A memory device includes a cross-point array of spin-torque transfer MRAM cells. First rail structures laterally extend along a first horizontal direction. Each of the first rail structures includes a vertical stack including, from bottom to top, a first electrically conductive line, a reference layer having a fixed magnetization direction, and a tunnel barrier layer. Second rail structures laterally extend along a second horizontal direction. Each of the second rail structures includes a second electrically conductive line that overlies the first rail structures. A two-dimensional array of pillar structures is located between a respective one of the first rail structures and a respective one of the second rail structures. Each of the pillar structures includes a free layer having energetically stable magnetization orientations that are parallel or antiparallel to the fixed magnetization direction.