# Conserved momenta of a ferromagnetic soliton

### APA

Tchernyshyov, O. (2015). Conserved momenta of a ferromagnetic soliton. Perimeter Institute. https://pirsa.org/15110091

### MLA

Tchernyshyov, Oleg. Conserved momenta of a ferromagnetic soliton. Perimeter Institute, Nov. 13, 2015, https://pirsa.org/15110091

### BibTex

@misc{ pirsa_PIRSA:15110091, doi = {10.48660/15110091}, url = {https://pirsa.org/15110091}, author = {Tchernyshyov, Oleg}, keywords = {Condensed Matter}, language = {en}, title = {Conserved momenta of a ferromagnetic soliton}, publisher = {Perimeter Institute}, year = {2015}, month = {nov}, note = {PIRSA:15110091 see, \url{https://pirsa.org}} }

**Collection**

**Subject**

Solitons in a ferromagnet have interesting dynamics because atomic magnetic moments behave like little gyroscopes. A domain wall in a magnetic wire can be modeled as a bead on a string: it has two soft modes, position and orientation. This "bead" rotates when it is pushed and moves when twisted.

From that one can deduce that the angular momentum is proportional to the domain wall's coordinate and the linear momentum to its azimuthal angle. In fact, the definition of conserved momenta for magnetic solitons has been discussed in the scientific literature for 40 years. A naive attempt to derive them from the application of Noether's theorem yields unphysical, gauge-dependent answers. To resolve this problem, we exploit a similarity between the dynamics of a ferromagnetic soliton and that of a charged particle in a magnetic field. For the latter, canonical momentum is also gauge-dependent and thus unphysical; the physical momentum is the generator of magnetic translations, a symmetry combining physical translations with gauge transformations. We use this analogy to unambiguously define conserved momenta for ferromagnetic solitons.