  (Abridged) Debris disks trace remnant reservoirs of leftover planetesimals in
planetary systems. A handful of "warm" debris disks have been discovered in the
last years, where emission in excess starts in the mid-infrared. An interesting
subset within these warm debris disks are those where emission features are
detected in mid-IR spectra, which points towards the presence of warm
micron-sized dust grains. Given the ages of the host stars, the presence of
these grains is puzzling, and questions their origin and survival in time. This
study focuses on determining the mineralogy of the dust around 7 debris disks
with evidence for warm dust, based on Spitzer/IRS spectroscopic data, in order
to provide new insights into the origin of the dust grains. We present a new
radiative transfer code dedicated to SED modeling of optically thin disks. We
make use of this code on the SEDs of seven warm debris disks, in combination
with recent laboratory experiments on dust optical properties. We find that
most, if not all, debris disks in our sample are experiencing a transient
phase, suggesting a production of small dust grains on relatively short
timescales. From a mineralogical point of view, we find that enstatite grains
have small abundances compared to crystalline olivine grains. The main result
of our study is that we find evidences for Fe-rich crystalline olivine grains
(Fe / [Mg + Fe] ~ 0.2) for several debris disks. This finding contrasts with
studies of gas-rich protoplanetary disks. The presence of Fe-rich olivine
grains, and the overall differences between the mineralogy of dust in Class II
disks compared to debris disks suggest that the transient crystalline dust is
of a new generation. We discuss possible crystallization routes to explain our
results, and comment on the mechanisms that may be responsible for the
production of small dust grains.
