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Magnetic Neutron Scattering

Magnetic Neutron Scattering. Martin Rotter. Institut für Physikalische Chemie, Universität Wien. Introduction: Neutrons and Magnetism Elastic Magnetic Scattering Inelastic Magnetic Scattering. Contents. Neutrons and Magnetism. Macro-Magnetism:

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Magnetic Neutron Scattering

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  1. Magnetic Neutron Scattering Martin Rotter NESY Winter School 2007 Institut für Physikalische Chemie, Universität Wien

  2. Introduction: Neutrons and Magnetism Elastic Magnetic Scattering Inelastic Magnetic Scattering Contents NESY Winter School 2007

  3. Neutrons and Magnetism Macro-Magnetism: Solution of Maxwell´s Equations – Engineering of (electro)magnetic devices 10-1m 10-3m 10-5m 10-7m 10-9m 10-11m MFM image Micromagnetic simulation. Micromagnetism: Domain Dynamics, Hysteresis Atomic Magnetism: Instrinsic Magnetic Properties Hall Probe VSM SQUID MOKE MFM NMR FMR SR NS NESY Winter School 2007

  4. 2/l k 2q τ=Q k‘ q Incoming Neutron Scattered Neutron Bragg’s Law in Reciprocal Space (Ewald Sphere) O a* c*

  5. Single Crystal DiffractionE2 – HMI, Berlin k Q O NESY Winter School 2007

  6. The Scattering Cross Section Scattering Cross Sections Total Differential Double Differential Scattering Law S .... Scattering function Units: 1 barn=10-28 m2 (ca. Nuclear radius2) NESY Winter School 2007

  7. (follows from Fermis golden rule) M neutron mass k wavevector |sn>Spin state of the neutron Psn Polarisation |i>,|f> Initial-,final- state of the targets Ei,EfEnergies of –‘‘- Pi thermal population of state |i> Hint Interaction -operator S. W. Lovesey „Theory of Neutron Scattering from Condensed Matter“,Oxford University Press, 1984 NESY Winter School 2007

  8. Interaction of Neutrons with Matter NESY Winter School 2007

  9. Splitting of S into elastic and inelastic part Unpolarised Neutrons - Van Hove Scattering function S(Q,ω) • for the following we assume that there is no nuclear order - <I>=0:

  10. Lattice G with basis B: Latticefactor Structurefactor Independent ofQ: „Isotope-incoherent-Scattering“ „Spin-incoherent-Scattering“ one element(NB=1): Neutron – Diffraction

  11. Difference to nuclear scattering: Formfactor ... no magnetic signal at high angles Polarisationfactor ... only moment components normal to κ contribute Magnetic Diffraction NESY Winter School 2007

  12. Formfactor Q= NESY Winter School 2007

  13. Atomic Lattice Magnetic Lattice ferro antiferro NESY Winter School 2007

  14. Atomic Lattice Magnetic Lattice ferro antiferro NESY Winter School 2007

  15. Atomic Lattice Magnetic Lattice ferro antiferro NESY Winter School 2007

  16. The Nobel Prize in Physics 1994 In 1949 Shull showed the magnetic structure of the MnO crystal, which led to the discovery of antiferromagnetism (where the magnetic moments of someatoms point up and some point down).

  17. Arrangement of Magnetic Moments in Matter Paramagnet Ferromagnet Antiferromagnet And many more .... Ferrimagnet, Helimagnet, Spinglass ...collinear, commensurate etc. NESY Winter School 2007

  18. GdCu2 TN= 42 K M [010] TR= 10 K q = (2/3 1 0) Magnetic Structure from Neutron Scattering Rotter et.al. J. Magn. Mag. Mat. 214 (2000) 281 NESY Winter School 2007

  19. GdCu2 TN= 42 K M [010] TR= 10 K q = (2/3 1 0) Magnetic Structure from Neutron Scattering Rotter et.al. J. Magn. Mag. Mat. 214 (2000) 281 NESY Winter School 2007

  20. GdCu2 TN= 42 K M [010] TR= 10 K q = (2/3 1 0) Magnetic Structure from Neutron Scattering Rotter et.al. J. Magn. Mag. Mat. 214 (2000) 281 NESY Winter School 2007

  21. GdCu2 TN= 42 K M [010] TR= 10 K q = (2/3 1 0) Magnetic Structure from Neutron Scattering Rotter et.al. J. Magn. Mag. Mat. 214 (2000) 281 NESY Winter School 2007

  22. GdCu2 TN= 42 K M [010] TR= 10 K q = (2/3 1 0) Magnetic Structure from Neutron Scattering Rotter et.al. J. Magn. Mag. Mat. 214 (2000) 281 NESY Winter School 2007

  23. GdCu2 TN= 42 K M [010] TR= 10 K q = (2/3 1 0) Magnetic Structure from Neutron Scattering Rotter et.al. J. Magn. Mag. Mat. 214 (2000) 281 NESY Winter School 2007

  24. NdCu2 Magnetic Phasediagram (Field along b-direction) NESY Winter School 2007

  25. Complex Structures AF1 Q= NESY Winter School 2007

  26. Complex Structures F1 Q= NESY Winter School 2007

  27. Complex Structures F2 Q= NESY Winter School 2007

  28. NdCu2 Magnetic PhasediagramH||b F1    F3  c F1  b a AF1  Lines=Experiment Colors=Theory NESY Winter School 2007

  29. Inelastic Magnetic Scattering • Dreiachsenspektometer – PANDA • Dynamik magnetischer Systeme: • Magnonen • Kristallfelder • Multipolare Anregungen NESY Winter School 2007

  30. Three Axes Spectrometer (TAS) k Q Ghkl k‘ q NESY Winter School 2007

  31. PANDA – TAS for Polarized Neutronsat the FRM-II, Munich NESY Winter School 2007

  32. PANDA – TAS for Polarized Neutrons at the FRM-II, Munich beam-channel monochromator-shielding with platform Cabin with computer work-placesand electronics secondary spectrometer with surrounding radioprotection, 15 Tesla / 30mK Cryomagnet NESY Winter School 2007

  33. The Nobel Prize in Physics 1994 E Q Movement of Atoms [Sound, Phonons] Brockhouse 1950 ... π/a Phonon Spectroscopy: 1) neutrons 2) high resolution X-rays NESY Winter School 2007

  34. Movement of Spins - Magnons 153 MF - Zeeman Ansatz (for S=1/2) T=1.3 K NESY Winter School 2007

  35. Movement of Spins - Magnons 153 T=1.3 K Bohn et. al. PRB 22 (1980) 5447 NESY Winter School 2007

  36. Movement of Spins - Magnons 153 a T=1.3 K Bohn et. al. PRB 22 (1980) 5447 NESY Winter School 2007

  37. + + + + + + + + + + E Hamiltonian Q Movement of Charges - the Crystal Field Concept 4f –charge density NESY Winter School 2007

  38. NdCu2 – Crystal Field Excitations orthorhombic, TN=6.5 K, Nd3+: J=9/2, Kramers-ion Gratz et. al., J. Phys.: Cond. Mat. 3 (1991) 9297 NESY Winter School 2007

  39. T=100 K T=40 K T=10 K NdCu2 - 4f Charge Density NESY Winter School 2007

  40. Linear Response Theory, MF-RPA Calculate Magnetic Excitations and the Neutron Scattering Cross Section NESY Winter School 2007

  41. F3  F1  AF1  NdCu2 F3: measured dispersion was fitted to get exchange constants J(ij)

  42. Movements of Atoms [Sound, Phonons] 1970 Movement of Spins [Magnons] ? Movement of Orbitals [Orbitons] a a τorbiton τorbiton Description: quadrupolar (+higher order) interactions NESY Winter School 2007

  43. M. Rotter, Institut für physikalische Chemie, Universität Wien NESY Winter School 2007

  44. McPhase-theWorldofRareEarthMagnetism McPhase is a program package for the calculation of magnetic properties of rare earth based systems. Magnetization Magnetic Phasediagrams Magnetic StructuresElastic/Inelastic/Diffuse                                              Neutron Scattering                                             Cross Section NESY Winter School 2007

  45. Crystal Field/Magnetic/Orbital Excitations Magnetostriction and much more.... NESY Winter School 2007

  46. McPhase runs on Linux and Windows and is available as freeware. • McPhase is being developed by • M. Rotter, Institut für Physikalische Chemie, Universität Wien, Austria M. Doerr, Technische Universität Dresden, Germany • R. Schedler, Hahn Meitner Institut, Berlin, Germany P. Fabi né Hoffmann, Forschungszentrum Jülich, Germany S. Rotter, Wien, Austria • M. Banks, Max Planck Institute, Stuttgart, Germany • Duc Manh Le, University of London, U.K. • Important Publications referencing McPhase: • M. Rotter, S. Kramp, M. Loewenhaupt, E. Gratz, W. Schmidt, N. M. Pyka, B. Hennion, R. v.d.Kamp Magnetic Excitations in the antiferromagnetic phase of NdCu2Appl. Phys. A74 (2002) S751     • M. Rotter, M. Doerr, M. Loewenhaupt, P. Svoboda, Modeling Magnetostriction in RCu2 Compounds using McPhase J. of Applied Physics 91 (2002) 8885 • M. Rotter Using McPhase to calculate Magnetic Phase Diagrams of Rare Earth Compounds J. Magn. Magn. Mat. 272-276 (2004) 481 • M. Rotter High Speed Algorithm for the calculation of Magnetic and Orbital Excitations in Rare Earth based Systems  Computational Materials Science38 (2006) 400 NESY Winter School 2007

  47. Workshop Magnetostrictive Materials and Magnetic Refrigeration (MMMR) 13.-15. August 2007, Vienna, Austria http://www.univie.ac.at/MMMR/

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