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PROBLEM TO BE SOLVED : To obtain a magnetic thin film memory employing a magnetoresistive effect element 41 as a memory element in which erroneous writing or incomplete writing due to saturation magnetization of a magnetic film or variation of coercive force incident to variation working temperature dependent significantly on the environment is reduced. SOLUTION : The nonvolatile magnetic thin film memory uses a magnetoresistive effect element 41 having a vertical magnetization film as a memory element, employs a ferrimagnetic body where rare earth element magnetization is dominant in the vertical magnetization film and has a compensation temperature between a room temperature and a Curie point. A magnetic thin film memory comprises means for controlling the level of a current required for writing information stepwise, and a temperature sensor sensing the temperature of the magnetoresistive effect element. In the recording/reproducing method of the magnetic thin film memory, test writing of information in the memory cell is performed before the information is recorded and normal data is recorded after recording the test writing is confirmed.