  In the last decade, nanoscale resistive devices with memory have been the
subject of intense study because of their possible use in brain-inspired
computing. However, operational endurance is one of the limiting factors in the
adoption of such technology. For this reason, we discuss the emergence of
current-induced memristance in magnetic materials, known for their durability.
We show analytically and numerically that a single ferromagnetic layer can
possess GHz memristance, due to a combination of two factors: a current-induced
transfer of angular momentum (Zhang-Li torque) and the anisotropic
magnetoresistance (AMR). We term the resulting effect the anisotropic
magneto-memristance (AMM). We connect the AMM to the topology of the
magnetization state, within a simple model of a 1-dimensional annulus-shaped
magnetic layer, confirming the analytical results with micromagnetic
simulations for permalloy. Our results open a new path towards the realization
of single-layer magnetic memristive devices operating at GHz frequencies.
