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We compute the spin torque acting on elongated magnetic layers inrecently proposed ultra-scaled STT-MRAM devices. For thispurpose we evaluate the non-equilibrium spin accumulation bysolving the coupled spin and charge transport equations. This goesbeyond the Slonczewski torque approximation which describestorques localized at the interface of the tunnel barrier and themagnetic free layer as well as the Zhang-Li torque approximationmodeling the torque acting on a magnetic texture (a domain wall)in the layer’s bulk. We show that the torque contributions frominterface and bulk are not independent from each other and ourgeneralized approach is necessary to accurately model the torquein the presence of a magnetic domain wall inside the magnetic freelayer. We implemented a numerical solution of the spin and chargetransport equations in a finite element-based framework.

Emerging spin transfer torque magnetoresistive random access memories (STT MRAM) are nonvolatile and offer high speed and endurance. MRAM cells include a fixed reference magnetic layer and a free-to-switch ferromagnetic layer (FL), separated by a tunnel barrier. The FL usually consists of several sub-layers separated by nonmagnetic buffer layers. The magnetization dynamics is governed by the Landau-Lifshitz-Gilbert (LLG) equation supplemented with the corresponding torques. To accurately design MRAM cells it is necessary to evaluate the torques in composite magnetic layers, which depend on nonequilibrium spin accumulation generated by an electric current. Spin accumulation and current also depend on the magnetization. Therefore, the LLG and the spin-charge transport equations must be solved simultaneously. We apply the finite element method (FEM) to numerically solve this coupled system of partial differential equations. We follow a modular approach and use well-developed C++ FEM libraries. For the computation of the torques acting in a magnetic tunnel junction (MTJ), a magnetization-dependent resistivity of the tunnel barrier is introduced. A fully three-dimensional solution of the equations is performed to accurately model the torques acting on the magnetization. The use of a unique set of equations for the whole memory cell is an ultimate advantage of our approach.

Spin-transfer torque magnetoresistive random access memory (STT-MRAM) is among the most promising candidates for emerging memories. Thus, reliable simulation tools are mandatory to provide an important aid for understanding and improving the design of such devices. In this work we are concerned with the simulation of STT-MRAM. The well-known Landau-Lifshitz-Gilbert (LLG) equation describes the magnetization dynamics. Since we are dealing with STT-MRAM, an additional torque term must be added to the LLG equation. The torque acting on the magnetization is generated by the nonequilibrium spin accumulation due to the electric current flowing through the structure. The partial differential LLG equation with the additional torque computed from the spin accumulation is solved using the highly efficient finite element method (FEM). We implemented several time integration schemes using an open-source FEM library. In order to verify and calibrate the FEM implementation, we compared it to a finite difference method (FDM) implementation used as a reference. By properly tailoring the time integration scheme and the time step size, almost identical simulation results as with the FDM are achieved. Proper calibration is essential in order to simulate a more realistic multi-layer structure with a composite switching layer consisting of ferromagnetic layers separated by nonmagnetic buffers.

We present the use of reinforcement learning for the discovery of pulse sequences for optimal switching of spin-orbit torque magnetoresistive memory devices. A neural network trained on fixed material parameters is able to switch a memory cell for a wide range of material parameter variations as well as for sub-critical current values. Micromagnetic simulations are used to prove the reliability of the trained neural network.

As the interest in spin-transfer torque magnetoresistive memories for embedded and stand-alone applications is growing, reliable simulation tools are needed to help design and improve these devices. In this paper, we present a finite element implementation of the drift-diffusion approach for coupled spin and charge transport, commonly applied in metallic valves, to compute the torques acting in a magnetic tunnel junction which constitutes the cell of modern spin-transfer torque memories. We investigate the dependence of the torques on system parameters and demonstrate that it is possible to employ the drift-diffusion approach to reproduce the torque magnitude expected in magnetic tunnel junctions. We further show that a full 3D solution of the equations is necessary in order to accurately model the torques acting on the magnetization. The use of a unique set of equations for the whole memory cell constitutes the basis of an efficient finite element based approach to rigorously describe the switching process of novel spin-transfer torque memories.

We employ a reinforcement learning strategy for finding switching schemes for deterministic switching of a spin-orbit torque magnetoresistive random access memory cell. The free layer of the memory cell is perpendicularly magnetized, and the spin-orbit torques are generated by currents through two orthogonal heavy metal wires. A rewarding scheme for the reinforcement learning approach is defined such that the objective of the algorithm is to find a pulse sequence that leads to fast deterministic field-free switching of the memory cell. The reliability of the found switching scheme is tested by performing micromagnetic simulations. The results show that a neural network model trained on fixed material parameters is able to reverse the memory cell magnetization for a wide range of material parameters and can be used to derive a writing pulse sequence for fast and deterministic spin-orbit torque switching of a perpendicular free layer.

Micromagnetic simulations of MRAM cells are a computationally demanding task. Different methods exist to handle the computational complexity of the demagnetizing field, the most expensive magnetic field contribution. In this work we show how the demagnetizing field can efficiently be calculated in complex memory structures and how this procedure can be further used to simulate spin-transfer torque switching in magnetic tunnel junctions.

Spin-transfer torque based devices are among the most promising candidates for emerging nonvolatile memory. Reliable simulation tools can help understand and improve the design of such devices. In this paper, we extend the drift-diffusion approach for coupled spin and charge transport, commonly applied to determine the torque in metallic valves, to the case of magnetic tunnel junctions, which constitute the cell of modern spin-transfer torque memories. We demonstrate that, by introducing a magnetization dependent conductivity and properly choosing the spin diffusion coefficient in the tunnel barrier, the expected behavior of both, the electric current and the spin accumulation, is properly reproduced. The spin torque values’ dependence on the system parameters is investigated. As a unique set of equations is used for the entire memory cell, this constitutes the basis of an efficient finite element based approach to rigorously describe the magnetization dynamics in emerging spin-transfer torque memories.

We demonstrate the switching of a perpendicularly magnetized free layer by spin-orbit torques. The switching is accomplished by a purely electrical, two-current pulse scheme. The first pulse realizes the selection of the cell, while the second pulse, with a lower current, completes the switching deterministically. The second current is reduced by 50% without affecting the switching performance. This current reduction results in a reduction of about 80% of the power consumption by the second pulse. Even with such a large decrease of current and power, the switching time remains robust and fast, resulting in a very efficient switching scheme.

A drift-diffusion approach to coupled spin and charge transport has been commonly applied to determine the spin-transfer torque acting on the magnetization in metallic valves. This approach, however, is not suitable to describe the predominant tunnel transport in magnetic tunnel junctions. Here we demonstrate that by introducing a magnetization dependent resistivity and adjusting the spin diffusion coefficient one can successfully apply the generalized spin and charge drift-diffusion approach also to magnetic tunnel junctions. As a unique set of equations is used for the entire structure, this paves the way to develop an efficient finite element based approach to describe the magnetization dynamics in emerging spin-transfer torque memories.

We employ a finite element discretization scheme to solve numerically the coupled spin and charge transport equations in spin-transfer torque magnetoresistive random access memory cells. To adapt the drift-diffusion formalism to the case of a magnetic tunnel junction, we model the tunnel barrier as a material with a low magnetization-dependent conductivity and a large spin diffusion constant. This generalized spin and charge drift-diffusion approach is applied to determine the torques entering the Landau-Lifshitz-Gilbert equation to describe the magnetization dynamics. In particular, the switching times under a fixed voltage, a fixed current, and a fixed current density are compared.

The magnetization dynamics of a free layer in spin-transfer torque MRAM is usually determined by the torque created by a position-independent current density. In circuits, the voltage, not current density, is fixed during switching. Therefore, the approximate evaluation of the torque based on the fixed current density becomes questionable in modern magnetic tunnel junctions with a tunneling magnetoresistance ratio of about 200%, where the current densities across the structure can vary by a factor of three. We compare the switching times obtained within a fixed voltage assumption with those from the approximate fixed current density approach. We demonstrate that the fixed current approach can reproduce the correct switching also in the case of high TMR, if the current is appropriately adjusted. It is shown that the correction to the current is not universal and depends on the temperature and the switching speed.

As scaling of electronic semiconductor devices - the main driving force behind an outstanding increase of computing power of modern electronic circuits - displays signs of saturation, the main focus of engineering research in microelectronics shifts towards finding new computing paradigms. The future solutions must be scalable and energy efficient while delivering high computational performance, superior to that of CMOS-based circuits. In order to benefit from the outstanding potential of highly advanced silicon processing technology, the emerging solutions must be CMOS compatible. Emerging nonvolatile memories, including magnetoresistive memories, satisfy the necessary requirements: Purely electrically addressable magnetoresistive random access memories yield all aforementioned conditions. They possess a simple structure, require fewer extra masks for fabrication, and offer endurance and speed superior to those of flash memory. Fast operation of magnetoresistive memories makes them a viable contender to static random access memory and flash memory for embedded applications in Systems on Chip. Having nonvolatile memory very close to CMOS removes the necessity of the energy-intensive data transfer from the main memory to the CPU and offers a prospect of data processing in the nonvolatile segment, where the same elements are used to store and to process the information. This opens perspectives for conceptually new low power and highperformance computing paradigms based on logic-in-memory and in-memory computing.

A drift-diffusion approach to coupled spin and charge transport has been commonly applied to determine the spin-transfer torque acting on the magnetization in metallic valves. This approach, however, is not suitable to describe the predominant tunnel transport in magnetic tunnel junctions. In this work we present a coupled Finite Element solution to the spin and charge drift–diffusion equations. We demonstrate that by introducing a magnetization dependent resistivity one can successfully reproduce the resistance dependence on the magnetization orientation in the ferromagnetic layers. We then investigate the dependence of the resulting torques on system parameters, and show that the approach is able to reproduce the torque magnitude expected in a magnetic tunnel junction. As a unique set of equations is used for the entire structure, this constitutes an efficient Finite Element based approach to describe the magnetization dynamics in emerging spin-transfer torque memories.

Finding and optimizing robust schemes for field-free switching remains a challenging problem in spin-orbit torque magnetoresistive random access memories. In this work reinforcement learning is employed for the optimization of switching schemes for such memory cells. A cell is switched purely electrically by applying pulses to two orthogonal metal wires. It is shown that a neural network model trained on a fixed material parameter set is suitable to determine optimal pulse sequences for reliable switching in the presence of thermal fluctuations, material parameter variations and reduction of the current to a sub-critical value. Multiple realizations of switching by means of simulation prove the reliability of magnetization reversal based on the pulse sequences found via reinforcement learning and show that the failure rate due to material parameter variations in these memory devices can be significantly reduced.

We demonstrate by means of numerical simulations the switching of a perpendicularly magnetized free layer by spin–orbit torques based on a two-pulse switching scheme with improved writing power efficiency. In this scheme, the first pulse selects the cell, while the second pulse completes the switching deterministically. It is shown that the magnitude of the second current pulse can be reduced to about 50% of the critical current and the switching remains reliable with a switching time of 300 ps. With such a significant current reduction the writing power required for switching decreases by 40%, which results in a very energy efficient scheme. In addition, we develop a reinforcement learning approach to optimize the pulse configuration with the goal of achieving the shortest switching time. With this approach a switching time of 146 ps has been obtained, a reduction of 50% in relation to the non-optimized configuration. These research findings confirm that reinforcement learning is a promising tool to simplify and automate the search for a faster, energy efficient scheme in the two-pulse switching approach.

Simulations of free-layer switching in spin - transfer torque MRAM are usually performed with the torque computed approximately by assuming a position-independent electric current density through the structure. For high values of the tunneling magnetoresistance, this description is not accurate anymore, and one needs to solve the spin and charge drift-diffusion equations in the whole structure self-consistently. We compute the switching time distribution obtained by the self-consistent model and compare it to the switching times from the fixed current density approach. We show that, provided the current is appropriately adjusted, the simplified model can mimic the correct switching time distribution even in the case of high TMR.

We investigate the switching of a symmetric square and an elongated rectangular perpendicular free layer by spin-orbit torque with a magnetic field-free two-pulse scheme. The switching of the layer is achieved by utilizing the in-plane shape anisotropic magnetic field. For making the switching of a symmetric square layer deterministic, an in-plane stray field created in a part of the layer is used. The combination of the shape and stray fields accelerates the switching of the free layer significantly. A switching speedup factor of 3 to 5 has been obtained. The strategy also improves the robustness of the scheme allowing fast, sub-0.5 ns switching, less sensitive to the pulses’ properties.

A long-standing problem of magnetic field-free switching of a symmetric perpendicular free layer by spin-orbit torque is resolved by employing two perpendicular consecutive current pulses. The optimal overlap of the second pulse line is found to be around 50%. The robustness of switching with respect to fluctuations of the second current pulse duration and of the overlap with the free layer is demonstrated.

We investigate the robustness of a purely electrical field-free switching of a perpendicularly magnetized free layer based on SOT. The effective magnetic field which leads to deterministic switching of a rectangular as well as of a square free layer is created dynamically by a two-current pulse scheme. It is demonstrated that the switching is very robust, being insensitive to fluctuations of the write pulses’ durations and to relatively large variations of the heavy metal wires’ dimensions. Furthermore, it remains reliable for a wide range of synchronization failures between the pulses. The combination of a rectangular free layer shape with a partial overlap with the second current line accelerates the switching of the cell allowing a fast, 0.25 ns, switching.

The outstanding improvement in the performance of modern integrated circuits is supported by the continuous down-scaling of semiconductor devices. However, this leads to a substantial increase in leakages, which results in growing stand-by power consumption. A viable path to mitigate these issues is the introduction of nonvolatility in integrated circuits. Spin-transfer torque (STT) magnetoresistive random access memory (MRAM) is a promising candidate. It is competitive with conventional nonvolatile flash memory as it combines high-speed, excellent endurance, and low costs. The range of potential STT-MRAM applications goes from automotive and Internet-of-Things to embedded memories on System-on-Chips and L3 caches [1]. The core of an STT-MRAM device is a magnetic tunnel junction, where the relative orientation of its magnetic layers provides a way of storing the binary information. Switching between the two possible configurations is achieved by passing an electric current through the structure. The electrons get spin-polarized by the reference layer and, when entering the free layer, act via the exchange interaction on its magnetization providing the torque. With a sufficiently large current density, the magnetization of the free layer can be flipped. The usual approach for micromagnetic simulations of STT switching is to assume a constant and uniform current density [2]. In circuits and applications, however, the voltage, rather than the current density, is fixed during the switching process. As the tunneling resistance in an MTJ depends on the relative magnetization orientation of the two layers, the current depends on time. Moreover, the magnetization of the free layer is nonuniform during switching, which results in a position (and time) dependent current density J(r,t) (Fig. 1). In order to evaluate the validity and the limits of the fixed current density approach in computing the switching time, we compare it with a model in which the total current is fixed, but redistributed according to the position-dependent resistance [3], determined by the local magnetization orientation. In addition, the fixed current and the fixed current density models are compared with a realistic approach in which the voltage during switching is kept constant. Herein, the value of the current in the fixed current/current density models is equal to the voltage in the fixed voltage model divided by the resistance in the initial parallel (P) or anti-parallel (AP) state. The free layer is perpendicularly magnetized. The switching time depends on the realization of the stochastic magnetic field which mimics the magnetization fluctuations at room temperature. It is demonstrated that, by slightly increasing the current from its initial value for AP to P switching and decreasing it for P to AP switching, the switching time distributions can be matched [4] for any value of the stray field induced by the pinned layer (Fig.2). Here, we systematically study the dependence of this current correction on system parameters. The dependence of the current correction on the tunneling magnetoresistance ratio (TMR) at room temperature is reported in Fig. 3. It is observed that the value of the correction increases with higher TMR. We then performed simulations at zero temperature, and in this case, the correction required to reproduce the fixed voltage results is lower than the one at room temperature (Fig. 4). However, the switching is also slower. This proves that the correction to the current is not universal and depends on the system parameters. To elaborate on the physical origin of this dependence we performed macrospin simulations. The initial magnetization orientation is slightly tilted from its perfect perpendicular orientation in order to reduce the incubation time of switching. By changing the initial tilting of the magnetization, we demonstrate that a faster switching requires a higher correction to the current value, which explains the difference between the room and zero temperature simulations (Fig. 5). Simulation results for the current correction as a function of the surface area of the structure at room temperature are shown in Fig. 6. The switching is faster for higher values of the area, and the current correction required is consequently higher, in agreement with the macrospin results. We conclude that it is possible to reproduce the switching times obtained within the realistic fixed voltage approach with the approximate fixed current density approach for a wide range of system parameters, provided that the dependence of the current correction on such parameters is taken into consideration. REFERENCES [1] S.Sakhare, M.Perumkunnil, T.H.Bao, S.Rao, W.Kim et al., Proc.IEDM, 420 (2018). [2] A.Makarov, T.Windbacher, V.Sverdlov, S.Selberherr, Semic.Sci.Tec. 31, 113006 (2016). [3] D.Aurelio, L.Torres, G.Finocchio, J.Magn.Magn.Mat. 321, 3913 (2009). [4] S.Fiorentini, R.Orio, W.Goes, J.Ender, V.Sverdlov, Proc.SISPAD, 57 (2019). Figure 1

A magnetic field-free switching of a symmetric square free layer with perpendicular magnetization by spin–orbit torque is demonstrated based on micromagnetic modeling and numerical simulations. The field-free switching is accomplished by using a two-pulse switching scheme. An appropriate design of the cell structure yields a deterministic and fast switching, about 0.6 ns, of the magnetized free layer. It is shown that the switching is robust with respect to fluctuations of the current pulse duration and, furthermore, very robust in case of delays or overlaps between the writing current pulses.

1,2,4-Triferrocenylbenzene was isolated and fully characterized for the first time. It was obtained, together with 1,3,5-triferrocenylbenzene, by cyclotrimerization reaction, catalyzed either by metalloporphyrins or cobaltocene. the latter catalyst gave better results. The isomerically different triferrocenylbenzene exhibit different properties.

A product and time-resolved kinetic study on the reactivity of the radical cations generated from cyclopropyl(4-methoxyphenyl)phenylmethanol (1) and cyclopropyl[bis(4-methoxyphenyl)]methanol (2) has been carried out in aqueous solution. In acidic solution, 1*+ and 2*+ display very low reactivities toward fragmentation, consistent with the presence of groups at Calpha (aryl and cyclopropyl) that after Calpha-Cbeta bond cleavage would produce relatively unstable carbon-centered radicals. In basic solution, 1*+ and 2*+ display oxygen acidity, undergoing -OH-induced deprotonation from the alpha-OH group, leading to the corresponding 1,1-diarylalkoxyl radicals 1r* and 2r*, respectively, as directly observed by time-resolved spectroscopy. The product distributions observed in the reactions of 1*+ and 2*+ under these conditions (cyclopropyl phenyl ketone, cyclopropyl(4-methoxyphenyl) ketone, and 4-methoxybenzophenone from 1*+; cyclopropyl(4-methoxyphenyl) ketone and 4,4'-dimethoxybenzophenone from 2*+) have been rationalized in terms of a water-induced competition between O-neophyl shift and C-cyclopropyl beta-scission in the intermediate 1,1-diarylalkoxyl radicals 1r* and 2r*.