All optical writing and current-driven shifting of bits in ferrimagnetic strips: A micromagnetic study

[EN]Nucleation of domains and domain walls by means of ultrashort laser pulses, and their current-driven shifting along a ferrimagnetic strip with high perpendicular magnetic anisotropy on top of a heavy metal, are both explored here by means of advanced micromagnetic modeling. Our results indicate that these systems are ideal candidates to develop high-density and high-efficient domain wall-based memory devices where the information is coded in series of bits in the form of perpendicular up and down domains flanked by chiral domain walls.This work was supported by Grant MAT2017-87072-C4-1-P funded by Ministerio de Ciencia e Innovacion and No. PID20 20117024GB-C41 funded by MCIN/AEI/10.13039/501100011033, both from the Spanish government, Projects No. SA299P18 and No. SA114P20 from Consejeria de Educacion of Junta de Castilla y León, and project MagnEFi, Grant Agreement No. 860060, (H2020-MSCA-ITN-2019) funded by the European Commission

Current-driven domain wall dynamics in ferrimagnets: Micromagnetic approach and collective coordinates model

[EN] Theoretical studies dealing with current-driven domain wall dynamics in ferrimagnetic alloys and, by extension, other antiferromagnetically coupled systems as some multilayers, are here presented. The analysis has been made by means of micromagnetic simulations that consider these systems as constituted by two subsystems coupled in terms of an additional exchange interlacing them. Both subsystems differ in their respective gyromagnetic ratios and temperature dependence. Other interactions, as for example anisotropic exchange or spin-orbit torques, can be accounted for differently within each subsystem according to the physical structure. Micromagnetic simulations are also endorsed by means of a collective coordinates model which, in contrast with some previous approaches to these antiferromagnetically coupled systems, based on effective parameters, also considers them as formed by two coupled subsystems with experimentally definite parameters. Both simulations and the collective model reinforce the angular moment compensation argument as accountable for the linear increase with current of domain wall velocities in these alloys at a certain temperature or composition. Importantly, the proposed approach by means of two coupled subsystems permits to infer relevant results in the development of future experimental setups that are unattainable by means of effective models.MAT2017-87072-C4-1-P from the Spanish government SA299P18 from the Junta de Castillay León

Novel interpretation of recent experiments on the dynamics of domain walls along ferrimagnetic strips

[EN] Domain wall motion along ferrimagnets is evaluated using micromagnetic simulations and a collective-coordinates model, both considering two sublattices with independent parameters. Analytical expressions are derived for strips on top of either a heavy metal or a substrate with negligible interfacial Dzyaloshinskii-Moriya Interaction. The work focuses its ndings in this latter case, with a eld-driven domain wall motion depicting precessional dynamics which become rigid at the angular momentum compensation temperature, and a current-driven dynamics presenting more complex behavior, depending on the polarization factors for each sublattice. Importantly, our analyses provide also novel interpretation of recent evidence on current-driven domain wall motion, where walls move either along or against the current depending on temperature. Besides, our approach is able to substantiate the large non-adiabatic efective parameters found for these systems.Project No. MAT2017-87072-C4-1-P from the (Ministerio de Economía y Competitividad) Spanish Government Project No. SA299P18 from the (Consejería de Educación of) Junta de Castilla y León

Current driven domain wall dynamics in ferrimagnetic strips explained by means of a two interacting sublattices model

[EN] The current-driven domain wall dynamics along ferrimagnetic elements are here theoretically analyzed as a function of temperature by means of micromagnetic simulations and a one dimensional model. Contrarily to conventional effective approaches, our model takes into account the two coupled ferromagnetic sublattices forming the ferrimagnetic element. Although the model is suitable for elements with asymmetric exchange interaction and spin-orbit coupling effects due to adjacent heavy metal layers, we here focus our attention on the case of single-layer ferrimagnetic strips where domain walls adopt achiral Bloch configurations at rest. Such domain walls can be driven by either out-of-plane fields or spin transfer torques upon bulk current injection. Our results indicate that the domain wall velocity is optimized at the angular compensation temperature for both field-driven and current-driven cases. Our advanced models allow us to infer that the precession of the internal domain wall moments is suppressed at such compensation temperature, and they will be useful to interpret state-of-the art experiments on these elements.MAT2017- 87072-C4-1-P from the (Ministerio de Economía y Competitividad) Spanish Government SA299P18 from the (Consejería de Educación) of Junta de Castilla y León

Current-Driven Domain Wall Motion in Curved Ferrimagnetic Strips Above and Below the Angular Momentum Compensation

[EN] Current driven domain wall motion in curved Heavy Metal/Ferrimagnetic/Oxide multilayer strips is investigated using systematic micromagnetic simulations which account for spinorbit coupling phenomena. Domain wall velocity and characteristic relaxation times are studied as functions of the geometry, curvature and width of the strip, at and out of the angular momentum compensation. Results show that domain walls can propagate faster and without a significant distortion in such strips in contrast to their ferromagnetic counterparts. Using an artificial system based on a straight strip with an equivalent current density distribution, we can discern its influence on the wall terminal velocity, as part of a more general geometrical influence due to the curved shape. Curved and narrow ferrimagnetic strips are promising candidates for designing high speed and fast response spintronic circuitry based on current-driven domain wall motion.Projects SA114P20 and SA299P18 from Junta de Castilla y Leon (JCyL) MAT2017-87072-C4-1-P and PID2020-117024GB-C41 from the Ministry of Economy, Spanish government MAGNEFI, from the European Commission (European Union

Geometrical design for pure current-driven domain wall nucleation and shifting

[EN]Nucleation of domain walls by current-driving a single domain wall, confined to the junction area of two symmetrical strips, is investigated using systematic micromagnetic simulations. Secondary domain walls (equivalently, bits encoded in domains) are simultaneously nucleated and driven by alternatively applying current pulses between two terminals in the structure. Simulations show that nanosecond-duration current pulses nucleate and drive series of robust up/down domains even under realistic conditions. These results demonstrate a technique for sequentially nucleating and shifting domain walls without using attached external “bit lines,” fields, or modifying the ferromagnetic strip

Micromagnetic Modeling of All-Optical Switching

[EN] The control of the magnetization at the microscale by pure optical means is fundamentally interesting and promises faster speeds for data storage devices. Although several experiments have shown that it is possible to locally reverse the magnetization of a ferromagnetic system by means of laser pulses, a completely theoretical description of these All Optical Switching processes is still lacking. Here, we develop an advanced micromagnetic solver that is applied to the numerical study of the All Optical Switching. The solver is based on the Landau-Lifshitz-Bloch equation that governs the dynamics of the magnetization coupled the microscopic three temperatures model, which describes the temporal evolution of the temperatures of the subsystems as caused by laser heating. The helicity-dependent magnetization switching is evaluated by a magneto-optical effective field caused by the Inverse Faraday Effect when a circularly polarized laser is applied to the sample. All the other usual terms of a full micromagnetic model are included (exchange, anisotropy, DMI…). As a test, the model is used to describe the local magnetization switching of thin film samples with high perpendicular anisotropy. The results are in good agreement with available experimental observations.MAT2014- 52477-C5-4-P, MAT2017-87072-C4-1-P, and MAT2017-90771-REDT from the Spanish government SA090U16 and SA299P18 from the Junta de Castilla y Leon

Micro and nanostrips in spintronics: How to keep them cool

[EN] This tutorial explores the problem of Joule heating on metallic micro or nanostrips, still one of the most popular geometries in modern spintronics. Many of the effects that result from the interaction of a spin polarized current and the local magnetization, require of a sizeable current density. This implies, quite often, an unneglectable Joule heating. Despite the few articles devoted to some aspects of Joule heating, there is still disinformation and many misconceptions in this topic, which is key for the correct interpretation of the scientific results. In this tutorial, we highlight the material parameters that are important to keep the temperature of the strip under control and those that give only a marginal advantage. In the vast majority of papers, at least one of these parameters is missing. We also focus on some misconceptions, such as the belief that performing the measurement on a cryostat, rules Joule heating out. In fact, for a fixed current density, measuring in a cryostat decreases the temperature but not enough to justify the use of such a costly measuring set-up. At the practical level, we put forward a 1D model to calculate, in few seconds, if Joule heating is present and if it should be taken into account when interpreting the results. Finally, and importantly, we describe a simple fabrication route to enhance the dissipation of heat in the strip considerably. This fabrication strategy is more effective at keeping the temperature under control than performing the experiment at cryogenic temperatures.Project MAT2017-87072-C4-3-P and MAT2017-87072-C4-1-P from the Spanish government Project No. SA299P18 from Consejería de Educación Junta de Castilla y Leó

Current-Driven Skyrmion Dynamics Along Curved Tracks

[EN] The current-driven skyrmion (Sk) motion along two exchange-coupled ferromagnetic (FM) layers with perpendicular magnetic anisotropy is studied by means of micromagnetic simulations and compared to the conventional case of a single FM layer. Our results indicate that the two coupled Sks can be synchronously driven along each FM layer in the presence of a strong interlayer exchange coupling and that the velocity is significantly enhanced due to the antiferromagnetic (AF) exchange coupling as compared with the single-FM-layer case. The interfacial Dzyaloshinskii–Moriya interaction gives the required chirality to the magnetization textures, while the interlayer exchange coupling favors the synchronous movement of the coupled Sks by a dragging mechanism, without depicting the unwanted Sk Hall effect. This observation is particularly relevant to drive Sks along curved strips, which are also evaluated here. Sks move with different velocities along single FM stacks with curved parts. On the contrary, the AF coupling between the FM layers mitigates the Sk Hall effect, which suggests these systems to achieve efficient and highly packed displacement of trains of Sks for spintronics devices. A study taking into account defects and thermal fluctuations analyzes the validity range of these claims.Spanish Governmentunder Project MAT2014-52477-C5-4-P, Project MAT2017- 87072-C4-1-P, and Project MAT2017-90771-REDT Junta de Castilla y Leon under Project SA090U16 and Project SA299P18

Realistic micromagnetic description of all-optical ultrafast switching processes in ferrimagnetic alloys

[EN]Both helicity-independent and helicity-dependent all-optical switching processes driven by single ultrashort laser pulse have been experimentally demonstrated in ferrimagnetic alloys as GdFeCo. Although the switching has been previously reproduced by atomistic simulations, the lack of a robust micromagnetic framework for ferrimagnets limits the predictions to small nanosystems, whereas the experiments are usually performed with lasers and samples of tens of micrometers. Here we develop a micromagnetic model based on the extended Landau-Lifshitz-Bloch equation, which is firstly validated by directly reproducing atomistic results for small samples and uniform laser heating. After that, the model is used to study ultrafast single shot all-optical switching in ferrimagnetic alloys under realistic conditions.We find that the helicity-independent switching under a linearly polarized laser pulse is a pure thermal phenomenon, in which the size of inverted area directly correlates with the maximum electron temperature in the sample. On the other hand, the analysis of the helicity-dependent processes under circular polarized pulses in ferrimagnetic alloys with different composition indicates qualitative differences between the results predicted by the magnetic circular dichroism and the ones from inverse Faraday effect. Based on these predictions, we propose experiments that would allow one to resolve the controversy over the physical phenomenon that underlies these helicity-dependent all optical processes.This work was supported by Projects No. MAT2017- 87072-C4-1-P funded by Ministerio de Educacion y Ciencia and No. PID2020117024GB-C41 funded by Ministerio de Ciencia e Innovacion, both from the Spanish government, Projects No. SA299P18 and No. SA114P20 from Consejeria de Educacion of Junta de Castilla y León, and project MagnEFi, Grant Agreement No. 860060, (H2020-MSCAITN- 2019) funded by the European Commission. U.A. would like to acknowledge funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—Project- ID 328545488—TRR 227, Project No. A08