  Resolving the interplay between magnetic interactions and structural
properties in strongly correlated materials through a quantitatively accurate
approach has been a major challenge in condensed matter physics. Here we apply
highly accurate first principles quantum Monte Carlo (QMC) techniques to obtain
structural and magnetic properties of the iron selenide (FeSe) superconductor
under pressure. Where comparable, the computed properties are very close to the
experimental values. Of potential ordered magnetic configurations, collinear
spin configurations are the most energetically favorable over the explored
pressure range. They become nearly degenerate in energy with bicollinear spin
orderings at around 7 GPa, when the experimental critical temperature $T_c$ is
the highest. On the other hand, ferromagnetic, checkerboard, and staggered
dimer configurations become relatively higher in energy as the pressure
increases. The behavior under pressure is explained by an accurate analysis of
the charge compressibility and the orbital occupation as described by the QMC
many-body wave function, which reveals how spin, charge and orbital degrees of
freedom are strongly coupled in this compound. This remarkable pressure
evolution suggests that stripe-like magnetic fluctuations may be responsible
for the enhanced $T_c$ in FeSe and that higher T$_c$ is associated with
nearness to a crossover between collinear and bicollinear ordering.
