RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



TMF:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


TMF, 2017, Volume 193, Number 1, Pages 162–176 (Mi tmf9301)  

This article is cited in 4 scientific papers (total in 4 papers)

Real meromorphic differentials: A language for describing meron configurations in planar magnetic nanoelements

A. B. Bogatyrevabc

a Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow Oblast, Russia
b Lomonosov Moscow State University, Moscow, Russia
c Institute for Numerical Mathematics, RAS, Moscow, Russia

Abstract: We use the language of real meromorphic differentials from the theory of Klein surfaces to describe the metastable states of multiply connected planar ferromagnetic nanoelements that minimize the exchange energy and have no side magnetic charges. These solutions still have sufficient internal degrees of freedom, which can be used as Ritz parameters to minimize other contributions to the total energy or as slow dynamical variables in the adiabatic approximation. The nontrivial topology of the magnet itself leads to several effects first described for the annulus and observed in the experiment. We explain the connection between the numbers of topological singularities of various types in the magnet and the constraints on the positions of these singularities following from the Abel theorem. Using multivalued Prym differentials leads to new meron configurations that were not considered in the classic work by Gross.

Keywords: spintronic, planar nanoelement, magnetic vortex, meron, Klein surface, Prym differential.

Funding Agency Grant Number
Russian Science Foundation 16-11-10349
This research was supported by a grant from the Russian Science Foundation (Project No. 16-11-10349).


DOI: https://doi.org/10.4213/tmf9301

Full text: PDF file (495 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 2017, 193:1, 1547–1559

Bibliographic databases:

ArXiv: 1610.04984
Received: 10.11.2016

Citation: A. B. Bogatyrev, “Real meromorphic differentials: A language for describing meron configurations in planar magnetic nanoelements”, TMF, 193:1 (2017), 162–176; Theoret. and Math. Phys., 193:1 (2017), 1547–1559

Citation in format AMSBIB
\Bibitem{Bog17}
\by A.~B.~Bogatyrev
\paper Real meromorphic differentials: A~language for describing meron configurations in planar magnetic nanoelements
\jour TMF
\yr 2017
\vol 193
\issue 1
\pages 162--176
\mathnet{http://mi.mathnet.ru/tmf9301}
\crossref{https://doi.org/10.4213/tmf9301}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3716532}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2017TMP...193.1547B}
\elib{http://elibrary.ru/item.asp?id=30512360}
\transl
\jour Theoret. and Math. Phys.
\yr 2017
\vol 193
\issue 1
\pages 1547--1559
\crossref{https://doi.org/10.1134/S0040577917100117}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000415198200011}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85034442808}


Linking options:
  • http://mi.mathnet.ru/eng/tmf9301
  • https://doi.org/10.4213/tmf9301
  • http://mi.mathnet.ru/eng/tmf/v193/i1/p162

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Alexander V. Chueshev, Victor V. Chueshev, “Prym differentials and Teichmüller spaces”, Zhurn. SFU. Ser. Matem. i fiz., 11:6 (2018), 686–691  mathnet  crossref
    2. Bezrodnykh S., Bogatyrev A., Goreinov S., Grigor'ev O., Hakula H., Vuorinen M., “On Capacity Computation For Symmetric Polygonal Condensers”, J. Comput. Appl. Math., 361 (2019), 271–282  crossref  isi
    3. Bogatyrev A.B., Metlov K.L., “Metastable States of Sub-Micron Scale Ferromagnetic Periodic Antidot Arrays”, J. Magn. Magn. Mater., 489 (2019), 165416  crossref  isi
    4. Alexander V. Chueshev, Victor V. Chueshev, “Vector bundle of prym differentials over Teichmüller spaces of surfaces with punctures”, Zhurn. SFU. Ser. Matem. i fiz., 12:3 (2019), 263–275  mathnet  crossref
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
    Number of views:
    This page:206
    References:24
    First page:21

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020