Calculation of energy-barrier lowering by incoherent switching in STT-MRAM

To make a useful STT-MRAM (spin-transfer torque magnetoresistive random-access memory) device, it is necessary to be able to calculate switching rates, which determine the error rates of the device. In a single-macrospin model, one can use a Fokker-Planck equation to obtain a low-current thermally activated rate $\propto \exp(-E_{eff}/k_B T)$. Here the effective energy barrier $E_{eff}$ scales with the single-macrospin energy barrier $KV$, where $K$ is the effective anisotropy energy density and $V$ the volume. A long-standing paradox in this field is that the actual energy barrier appears to be much smaller than this. It has been suggested that incoherent motions may lower the barrier, but this has proved difficult to quantify. In the present paper, we show that the coherent precession has a magnetostatic instability, which allows quantitative estimation of the energy barrier and may resolve the paradox.