1. Neutron and X-ray Scattering Studies of Spin, Charge and Orbital Order in TM Oxides Andrew Boothroyd Department of Physics, Oxford University magnetization resistivity La 5/3 Sr 1/3 NiO 4

2. Transition Metal Oxide Research in Oxford Physics Department Sample Preparation lab. Single Crystals Dr Prabhakaran Neutron Scattering Dr Boothroyd Dr Coldea Prof Cowley Muon-spin Rotation Dr Blundell X-ray scattering Dr Hatton (Durham) Prof Cowley Characterization Magnetization Transport etc

3. Crystal growth — floating-zone method Image furnace (Clarendon Laboratory)

4. Oxford single crystals of TM oxides La 5/3 Sr 1/3 NiO 4 La 0.7 Sr 0.3 MnO 3 CoNb 2 O 6 La 3/2 Sr 1/2 CoO 4 Na 0.7 CoO 2

5. Neutron scattering studies of stripe-ordered nickelates D. Prabhakaran Oxford University Paul Freeman  Mechthild Enderle Institut Laue-Langevin Jiri Kulda  Arno Hiess  Louis-Pierre Regnault CEA, Grenoble, Felix AltorferPaul-Scherrer Institut,Switzerland Christof Niedermayer  Chris FrostISIS Hyungje Woo Brookhaven National Lab/ISIS Kenji NakajimaUniversity of Tokyo John Tranquada Brookhaven National Lab collaborators

6. Outline  Overview of stripe phenomena in La 2–x Sr x NiO 4  What can be learned by neutron diffraction ?  Interesting aspects of magnetic ordering  Interesting features in magnetic excitation spectra

7. 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

8. Neutron Diffraction Bragg n = 2d sin  Laue Q =  (1) Scattering from nuclei  Q Q = k i - k f Applications: Crystal structure refinement Structural distortions (e.g. charge order)

9. Neutron diffraction (2) Scattering from magnetic moments V(r) = –  n.B(r) Neutrons scatter from component of magnetization perpendicular to Q Q m m No! Yes! Applications: Spin arrangements in ordered phases Magnetic form factors

10. Polarized neutron scattering x y z Q P 1. P || Q SF: M yy + M zz NSF: N x y z P Q x y z Q P 2. P  Q (in plane) 3. P  Q (vertical) SF: M zz NSF: N + M yy SF: M yy NSF: N + M zz Magnetic field defines polarization axis, P Incident neutrons Scattered neutrons Spin-flip (SF) Non-spin-flip (NSF)

11. Advantages of polarized neutron scattering for studying complex order  static: charge vs magnetic order  dynamic: spin fluctuations vs phonons 1. Distinguishing magnetic and non-magnetic scattering 2. Separating different magnetic components  static: determining moment directions  dynamic: identifying anisotropy gaps and anisotropic fluctuations La 5/3 Sr 1/3 NiO 4

12. Spin & charge order in La 3/2 Sr 1/2 NiO 4 170 K < T < 460 K ‘checkerboard’ charge ordering charge ordermagnetic order T < 170 K spin & charge ordering Not simple checkerboard pattern Freeman et al, Phys. Rev. B 66 (2002) 212405 Kajimoto et al, Phys. Rev. B 67 (2003) 14511 Half-doping: Correlation length  35 Å

13. Models for spin-charge order in La 3/2 Sr 1/2 NiO 4 Possible diagonal stripe pattern: Charge peaks at Q co = (½, ½) and  ),  4/9 Magnetic peaks at Q m = (½, ½) ±  )

14. Spin reorientations La 3/2 Sr 1/2 NiO 4  La 1.63 Sr 0.37 NiO 4 Similar results for La 5/3 Sr 1/3 NiO 4 reported by Lee et al, Phys. Rev. B 63 (2001) 60405(R) [T SR = 50 K,  = 13 deg]

15. Overview of spin dynamics in La 2–x Sr x NiO 4 e.g. La 5/3 Sr 1/3 NiO 4 Spin wavesGap-like features2 components

16. Low energy quasi-1D spin fluctuation in La 5/3 Sr 1/3 NiO 4 Diffuse inelastic scattering Scans along line A  Ni 3+ ions (probably) carry spin S = ½  Consistent with quasi-1D AFM chains Scans along line B

17. Soft X-ray scattering studies of manganates Peter Hatton University of Durham Philip Spencer  Stuart WilkinsInstitute of Transuranium Elements,Karlsruhe, and European Synchrotron Radiation Facility, Grenoble D. Prabhakaran Oxford University Steve CollinsDaresbury Laboratory Mark Roper  collaborators

18. X-ray Scattering Non-resonant scattering X-rays can probe charge density (Thomson) – very strong! X-rays also scatter from spin and orbital moments – very weak! Resonant scattering Strong enhancements at atomic absorption edges Resonant scattering from spin and orbital moments Element specific Higher-order ‘anomalous’ scattering processes observable

19. Examples of X-ray resonant magnetic scattering Antiferromagnetic order in PrBa 2 Cu 3 O 6+x J.P. Hill et al, Phys. Rev. B 61 (2000) 1251 Cu K edge Pr L II edge J.P. Hill et al, Phys. Rev. B 58 (1998) 11211

20. X-ray resonant scattering from Mn 1s1s 4p4p E A = 6.55 keV  = 1.9 Å K edge resonance 2p2p 3d3d E A = 0.65 keV = 19 Å L edge resonance  Soft X-rays  Long period structures only Probes 3d orbitals directly Very large resonant enhancements Long wavelengths Indirect probe of 3d magnetism

21. Daresbury Laboratory 2 GeV Machine 5U1 – Soft X-ray Undulator Good Sample Environment Awful Food

22. Soft X-ray scattering at 5U1, SRS Air absorption at 650 eV is severe!

23. Soft X-ray resonant scattering from La 2–2x Sr 1+2x Mn 2 O 7 (x = 0.45) L III L II T = 83 K Charge order between 120 K and 220 K Antiferromagnetic order below 170 K (001) AFM Bragg peak S.B. Wilkins et al Phys. Rev. Lett. 90 (2003) 187201

24. Orbital ordering in La 0.5 Sr 1.5 MnO 4 Spin, charge and orbital order below 240 K; Jahn-Teller distortion very small AFM order

25. Soft X-ray scattering & theory (Castelton & Altarelli, Phys. Rev. B 62 (2000) 1033) Theoretical predictions No Jahn-Teller distortion Strong JT distortion (¼, ¼, 0) Soft X-ray resonant scattering At the orbital ordering Bragg peak (S.B. Wilkins et al, to appear in Phys. Rev Lett.) Conclusion: scattering is due to combined orbital ordering and cooperative Jahn-Teller distortions

26. Conclusions Spin and charge order – La 3/2 Sr 1/2 NiO 4 not checkerboard! Spin reorientations occur Evidence for coupling of spin excitations to charge stripes AFM spin correlations on the charge stripes Neutron scattering studies of stripe-ordered nickelates Soft X-ray studies of spin-charge-orbital ordered manganates Large resonant enhancements at L edge Can probe ordering of 3d orbitals directly Limited to ordering phenomena with period d > 10 Å Jahn-Teller mechanism important in driving orbital order