  Micro-physical processes on interstellar dust surfaces are tightly connected
to dust properties (i.e. dust composition, size and shape) and play a key role
in numerous phenomena in the interstellar medium (ISM). The large disparity in
physical conditions (i.e. density, gas temperature) in the ISM triggers an
evolution of dust properties. The analysis of how dust evolves with the
physical conditions is a stepping-stone towards a more thorough understanding
of interstellar dust. The aim of this paper is to highlight dust evolution in
the Horsehead Nebula PDR region. We use Spitzer/IRAC (3.6, 4.5, 5.8 and 8
{\mu}m), Spitzer/MIPS (24 {\mu}m) together with Herschel/PACS (70 and 160
{\mu}m) and Herschel/SPIRE (250, 350 and 500 {\mu}m) to map the spatial
distribution of dust in the Horsehead over the entire emission spectral range.
We model dust emission and scattering using the THEMIS interstellar dust model
together with the 3D radiative transfer code SOC. We find that the nano-grains
dust-to-gas ratio in the irradiated outer part of the Horsehead is 6 to 10
times lower than in the diffuse ISM. Their minimum size is 2 to 2.25 times
larger than in the diffuse ISM and the power-law exponent of their size
distribution, 1.1 to 1.4 times lower than in the diffuse ISM. Regarding the
denser part of the Horsehead, it is necessary to use evolved grains (i.e.
aggregates, with or without an ice mantle). It is not possible to explain the
observations using grains from the diffuse medium. We therefore propose the
following scenario to explain our results. In the outer part of the Horsehead,
all the nano-grains have not yet had time to re-form completely through
photo-fragmentation of aggregates and the smallest of the nano-grains that are
sensitive to the radiation field are photo-destroyed. In the inner part of the
Horsehead, grains most likely consist of multi-compositional, mantled
aggregates.
