Quantum effects in Magnetic Salts

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Quantum effects in Magnetic Salts

• G. Aeppli (LCN)
• N-B. Christensen (PSI)
• H. Ronnow (PSI)
• D. McMorrow (LCN)
• S.M. Hayden (Bristol)
• R. Coldea (Bristol)
• T.G. Perring (RAL)
• Z.Fisk (UC)
• S-W. Cheong (Rutgers)
• Harrison (Edinburgh)
• et al.

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outline

• Introduction salts?quantum mechanics?classical
  magnetism
• RE fluoride magnet LiHoF4 model quantum phase
  transition
• 1d model magnets
• 2d model magnets Heisenberg Hubbard models

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Experimental program

• Observe dynamics
• Is there anything other than Neel state
• and spin waves?
• Over what length scale do quantum degrees of
  freedom matter?

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Pictures are essential cant understand nor use
what we cant visualize-difficulty is that
antiferromagnet has no external field-need
atomic-scale object which interacts with spins

• Subatomic bar magnet neutron
• Atomic scale light X-rays

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Scattering experiments
kf,Ef,sf
ki,Ei,si
Qki-kf hwEi-Ef
Measure differential cross-sectionratio of
outgoing flux per unit solid angle and energy to
ingoing fluxd2s/dWdw
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inelastic neutron scatteringFermis Golden Rule

• at T0,
• d2s/dWdwSfltfS(Q)0gt2d(w-E0Ef) where S(Q)
  SmSmexpiq.rm
• for finite T
• d2s/dWdw kf/ki S(Q,w) where S(Q,w)(n(w)1)Imc(
  Q,w)
• S(Q,w)Fourier transform in space and time of
  2-spin correlation function
• ltSi(0)Sj(t)gt
• Int dt Sij expiQ(ri-rj)expiwt ltSi(0)Sj(t)gt

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ISIS Spallation Neutron Source
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ISIS - UK Pulsed Neutron Source
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Information
576 detectors 147,456 total pixels 36,864
spectra 0.5Gb
Typically collect 100 million data points
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The Samples
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Two-dimensional Heisenberg AFM is stable for
S1/2 square lattice
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Copper formate tetrahydrate
2D XRD mapping (still some texture present
because crystals have not been crushed fully)
Crystallites (copper carbonate formic acid)
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H. Ronnow et al. Physical Review Letters 87(3),
pp. 037202/1, (2001)
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• Copper formate tetradeuterate

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Christensen et al, unpub (2006)
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(p,0) (3p/2,p/2) (p,p)
Christensen et al, unpub (2006)
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Why is there softening of the mode at (p,0) ZB
relative to (3p/2,p/2) ?

• Neel state is not a good eigenstate
• 0gtNeelgt SaiNeel states with 1 spin flippedgt
  
• SbiNeel states with 2 spins flippedgt
• real space basis entanglement
• 0gtNeelgtSkakspin wave with momentum kgt
• momentum space basis
• What are consequences for spin waves?

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Neelgt
correctiongt
0gt
whereas flips along (0,p) and (p,0) cost 4J,2J
or 0 e.g. -
All diagonal flips along diagonal still cost 4J
SWgt
?SW energy lower for (p,0) than for (3p/2,p)
C. Broholm and G. Aeppli, Chapter 2 in "Strong
Interactions in Low Dimensions (Physics and
Chemistry of Materials With Low Dimensional
Structures)", D. Baeriswyl and L. Degiorgi,Eds.
Kluwer ISBN 1402017987 (2004)
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How to verify?

• Need to look at wavefunctions
• info contained in matrix elements ltkSk0gt
• measured directly by neutrons

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Christensen et al, unpub (2006)
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Spin wave theory predicts not only energies, but
also ltkSk0gt
Christensen et al, unpub (2006)
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Discrepancies exactly where dispersion deviates
the most!
Christensen et al, unpub (2006)
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Another consequence of mixing of classical
eigenstates to form quantum states-

• multimagnon continuum
• Sk0gtSkakSkkgt
• Skakk-kgt
• ?many magnons produced by Sk
• ?multimagnon continuum
• Can we see?

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Christensen et al, unpub (2006)
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Christensen et al, unpub (2006)
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Christensen et al, unpub (2006)
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2-d Heisenberg model

• Ordered AFM moment
• Propagating spin waves
• Corrections to Neel state (aka RVB, entanglement)
  
• seen explicitly in
• Zone boundary dispersion
• Single particle pole(spin wave amplitude)
• Multiparticle continuum

Theory Singh et al, Anderson et al
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Now add carriers but still keep it insulating

• Is the parent of the hi-Tc materials really a
  S1/2 AFM on a square lattice?

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2d Hubbard model at half filling
non-zero t/U, so charges can move around still
antiferromagnetic why?
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gt
...

gt
t2/UJ
gt
t0
t nonzero
FM and AFM degenerate
FM and AFM degeneracy split by t
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• consider case of La2CuO4 for which t0.3eV and
  U3eV from electron spectroscopy,
• but ordered moment is as expected for 2D
  Heisenberg model

R.Coldea, S. M. Hayden, G. Aeppli, T. G. Perring,
C. D. Frost, T. E. Mason, S.-W. Cheong, Z. Fisk,
Physical Review Letters 86(23), pp. 5377-5380,
(2001)
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(p,p) (p,0) (3p/2,p/2)
(3p/2,p/2) (p,0) (p,p)
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Why? Try simple AFM model with nnn interactions-
? Most probable fits have ferromagnetic J
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ferromagnetic next nearest neighbor coupling

• not expected based on quantum chemistry
• are we using the wrong Hamiltonian?
• consider ring exchange terms which provide much
  better fit to
• small cluster calculations and explain light
  scattering anomalies , i.e. HSJSiSjJcSiSjSkSl

Si
Sl
Sj
Sk
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R.Coldea et al., Physical Review Letters 86(23),
pp. 5377-5380, (2001)
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Where can Jc come from?
Girvin, Mcdonald et al, PRB
From our NS expmts-
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Is there intuitive way to see where ZB dispersion
comes from?
C. Broholm and G. Aeppli, Chapter 2 in "Strong
Interactions in Low Dimensions (Physics and
Chemistry of Materials With Low Dimensional
Structures)", D. Baeriswyl and L. Degiorgi,Eds.
Kluwer ISBN 1402017987 (2004)
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For Heisenberg AFM, there was softening of the
mode at (1/2,0) ZB relative to (1/4,1/4)
Neelgt
correctiongt
0gt
whereas flips along (0,1) and (1,0) cost 4J,2J
or 0 e.g. -
All diagonal flips along diagonal still cost 4J
SWgt
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Hubbard model- hardening of the mode at (1/2,0)
ZB relative to (1/4,1/4)
Neelgt
correctiongt
0gt
whereas flips along (0,1) cost 3J or more because
of electron confinement
flips along diagonal away from doubly occupied
site cost lt3J
SWgt
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summary

• For most FM, QM hardly matters when we go much
  beyond ao,
• QM does matter for real FM, LiHoF4 in a
  transverse field
• For AFM, QM can matter hugely and create new
• interesting composite degrees of freedom 1d
  physics especially interesting
• 2d Heisenberg AFM is more interesting than we
  thought, different from Hubbard
• model
• IENS basic probe of entanglement and quantum
  coherence
• because x-section ltfS(Q)0gt2 where S(Q)
  SmSmexpiq.rm