Linear dynamics of classical spin as Mobius transformation
Abstract
Though the overwhelming majority of natural processes occur far from the equilibrium, general theoretical approaches to non-equilibrium phase transitions remain scarce. Recent breakthroughs introduced a description of open dissipative systems in terms of non-Hermitian quantum mechanics enabling the identification of a class of non-equilibrium phase transitions associated with the loss of combined parity (reflection) and time-reversal symmetries. Here we report that the time evolution of a single classical spin (e.g. monodomain ferromagnet) governed by the Landau-Lifshitz-Gilbert-Slonczewski equation in the absence of magnetic anisotropy terms is described by a Mobius transformation in complex stereographic coordinates. We identify the parity-time symmetry-breaking phase transition occurring in spin-transfer torque-driven linear spin systems as a transition between hyperbolic and loxodromic classes of Mobius transformations, with the critical point of the transition corresponding to the parabolic transformation. However, this establishes the understanding of non-equilibrium phase transitions as topological transitions in configuration space.
- Authors:
-
[1]
- Univ. of Chicago, Chicago, IL (United States); Argonne National Lab. (ANL), Argonne, IL (United States)
- Publication Date:
- Research Org.:
- Argonne National Laboratory (ANL), Argonne, IL (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22), Materials Sciences and Engineering Division
- OSTI Identifier:
- 1372900
- Grant/Contract Number:
- AC02-06CH11357
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Scientific Reports
- Additional Journal Information:
- Journal Volume: 7; Journal Issue: 1; Journal ID: ISSN 2045-2322
- Publisher:
- Nature Publishing Group
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Citation Formats
Galda, Alexey, and Vinokur, Valerii Ð. Linear dynamics of classical spin as Mobius transformation. United States: N. p., 2017.
Web. doi:10.1038/s41598-017-01326-x.
Galda, Alexey, & Vinokur, Valerii Ð. Linear dynamics of classical spin as Mobius transformation. United States. https://doi.org/10.1038/s41598-017-01326-x
Galda, Alexey, and Vinokur, Valerii Ð. Wed .
"Linear dynamics of classical spin as Mobius transformation". United States. https://doi.org/10.1038/s41598-017-01326-x. https://www.osti.gov/servlets/purl/1372900.
@article{osti_1372900,
title = {Linear dynamics of classical spin as Mobius transformation},
author = {Galda, Alexey and Vinokur, Valerii Ð.},
abstractNote = {Though the overwhelming majority of natural processes occur far from the equilibrium, general theoretical approaches to non-equilibrium phase transitions remain scarce. Recent breakthroughs introduced a description of open dissipative systems in terms of non-Hermitian quantum mechanics enabling the identification of a class of non-equilibrium phase transitions associated with the loss of combined parity (reflection) and time-reversal symmetries. Here we report that the time evolution of a single classical spin (e.g. monodomain ferromagnet) governed by the Landau-Lifshitz-Gilbert-Slonczewski equation in the absence of magnetic anisotropy terms is described by a Mobius transformation in complex stereographic coordinates. We identify the parity-time symmetry-breaking phase transition occurring in spin-transfer torque-driven linear spin systems as a transition between hyperbolic and loxodromic classes of Mobius transformations, with the critical point of the transition corresponding to the parabolic transformation. However, this establishes the understanding of non-equilibrium phase transitions as topological transitions in configuration space.},
doi = {10.1038/s41598-017-01326-x},
journal = {Scientific Reports},
number = 1,
volume = 7,
place = {United States},
year = {Wed Apr 26 00:00:00 EDT 2017},
month = {Wed Apr 26 00:00:00 EDT 2017}
}
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Works referenced in this record:
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Works referencing / citing this record:
Exceptional points in classical spin dynamics
preprint, January 2019
- Galda, Alexey; Vinokur, Valerii M.
- arXiv
Exceptional points in classical spin dynamics
journal, November 2019
- Galda, Alexey; Vinokur, Valerii M.
- Scientific Reports, Vol. 9, Issue 1
Dynamic Vortex-Mott Transition in 2D Superconducting Proximity Arrays
preprint, January 2020
- Glatz, Andreas; Vinokur, Valerii
- arXiv
Antiferromagnetism Emerging in a Ferromagnet with Gain
journal, November 2018
- Yang, Huanhuan; Wang, C.; Yu, Tianlin
- Physical Review Letters, Vol. 121, Issue 19
Exceptional points in classical spin dynamics
journal, November 2019
- Galda, Alexey; Vinokur, Valerii M.
- Scientific Reports, Vol. 9, Issue 1
Antiferromagnetism emerging in a ferromagnet with gain
text, January 2018
- Yang, Huanhuan; Wang, C.; Yu, Tianlin
- arXiv