Urmimala Roy

Micromagnetic study of spin-transfer-torque switching of a ferromagnetic cross towards multi-state spin-transfer-torque based random access memory

We study spin-transfer-torque (STT) switching of a cross-shaped ferromagnet with unequal branches as the free layer in a magnetic tunnel junction using micromagnetic simulations. The free layer in the magnetic tunnel junction is thus designed to have four stable energy states using shape anisotropy. Switching shows distinct regions with increasing current density. Stability of the states against thermal fluctuations is considered, and the validity of the results for different dimensions and material parameters of the free layer ferromagnet is investigated. The results could be useful for a multi-bit STT-based memory.

Spin-transfer-torque switching in spin valve structures with perpendicular, canted, and in-plane magnetic anisotropies

We exploit canted anisotropies as possible means to enhance spin-transfer-torque (STT) and reduce switching currents. The STTs in spin-valve structures with perpendicular, canted, and, as a reference, in-plane magnetic anisotropies were studied. For perpendicular magnetic anisotropy and canted spin valves the thicknesses and number of Co and Pt layers were varied to obtain different angles of the magnetic anisotropy with respect to the sample plane. Point contact measurements were used to measure the change in the switching-field of the magnetization with the change in the bias current applied to the point contact. A larger STT effect, as evidenced by a larger change in the switching magnetic field for the unit change in the dc bias current, was observed for the sample with 45∘ tilt in magnetization compared to a sample with 12∘ tilt. Tilted magnetization of the reference layer causes precessional switching, decreasing the switching energy and time. Micromagnetic simulations were performed to explain the ...

Magnetization switching of a metallic nanomagnet via current-induced surface spin-polarization of an underlying topological insulator

We consider a thermally stable, metallic nanoscale ferromagnet (FM) subject to spin-polarized current injection and exchange coupling from the spin-helically locked surface states of a topological insulator (TI) to evaluate possible non-volatile memory applications. We consider parallel transport in the TI and the metallic FM, and focus on the efficiency of magnetization switching as a function of transport between the TI and the FM. Transport is modeled as diffusive in the TI beneath the FM, consistent with the mobility in the TI at room temperature, and in the FM, which essentially serves as a constant potential region albeit spin-dependent except in the low conductivity, diffusive limit. Thus, it can be captured by drift-diffusion simulation, which allows for ready interpretation of the results. We calculate switching time and energy consumed per write operation using self-consistent transport, spin-transfer-torque (STT), and magnetization dynamics calculations. Calculated switching energies and times compare favorably to conventional spin-torque memory schemes for substantial interlayer conductivity. Nevertheless, we find that shunting of current from the TI to a metallic nanomagnet can substantially limit efficiency. Exacerbating the problem, STT from the TI effectively increases the TI resistivity. We show that for optimum performance, the sheet resistivity of the FM layer should be comparable to or larger than that of the TI surface layer. Thus, the effective conductivity of the FM layer becomes a critical design consideration for TI-based non-volatile memory.

Write Error Rate of Spin-Transfer-Torque Random Access Memory Including Micromagnetic Effects Using Rare Event Enhancement

Spin-transfer-torque random access memory (STT-RAM) is a promising candidate for the next generation of random access memory due to improved scalability, read-write speeds, and endurance. However, the write pulse duration must be long enough to ensure a low write error rate (WER), the probability that a bit will remain unswitched after the write pulse is turned OFF, in the presence of stochastic thermal effects. WERs on the scale of 10-9 or lower are desired. Within a macrospin approximation, WERs can be calculated analytically using the Fokker-Planck method to this point and beyond. However, dynamic micromagnetic effects within the bit can affect and lead to faster switching. Such micromagnetic effects can be addressed via numerical solution of the stochastic Landau-Lifshitz-Gilbert-Slonczewski (LLGS) equation. However, determining WERs approaching 10-9 would require well over 109 such independent simulations, which is infeasible. In this paper, we explore the calculation of WER using rare event enhancement (REE), an approach that has been used for Monte Carlo simulation of other systems where rare events nevertheless remain important. Using a prototype REE approach tailored to the STT-RAM switching physics, we demonstrate reliable calculation of a WER to 10-9 with sets of only approximately 103 ongoing stochastic LLGS simulations, and the apparent ability to go further.

Proposal of a Multistate Memory Using Voltage Controlled Magnetic Anisotropy of a Cross-Shaped Ferromagnet

Voltage controlled magnetic anisotropy (VCMA)-induced precessional magnetization dynamics of a cross-shaped ferromagnet (FM) is studied by micromagnetic simulation. A cross-shaped FM, which has four minima in its energy landscape, can be used to store two bits. We show that, by selecting appropriate dimensions and taking into account interfacial perpendicular magnetic anisotropy, the cross-shaped FM can be switched from one state to the other states using VCMA, while the in-plane component of magnetization provides multistate functionality. VCMA-induced switching provides a low-power alternative to spin-transfer-torque switching of a similar cross-shaped FM studied previously. We estimate the thermal stability using the string method to capture the complex micromagnetic nature of the switching along the minimum energy path. The results could be useful toward development of a low-power multistate nonvolatile memory.

Micromagnetic simulations of spin-wave normal modes and the spin-transfer-torque driven magnetization dynamics of a ferromagnetic cross

We studied spin-transfer-torque (STT) switching of a cross-shaped magnetic tunnel junction in a recent report [Roy et al., J. Appl. Phys. 113, 223904 (2013)]. In that structure, the free layer is designed to have four stable energy states using the shape anisotropy of a cross. STT switching showed different regions with increasing current density. Here, we employ the micromagnetic spectral mapping technique in an attempt to understand how the asymmetry of cross dimensions and spin polarization direction of the injected current affect the magnetization dynamics. We compute spatially averaged frequency-domain spectrum of the time-domain magnetization dynamics in the presence of the current-induced STT term. At low currents, the asymmetry of polarization direction and that of the arms are observed to cause a splitting of the excited frequency modes. Higher harmonics are also observed, presumably due to spin-wave wells caused by the regions of spatially non-uniform effective magnetic field. The results could be used towards designing a multi-bit-per-cell STT-based random access memory with an improved storage density.

Write error rate in spin-transfer-torque random access memory including micromagnetic effects

Spin-transfer-torque (STT) random access memory (STTRAM) is considered to be one of the promising candidates for a non-volatile memory for improved scalability and access speed. Write error rate (WER) in an STTRAM is the probability that the free layer magnetization of the STTRAM bit does not flip when a write current is applied because of random thermal fluctuations. The WER needs to be below a certain acceptable limit for reliable write operation. Previously, WER have been studied using Fokker-Planck (FP) calculations for perpendicular bit [1] and using Landau-Lifshitz-Gilbert (LLG) simulations for the magnetization dynamics including a random thermal magnetic field and an STT term, for an in-plane bit with and without perpendicular magnetic anisotropy (PMA) [2]. These studies however assumed the free layer magnetization to be a macrospin, thereby neglecting the spatial variation in spin across the free layer (micromagnetic effects). Several important experimental observations related to WER in STTRAM have, however, been attributed to spatially varying spin-texture in the free layer magnet, for example, sub-volume excitations [3] and higher order spin wave modes related to branching of WER [4, 5].

Machine learning for variability aware statistical device design: The case of perpendicular spin-transfer-torque random access memory

Spin-transfer-torque random access memory (STT RAM) is a promising memory technology due to its scalability, endurance and non-volatility. Addressing the process induced variations during realistic device fabrication process is a challenge, while trying to meet performance specifications, more so with the technology scaling leading to smaller device dimensions. In a simplified picture, the performance parameters of an STT RAM cell such as switching current density for a given pulse length or the switching delay for a given applied current density, depend on a variety of material parameters such as magnetic anisotropy and damping constant of the “free layer” (FL), the information storage layer. Besides material parameters, device dimensions, such as the diameter and the thickness of FL also vary about the target values, due to imperfections during thin-film deposition, lithography and ion-beam etching, among other process steps. To consider process variations in such parameters, Monte-Carlo simulations can be used, where each of the parameters can be, e.g., a random number from a Gaussian distribution about its target value. However, a modest number of 5 parameters and 100 values for each of them would require (102)5 = 1010 device simulations, and would be computationally infeasible for e.g., micromagnetic simulation. A possible route to circumvent such a prohibitively large computational load would be to use a compact model [1, 2]. However, a method like this relies on the so-called macrospin approximation and assumes spins across FL to be parallel to each other at all times during switching and might not be a true representation. Also, for many emerging devices, a compact model still is not available. Machine learning (ML) has been used in the past to model array of resistive random access memory (RRAM) [3]. In this work, we propose an ML driven simulation methodology to take the effect of process variation into account using micromagnetic simulations with reasonable computational effort. We employ support vector regression (SVR), a method used in supervised learning to anticipate the behavior of a system based on previously obtained “training data”, to predict performance of an STT RAM cell. We use STT RAM as a model system, although the proposed scheme should be usable for other devices too.