bond of strength JO-Ni 2

S(Q)=cos2(Q) peaks at 2n, nodes at (2n+1)

-4 -3 -2 -1 0 1 2 3 40

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

but really JHund>>JNi-Ni

Jhund<<JNi-Ni

dispersionless VB state real S=1 chain

•antiferromagnetism survives on a length scale >lattice spacing•edge states are more extended than single lattice spacing

Therefore-

2

coscosh

2/cos)1()()(

Q

QeQFQS

1/

1 2 3 4 50

5

10

15

202

…interference between left and right hand side of bound state wavefunction produces two incommensurate peaks centered around

for finite(rather than infinitesimal) impurity density, interference effect no longer perfect, and node at

partially relieved

Test: No interference effect when chain is cut rather than FM bond inserted -

Direct observation of effective S=1/2 edge state for chain cut by substitution of

nonmagnetic Mg for magnetic Ni

M. Kenzelmann et al. Physical Review Letters , 90, 087202/1-4, (2003)

Immobile holes in 1-d quantum spin liquid nucleate subgap edge states

Incommensurate structure factor

- not from charge ordering Fermi surface etc.

- but from delocalized quantum spin degree of freedom which extendsover several Ni-Ni spacings into QSF and accounts for large spectral weight

summary

Antiferromagnets in 1d avoid classical order & display mesoscopic quantum effects

1d magnets a good experimental laboratory for edge states in quantum systems