  The recently discovered superconductor UTe$_2$, with a T$_c$ between 1.5~K
and 2~K, is attracting much attention due to strong suspicion of spin-triplet
and topological superconductivity. Its properties under magnetic field are also
remarkable, with field-reinforced and field-induced superconducting phases.
Here, we report the first complete thermodynamic determination of the phase
diagram for fields applied along the three crystallographic directions.
Measurements were performed up to 36~T along the hard magnetisation $b$~axis in
order to follow the superconducting transition up to the metamagnetic
transition at $H_{m} = 34.75$~T. They reveal the existence of a phase
transition line within the superconducting phase, and drastic differences
occurring between these two phases. Detailed analysis supports a different spin
state between the two phases, implying a low-field spin-triplet to high-field
spin-singlet transition, a unique case among superconductors, giving insight on
the mechanisms leading to spin-triplet superconductivity.
