  We report the magnetoresistance in the novel spin-triplet superconductor UTe2
under pressure close to the critical pressure Pc, where the superconducting
phase terminates, for field along the three a, b and c-axes in the orthorhombic
structure. The superconducting phase for H // a-axis just below Pc shows a
field-reentrant behavior due to the competition with the emergence of magnetic
order at low fields. The upper critical field Hc2 for H // c-axis shows a
quasi-vertical increase in the H-T phase diagram just below Pc, indicating that
superconductivity is reinforced by the strong fluctuations which persist even
at high fields above 20T. Increasing pressure leads to the disappearance of
superconductivity at zero field with the emergence of magnetic order.
Surprisingly, field-induced superconductivity is observed at high fields, where
a spin-polarized state is realized due to the suppression of the magnetic
ordered phases; the spin-polarized state is favorable for superconductivity,
whereas the magnetic ordered phase at low field seems to be unfavorable. The
huge Hc2 in the spin-polarized state seems to imply a spin-triplet state.
Contrary to the a- and c-axes, no field-reinforcement of superconductivity
occurs for magnetic field along the b-axis. We compare the results with the
field-reentrant superconductivity above the metamagnetic field, Hm for the
field direction tilted by about 30 deg. from b to c-axis at ambient pressure as
well as the field-reentrant (-reinforced) superconductivity in ferromagnetic
superconductors, URhGe and UCoGe.
