Faculty of Mathematics, Physics
and Informatics
Comenius University Bratislava

Magnetic devices and their energy landscapes

Elimination of mechanical parts in hard drives would allow us to significantly increase their speed, reliability and lifespan. Indeed, it is possible to replace mechanical read and write heads with electrical impulses, however, the question arises whether information stored in this way would be stable in a long term. This is the question investigated by a team of researchers from FMPHI (Roman Martoňák) and the Institute of Electrical Engineering of Slovak Academy of Sciences (Jaroslav Tóbik and Vladimír Cambel) in a study recently published in Physical Review B: Rapid Communications.

02. 11. 2017 15.24 hod.
By: Roman Martoňák

An important application of magnetic materials, commonly encountered in everyday life, is magnetic storage of data. Currently the most widespread storage medium is hard disk. Standard hard disks make use of mechanical motion of magnetic medium as well as of the read/write heads which is not optimal from the point of view of low energy consumption and noise and high speed and reliability. Recently new technologies and trends entered into the field of magnetic storage media. It was demonstrated that the magnetic state of magnetic elements can be switched purely electrically, by current pulses, eliminating the need for mechanical motion and read/write heads. Several concepts of modern design of future magnetic storage media were proposed [1]. They should be fast and voltage independent to be able to keep the stored information without external energy source. Different exotic magnetic textures are being considered, such as e.g. magnetic vortices[2], skyrmions[3], magnetic bobbers[4], etc. Their applicability is motivated by their stability which is of topological origin. A long-term stability of the magnetic state is critically important since we want to reliably retrieve the stored information anytime, in one minute or in one year. But how do we know whether the stored magnetization persists long enough? 

Computer simulations are likely to be of help, but even they can't solve the problem by brute force. It might appear surprising but a direct simulation of a 1 second time interval is impossible. Time scales in microscopic and macroscopic world are simply too different and a more sophisticated approach is necessary. According to statistical physics, the dynamics or time evolution of a system is determined by its free energy. Its landscape can be represented in the form of an energy map, which could be imagined as similar to a standard geographic map. The stable states correspond to deep or shallow valleys separated by mountain ridges. On the ridges one finds low-lying saddle points through which the transitions between the different states take place. The height of these points determines the so-called energetic barrier which decides how long it takes until the transition occurs and therefore also how stable is the stored information. The determination of the free-energy map and identification of valleys and saddle points is therefore a key to the solution of our problem. The problem of barrier crossing is, however, not specific to micromagnetism. It appears in various forms in many field of physics and chemistry and a number of approaches were proposed to study it. Among the most efficient ones is the metadynamics algorithm [5] which was successfully applied  to study a broad class of problems such as protein folding, crystallization, structural transformations, chemical reactions etc. A team of researchers from the Institute of Electrical Engineering of the Slovak Academy of Sciences (Jaroslav Tóbik and Vladimír Cambel) and from the Department of Experimental Physics, Faculty of Mathematics, Physics and Informatics of the Comenius University in Bratislava showed for the first time that this powerful approach is applicable also in the field of micromagnetism and employed it to determine the free-energy map of a nanomagnetic device. The general approach had to be adapted by a suitable choice of the so-called collective variables. It was shown that the metadynamics algorithm allows an efficient and detailed simulation of the process in which a magnetic vortex enters or leaves the nanodevice as well as the determination of the free-energy map (Fig.1). This was so far not possible with the use of previous techniques. The results suggest that metadynamics opens new possibilities of research in the field of micro/nanomagnetism. Besides determining the energy maps it will also allow a search for new types of magnetic structures and a detailed control of magnetization. Applications to the above mentioned exotic textures, which currently represent very perspective directions of research, can be expected as well. The work was published in the Rapid Communications section of Physical Review B which is devoted to the publication of short papers presenting highly original and significant material.

Jaroslav Tóbik, Roman Martoňák, and Vladimír Cambel: Free-energy landscapes in magnetic systems from metadynamics. Phys. Rev. B 96, 140413(R) zalinkovane na https://doi.org/10.1103/PhysRevB.96.140413

[1] Racetrack memory: https://en.wikipedia.org/wiki/Racetrack_memory
[2] Magnetic Vortex: https://en.wikipedia.org/wiki/Magnetic_spin_vortex_disc
[3] Magnetic skyrmion: https://en.wikipedia.org/wiki/Magnetic_skyrmion
[4] F. Zheng,et.al.: Experimental observation of magnetic bobbers for a new concept of magnetic solid-state memory, arxiv:1706.04654, https://arxiv.org/abs/1706.04654
[5] A. Laio and M. Parrinello, Proc. Natl. Acad. Sci. U.S.A. 99, 12562 (2002).