Magnetic order refinement in high field

Probing Matter with X-Rays and Neutrons Probing Matter with X-Rays and Neutrons Tallahassee, May 10-12, 2005 Tallahassee, May 10-12, 2005

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


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


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


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


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


Coupled Haldane chains: magnetic field enhances Coupled Haldane chains: magnetic field enhances antiferromagnetic order. antiferromagnetic order.

Hc

Spin-flop


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


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


Spin realignment: powder in magnetic fieldSpin realignment: powder in magnetic field


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


The right way: do the real thingThe right way: do the real thing

15 T magnet on D23 @ ILL(courtesy B. Grenier)


Cavalry approach: just follow the Bragg peaks Cavalry approach: just follow the Bragg peaks

Not satisfactory!

H perpendicular to the easy axis

single-domenization


Full refinement in mangetic field Full refinement in mangetic field


Full refinement in mangetic field Full refinement in mangetic field

Haldane gap in CsNiCl3


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).


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


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


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


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


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)


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


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)


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


Spin-quasiparticles in Haldane chains in CsNiClSpin-quasiparticles in Haldane chains in CsNiCl33


Spectrum termination point in CsNiClSpectrum termination point in CsNiCl33

I. A. Zaliznyak, S.-H. Lee, S. V. Petrov, PRL 017202 (2001)


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


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

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Magnetic order refinement in high field