Accurate Torque Evaluation in Elongated Ultra-Scaled STT-MRAM Devices
Authors: Fiorentini Simone , Pruckner Bernhard , Goes Wolfgang , Selberherr Siegfried , Sverdlov Viktor 
Published: September 2023

Emerging spin-transfer torque magnetoresistive random access memory (STT-MRAM) is attractive for stand-alone and embedded applications. STT-MRAM is nonvolatile, operates fast, and possesses excellent endurance. STT-MRAM is compatible with CMOS technology and can be integrated during the back-end-of-line process. This makes STT-MRAM promising for automotive and IoT applications, microcontrollers, frame buffer memory, and last level cache. The core of modern STT-MRAM cells consists of a magnetic tunnel junction (MTJ), which is a sandwich of two ferromagnetic (FM) layers separated by a tunnel barrier (TB). The FM layers are referred to as reference layer (RL) and free layer (FL). The magnetization of the RL is fixed, while the magnetization of the FL can be reversed. The use of MTJs with perpendicular magnetic anisotropy (PMA) permits to obtain better scalability and lower switching currents. When the magnetization vectors of the FL and RL are parallel (P), the electrical resistance is lower than when the vectors are anti-parallel (AP), which provides a way to store binary information. Importantly, the switching between these two stable configurations is achieved by purely electrical means.
To reduce the footprint and benefit from shape-induced anisotropy, an ultra-scaled MRAM cell with a composite FL made of several elongated ferromagnetic pieces, separated by multiple MgO barriers, was proposed and demonstrated [1]. In elongated FLs, shown in Fig.1a, domain walls or magnetization textures can be generated during switching. In this case, additional spin torques created by the presence of magnetization gradients inside the ferromagnetic parts must be considered. This type of torque is typically modeled by the Zhang-Li expression [2]. If the spin dephasing length correctly describes the coupled charge and spin transport through the device, the expression for bulk torque must be generalized [3].
In MTJs, however, there exists another torque acting on a FL close to the interface with MgO. This torque, predicted by Slonczewski [4] and Berger [5], was utilized to flip the magnetization in traditional MTJs with a FL fabricated as a flat and thin disk. It is due to the spin-polarized current coming across the TB from the RL. Electrons tunneling from the RL become spin-polarized. When entering the FL, the spin polarized electrons interact with the magnetization via the exchange interaction. When the magnetization vectors in the RL and FL are not aligned, the spin current components normal to the FL magnetization are quickly absorbed. Due to conservation of the angular momentum, the absorption of the normal component of the spin current results in a torque acting on the FL magnetization in the opposite sense. If the current is sufficiently strong, the magnetization of the FL can be switched between the two stable P and AP configurations relative to the RL.
As the Slonczewski torque is localized at the interface and Zhang-Li (ZL) torque is acting in the bulk, the two torques are usually assumed to be independent. However, this is not correct [5]. Although the spin component normal to the FL magnetization is indeed quickly absorbed, the interface-polarization induced spin current parallel to the magnetization propagates into the FL at a longer distance determined by the spin-flipping length. This length is about 10nm in typical FL materials. As the interface-polarization induced spin current hits the spin texture, it modifies the ZL torque value determined by the spin polarization in the bulk. The FL in ultra-scaled MRAM cells contains a TB on both interfaces. Here, we compare the ZL torque acting on the domain wall (Fig.1b) for the case, when the interface polarization at the second TB is lower than the spin polarization in the bulk (Fig.1c) or higher (Fig.1d). It is demonstrated that the torque acting on the domain wall can be enhanced compared to the ZL value for the case of larger interface polarization than spin polarization in the bulk.

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Figure 1