Micromagnetic study of strain-induced magnetization switching in FeGaB nanomagnets for self-biased MRAM applications

Abstract

Lately, Magnetic Random-Access Memory (MRAM) has stimulated significant interests compared to traditional semiconductor memory devices due to its non-volatility combined with expeditious read and write endurance. In the preceding studies, conventional methods that had been investigated widely include spin-orbit torque (SOT)1, spin-transfer torque (STT)2 and current-driven switching. However, magnetization switching in MRAM utilizing such techniques fall short to observe the desired switching and inevitably supplemented by thermal issues, leading to inefficient functionality. Recently, considerable endeavour towards a new paradigm of straintronic devices (STR)3 for efficient magnetization switching is explored. A magnetoelectric STR constitutes of ferromagnetic and piezoelectric order parameters, in which an applied electric field across the piezoelectric order parameter instigate mechanical strain at the heterostructure interface giving rise to the magnetization switching due to the Villari effect. Though both out-of-plane and in-plane magnetization switching are examined in the aforementioned studies to explore the STR devices, magnetization switching in the in-plane direction is obscured on account of thermal instability in smaller element size and multi-domain formation in larger element size. Also, the self-biased STR-MRAM device that extinguishes the external bias magnetic field is still undiscovered.In this work, we investigated the size-dependent in-plane magnetization switching of FeGaB/PMN-PT (ferromagnetic/piezoelectric) heterostructure (Fig. 1(a)) using micromagnetic finite element method (FEM) coupled with electrodynamic and elastic analysis. Three elliptical nanodiscs of FeGaB magnetoelastic material having cross-sectional areas 100×90.9 nm2, 100×66.67 nm2, and 100×50 nm2 are investigated by varying the thickness from 2 nm to 28 nm on a 10×10×0.5 mm3 single-crystal PMN-PT (011) piezoelectric substrate. Initially, minimum thickness (dmin) at pre-stress condition for three elliptical nanodiscs are investigated (Fig. 1(b)) using in-plane induced energy well (△E) scaled by kbT (where kb is Boltzmann constant and T is the temperature in Kelvin). △E/kbT≤70 is an assumed condition for thermal instability to ensure dmin for STR-MRAM devices. To explore the maximum thickness related to self-biasing (dsb), pre-stress equilibrium exchange and demagnetization energies associated with the three elliptical nanodiscs are analyzed against thickness. The larger size magnets make an effort to minimize the energy by aligning the magnetization with the elliptical nanodisc boundary and gives rise to vortex state. On contrary, smaller size magnets minimize the energy by aligning the magnetization along the easy axis (0° or 180°) of the elliptical FeGaB nanomagnets without applying the external magnetic bias field (Fig. 2). This result is pivotal as such self-biasing would give primacy to future STR-MRAM devices by omitting the necessity for an extrinsic magnetic bias field.Although the above analysis is performed to obtain optimum size where STR-MRAM device is stable and self-biased, the maximum thickness (dmax) for in-plane 180° magnetization switching is limited by the critical stress requirement. It is observed that dsb is not necessarily the same as dmax for in-plane 180° magnetization switching. When compressive strain equal or greater than the critical compressive strain is applied from the pre-stress state, where magnetization is along the easy axis, in-plane 90° magnetization switching (along 90° or 270°) is observed. This happens as exchange and stress anisotropy energies are almost negligible and the demagnetization energy rises as the magnetization is switched from the easy to the hard axis. Magnetic precession is used to obtain in-plane 180o switching. When the magnetization component along the x-axis is negative during the precession, removal of external strain causes another 90o switching because the ferromagnet tries to reduce its total energy by gravitating to its nearest easy axis. In-plane fastest 180o magnetization switching time and associated external strain are investigated also. For fixed thickness, compressive strain requirement rises with increasing cross-sectional area. As the thickness is increased, tradeoff between fastest switching time and associated switching energy is observed for the same cross-sectional area. Whereas faster switching time and lesser switching energy are required for larger cross-sectional nanodiscs having the same thickness.This work can be potentially useful in the future STR-MRAM devices that eliminates the necessity of extrinsic magnetic field bias and completes in-plane 180o magnetization switching. **