1. Spin dynamics of stripe-ordered layered nickelates Andrew Boothroyd Department of Physics, Oxford University Ni 2+ (S=1) Ni 3+ (S=1/2) Cu 2+ (S=1/2) Cu ~2.5+ La 2–x Sr x NiO 4 (La,Nd) 2–x (Sr,Ba) x CuO 4 (x~1/8) ● Spin waves in La 5/3 Sr 1/3 NiO 4 ● Magnetic ‘resonance’ ● quasi 1D spin correlations ● Inward dispersion in La 2 NiO 4.11 ● Low energy charge dynamics

2. Acknowledgements Paul Freeman Institut Laue-Langevin / Oxford University D. Prabhakaran Oxford University(Single crystals) Stephen HaydenUniversity of Bristol Hyungje Woo Brookhaven National Lab / ISIS / Oak Ridge John Tranquada Brookhaven National Lab Marcus Huecker  Kenji NakajimaUniversity of Tokyo Michael JohnstonUniversity of Oxford James Lloyd-Hughes  Mechthild Enderle Institut Laue-Langevin Jiri Kulda  Arno Hiess  Felix AltorferPaul-Scherrer Institut,Switzerland Christof Niedermayer  Chris FrostISIS Facility Toby Perring 

3. Stripe order in La 2–x Sr x NiO 4 x = 0 x = 1/4x = 1/3x = 1/2 (Tranquada et al, Cheong et al, Yoshizawa et al) ideal stripe structures Ni 2+ (S = 1) Ni 3+ (S = ½)

4. Stripe order in La 5/3 Sr 1/3 NiO 4

5. Constant-energy slices projected onto the a*b* plane. Data from MAPS spectrometer. Neutron scattering from La 5/3 Sr 1/3 NiO 4

6. Woo et al. PRB 72, 064437 (2005) 1. Spin wave model for La 5/3 Sr 1/3 NiO 4

7. Spin wave dispersion in La 5/3 Sr 1/3 NiO 4 0 0.5 1 1 Q x (r.l.u.) Q y (r.l.u.) Linear spin wave model provides good description of Spin excitation spectrum for energies > ~30 meV

8. 2. Mystery ‘resonance’ in spin excitation spectrum of La 5/3 Sr 1/3 NiO 4 unpolarized neutrons (MAPS time-of-flight, RAL) polarized neutrons (IN20 triple-axis, ILL) Boothroyd et al, PRB 67, 100407(R) (2003) Out-of-plane anisotropy gap Broadening above 6 meV 0 0.5 1 1 Q x (r.l.u.) Q y (r.l.u.)

9. Spin wave dispersion in La 5/3 Sr 1/3 NiO 4 0 0.5 1 1 Q x (r.l.u.) Q y (r.l.u.)

10. E = 2.5 meV 3. Low energy spin fluctuations in La 5/3 Sr 1/3 NiO 4 Boothroyd et al, PRL 91, 257201 (2003) E = 5 meV E = 0 meV (elastic)

11. Diffuse inelastic scattering  Consistent with quasi-1D AFM chains Low energy quasi-1D spin fluctuation in La 5/3 Sr 1/3 NiO 4 Scans along line B Scan along line A B

12. 4. Inward dispersion of spin waves in La 2 NiO 4.11 Christensen et al. PRL 93, 147002 (2004) Vignolle et al. Nature Phys. 3, 163 (2007) Spin excitation spectrum of La 1.84 Sr 0.16 CuO 4 0 0.5 1 1 Q x (r.l.u.) Q y (r.l.u.)

13. Inward dispersion of spin waves in La 2 NiO 4.11 0 0.5 1 1 Q x (r.l.u.) Q y (r.l.u.) Freeman et al., JMMM 310, 760 (2007)

14. Inward dispersion of spin waves in La 2 NiO 4.11 Yao and Carlson, PRB 73, 224525 (2006) Linear spin wave theory J 1 = 0.1J J 1 = 0.5J

15. Lloyd-Hughes, PRB 77, 195114 (2008) Optical conductivity, THz spectroscopy x = 0.333 x = 0.275 5. Low energy charge dynamics in La 2–x Sr x NiO 4

16. Lloyd-Hughes, PRB 77, 195114 (2008) x = 0.333 x = 0.275 Low energy charge dynamics in La 2–x Sr x NiO 4 Thermally activated charge response with energy ~5meV

17. Summary — spin and charge excitations in La 2–x Sr x NiO 4 Summary — spin and charge excitations in La 2–x Sr x NiO 4 1. E > 30 meV: spin-wave-like modes on a rigid stripe superlattice; spin wave model for La 5/3 Sr 1/3 NiO 4  intra- and inter-stripe exchange 2. Mysterious magnetic ‘resonance’ peak at ~25 meV 3. AFM spin fluctuations along charge stripes 4. Inward magnetic dispersion observed at x ~ ¼ 5. Low energy charge mode at ~5 meV

18. Hybridization with another excitation?

19. Possible magnetic ground state for La 5/3 Sr 1/3 NiO 4 ? Klingeler et al; M. Long (unpublished) 0 0.5 1 1 Q x (r.l.u.) Q y (r.l.u.) Non-collinear magnetic structure

20. Spin reorientation transition La 3/2 Sr 1/2 NiO 4  La 1.67 Sr 0.33 NiO 4 ● On cooling, spins rotate away from stripe direction ● Reorientation observed for 0.275 < x < 0.5 ● Most prominent for x = 1/3 ( Df = 13 deg) and x = 1/2 ( Df = 26 deg) Freeman et al, PRB 66, 212405 (2002), Freeman et al, PRB 70, 024413 (2004) Lee et al, Phys. Rev. B 63, 60405(R) (2001),

21. Spin wave model for La 5/3 Sr 1/3 NiO 4 J = 15 ± 1.5 meV J’ = 7.5 ± 1.5 meV K c = 0.07 ± 0.01 meV Boothroyd et al. PRB 67, 100407 (2003)

22. Temperature dependence of 25meV mode Freeman et al, JPCM 20, 104229 (2008) Polarised neutron scattering

23. Determination of out-of-plane anisotropy gap 1.Compare spectra obtained with in-plane and out-of-plane scattering vectors 2.Separate different directional components of spin fluctuations by neutron polarization analysis S c = spin fluctuations along c axis S || = … … parallel to stripes x = 0.33

24. Spin excitations as function of x in La 2–x Sr x NiO 4 E = 40 meV Broadening when x  1/3 dispersion

25. Energy gap D = 1.45 ± 0.07 meV G = 1.54 ± 0.14 meV Fit to Lorentzian with gap D

26. Scans along line B Temperature dependence Diffuse inelastic scattering

27. Low energy mode follows zone boundary

28. Polarization of low energy mode Neutron polarization analysis of low energy mode: Intensity of spin fluctuations along c axis is factor 2.3 ± 0.4 larger than in plane