A magnetic memory cell having read-write conductor that is wholly clad with a high magnetic permeability soft magnetic material for a pinned-on-the-fly soft ferromagnetic reference layer is disclosed. The magnetic memory cell includes a ferromagnetic data layer, an intermediate layer formed on the ferromagnetic data layer, and a soft ferromagnetic reference layer having a non-pinned orientation of magnetization formed on the intermediate layer. The soft ferromagnetic reference layer includes a read-write conductor and a ferromagnetic cladding that completely surrounds the read-write conductor to form a cladded read-write conductor. During a read operation, a read current flowing through the read-write conductor generates a read magnetic field that does not saturate the ferromagnetic cladding. During a write operation, a write current flowing through the read-write conductor generates a write magnetic field that saturates the ferromagnetic cladding and extends to the ferromagnetic data layer.