Magnetic Domain Wall Dynamics

Abstract

Some calculations exist for the mobility and the effective mass of ferromagnetic domain walls of special wall structures. More generally valid derivations and formulas are presented here, which are not restricted to a special wall structure. It is shown that the nonlinearity observed by several authors in the dependence of the wall velocity on the field can be predicted theoretically if the material inhomogeneities causing the coercivity are taken into account in an appropriate manner. For a special example the existence of the wall contraction and the velocity limit shown by Enz for a wall without damping and without field is shown for a wall with damping and with field. As is the approximation by Enz, the present approximation also is not able to indicate the value of this velocity limit.Fur die Beweglichkeit und die effektive Masse ferromagnetischer DomiinenwLnde sind einige Berechnungen fur spezielle Wandstrukturbeispiele bekannt geworden. Die hier wiedergegebene Rechnung ist allgemeingiiltiger und bezieht sich nicht auf eine bestimmte Wandstruktur. Es wird gezeigt, daB die verschiedentlich beobachtete Nichtlinearitiit in der AbhLngigkeit der Wandgeschwindigkeit vom angelegten Feld theoretisch zu erwarten ist, wenn man die die Koerzitivfeldstirke bestimmenden Inhomogenititen des Materials in geeigneter Weise beriicksichtigt. An einem speziellen Beispiel wird aul3erdem gezeigt, daB die von Enz fiir eine ungediimpfte Wand ohne Feld berechnete Wandkontraktion und Maximalgeschwindigkeit auch fur eine gedimpfte Wand im Feld existiert. Beide Niherungen sind jedoch nicht in der Lage, die Hohe der Grenzgeschwindigkeit sicher anzugeben.

A symmetry breaking mechanism for selecting the speed of relativistic solitons

“…On the phenomenological side, SG solitons have wide range of applicability: non linear molecular [7] and DNA dynamics [8,9,10,11], Josephson effect [12], ferromagnetic waves [13,14], non linear optics [15,16], superconductivity [17] and many others [18].…”

10.1007/s11451-008-2001-4

“…(19) for various values of Q. At Q < 1, this dependence becomes nonlinear, which can be explained [43] in terms of the dynamic decrease in the DW width with increasing H according to the formula ∆ = (A/K) 1/2 (1 + H 2 /2αK) -1/2 .…”

Thermal diffusion of sine-Gordon solitons

“…Among those, stochastic perturbations are very much of interest in view of their highly non trivial effects on nonlinear systems [8], and a great deal of work has been devoted to them [2,4,5]. In particular, of the very many nonlinear models applied to physical problems, the sine-Gordon (sG) equation has been considered in much detail in this context, as it applies to, e.g., propagation of ultra-short optical pulses in resonant laser media [9], a unitary theory of elementary particles [10][11][12][13], propagation of magnetic flux in Josephson junctions [14], transmission of ferromagnetic waves [15], epitaxial growth of thin films [16][17][18], motion of dislocations in crystals [19,20], flux-line unlocking in type II superconductors [21], or DNA dynamics [22][23][24], situations in which noise (of different origins) can play, and often does, a crucial role. As an example, let us mention the recent work on long Josephson junctions reported in [25], where the authors calculated the escape rate from the zero-voltage a e-mail: anxo@math.uc3m.es state induced by thermal fluctuations, obtaining very satisfactory results compared with the experimental ones.…”