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Magnetic order refinement in high field

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

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Magnetic order refinement in high field

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  1. 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 • Magnetic order refinement in high field: challenges and caveats

  2. 3,5,…-particle continuum 3,5,…-particle continuum H=0 H~Hc ? particles particles holes H>Hc Haldane chain in magnetic field. Haldane (Quantum) Critical Luttinger Liquid Macroscopic quantum phase in the string operator at H>Hc results in the shift in q-space between fermions and magnons.

  3. Haldane chain in magnetic field. Luttinger Liquid L.P. Regnault, I. Zaliznyak, J.P. Renard, C. Vettier, PRB 50, 9174 (1994).

  4. Coupled Haldane chains in (Cs,Rb)NiCl3: weak antiferromagnetic order in zero field <m> ≈ 1mB 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

  5. Field perpendicular to easy axis: no spin-flop, just increase in magnetic order Coupled Haldane chains in (Cs,Rb)NiCl3 in magnetic field Field along easy axis: spin-flop + increase in magnetic order

  6. Spin-flop Hc Coupled Haldane chains: magnetic field enhances antiferromagnetic order.

  7. 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

  8. 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

  9. Spin realignment: powder in magnetic field

  10. Red: H = 6.8 T Black: H = 0 T Red: H = 6.8 T Black: H = 1 T Brave attempt: refine on powder

  11. The right way: do the real thing 15 T magnet on D23 @ ILL (courtesy B. Grenier)

  12. single-domenization Cavalry approach: just follow the Bragg peaks H perpendicular to the easy axis Not satisfactory!

  13. Full refinement in mangetic field

  14. Full refinement in mangetic field Haldane gap in CsNiCl3

  15. E. Demler, S. Sachdev, and Y. Zhang, PRL 87 (2001). B. Khaykovich, Y. S. Lee, et. al., PRB 66 (2002). Compare to LCO superconductors

  16. 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

  17. / U. Maryland Acknowledgements: thanks go to • S. V. Petrov • B. Grenier and L.-P. Regnault • R. Erwin and C. Quang • C. Broholm • A. Savici

  18. What is liquid? • no shear modulus • no elastic scattering = no static density-density correlation ‹ρq(0)ρ-q(t)›→ 0 t → ∞ • Quantum liquid state for a system of Heisenberg spins H = J||SSiSi+||+ JS SiSi+D+ DS(Siz)2 • no static spin correlations ‹Sqα(0)S-βq(t)›→ 0, i.e. ‹Sqα(0)S-βq (t)›= 0 • hence, no elastic scattering (e.g. no magnetic Bragg peaks) t → ∞ J||/J>> 1 (<<1) parameterize quasi-1D (quasi-2D) case 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)

  19. has Neel-ordered ground state with elastic Bragg scattering at q=π • and quasiparticles that are gapless Goldstone magnons e(q) = 2J(S(S+1))1/2sin(q) e(q)/J/(S(S+1))1/2 What would be a “spin solid” Heisenberg antiferromagnet with classical spins, S >> 1

  20. short-range-correlated “spin liquid” Haldane ground state • quasiparticles with a gap  ≈ 0.4J at q=π e2 (q) = D2 + (cq)2 e(q)/J/(S(S+1))1/2 Quantum Monte-Carlo for 128 spins. Regnault, Zaliznyak & Meshkov, J. Phys. C (1993)  1D quantum spin liquid: Haldane spin chain Heisenberg antiferromagnetic chain with S = 1

  21. strong interaction weak interaction   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

  22. Typical geometry of a scattering experiment, (a) elastic, (b) inelastic. How do neutrons measure quasiparticles. I. A. Zaliznyak and S.-H. Lee, in Modern Techniques for Characterizing Magnetic Materials, Ed. Y. Zhu, Springer (2005)

  23. 0 π q 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

  24. Spin-quasiparticles in Haldane chains in CsNiCl3

  25. Spectrum termination point in CsNiCl3 I. A. Zaliznyak, S.-H. Lee, S. V. Petrov, PRL 017202 (2001)

  26. Quasiparticle spectrum termination line in PHCC max{E2-particle (q)} min{E2-particle (q)} Spectrum termination line E1-particle(q)

  27. 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

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