The present invention relates to a Bloch-line memory element and a nonvolatile RAM memory using such a Bloch-line memory element. The Bloch-line memory element comprises a planar magnetic memory element having magnetic domains separated by a wall which contains a Bloch-line disposed within the individual memory element. Coincident write lines interact with the magnetic element for writing a Bloch-line to a predetermined area within the memory element. For sensing the presence or absence of a Bloch-line within the predetermined area, one write conductor and a sense line are used for determining the logic state of the particular memory element. A plurality of memory elements are disposed in an address matrix and can be selected for reading from or writing to the particular Bloch-line RAM memory element for determining or writing bits of words.