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We present a theoretical description of the London penetration depth of amulti-band superconductor in the case when both superconducting andspin-density wave orders coexist. We focus on clean systems and zerotemperature to emphasize the effect of the two competing orders. Ourcalculation shows that the supefluid density closely follows the evolution ofthe superconducting order parameter as doping is increased, saturating to a BCSvalue in the pure superconducting state. Furthermore, we predict a stronganisotropic in-pane penetration depth induced by the spin-density wave order.

Magnetic penetration depth in the presence of a spin-density wave in multiband superconductors at zero temperature