Low power magnetoelectronic device structures and methods therefore are provided. The magnetoelectronic device structure (100, 150, 450, 451) comprises a programming line (104, 154, 156, 454, 456), a magnetoelectronic device (102, 152, 452) magnetically coupled to the programming line (104, 154, 156, 454, 456), and an enhanced permeability dielectric (EPD) material (106, 108, 110, 158, 160, 162, 458, 460, 462) disposed adjacent the magnetoelectronic device. The EPD material (106, 108, 110, 158, 160, 162, 458, 460, 462) comprises multiple composite layers (408) of magnetic nano-particles (406) embedded in a dielectric matrix (409). The composition of the composite layers is chosen to provide a predetermined permeability profile. A method for making a magnetoelectronic device structure is also provided. The method comprises fabricating the magnetoelectronic device (102, 152, 452) and depositing the programming line (104, 154, 156, 454, 456). The EPD material (106, 108, 110, 158, 160, 162, 458, 460, 462) comprising the multiple composite layers (408) is formed around the magnetoelectronic device (102, 152, 452) and/or between the device (102, 152, 452) and the programming line (104, 154, 156, 454, 456). The presence of the EPD structure (470, 480, 490) in proximity to the programming line (104, 154, 156, 454, 456) and/or the magnetoelectronic device (102, 152, 452) reduces the required programming current.