A stacked-thin-film structure that includes an Llo-ordered MnAl layer having high perpendicular magnetic anisotropy (PMA). In some embodiments, the Ll0-ordered MnAl layer has an Mn content in a range of about 35% to about 65%, a thickness less than about 50 nm, a saturation magnetization of about 100 emu/cm3 to about 600 emu/cm3 and a magnetocrystalline anisotropy of at least 1×106 erg/cm. In some embodiments, the high-PMA Llo-ordered MnAl material is incorporated in magnetic tunneling junction stacked-film structures that are part of magnetoelectronic circuitry, such as spin-transfer-torque magnetoresistive random access memory circuitry and magnetic logic circuitry. In some embodiments, the high-PMA Llo-ordered MnAl material is incorporated into other devices, such as into read/write heads and/or recording media of hard-disk-drive devices.