movement of atoms [sound, phonons] brockhouse 1950... e q π/a the nobel prize in physics 1994...
TRANSCRIPT
Movement of Atoms [Sound, Phonons]
Brockhouse 1950 ...
E
Q
π/a
The Nobel Prize in Physics 1994
Phonon Spectroscopy: 1) neutrons 2) high resolution X-rays
Movement of Spins - Magnons
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jiijJH SS)(2
1
153
T=1.3 KMF - Zeeman Ansatz (for S=1/2)
Movement of Spins - Magnons
ij
jiijJH SS)(2
1
Bohn et. al. PRB 22 (1980) 5447
T=1.3 K
153
Movement of Spins - Magnons
ij
jiijJH SS)(2
1
Bohn et. al. PRB 22 (1980) 5447
T=1.3 Ka
153
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 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.
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.
Movement of Charges - the Crystal Field Concept
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Hamiltonian ilm
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4f –charge density
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
T=10 KT=40 KT=100 K
NdCu2 - 4f Charge Density)()(|)(|)(ˆ
,...,06,4,2,0
24
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nmn
mnnnmf ZOecrR Jr
Magnetische Anregungen
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Calculate Magnetic Excitations and the Neutron Scattering Cross Section
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NdCu2 Magnetic Phasediagram(Field along b-direction)
Complex Structures
AF1
Q=
Complex Structures
F1
Q=
Complex Structures
F2
Q=
NdCu2 Magnetic PhasediagramH||b
F3
AF1
F1
ab
c
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Lines=ExperimentColors=Theory
Magnetische Anregungen– NdCu2
H=3T||b
τ
NdCu2F3
AF1
F1
F3: measured dispersion was fitted to get exchange constants J(ij)
1950 Movements of Atoms [Sound, Phonons]
a
τorbiton
lmij
jmli
mlQ OOijCH
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)()()( JJDescription: quadrupolar (+higher order) interactions
a
τorbiton
1970 Movement of Spins [Magnons]
? Movement of Orbitals [Orbitons]
M. Rotter, Institut für physikalische Chemie, Universität Wien
McPhase - the World of Rare Earth MagnetismMcPhase 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
and much more....
Magnetostriction
Crystal Field/Magnetic/Orbital Excitations
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, 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) 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