excited states have become populated, allowing higher
transitions to have greater spectral weight, and shifting
the observed peak to a higher energy. However, the data
is much broader than the instrumental resolution, and
MF-RPA theory we have used to analyse the low temperature data does not account for thermal broadening
of the excitations. Instead we have convoluted the calculation with Gaussian curves with a full width at half
maximum of 1.2 meV to obtain the curves in figure 4,
whereas instrumental resolution at these energy transfers
is expected to be less than 0.5 meV. It can be seen that
this still does not fully account for the measurements.
In addition, the calculations predict that the intensity
should fall off much faster with increasing temperature
than is observed: the calculate intensity ratio of the peak
area at 720 K vs 100 K is 0.35, which is half that observed (I720K /I100K ≈ 0.7). Thus, whilst the energies of
the peaks observed at high temperatures may be satisfactorily explained by the MF-RPA theory, their intensity
and linewidths needs a more sophisticated approach.
Fe2+ due to splitting of the S = 2 levels that arise from
the effects of the crystal field and spin-orbit interactions
amplified by the highly distorted nature of the oxygen octahedron surrounding the iron spins. Above TN the magnetic fluctuations are observed to relatively high temperatures, with little temperature dependence between 100
and 720 K. Additional excitations, broad in energy, are
observed around ± 4 meV that are due to the single-ion
splittings caused by the spin-orbit and crystal field interactions. These excitations weaken slightly at 720 K
compared to 100 K, consistent with the calculated crosssections from our single-ion model. Our theoretical analysis using the MF-RPA model provides detailed spectra
of the d−shell in LiFePO4 and also enables estimates of
the average ordered magnetic moment and TN . Applying
it to spin-wave results of other members of the LiM PO4
(M = Mn, Co, and Ni) compounds provides reasonable
ordered moments and transition temperatures showing
the approach is robust.
In summary, we present a inelastic neutron scattering study in LiFePO4 that complements a previous spin
wave excitations study. In particular, we find an extra
excitation at 4.5 meV at T = 35 K < TN that is nearly
dispersionless and is most intense around magnetic zone
centers. We show that these excitations correspond to
transitions between thermally occupied excited states of
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