  UTe$_2$ is a recently discovered unconventional superconductor that has
attracted much interest due to its many intriguing properties - a large
residual density-of-states in the superconducting state, re-entrant
superconductivity in high magnetic fields, and potentially spin-triplet
topological superconductivity. Our ac calorimetry, electrical resistivity, and
x-ray absorption study of UTe$_2$ under applied pressure reveals key new
insights on the superconducting and magnetic states surrounding
pressure-induced quantum criticality at P$_{c1}$ = 1.3 GPa. First, our specific
heat data at low pressures, combined with a phenomenological model, show that
pressure alters the balance between two closely competing superconducting
orders. Second, near 1.5 GPa we detect two bulk transitions that trigger
changes in the resistivity which are consistent with antiferromagnetic order,
rather than ferromagnetism. The presence of both bulk magnetism and
superconductivity at pressures above P$_{c2}$ = 1.4 GPa results in a
significant temperature difference between resistively and thermodynamically
determined transitions into the superconducting state, which indicates a
suppression of the superconducting volume fraction by magnetic order. Third,
the emergence of magnetism is accompanied by an increase in valence towards a
U$^{4+}$ (5f2) state, which indicates that UTe$_2$ exhibits intermediate
valence at ambient pressure. Our results suggest that antiferromagnetic
fluctuations may play a more significant role on the superconducting state of
UTe$_2$ than previously thought.
