Linear dynamics of classical spin as Mobius transformation

Galda, Alexey; Vinokur, Valerii Ð.

doi:10.1038/s41598-017-01326-x

Linear dynamics of classical spin as Mobius transformation

Journal Article · Wed Apr 26 00:00:00 EDT 2017 · Scientific Reports

DOI:https://doi.org/10.1038/s41598-017-01326-x· OSTI ID:1372900

Galda, Alexey ^[1]; ^[1]

Univ. of Chicago, Chicago, IL (United States); Argonne National Lab. (ANL), Argonne, IL (United States)

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.

View Accepted Manuscript (DOE)

Research Organization:: Argonne National Laboratory (ANL)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22), Materials Sciences and Engineering Division

Grant/Contract Number:: AC02-06CH11357

OSTI ID:: 1372900

Journal Information:: Scientific Reports, Journal Name: Scientific Reports Journal Issue: 1 Vol. 7; ISSN 2045-2322

Publisher:: Nature Publishing GroupCopyright Statement

Country of Publication:: United States

Language:: English

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Cited By (5)

Exceptional points in classical spin dynamics Galda, Alexey; Vinokur, Valerii M. Scientific Reports, Vol. 9, Issue 1 https://doi.org/10.1038/s41598-019-53455-0	journal	November 2019
Dynamic Vortex-Mott Transition in 2D Superconducting Proximity Arrays Glatz, Andreas; Vinokur, Valerii arXiv https://doi.org/10.48550/arxiv.2005.13184	preprint	January 2020
Antiferromagnetism Emerging in a Ferromagnet with Gain Yang, Huanhuan; Wang, C.; Yu, Tianlin Physical Review Letters, Vol. 121, Issue 19 https://doi.org/10.1103/physrevlett.121.197201	journal	November 2018
Antiferromagnetism emerging in a ferromagnet with gain Yang, Huanhuan; Wang, C.; Yu, Tianlin arXiv https://doi.org/10.48550/arxiv.1807.01048	text	January 2018
Exceptional points in classical spin dynamics Galda, Alexey; Vinokur, Valerii M. arXiv https://doi.org/10.48550/arxiv.1903.09729	preprint	January 2019

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