  We present a theoretical description of the London penetration depth of a
multi-band superconductor in the case when both superconducting and
spin-density wave orders coexist. We focus on clean systems and zero
temperature to emphasize the effect of the two competing orders. Our
calculation shows that the supefluid density closely follows the evolution of
the superconducting order parameter as doping is increased, saturating to a BCS
value in the pure superconducting state. Furthermore, we predict a strong
anisotropic in-pane penetration depth induced by the spin-density wave order.
