Abstract: A magnetoresistive sensor includes a magnetoresistive element and equipment which generates a magnetic field in the magnetoresistive element thereby inducing a biasing magnetic field in the element, where the magnetoresistive element comprises a high electron mobility semiconductor and electrodes which are connected to the semiconductor. If it is an insulator, the equipment, which generates the biasing magnetic field and supplies it to the magnetoresistive element, may contact directly to the magnetoresistive element. If it is a conductor, an insulating separation layer must be set between the equipment and the element. A magnetoresistive element is representatively Corbino disk type or a bar type magnetoresistive element. Another candidate of the magnetoresistive element is an element consisting of a high electron mobility semiconductor, a pair of electrodes which make a current path in the high electron mobility semiconductor, and another pair of electrodes to detect the induced voltage by the current.