Memristors are non-volatile nano-resistors which resistance can be tuned by applied currents or voltages and set to a large number of levels. Thanks to these properties, memristors are ideal building blocks for a number of applications such as multilevel non-volatile memories and artificial nano-synapses, which are the focus of this work. A key point towards the development of large scale memristive neuromorphic hardware is to build these neural networks with a memristor technology compatible with the best candidates for the future mainstream non-volatile memories. Here we show the first experimental achievement of a multilevel memristor compatible with spin-torque magnetic random access memories. The resistive switching in our spin-torque memristor is linked to the displacement of a magnetic domain wall by spin-torques in a perpendicularly magnetized magnetic tunnel junction. We demonstrate that our magnetic synapse has a large number of intermediate resistance states, sufficient for neural computation. Moreover, we show that engineering the device geometry allows leveraging the most efficient spin torque to displace the magnetic domain wall at low current densities and thus to minimize the energy cost of our memristor. Our results pave the way for spin-torque based analog magnetic neural computation.

Shifting electrically a magnetic domain wall (DW) by the spin transfer mechanism [1-4] is one of the future ways foreseen for the switching of spintronic memories or registers [5,6]. The classical geometries where the current is injected in the plane of the magnetic layers suffer from a poor efficiency of the intrinsic torques [12,13] acting on the DWs. A way to circumvent this problem is to use vertical current injection [7,8,11]. In that case, theoretical calculations [9] attribute the microscopic origin of DW displacements to the out-of-plane (field-like) spin transfer torque [17,18]. Here we report experiments in which we controllably displace a DW in the planar electrode of a magnetic tunnel junction by vertical current injection. Our measurements confirm the major role of the out-of-plane spin torque for DW motion, and allow to quantify this term precisely. The involved current densities are about 100 times smaller than the one commonly observed with in-plane currents [10].Step by step resistance switching of the magnetic tunnel junction opens a new way for the realization of spintronic memristive devices [14][15][16].We devise an optimized sample geometry for efficient current DW motion using a magnetic tunnel junction with an MgO barrier sandwiched between two ferromagnetic layers, one free, the other fixed. Such junctions are already the building block of magnetic random-access memories (M-RAMs), which makes our device suitable for memory applications. The large tunnel magnetoresistance [19,20] allows us to detect clearly DW motions when they propagate in the free layer of the stack [21]. The additional advantage of magnetic tunnel junctions is that the out-of-plane field-like torque T OOP can reach large amplitudes, up to 30% of the classical in-plane torque T IP [22,23], in contrast to metallic spin-valve structures, in which the out-of-plane torque is only a few % of the in-plane torque [24,25]. This is of fundamental importance since theoretical calculations predict that, when the free and reference layers are based on materials with the same magnetization orientation (either inplane or perpendicular), the driving torque for steady domain wall motion by vertical current injection is the OOP field-like torque [9]. Indeed, T OOP is equivalent to the torque of a magnetic field in the direction of the reference layer, that has the proper symmetry to push the DW along the free layer. On the contrary, the inplane torque T IP can only induce a small shift of the DW of a few nm. In magnetic tunnel junctions with the same composition for the top free and bottom reference layers, the OOP field-like torque exhibits a quadratic dependence with bias [22,23], which could not allow us to reverse the DW motion by current inversion. Therefore we use asymmetric layer composition to obtain an asymmetric OOP field-like torque [26,27].The magnetic stack is sketched in Fig.