Energy landscape of noncollinear exchange coupled magnetic multilayers

We conduct an exploration of the energy landscape of two coupled ferromagnetic layers with perpendicular-to-plane uniaxial anisotropy using finite-element micromagnetic simulations. These multilayers can be used to produce noncollinearity in spin-transfer torque magnetic random-access memory cells, which has been shown to increase the performance of this class of computer memory. We show that there exists a range of values of the interlayer exchange coupling constants for which the magnetic state of these multilayers can relax into two energy minima. The size of this region is determined by the difference in the magnitude of the layer anisotropies and is minimized when this difference is large. In this case, there is a wide range of experimentally achievable coupling constants that can produce desirable and stable noncollinear alignment. We investigate the energy barriers separating the local and global minima using string method simulations, showing that the stabilities of the minima increase with increasing difference in the anisotropy of the ferromagnetic layers. We provide an analytical solution to the location of the minima in the energy landscape of coupled macrospins, which has good agreement with our micromagnetic results for a case involving ferromagnetic layers with the same thickness and anisotropy, no demagnetization field, and large exchange stiffness. These results are important to understand how best to employ noncollinear coupling in the next generation of thin-film magnetic devices.