  We performed AC calorimetry and magnetoresistance measurements under pressure
for H || a-axis (easy-magnetization axis) in the novel heavy-fermion
superconductor UTe2. Thanks to the thermodynamic information, multiple
superconducting phases have been revealed under pressure and magnetic field.
The (H,T) phase diagram of superconductivity under pressure displays an abrupt
increase of the upper critical field (Hc2) at low temperature and in the high
field region, and a strong convex curvature of Hc2 at high temperature. This
behavior of Hc2 and the multiple superconducting phases require a state for the
superconducting order parameter more complex than a spin-triplet equal spin
pairing. Above the superconducting critical pressure, Pc, we find strong
indications that the possible magnetic order is closer to antiferromagnetism
than to ferromagnetism.
