Ph.D. thesis (pdf) - dirac

158 Boson Peak
g(ω)/ω 2 [arb. unit]
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0 5 10 15
ω [meV]
g(ω)− g D
(ω) [arb. units]
60
40
20
0
−20
−40
Patm
−60
0.41GPa
0.8GPa
1.4GPa
−80
0 5 10 15 20
ω [meV]
Figure 8.9: Left: the rDOS (g(ω)/ω 2 ) of PIB at different pressures. The Debye level
is indicated with horizontal lines (see the text). Right: the excess density of states.
Atmospheric pressure (•), 4 MPa () 8 MPa (), and 14 MPa ().
8.2.4 Shape of the boson peak
It has been found that the boson peak had a universal shape [Malinovsky et al., 1990]
when comparing the boson peak in various materials. In line with this, Chumakov
et al. [2004] find a universal exp(−ω/ω 0 ) behavior at frequencies above the boson
peak in g(ω)/ω 2 . The exp(−ω/ω 0 ) behavior is also expected from the FEC model
[Maurer and Schirmacher, 2004]. Based on the SPM model, Schober and coworkers
predict that the universal behavior above the boson peak at ambient pressure should
follow a ω −1 power law [Gurevich et al., 2003].
The neutron data allow us to analyze the influence of pressure on the shape and
intensity of the boson peak without the uncertainty from the unknown frequency
dependence of the light to vibration coupling factor which influences the Raman
spectra.
In figure 8.10 we show the boson peak at different pressures with the axis scaled by
the boson peak position (ω BP ) and intensity respectively. The data overlap on a
master curve roughly above ω BP /2. This is consistent with the picture of a universal
shape of the boson peak not only on the high frequency part but also in the region
of the peak itself. We find that the shape follows a exp(−ω/ω 0 ) behavior from
ω BP up to approximately 5ω BP . This suggests that the mechanisms responsible for
the boson peak are not altered as pressure is applied but rather pushed to higher
frequencies due to an increase of the force constants in the material.