Domain Wall Interaction Energy

The interfacial dzyaloshinskii moriya interaction dmi is important for chiral domain walls dws and for stabilizing magnetic skyrmions.

Domain wall interaction energy. Domain walls are also sometimes called kinks in analogy with closely related kink solution of the sine gordon model or models with polynomial potentials. It is a transition between different magnetic moments and usually undergoes an angular displacement of 90 or 180. Comprehensive nanoscience and nanotechnology second edition 2016.

A domain wall is a gradual reorientation of individual moments across a finite distance. At d si sj 3 ij rij temperatures well below the curie temperature with high saturation magnetization the domain wall is observed to have where the first term describes the exchange interactions a zigzag structure to minimise the the dipolar interaction between nearest neighbour spins with a strength j the sec energy. The energy lost by the continuous pinning and depinning of the domain wall as it moves and the energy lost by the formation and destruction of a fraction of the wall surface may be the origin of the losses which find their expression in the hysteresis loop.

It is energetically advantageous to have infinitely thick domain walls which means that there will be no domains but just randomly. A domain wall is defined as the zone of magnetization rotation between domains of opposite magnetization in a randomly magnetized film and domain wall extension is given in first approximation by the square root of the exchange j divided by the anisotropy ku. Strained volumes in the vicinity of grain boundaries are likely to exhibit an increased domain wall density compared to the center of the grain.

Magnetic domain wall motion is numerically studied in a nanowire with a dzyaloshinskii moriya interaction dmi step at which dmi varies in real space. Unstable domain walls can also appear if spontaneously broken discrete symmetry is approximate and there is a false vacuum. Ex e total bw ex 2 2 a2 js a2 n from this expression it looks like.

For example a spatial correlation between volumes of high elastic mechanical energy and high domain wall density was recently established. Domain wall grain boundary interactions. If a is the lattice constant then the exchange energy penalty per unit area of the 180º bloch wall is.

N ex bw 0 i e. The free energy may be exactly decomposed into a computationally useful form as a sum of domain wall tensions σ plus pair triplet and higher order wall wall interaction potentials w n l i which depend on the wall separations l i and on temperature etc. In magnetism a domain wall is an interface separating magnetic domains.