Ferromagnetism is the property by which a material such as iron develops magnetic properties. This property finds use in various applications such as electromagnets, electric motors, hard disks, generators, and transformers.
Taking ferromagnetism to another level are ferromagnetic nanostructures which are gaining lots of attention due to their applications in magnetic memory and logic devices.
One of the main aspects of this type of magnetism is known as magnetic domain walls (DWs). Domain walls act like a transition layer that separates the uniformly magnetized regions of a magnetic material. The interesting fact is that several reports suggest that magnetic domain walls can be manipulated with an external magnetic field and/or electric current.
An equation known as the Landau-Lifshitz-Gilbert (LLG) equation can theoretically explain the mathematical modelling of the magnetization configuration in magnetic devices.
However, this equation is physically inconsistent with characterizing the magnetization dynamics in the nonlinear regime. It is also physically inadequate to describe the magnetization dynamics below the typical time scale.
These drawbacks have given birth to the field of ultrafast magnetism.
Ultrafast magnetism has given rise to a lot of debate about the fundamental understanding of magnetism and possible applications for faster and more energy-efficient data manipulation.
Because of this, the governing LLG equation is extended by an inertial term describing the domain wall motion in such a small timescale called inertial Landau-Lifshitz-Gilbert (iLLG) equation.
In this study conducted by Mr. Chiranjeev K. Shahu and Prof. Shruti Dubey from the Department of Mathematics, Indian Institute of Technology (IIT) Madras, Chennai, India, and Dr. Sharad Dwivedi from the Department of Mathematics, School of Sciences, National Institute of Technology (NIT) Andhra Pradesh, Tadepalligudem, India, the field-driven motion of curved domain walls in ferromagnetic nanostructures under the framework of the modified LLG equation (iLLG) was studied.
Domain wall motion can be either steady-state or precessional. The maximum (minimum) value of the external sources for domain wall motion that remains in the steady-state regime is what is known as the Walker breakdown (threshold). A precessional regime occurs above the Walker breakdown value.
The most relevant dynamical features in the steady dynamical regime for the considered model was studied by employing the reductive perturbation technique. It was found that the curvature, nonlinear dissipative, and inertial effects affect the domain wall velocity.
The nonlinear dissipative and inertial effects play an important role in propagating the curved domain walls at an appropriate position along the magnetic nanostructures to encode the data more efficiently.
This study of the curved domain walls motions under the influence of nonlinear dissipative and inertial effects is advantageous in enhancing magnetic storage and logic devices.
The results for various domain wall surfaces such as plane, cylinder, and sphere were shown numerically and their physical significance was noted. The results obtained here agree with the recent theoretical and experimental observations.
Future studies could include studying curved domain wall motion above the breakdown limit and further research is required along these lines. The authors aim to work on this issue in future tasks.
Prof. Giancarlo Consolo, Associate Professor of Mathematical Physics, from the Department of Mathematical, Computer, Physical and Earth Sciences, University of Messina, Italy, gave his analysis of the study and appreciated the authors’ efforts with the following comments: “I’ve read with interest the manuscript “Dynamics of curved domain walls in hard ferromagnets with nonlinear dissipative and inertial effects” recently published in Physica D (vol.448, 133737, Year 2023).
This paper focuses on the “control of position and velocity of magnetic domain walls in ferromagnetic nanostructures”, a topic which has been attracting a lot of efforts by mathematicians, physicists and engineers in the last decades, since many industrial applications (in the field of magnetic memories, sensors and oscillators) rely on theoretical findings.
In particular, authors tackled a theoretical study, based on a modified framework of the Landau–Lifshitz–Gilbert equation, where some previous results existing in the literature for curved domain walls (e.g. Appl. Math. Model. 38, 1001 (2014)) have been generalized to include the effects arising from nonlinear dissipation and inertia. I believe that analytical and numerical results here contained might provide some insights to experimentalists for the optimization of the performances of these nanodevices.”
Article by Akshay Anantharaman
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