The present invention is directed to a magnetic memory cell including a magnetic tunnel junction (MTJ) memory element and a two-terminal bidirectional selector coupled in series between two conductive lines. The MTJ memory element includes a magnetic free layer; a magnetic reference layer; and an insulating tunnel junction layer interposed therebetween. The two-terminal bidirectional selector includes a bottom electrode; a top electrode; a load-resistance layer interposed between the bottom and top electrodes and comprising a first tantalum oxide; a first volatile switching layer interposed between the bottom and top electrodes and comprising a metal dopant and a second tantalum oxide that has a higher oxygen content than the first tantalum oxide; and a second volatile switching layer in contact with the first volatile switching layer and comprising a third tantalum oxide that has a higher oxygen content than the first tantalum oxide.