Mathematical Analysis of Domain Wall Motion in Nanowires

Lead Research Organisation: Northumbria University
Department Name: Fac of Engineering and Environment

Abstract

Ferromagnetism is a striking and subtle phenomenon. Observable on the macroscopic scale, its origins lie outside the scope of classical physics, and are consequences of two quintessentially quantum mechanical properties of matter, namely electron spin and the Pauli exclusion principle. The quantum mechanical origin of ferromagnetism accounts for the existence of ferromagnetic domains -- regions of distinct and nearly uniform magnetisation -- on microscopic, indeed nanometer scales. The size of ferromagnetic domains, along with the modest energy required to manipulate (i.e., read and write) them has led to far-reaching applications in information technology, proceeding over the last half-century from magnetic tape drives to the current frontier, for example race-track memory: a three-dimensional memory on which domains -- ''bits'' -- may be read, moved, and written around nanowire loops.

The last two decades have witnessed a revolution in micromagnetics, both in fundamental science as well as consequent technological breakthroughs. It has long been understood how ferromagnetic domains can be controlled through external magnetic fields. More recent is the discovery of a wholly new mechanism for domain wall dynamics through the interaction of magnetisation and spin-polarised currents.

For length scales down to tens of nanometers, there is a well established and extremely successful continuum theory of micromagnetism, namely the micromagnetic variational principle and its dynamic counterpart, the Landau-Lifshitz-Gilbert equation. The theory is mathematically complex (the equations are both nonlinear and nonlocal), and encompasses a range of diverse regimes. These regimes can be separately investigated analytically using modern techniques from the calculus of variations and partial differential equations. Models on the scale of individual atoms are necessarily quantum mechanical, and require additional physical concepts and mathematical apparatus.

The first aim of this project is an analytic study of domain-wall motion in nanowires and nanotubes induced by currents and applied magnetic fields. We will establish mathematically the existence and wide range of physical behaviours, and derive formulas which describe their properties. The second aim is to elucidate the underlying quantum mechanical mechanisms of domain-wall propagation through a semiclassical analysis of the electron dynamics, including spin, in a ferromagnetic medium.

Publications

10 25 50

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Dubertrand R (2014) Origin of the exponential decay of the Loschmidt echo in integrable systems. in Physical review. E, Statistical, nonlinear, and soft matter physics

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Gaididei Y (2017) Magnetization in narrow ribbons: curvature effects in Journal of Physics A: Mathematical and Theoretical

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Goussev A (2020) Dynamics of ferromagnetic domain walls under extreme fields in Physical Review B

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Goussev A (2017) Rotating Gaussian wave packets in weak external potentials in Physical Review A

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Goussev A (2016) Loschmidt echo and time reversal in complex systems. in Philosophical transactions. Series A, Mathematical, physical, and engineering sciences

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Goussev A (2014) Domain wall motion in thin ferromagnetic nanotubes: Analytic results in EPL (Europhysics Letters)

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Goussev A (2016) Dzyaloshinskii-Moriya domain walls in magnetic nanotubes in Physical Review B

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Reck P (2018) Towards a quantum time mirror for non-relativistic wave packets in New Journal of Physics

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Reck P (2017) Dirac quantum time mirror in Physical Review B

 
Description A domain wall is an interface separating magnetic domains. Domain walls can be set in motion by application of external magnetic fields or electric currents. The field and current control of domain wall motion has been proposed as a basis for next generation memory devices in which domain walls are used for the information storage.

We have addressed domain wall dynamics in nano/micro-scale ferromagnets of various geometries and topolgies with and without spin-orbit-induced Dzyaloshinskii-Moriya interaction, and obtained, for the first time, several exact analytical results concerning the domain wall profiles and their propagation velocity.
Exploitation Route Our analytical results may be used in guiding experimental and numerical studies of ferromagnetic nanostructures and in developing future technological applications (e.g. magnetic memory devices).
Sectors Education,Electronics,Other

 
Description Dr Denis D Sheka (Taras Shevchenko National University of Kyiv, Kiev, Ukraine) 
Organisation Taras Shevchenko National University of Kyiv
Country Ukraine 
Sector Academic/University 
PI Contribution I collaborated with Dr Sheka and his research group on the topic of geometrically-constrained ferromagnets and published a joint paper: "Magnetization in narrow ribbons: curvature effects", J. Phys. A: Math. Theor. 50, 385401 (2017).
Collaborator Contribution Dr Sheka collaborated with me on the topic of geometrically-constrained ferromagnets and published a joint paper: "Magnetization in narrow ribbons: curvature effects", J. Phys. A: Math. Theor. 50, 385401 (2017).
Impact "Magnetization in narrow ribbons: curvature effects", J. Phys. A: Math. Theor. 50, 385401 (2017)
Start Year 2016
 
Description Dr J. M. Robbins and Dr V. Slastikov (Department of Mathematics, University of Bristol) 
Organisation University of Bristol
Country United Kingdom 
Sector Academic/University 
PI Contribution Contributed with research expertise and intellectual input.
Collaborator Contribution Contributed with research expertise and intellectual input.
Impact Research paper output: "Magnetization in narrow ribbons: curvature effects", Y. Gaididei, A. Goussev, V. P. Kravchuk, O. V. Pylypovskyi, J. M. Robbins, D. D. Sheka, V. Slastikov, S. Vasylkevych, J. Phys. A: Math. Theor. 50, 385401 (2017) "Dzyaloshinskii-Moriya domain walls in magnetic nanotubes", A. Goussev, J. M. Robbins, V. Slastikov, O. A. Tretiakov, Phys. Rev. B 93, 054418 (2016) "Domain wall motion in thin ferromagnetic nanotubes: Analytic results", A. Goussev, J. M. Robbins, V. Slastikov, EPL (Europhys. Lett.) 105, 67006 (2014)
Start Year 2013
 
Description Dr Oleg Tretiakov (Institute for Matetials Research, Tohoku University, Sendai, Japan) 
Organisation University of Hasselt
Department Institute for Materials Research
Country Belgium 
Sector Academic/University 
PI Contribution I collaborated with Dr Tretiakov on ferromagnetic nanotubes and published a joint paper: "Dzyaloshinskii-Moriya domain walls in magnetic nanotubes", A. Goussev, J. M. Robbins, V. Slastikov, O. A. Tretiakov, Phys. Rev. B 93, 054418 (2016)
Collaborator Contribution Dr Tretiakov collaborated with me on ferromagnetic nanotubes and published a joint paper: "Dzyaloshinskii-Moriya domain walls in magnetic nanotubes", A. Goussev, J. M. Robbins, V. Slastikov, O. A. Tretiakov, Phys. Rev. B 93, 054418 (2016)
Impact "Dzyaloshinskii-Moriya domain walls in magnetic nanotubes", A. Goussev, J. M. Robbins, V. Slastikov, O. A. Tretiakov, Phys. Rev. B 93, 054418 (2016)
Start Year 2014