part 9

Energy levels visible in Inelastic Neutron Scattering

The fine electronic structure can be derived from different experiments (ESR, Mössbauer spectroscopy, Raman scattering). However, the most powerful tool to study the CEF effects is given by the Inelastic Neutron Scattering (INS) technique, especially in optically opaque metallic systems. For a system of N identical ions in a single-ion approximation the cross section is:

were:
γB– Bohr magneton
gL= Lande factor
(ki-kf) is the neutron momentum transfer.
For (ki-kf)||c only transverse transitions appear, whereas for (ki-kf) is perpendicular to c axis, both transverse and longitudinal transitions can be observed.

For experiments on polycrystalline materials, due to averaging in (ki-kf) space, the relation between matrix elements above, can be replaced by:

For monocrystals, the intensity of neutron dispersion for transition between CEF states Γj, Γk has the form:

where:
θ – angle between z-axis and the neutron beam.

Details of Theory

• Hamiltonian
• Fine electronic structure Ei, Γi(|LSLzSz>)
• The thermodynamic functions

Computable properties:

• Entropy S(T)
• Specific heat Cmol(T)
• Magnetic moment and influence of the external magnetic field for it m(B,T)
• Magnetic susceptibility along different crystal directions χi(T)
• Visibility of the energy levels in spectroscopy <Γi|J_|Γj>, <Γi|J+|Γj> , <Γi|JZ|Γj>
• Spin and orbital momenta of the magnetic ion in solid <Γi|L|Γi>, <Γi|S|Γi>