Thermal Stability of Magnetic States in Circular Thin-Film Nanomagnets with Large Perpendicular Magnetic Anisotropy

Abstract

The scaling of the energy barrier to magnetization reversal in thin film nanomagnets with perpendicular magnetization as a function of their lateral size is of great current interest for high-density magnetic random access memory devices. Here we determine the micromagnetic states that set the energy barrier to thermally activated magnetization reversal of circular thin film nanomagnets with large perpendicular magnetic anisotropy. We find a critical length in the problem that is set by the exchange and effective perpendicular magnetic anisotropy energies, with the latter including the size dependence of the demagnetization energy. For diameters smaller than this critical length the reversal occurs by nearly coherent magnetization rotation and the energy barrier scales with the square of the diameter normalized to the critical length (for fixed film thickness), while for larger diameters the transition state has a domain wall and the energy barrier depends linearly on the normalized diameter. Simple analytic expressions are derived for these two limiting cases and verified using full micromagnetic simulations with the String Method. Further, the effect of an applied field is considered and shown to lead to a plateau in the energy barrier versus diameter dependence at large diameters.

The 2017 Magnetism Roadmap

“…Thus far, STT-MRAM devices are larger than this scale. Recent experiments on large arrays of very uniform magnetic bits have found that the energy barrier (for fixed element thickness) scales with the element diameter (not the diameter squared) [146], consistent with the predictions of a recent micromagnetic model [144] and the reversal mode pictured in figure 19(b).…”

“…However, the device response clearly indicates more complex behaviour with intermediate multi-domain states (illustrated schematically in figure 19(b)), even in the switching of 50 nm diameter magnetic elements [143][144][145]. Further, thermal fluctuations play an important role in the dynamics, which can aid the switching process (e.g.…”

“…To achieve this, the magnetic anisotropy and exchange energy of the free layer materials must be increased. The expectation is that for very small sizes-in the macrospin or single domain limit-the energy barrier will be proportional to the volume of the magnetic element and, at larger sizes, there should be a crossover to a reverse domain expansion mediated reversal, in which the energy barrier scales with the element diameter times its thickness [144]. The length scale at which the crossover occurs depends on the exchange, anisotropy and magnetization of the elements.…”

Material Developments and Domain Wall-Based Nanosecond-Scale Switching Process in Perpendicularly Magnetized STT-MRAM Cells

“…For a given MTJ stack, the switching voltage is practically independent from the device size and shape in our interval of investigated sizes (not shown). This finding is consistent with the consensual conclusion that the switching energy barrier is almost independent from the device area 38,39 for device areas above 50 nm. In spite of this quasi-independence of the switching voltage and the device size, the switching duration was found to strongly depend on device size (Fig.…”

“…Using 42 , the domain wall stiffness field can be estimated to be at the most 20 mT in our devices. In circular devices, the domain wall has to elongate upon its propagation 38 such that the domain wall stiffness field H DW depends in principle on the DW position. It should be maximal when the wall is along the diameter of the free layer.…”