# Presentation: 473543

## Magnetic order refinement in high field 

- _Outline_
- 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 Zaliznyak
*Neutron Scattering Group, Brookhaven National Laboratory*

## Haldane chain in magnetic field.

- 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.

*L.P. Regnault, I. Zaliznyak, J.P. Renard,  C. Vettier, PRB 50, 9174 (1994). *

- Luttinger Liquid

## Coupled Haldane chains in (Cs,Rb)NiCl3: weak antiferromagnetic order in zero field

**CsNiCl****3****:**
- 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 K

**<********> ****≈ 1********B**

## Coupled Haldane chains in (Cs,Rb)NiCl3 in  magnetic field

- Field along easy axis: spin-flop + increase in magnetic order

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

## Measuring the field dependence of magnetic 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 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 field

## Brave attempt: refine on powder

## The right way: do the real thing

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

## Cavalry approach: just follow the Bragg peaks 

- Not satisfactory!

- H perpendicular to the easy axis

## Full refinement in mangetic field 

## Full refinement in mangetic field 

- Haldane gap in CsNiCl3

## Compare to LCO superconductors

## Summary 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 

- S. V. Petrov
- B. Grenier and L.-P. Regnault
- R. Erwin and C. Quang
- C. Broholm
- A. Savici

## What is quantum spin liquid?

-  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)

## What would be a “spin solid”

-  Heisenberg antiferromagnet with classical spins, **S >> 1**

## 1D quantum spin liquid: Haldane spin chain

-  Heisenberg antiferromagnetic chain with **S = 1**

## 2D quantum spin liquid: a lattice of frustrated dimers

- M. B. Stone, I. Zaliznyak, et. al. PRB (2001)
- (C4H12N2)Cu2Cl6 (PHCC)

-  singlet disordered ground state
-  gapped triplet spin excitation

## How do neutrons measure quasiparticles.

*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 CsNiCl3

- 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 K
*unimportant for high energies*

## Spin-quasiparticles in Haldane chains in CsNiCl3

- Spin-quasiparticles in Haldane chains in CsNiCl3

## Spectrum termination point in CsNiCl3

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

## Quasiparticle spectrum termination line in PHCC

- max{E2-particle (q)}

- min{E2-particle (q)}

- E1-particle(q)

- Spectrum termination line

## Summary 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