A hallmark of the iron-based superconductors is the strong coupling between magnetic, structural and electronic degrees of freedom. However, a universal picture of the normal state properties of these compounds has been confounded by recent investigations of FeSe where the nematic (structural) and magnetic transitions appear to be decoupled. Here, using synchrotron-based high-energy x-ray diffraction and time-domain Moessbauer spectroscopy, we show that nematicity and magnetism in FeSe under applied pressure are indeed strongly coupled. Distinct structural and magnetic transitions are observed for pressures, 1.0 GPa <= p <= 1.7 GPa, which merge into a single first-order phase line for p >= 1.7 GPa, reminiscent of what has been observed, both experimentally and theoretically, for the evolution of these transitions in the prototypical doped system, Ba(Fe[1-x]Co[x])2As2. Our results support a spin-driven mechanism for nematic order in FeSe and provide an important step towards a universal description of the normal state properties of the iron-based superconductors.
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