  We report muon spin rotation and magnetic susceptibility experiments on
in-plane stress effects on the static spin-stripe order and superconductivity
in the cuprate system La2-xBaxCuO4 with x = 0.115. An extremely low uniaxial
stress of 0.1 GPa induces a substantial decrease in the magnetic volume
fraction and a dramatic rise in the onset of 3D superconductivity, from 10 to
32 K; however, the onset of at-least-2D superconductivity is much less
sensitive to stress. These results show not only that large-volume-fraction
spin-stripe order is anti-correlated with 3D superconducting (SC) coherence,
but also that these states are energetically very finely balanced. Moreover,
the onset temperatures of 3D superconductivity and spin-stripe order are very
similar in the large stress regime. These results strongly suggest a similar
pairing mechanism for spin-stripe order, the spatially-modulated 2D and uniform
3D SC orders, imposing an important constraint on theoretical models.
