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Magnetic Neutron Scattering

Magnetic Neutron Scattering. Martin Rotter, University of Oxford. Introduction: Neutrons and Magnetism Elastic Magnetic Scattering Inelastic Magnetic Scattering. Contents. Neutrons and Magnetism. Macro-Magnetism: Solution of Maxwell´s Equations – Engineering of (electro)magnetic

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Magnetic Neutron Scattering

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  1. Magnetic Neutron Scattering Martin Rotter, University of Oxford NESY Winter School 2009

  2. Introduction: Neutrons and Magnetism Elastic Magnetic Scattering Inelastic Magnetic Scattering Contents NESY Winter School 2009

  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 2009

  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 2009

  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 2009

  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 2009

  8. Interaction of Neutrons with Matter NESY Winter School 2009

  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. A short Excursion to Fourier and Delta Functions .... it follows by extending the range of x to more than –L/2 ...L/2 and going to 3 dimensions (v0 the unit cell volume) NESY Winter School 2009

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

  12. Difference to nuclear scattering: Formfactor ... no magnetic signal at high angles Polarisationfactor ... only moment components normal to κ contribute Magnetic Diffraction NESY Winter School 2009

  13. Atomic Lattice Magnetic Lattice ferro antiferro NESY Winter School 2009

  14. Atomic Lattice Magnetic Lattice ferro antiferro NESY Winter School 2009

  15. Atomic Lattice Magnetic Lattice ferro antiferro NESY Winter School 2009

  16. Formfactor Q= Dipole Approximation (small Q): NESY Winter School 2009

  17. 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).

  18. Arrangement of Magnetic Moments in Matter Paramagnet Ferromagnet Antiferromagnet And many more .... Ferrimagnet, Helimagnet, Spinglass ...collinear, commensurate etc. NESY Winter School 2009

  19. GdCu2 TN= 42 K M [010] TR= 10 K q = (2/3 1 0) Magnetic Structure from Neutron Scattering Experimental data D4, ILL Calculation done by McPhase Rotter et.al. J. Magn. Mag. Mat. 214 (2000) 281 NESY Winter School 2009

  20. GdCu2 TN= 42 K M [010] TR= 10 K q = (2/3 1 0) Magnetic Structure from Neutron Scattering Experimental data D4, ILL Calculation done by McPhase Rotter et.al. J. Magn. Mag. Mat. 214 (2000) 281 NESY Winter School 2009

  21. GdCu2 TN= 42 K M [010] TR= 10 K q = (2/3 1 0) Magnetic Structure from Neutron Scattering Experimental data D4, ILL Calculation done by McPhase Rotter et.al. J. Magn. Mag. Mat. 214 (2000) 281 NESY Winter School 2009

  22. GdCu2 TN= 42 K M [010] TR= 10 K q = (2/3 1 0) Magnetic Structure from Neutron Scattering Experimental data D4, ILL Calculation done by McPhase Rotter et.al. J. Magn. Mag. Mat. 214 (2000) 281 NESY Winter School 2009

  23. GdCu2 TN= 42 K M [010] TR= 10 K q = (2/3 1 0) Magnetic Structure from Neutron Scattering Experimental data D4, ILL Calculation done by McPhase Rotter et.al. J. Magn. Mag. Mat. 214 (2000) 281 NESY Winter School 2009

  24. GdCu2 TN= 42 K M [010] TR= 10 K q = (2/3 1 0) Magnetic Structure from Neutron Scattering Rpnuc= 4.95% Rpmag= 6.21% Experimental data D4, ILL Calculation done by McPhase Goodness of fit Rotter et.al. J. Magn. Mag. Mat. 214 (2000) 281 NESY Winter School 2009

  25. NdCu2 Magnetic Phasediagram (Field along b-direction) NESY Winter School 2009

  26. Complex Structures μ0Hb=2.6T AF1 μ0Hb=1T μ0Hb=0 Q= Experimental data TAS6, Riso Loewenhaupt, Z. Phys. (1996) 499 NESY Winter School 2009

  27. Complex Structures μ0Hb=2.6T F1 μ0Hb=1T μ0Hb=0 Q= Experimental data TAS6, Riso Loewenhaupt, Z. Phys. (1996) 499 NESY Winter School 2009

  28. Complex Structures μ0Hb=2.6T F2 μ0Hb=1T μ0Hb=0 Q= Experimental data TAS6, Riso Loewenhaupt, Z. Phys. (1996) 499 NESY Winter School 2009

  29. NdCu2 Magnetic PhasediagramH||b F1    F3  c F1  b a AF1  Lines=Experiment Colors=Theory Calculation done by McPhase NESY Winter School 2009

  30. A caveat on the Dipole Approximation Dipole Approximation (small Q): E. Balcar derived accurate formulas for the S. W. Lovesey „Theory of Neutron Scattering from Condensed Matter“,Oxford University Press, 1984 Page 241-242 NESY Winter School 2009

  31. M. Rotter & A. Boothroyd 2008 did some calculations E. Balcar NESY Winter School 2009

  32. Comparison to experiment (σ-σdip)/σdip(%) Goodness of fit: Rpdip=15.6% Rpbey=8.4 % (Rpnuc=7.3%) Calculation done by McPhase CePd2Si2 bct ThCr2Si2 structure Space group I4/mmm Ce3+ (4f1)J=5/2 TN=8.5 K q=(½ ½ 0), M=0.66 μB/Ce M. Rotter, A. Boothroyd, PRB, submitted NESY Winter School 2009

  33. NdBa2Cu3O6.97 superconductor TC=96K orth YBa2Cu3O7-x structure Space group Pmmm Nd3+ (4f3)J=9/2 TN=0.6 K q=(½ ½ ½), M=1.4 μB/Nd ... using the dipole approximation may lead to a wrong magnetic structure ! M. Rotter, A. Boothroyd, PRB, submitted Calculation done by McPhase NESY Winter School 2009

  34. Inelastic Magnetic Scattering • Dreiachsenspektometer – PANDA • Dynamik magnetischer Systeme: • Magnonen • Kristallfelder • Multipolare Anregungen NESY Winter School 2009

  35. Three Axes Spectrometer (TAS) k Q Ghkl k‘ q NESY Winter School 2009

  36. PANDA – TAS for Polarized Neutronsat the FRM-II, Munich NESY Winter School 2009

  37. 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 2009

  38. 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 2009

  39. Movement of Spins - Magnons 153 MF - Zeeman Ansatz (for S=1/2) T=1.3 K NESY Winter School 2009

  40. Movement of Spins - Magnons 153 T=1.3 K Bohn et. al. PRB 22 (1980) 5447 NESY Winter School 2009

  41. Movement of Spins - Magnons 153 a T=1.3 K Bohn et. al. PRB 22 (1980) 5447 NESY Winter School 2009

  42. + + + + + + + + + + E Hamiltonian Q Movement of Charges - the Crystal Field Concept 4f –charge density NESY Winter School 2009

  43. 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 2009

  44. T=100 K T=40 K T=10 K NdCu2 - 4f Charge Density NESY Winter School 2009

  45. Linear Response Theory, MF-RPA Calculate Magnetic Excitations and the Neutron Scattering Cross Section .... High Speed (DMD) algorithm: M. Rotter Comp. Mat. Sci. 38 (2006) 400 NESY Winter School 2009

  46. F3  F1  AF1  NdCu2 F3: measured dispersion was fitted to get exchange constants J(ij) Calculations done by McPhase

  47. 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 2009

  48. Magnetic Diffraction Magnetic Structures Caveat on using the Dipole Approx. • Magnetic Spectroscopy • Magnons (Spin Waves) • Crystal Field Excitations • Orbitons Summary NESY Winter School 2009

  49. Martin Rotter, University of Oxford NESY Winter School 2009

  50. 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 2009

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