Ph.D. thesis (pdf) - dirac

8.2. The origin of the excess modes 157
mentioning that the studies by Monaco et al. were performed using nuclear inelastic
scattering, which might not be sensitive to all the modes in the vibrational density
of states [Chumakov et al., 2004].
The excess in the density of states
It is possible to define the excess of modes with respect to the Debye modes by the
total density of states minus the Debye density of states g ex (ω) = g ( ω) − g D (ω). If
the boson peak is due to modes that superimpose to Debye modes, then these modes
are described by g ex (ω) and the number of excess modes is given by the integral of
g ex (ω).
The shift of the excess to a higher frequency gives a decrease in the boson peak seen
in the rDOS. This is so because, as pointed out by Yannopoulos et al. [2006 a], the
division by ω 2 leads to an intrinsic suppression of the peak intensity.
Assuming that the excess density of states does not change in intensity but just
shifts to higher frequency then this effect will make the intensity of the boson peak
seen in the reduced excess density of states g ex (ω)/ω 2 inversely proportional to ωBP 2 .
Note however, that this is true for the intensity of g(ω)/ω 2 , because the Debye level
gives an additional term. The total reduced density of states will be given by
g(ω)/ω 2 = g D (ω)/ω 2 + g ex (ω)/ω 2 = rDOS D + g ex (ω)/ω 2 . (8.2.7)
It follows that the 1/ω 2 dependence of the intensity only will be seen if the excess
term g ex (ω)/ω 2 dominates over the Debye term, even in the most simple situation
where the Debye level itself is assumed to be pressure independent.
It is clear that to evaluate pressure dependence of the intensity the excess vibrational
density of states it is necessary to determine the Debye level. Our neutron
measurements do not give the vibrational density of states in absolute values, but
only the relative evolution with pressure. We therefore use the ratio of the boson
peak intensity over the Debye density of states at atmospheric pressure [Kanaya and
Kaji, 2001] in order to get comparable scales of the two. Based on this we estimated
excess densities of states at different pressures. The result is depicted in figure 8.9
b). The rather surprising result is that the number of excess states increases when
pressure increases. It is difficult to anticipate the mechanism which could lead to
such an increase in excess states. Our interpretation of the result is therefore that
it is not physically correct to view the vibrational density of states as Debye modes
plus excess modes.