Quantum effects in Magnetic Salts Part II G. Aeppli London Centre for Nanotechnology.
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Transcript of Quantum effects in Magnetic Salts Part II G. Aeppli London Centre for Nanotechnology.
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Quantum effects in Magnetic Salts Part II
G. Aeppli
London Centre for Nanotechnology
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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
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outline
Introduction – saltsquantum mechanicsclassical magnetism
RE fluoride magnet LiHoF4 – model quantum phase transition
1d model magnets
2d model magnets – Heisenberg & Hubbard models
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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)
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Example #2 - Heisenberg antiferromagnet
• H=JSiSj with J>0
• classical ground state
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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
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Antiferromagnets can self-destruct
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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
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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
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>,
<> - >
> + >J
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Consequence- antiferromagnetism can be
unstable, especially for low d
What do experiments say?
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S=1/2 chain AFM (CuGeO3)
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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…
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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
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Dender et al., Phys. Rev. Lett. 79(9), pp. 1750-1753, (1997)
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E=0.21meV
Dender et al., Phys. Rev. Lett. 79(9), pp. 1750-1753, (1997)
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Zeeman-split spinon Fermi surface
Dender et al., Phys. Rev. Lett. 79(9), pp. 1750-1753, (1997)
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Consider S=1 AFM chain compound YBaNiO5
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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
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An unstable antiferromagnet
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0
20
40
60
0 0.5 1 1.5 2
q
h (
meV
)
Xu et al, unpublished
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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
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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?
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0
20
40
60
0 0.5 1 1.5 2
q
h (
meV
)
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S(q
,
S(q
,
m
eV)
Xu et al, unpublished
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Theory by Sachdev et alXu et al, unpublished
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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
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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+ ...
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Subgap bound statesin Ca-doped YBaNiO5
Xu et al, unpublished
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G. Xu et al., Science, 289(5478), pp. 419-422, (2000)
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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
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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
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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
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but really JHund>>JNi-Ni
Jhund<<JNi-Ni
dispersionless VB state real S=1 chain
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•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/
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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
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for finite(rather than infinitesimal) impurity density, interference effect no longer perfect, and node at
partially relieved
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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)
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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
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summary
Antiferromagnets in 1d avoid classical order & display mesoscopic quantum effects
1d magnets a good experimental laboratory for edge states in quantum systems