  FeSe, despite being the structurally simplest compound in the family of
iron-based superconductors, shows an astoundingly rich interplay of physical
phenomena including nematicity and pressure-induced magnetism. Here, we present
a microscopic study of these two phenomena by high-energy x-ray diffraction and
time-domain M\"ossbauer spectroscopy on FeSe single crystals over a wide
temperature and pressure range. The topology of the pressure-temperature phase
diagram is a surprisingly close parallel to the well-known doping-temperature
phase diagram of BaFe2As2 generated through partial Fe/Co and Ba/Na
substitution. In FeSe with pressure p as a control parameter, the
magneto-structural ground state can be tuned from "pure" nematic - paramagnetic
with an orthorhombic lattice distortion - through a strongly coupled
magnetically ordered and orthorhombic state to a magnetically ordered state
without an orthorhombic lattice distortion. The magnetic hyperfine field
increases monotonically over a wide pressure range. However, the orthorhombic
distortion initially decreases under increasing pressure, but is stabilized by
cooperative coupling to the pressure-induced magnetic order. Close to the
reported maximum of the superconducting critical temperature Tc (occuring at p
= 6.8 GPa), the orthorhombic distortion suddenly disappears and FeSe remains
tetragonal down to the lowest temperature measured. Analysis of the structural
and magnetic order parameters suggests an independent origin of the structural
and magnetic ordering phenomena, and their cooperative coupling leads to the
similarity with the canonical phase diagram of iron pnictides.
