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**Movement of Atoms [Sound, Phonons]**

Brockhouse The Nobel Prize in Physics 1994 E Q π/a Phonon Spectroscopy: 1) neutrons 2) high resolution X-rays

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**Movement of Spins - Magnons**

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

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**Movement of Spins - Magnons**

153 T=1.3 K Bohn et. al. PRB 22 (1980) 5447

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**Movement of Spins - Magnons**

153 a T=1.3 K Bohn et. al. PRB 22 (1980) 5447

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(a) Crystal structure of La2-2xSr1+2xMn2O7. The Mn ions are at the centre of the MnO6 octahedra. Circles denote La and Sr. (b) Expanded view of MnO6 octahedra in a single bilayer, showing the Mn d3z2 -r2 and dx2-y2 orbitals. 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).

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**UO2:Spin wave dispersion curves measured at 16**

UO2: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**

+ 4f –charge density E Q Hamiltonian

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**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

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NdCu2 - 4f Charge Density T=100 K T=40 K T=10 K

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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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**NdCu2 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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**NdCu2 Magnetic Phasediagram H||b**

F1 F3 c F1 b a AF1 Lines=Experiment Colors=Theory

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**Magnetische Anregungen– NdCu2**

H=3T||b τ

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

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**Movements of Atoms [Sound, Phonons]**

Movement of Spins [Magnons] ? Movement of Orbitals [Orbitons] a a τorbiton τorbiton Description: quadrupolar (+higher order) interactions

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**M. Rotter, Institut für physikalische Chemie, Universität Wien**

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**McPhase - 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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**Crystal Field/Magnetic/Orbital Excitations**

Magnetostriction and much more....

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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 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 NdCu2 Appl. 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 (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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