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

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Movement of Spins - Magnons 153 T=1.3 K MF - Zeeman Ansatz (for S=1/2)

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

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

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Measured spin wave dispersion relations for x=0.35 and x=0.40. Solid lines show the best fits for the Heisenberg ferromagnet Hamiltonian with nearest neighbour exchange only. Dashed lines show the best fit including second neighbour interactions as well (i.e. hopping along Mn-O-Mn- O-Mn). (a) Crystal structure of La 2- 2x Sr 1+2x Mn 2 O 7. The Mn ions are at the centre of the MnO 6 octahedra. Circles denote La and Sr. (b) Expanded view of MnO 6 octahedra in a single bilayer, showing the Mn d 3z 2 -r 2 and d x 2 -y 2 orbitals.

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UO 2: Spin wave dispersion curves measured at 16.5 K along the principal crystallographic directions. Dashed lines and crosses correspond to acoustic phonon branches. Open symbols indicate qualitatively smaller magnon intensity than the filled points. The non-spin-flip cross-section was always found to be negligible.

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Movement of Charges - the Crystal Field Concept Hamiltonian E Q 4f –charge density

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NdCu 2 – Crystal Field Excitations orthorhombic, T N =6.5 K, Nd 3+ : J=9/2, Kramers-ion Gratz et. al., J. Phys.: Cond. Mat. 3 (1991) 9297

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T=10 KT=40 KT=100 K NdCu 2 - 4f Charge Density

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Magnetische Anregungen

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Calculate Magnetic Excitations and the Neutron Scattering Cross Section Linear Response Theory, MF-RPA

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Kristallfeld – übergänge Mittelung über Polykristall

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NdCu 2 Magnetic Phasediagram (Field along b-direction)

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Complex Structures AF1 Q=

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Complex Structures F1 Q=

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Complex Structures F2 Q=

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NdCu 2 Magnetic Phasediagram H||b F3 AF1 F1 a b c Lines=Experiment Colors=Theory

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Magnetische Anregungen– NdCu 2 H=3T||b τ

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NdCu 2 F3 AF1 F1 F3: measured dispersion was fitted to get exchange constants J(ij)

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1950 Movements of Atoms [Sound, Phonons] a τ orbiton Description: quadrupolar (+higher order) interactions a τ orbiton 1970 Movement of Spins [Magnons] ? Movement of Orbitals [Orbitons]

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M. Rotter, Institut für physikalische Chemie, Universität Wien

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McPhase - the World of Rare Earth MagnetismMcPhase - the World of Rare Earth Magnetism McPhase is a program package for the calculation of magnetic properties of rare earth based systems. Magnetization Magnetic Phasediagrams Magnetic Structures Elastic/Inelastic/Diffuse Neutron Scattering Cross Section

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and much more.... Magnetostriction Crystal Field/Magnetic/Orbital Excitations

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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 In stitute, 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 NdCu 2 Appl. Phys. A74 (2002) S751 M. Rotter, M. Doerr, M. Loewenhaupt, P. Svoboda, Modeling Magnetostriction in RCu 2 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 (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

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