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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

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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

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

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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

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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

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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

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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

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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)

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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

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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)

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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

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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

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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) ± )

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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]

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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

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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

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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

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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

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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

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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

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

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

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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

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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

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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

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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

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