  CeCoSi is an intermetallic antiferromagnet with a very unusual
temperature-pressure phase diagram: at ambient pressure it orders below
$T_{\mathrm{N}} = 8.8$ K, while application of hydrostatic pressure induces a
new magnetically ordered phase with exceptionally high transition temperature
of $\sim40$ K at 1.5 GPa. We studied the magnetic properties and the
pressure-induced magnetic phase of CeCoSi by means of elastic and inelastic
neutron scattering (INS) and heat capacity measurements. At ambient pressure
CeCoSi orders into a simple commensurate AFM structure with a reduced ordered
moment of only $m_{\mathrm{Ce}} = 0.37(6)$ $\mu_{\mathrm{B}}$. Specific heat
and low-energy INS indicate a significant gap in the low-energy magnon
excitation spectrum in the antiferromagnetic phase, with the CEF excitations
located above 10 meV. Hydrostatic pressure gradually shifts the energy of the
magnon band towards higher energies, and the temperature dependence of the
magnons measured at 1.5 GPa is consistent with the phase diagram. Moreover, the
CEF excitations are also drastically modified under pressure.
