A high-capacity magnetic memory capable of writing and reading a magnetic record in/from a magnetic recording film according to a perpendicular magnetic recording system at a high speed in a purely-electrically random access manner. In the magnetic memory, a writing-magnetic-field generating means 62 and a writing word line 43 are disposed relative to a perpendicular magnetic recording film 50, and a reading/writing bit-line conductor 41, a magnetoresistive-effect element 20 and a reading word lead conductor 42 are laminated in order on a probe substrate opposed to the perpendicular magnetic recording film 50. A magnetic probe 30 composed of a carbon nanotube containing a soft magnetic material is disposed relative to the magnetoresistive-effect element 20 in a standing manner, and electrically connected to the reading/writing bit-line conductor. During a writing operation, a micro-discharge is generated in a micro-gap G between the edge of the magnetic probe and the magnetic recording film under a writing magnetic field to allow a writing current to flow through the micro-gap G so as to heat a micro-region of the magnetic recording film in such a manner that it goes through its Curie point to thereby become magnetized in the direction of the recording magnetic field to form a magnetic record therein. During a reading operation, the magnetic record is read out through the magnetic probe in accordance with a current variation in the magnetoresistive-effect element.