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In this paper, we have calculated the intrinsic threshold current density of domain wall (DW) motion in nanostrips with perpendicular magnetic anisotropy (PMA) and have estimated writing properties of magnetic random access memories (MRAMs) with DW motion. Carrying out a micromagnetic simulation, we revealed that the intrinsic threshold current density decreases with decreases in the strip thickness, width, and magnetization, whereas it did not depend significantly on magnetocrystalline anisotropy and exchange stiffness. These results showed good agreement with one-dimensional (1-D) analysis. We also found that current-induced DW motion in PMA strips may have potential for use in low-write-current MRAMs. For a width of less than roughly 100 nm, comparable properties to those of existing memories can be obtained.