Double magnetic tunnel junctions and methods of forming the same include a bottom reference layer having a first fixed magnetization and a first thickness. A first tunnel barrier is formed on the bottom reference layer. A free layer is formed on the first tunnel barrier and has a changeable magnetization. A second tunnel barrier is formed on the free layer. A top reference layer is formed on the second tunnel barrier and has a second fixed magnetization that is opposite to the first fixed magnetization and a second thickness that is significantly smaller than the first thickness.