magnetic order refinement in high field
DESCRIPTION
Magnetic order refinement in high field. Igor Zaliznyak Neutron Scattering Group, Brookhaven National Laboratory. Outline Magnetic field as a source of Luttinger liquid alternate route to “quantum” criticality Enhancing weak antiferromagnetism in coupled Haldane chains - PowerPoint PPT PresentationTRANSCRIPT
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Magnetic order refinement in high field Magnetic order refinement in high field
OutlineOutline
• Magnetic field as a source of Luttinger liquid
– alternate route to “quantum” criticality
• Enhancing weak antiferromagnetism in coupled Haldane chains
• Magnetic order refinement in high field: challenges and caveats
Igor ZaliznyakIgor Zaliznyak
Neutron Scattering Group, Brookhaven National Laboratory
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Haldane chain in magnetic field.Haldane chain in magnetic field.3,5,…-particle continuum
3,5,…-particle continuum
H=0 H~Hc
H>Hc
?particles
holesparticles
Macroscopic quantum phase in the string operator at H>Hc results in the shift in q-space between fermions and magnons.
Haldane (Quantum) Critical
Luttinger Liquid
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Haldane chain in magnetic field.Haldane chain in magnetic field.
L.P. Regnault, I. Zaliznyak, J.P. Renard, C. Vettier, PRB 50, 9174 (1994).
Luttinger Liquid
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Coupled Haldane chains in (Cs,Rb)NiClCoupled Haldane chains in (Cs,Rb)NiCl33: weak : weak
antiferromagnetic order in zero fieldantiferromagnetic order in zero field
CsNiClCsNiCl33::J = 2.3 meV = 26 K J = 0.03 meV = 0.37 K = 0.014 JD = 0.002 meV = 0.023 K = 0.0009 J3D magnetic order below TN = 4.84 K
<<> > ≈ 1≈ 1BB
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Coupled Haldane chains in (Cs,Rb)NiClCoupled Haldane chains in (Cs,Rb)NiCl33 in in
magnetic fieldmagnetic field
Field along easy axis: spin-flop + increase in magnetic order
Field perpendicular to easy axis: no spin-flop, just increase in magnetic order
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Coupled Haldane chains: magnetic field enhances Coupled Haldane chains: magnetic field enhances antiferromagnetic order. antiferromagnetic order.
Hc
Spin-flop
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Measuring the field dependence of magnetic Measuring the field dependence of magnetic Bragg peaks: challenges and caveats.Bragg peaks: challenges and caveats.
• Equivalent “Friedel” reflections have different intensities– non-uniform illumination of absorbing sample is a source of the
dominant systematic error– sample/wavelength optimization is vital
• Realignment of spins in the spin-flop process greatly impacts intensities– very sensitive to magnetic field orientation with respect to
crystallographic “easy” axis– sensitive to sample mosaicity– different bias for different reflections
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Spin-flop is nothing new and is well understoodSpin-flop is nothing new and is well understood
J. W. Lynn, P. Heller, N. A. Lurie, PRB 16 (1977).
• ψ is misalignment of the magnetic field from the easy axis• φ is corresponding misalignment of staggered magnetization
• Eq. (14) is a venerable expression with long history dating back to L. Neel (J. Lynn et. al.)• It also is general: goes beyond simple quasiclassical approximation
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Spin realignment: powder in magnetic fieldSpin realignment: powder in magnetic field
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Brave attempt: refine on powderBrave attempt: refine on powder
Red:H = 6.8 TBlack:H = 0 T
Red:H = 6.8 TBlack:H = 1 T
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The right way: do the real thingThe right way: do the real thing
15 T magnet on D23 @ ILL(courtesy B. Grenier)
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Cavalry approach: just follow the Bragg peaks Cavalry approach: just follow the Bragg peaks
Not satisfactory!
H perpendicular to the easy axis
single-domenization
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Full refinement in mangetic field Full refinement in mangetic field
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Full refinement in mangetic field Full refinement in mangetic field
Haldane gap in CsNiCl3
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Compare to LCO superconductorsCompare to LCO superconductors
B. Khaykovich, Y. S. Lee, et. al., PRB 66 (2002).
E. Demler, S. Sachdev, and Y. Zhang, PRL 87 (2001).
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Summary and conclusionsSummary and conclusions
• Magnetic field brings about fascinating new phases
– Luttinger-liquid (quantum) critical state
– tunes antiferromagnetism in weakly ordered systems
• Refining field dependence of magnetic order is a challenging experimental task
– field-dependent variation of intensity is often smaller than systematic (not statistical!) errors
– only one reciprocal lattice (hkl) plane is typically available
– spin realignment is often a complication: serious science requires serious refinement
This work was carried out under Contract DE-AC02-98CH10886, Division of Materials Sciences, US Department of Energy. The work on SPINS was supported by NSF through DMR-9986442
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Acknowledgements: thanks go to Acknowledgements: thanks go to
• S. V. Petrov
• B. Grenier and L.-P. Regnault
• R. Erwin and C. Quang
• C. Broholm
• A. Savici
/ U. Maryland/ U. Maryland
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What is quantum spin liquid?What is quantum spin liquid?
• What is liquid?− no shear modulus− no elastic scattering = no static density-density correlation
‹ρq(0)ρ-q(t)› → 0t → ∞• What is quantum liquid?
− all of the above at T → 0 (i.e. at temperatures much lower than interactions between the particles in the system)
• Quantum liquid state for a system of Heisenberg spins
H = J|| SiSi+||+ JSiSi
D(Siz)2
• no static spin correlations
‹Sqα (0)S-
βq (t)› → 0, i.e. ‹Sq
α (0)S-β
q (t)› = 0
• hence, no elastic scattering (e.g. no magnetic Bragg peaks)
t → ∞
J||/J>> 1 (<<1) parameterize quasi-1D (quasi-2D) case
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What would be a “spin solid”What would be a “spin solid”
• Heisenberg antiferromagnet with classical spins, S >> 1S >> 1
− and quasiparticles that are gapless Goldstone magnons
(q) = 2J(S(S+1))1/2sin(q)
(q)
/J/(
S(S
+1)
)1/2
− has Neel-ordered ground state with elastic Bragg scattering at q=π
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1D quantum spin liquid: Haldane spin chain1D quantum spin liquid: Haldane spin chain
− short-range-correlated “spin liquid” Haldane ground state
• Heisenberg antiferromagnetic chain with S = 1S = 1
(q)
/J/(
S(S
+1)
)1/2
− quasiparticles with a gap ≈ 0.4J at q=π
2 (q) = 2 + (cq)2
Quantum Monte-Carlo for 128 spins.
Regnault, Zaliznyak & Meshkov, J. Phys. C (1993)
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weak interaction
2D quantum spin liquid: a lattice of frustrated 2D quantum spin liquid: a lattice of frustrated dimersdimers
M. B. Stone, I. Zaliznyak, et. al. PRB (2001)
(C4H12N2)Cu2Cl6 (PHCC)
− singlet disordered ground state
− gapped triplet spin excitation
strong interaction
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How do neutrons measure quasiparticles.How do neutrons measure quasiparticles.
E , kf f
sam pleE , ki i
Q =k -ki f
E , kf f
sam pleE , ki i
Q =k -ki f
s s
a ) b )
df
df
Typical geometry of a scattering experiment, (a) elastic, (b) inelastic.
M o n o ch ro m a to r
(2 s)
F o cu sin g an a ly ze r
S am p le
D e tec to r
M o n o ch ro m a to r
(2 s)
F o cu sin g an a ly ze r
S am p le
D e tec to r
(a ) (b )
R A
R
L S AL S A
L S DL S D
I. A. Zaliznyak and S.-H. Lee, in Modern Techniques for Characterizing Magnetic Materials, Ed. Y. Zhu, Springer (2005)
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Spin-quasiparticles in Haldane chains in CsNiClSpin-quasiparticles in Haldane chains in CsNiCl33
J = 2.3 meV = 26 K J = 0.03 meV = 0.37 K = 0.014 J
D = 0.002 meV = 0.023 K = 0.0009 J
3D magnetic order below TN = 4.84 Kunimportant for high energies
q0 π
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Spin-quasiparticles in Haldane chains in CsNiClSpin-quasiparticles in Haldane chains in CsNiCl33
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Spectrum termination point in CsNiClSpectrum termination point in CsNiCl33
I. A. Zaliznyak, S.-H. Lee, S. V. Petrov, PRL 017202 (2001)
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Quasiparticle spectrum termination line in PHCCQuasiparticle spectrum termination line in PHCC
max{E2-particle (q)}
min{E2-particle (q)}
E1-particle(q)
Spectrum termination line
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Summary and conclusionsSummary and conclusions
• Quasiparticle spectrum termination at E > 2 is a generic property of the quantum Bose (spin) fluids
– observed in the superfluid 4He
– observed in the Haldane spin chains in CsNiCl3
– observed in the 2D frustrated quantum spin liquid in PHCC
• A real physical alternative to the ad-hoc “excitation fractionalization” explanation of scattering continua
• Implications for the high-Tc cuprates: spin gap induces disappearance of the coherent quasiparticles at high E
This work was carried out under Contract DE-AC02-98CH10886, Division of Materials Sciences, US Department of Energy. The work on SPINS was supported by NSF through DMR-9986442