One time programmable memory units include a magnetic tunnel junction cell electrically coupled to a bit line and a word line. The magnetic tunnel junction cell is pre-programmed to a first resistance state, and is configured to switch only from the first resistance state to a second resistance state by passing a voltage across the magnetic tunnel junction cell. In some embodiments, a transistor is electrically coupled between the magnetic tunnel junction cell and the word line or the bit line. In other embodiments, a device having a rectifying switching characteristic, such as a diode or other non-ohmic device, is electrically coupled between the magnetic tunnel junction cell and the word line or the bit line. Methods of pre-programming the one time programmable memory units and reading and writing to the units are also disclosed.