  We investigate the coupling between the magnetic and superconducting order
parameters in an 8 m long meander line ("wire") made of a La1.94Sr0.06CuO4 film
with a cross section of 0.5 x 100 um^2. The magnetic order parameter is
determined using the Low-Energy muon spin relaxation technique. The
superconducting order parameter is characterized by transport measurements and
modified by high current density. We find that, when the superconducting order
parameter is suppressed by the current, the magnetic transition temperature,
Tm, increases. The extracted sign and magnitude of the Ginzburg-Landau coupling
constant indicate that the two orders are repulsive, and that our system is
located close to the border between first and second order phase transition.
