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 ðH; TÞ 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.
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