Low power magnetoelectronic device structures and methods for making the same are provided. One magnetoelectronic device structure (100) comprises a programming line (104), a magnetoelectronic device (102) magnetically coupled to the programming line, and an enhanced permeability dielectric material (106) disposed adjacent the magnetoelectronic device. The enhanced permeability dielectric material has a permeability no less than approximately 1.5. A method for making a magnetoelectronic device structure is also provided. The method comprises fabricating a magnetoelectronic device (102) and depositing a conducting line (104). A layer of enhanced permeability dielectric material (106) having a permeability no less than approximately 1.5 is formed, wherein after the step of fabricating a magnetoelectronic device and the step of depositing a conducting line, the layer of enhanced permeability dielectric material is situated adjacent the magnetoelectronic device.