  We present a combination of first-principles and experimental results
regarding the structural and magnetic properties of olivine-type LiFePO$_4$
under pressure. Our investigations indicate that the starting $Pbnm$ phase of
LiFePO$_4$ persists up to 70 GPa. Further compression leads to an isostructural
transition in the pressure range of ~70-75 GPa, inconsistent with a former
theoretical study. Considering our first-principles prediction for a high-spin
to low-spin transition of Fe$^{2+}$ close to 72 GPa, we attribute the
experimentally observed isostructural transition to a change on the spin state
of Fe$^{2+}$ in LiFePO$_4$. Compared to relevant Fe-bearing minerals,
LiFePO$_4$ exhibits the largest onset pressure for a pressure-induced spin
state transition.
