5(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).
6UO2: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.
7Movement of Charges - the Crystal Field Concept +4f –charge densityEQHamiltonian
8NdCu2 – Crystal Field Excitations orthorhombic, TN=6.5 K, Nd3+: J=9/2, Kramers-ionGratz et. al., J. Phys.: Cond. Mat. 3 (1991) 9297
20NdCu2F3 F3: measured dispersion was fitted to get exchange constants J(ij)F1 AF1
21Movements of Atoms [Sound, Phonons] Movement of Spins [Magnons]? Movement of Orbitals [Orbitons]aaτorbitonτorbitonDescription: quadrupolar(+higher order) interactions
22M. Rotter, Institut für physikalische Chemie, Universität Wien
23McPhase - the World of Rare Earth Magnetism McPhase is a program package for the calculation ofmagnetic properties of rare earth based systems. Magnetization Magnetic Phasediagrams Magnetic Structures Elastic/Inelastic/Diffuse Neutron Scattering Cross Section
24Crystal Field/Magnetic/Orbital Excitations Magnetostriction and much more....
25McPhase 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, GermanyR. Schedler, Hahn Meitner Institut, Berlin, Germany P. Fabi né Hoffmann, Forschungszentrum Jülich, Germany S. Rotter, Wien, AustriaM. Banks, Max Planck Institute, Stuttgart, GermanyDuc 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) 8885M. Rotter Using McPhase to calculate Magnetic Phase Diagrams of Rare Earth Compounds J. Magn. Magn. Mat (2004) 481M. Rotter High Speed Algorithm for the calculation of Magnetic and Orbital Excitations in Rare Earth based Systems Computational Materials Science38 (2006) 400