  The NaZn13 type itinerant magnet LaFe13-xSix has seen considerable interest
due to its unique combination of large magnetocaloric effect and low
hysteresis. Here we demonstrate, with a combination of magnetometry, bespoke
microcalorimetry and inelastic neutron scattering that this is due to the
presence of paramagnetic spin fluctuations, which build up as the critical
point is approached. While thermal measurements show significant latent heat
independent changes in the heat capacity, inelastic neutron scattering reveals
the presence of broad quasielastic scattering that persists above Tc, in
addition to a finite Q quasielastic peak at Q=0.52 A$^{-1}$ (close to a 100
Bragg reflection in this system at Q = 0.54 A$^{-1}$). This finite Q
quasielastic peak appears only in the paramagnetic state and when in proximity
to the itinerant metamagnetic transition. We associate these observations with
a hidden competing phase and spin fluctuations close to the transition
temperature and magnetic field, that persist across the magnetic transition.
