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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="en"><front><journal-meta><journal-id journal-id-type="publisher-id">najo</journal-id><journal-title-group><journal-title xml:lang="en">Nanosystems: Physics, Chemistry, Mathematics</journal-title><trans-title-group xml:lang="ru"><trans-title>Наносистемы: физика, химия, математика</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2220-8054</issn><issn pub-type="epub">2305-7971</issn><publisher><publisher-name>Университет ИТМО</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.17586/2220-8054-2024-15-3-332-339</article-id><article-id custom-type="elpub" pub-id-type="custom">najo-63</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>PHYSICS</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>ФИЗИКА</subject></subj-group></article-categories><title-group><article-title>Stability and transformations of domain walls in cylindrical wires</article-title><trans-title-group xml:lang="ru"><trans-title>Стабильность и трансформации доменных границ в цилиндрических проводах</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-6921-6075</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Чичай</surname><given-names>К. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Chichay</surname><given-names>K. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Ксения А. Чичай</p><p>физический факультет</p><p>197101; Санкт-Петербург</p></bio><bio xml:lang="en"><p>Ksenia A. Chichay</p><p>Department of Physics</p><p>197101; St. Petersburg</p></bio><email xlink:type="simple">ks.chichay@gmail.com</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-8789-3267</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Лобанов</surname><given-names>И. С.</given-names></name><name name-style="western" xml:lang="en"><surname>Lobanov</surname><given-names>I. S.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Игорь С. Лобанов</p><p>физический факультет</p><p>197101; Санкт-Петербург</p></bio><bio xml:lang="en"><p>Igor S. Lobanov</p><p>Department of Physics</p><p>197101; St. Petersburg</p></bio><email xlink:type="simple">lobanov.igor@gmail.com</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-9505-0996</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Уздин</surname><given-names>В. М.</given-names></name><name name-style="western" xml:lang="en"><surname>Uzdin</surname><given-names>V. M.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Валерий М. Уздин</p><p>физический факультет</p><p>197101; Санкт-Петербург</p></bio><bio xml:lang="en"><p>Valery M. Uzdin</p><p>Department of Physics</p><p>197101; St. Petersburg</p></bio><email xlink:type="simple">v.uzdin@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Университет ИТМО</institution></aff><aff xml:lang="en"><institution>ITMO University</institution></aff></aff-alternatives><pub-date pub-type="collection"><year>2024</year></pub-date><pub-date pub-type="epub"><day>01</day><month>06</month><year>2025</year></pub-date><volume>15</volume><issue>3</issue><fpage>332</fpage><lpage>339</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Chichay K.A., Lobanov I.S., Uzdin V.M., 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Чичай К.А., Лобанов И.С., Уздин В.М.</copyright-holder><copyright-holder xml:lang="en">Chichay K.A., Lobanov I.S., Uzdin V.M.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://nanojournal.ifmo.ru/jour/article/view/63">https://nanojournal.ifmo.ru/jour/article/view/63</self-uri><abstract><p>   For magnetic wires and other systems with cylindrical symmetry, algorithms have been proposed for constructing a multidimensional energy surface, searching for minimal energy paths between locally stable states and the activation energies of transitions between such states. The mechanisms of nucleation and transformation of domain walls of various types in amorphous ferromagnetic nanowires with a nonuniform anisotropy distribution have been studied. The stability of the domain walls structure with respect to thermal fluctuations and random external perturbations has been assessed.</p></abstract><trans-abstract xml:lang="ru"><p>   Предложены алгоритмы построения многомерной энергетической поверхности, поиска путей с минимальным перепадом энергии между локально устойчивыми состояниями и энергий активации переходов между такими состояниями для магнитных проводов и других систем с цилиндрической симметрией. Изучены механизмы зарождения и трансформации доменных границ различного типа в аморфных ферромагнитных нанопроводах с неоднородным распределением анизотропии. Оценена устойчивость структуры доменных стенок по отношению к тепловым флуктуациям и случайным внешним возмущениям.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>доменная граница</kwd><kwd>цилиндрические системы</kwd><kwd>аморфные ферромагнитные микропровода</kwd><kwd>микромагнетизм</kwd><kwd>трансформация доменной границы</kwd><kwd>теория переходного состояния</kwd></kwd-group><kwd-group xml:lang="en"><kwd>domain wall</kwd><kwd>cylindrical systems</kwd><kwd>amorphous ferromagnetic microwires</kwd><kwd>micromagnetics</kwd><kwd>domain wall transformation</kwd><kwd>transition state theory</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">Работа выполнена при финансовой поддержке Российского научного фонда (проект № 23-72-10028, https://rscf.ru/en/project/23-72-10028/)</funding-statement><funding-statement xml:lang="en">This work was funded by the Russian Science Foundation (project No. 23-72-10028, https://rscf.ru/en/project/23-72-10028/)</funding-statement></funding-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Foerster M., Boulle O., Esefelder S., Mattheis R., Kl¨aui M. Domain Wall Memory Device. In: Xu, Y., Awschalom, D., Nitta, J. (eds) Handbook of Spintronics. Springer, Dordrecht, 2016</mixed-citation><mixed-citation xml:lang="en">Foerster M., Boulle O., Esefelder S., Mattheis R., Kl¨aui M. Domain Wall Memory Device. In: Xu, Y., Awschalom, D., Nitta, J. (eds) Handbook of Spintronics. Springer, Dordrecht, 2016</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Parkin S.S.P., Hayashi M. and Thomas L. Magnetic Domain-Wall Racetrack Memory. Science, 2008, 320(5873), P. 190–194.</mixed-citation><mixed-citation xml:lang="en">Parkin S.S.P., Hayashi M. and Thomas L. Magnetic Domain-Wall Racetrack Memory. Science, 2008, 320(5873), P. 190–194.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Venkat G., Allwood D.A., Hayward T.J. Magnetic domain walls: types, processes and applications. J. Phys. D: Appl. Phys., 2024, 57, P. 1688.</mixed-citation><mixed-citation xml:lang="en">Venkat G., Allwood D.A., Hayward T.J. Magnetic domain walls: types, processes and applications. J. Phys. D: Appl. Phys., 2024, 57, P. 1688.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Parkin S., Yang S.H. Memory on the racetrack. Nature nanotechnology, 2015, 10(3), P. 195–198.</mixed-citation><mixed-citation xml:lang="en">Parkin S., Yang S.H. Memory on the racetrack. Nature nanotechnology, 2015, 10(3), P. 195–198.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Blasing R. et al. Magnetic Racetrack Memory: From Physics to the Cusp of Applications Within a Decade. Proc. IEEE 2020, 108, P. 1303–1321.</mixed-citation><mixed-citation xml:lang="en">Blasing R. et al. Magnetic Racetrack Memory: From Physics to the Cusp of Applications Within a Decade. Proc. IEEE 2020, 108, P. 1303–1321.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Hertel R. Ultrafast domain wall dynamics in magnetic nanotubes and nanowires. J. Phys.: Condens. Matter, 2016. 28, P. 483002.</mixed-citation><mixed-citation xml:lang="en">Hertel R. Ultrafast domain wall dynamics in magnetic nanotubes and nanowires. J. Phys.: Condens. Matter, 2016. 28, P. 483002.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Yan M., Andreas C., Kakay A., Garcıa-Sanchez F., Hertel R. Fast domain wall dynamics in magnetic nanotubes: Suppression of Walker breakdown and Cherenkov-like spin wave emission. Appl. Phys. Lett., 2011. 99, P. 122505.</mixed-citation><mixed-citation xml:lang="en">Yan M., Andreas C., Kakay A., Garcıa-Sanchez F., Hertel R. Fast domain wall dynamics in magnetic nanotubes: Suppression of Walker breakdown and Cherenkov-like spin wave emission. Appl. Phys. Lett., 2011. 99, P. 122505.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Corte-Le´on P., Gonzalez-Legarreta L., Zhukova V., Ipatov M., Blanco J.M., Churyukanova M., Taskaev S. and Zhukov A. Controlling the domain wall dynamics in Fe-, Ni- and Co- based magnetic microwires. J. Alloys Compound., 2020. 834, P. 155170.</mixed-citation><mixed-citation xml:lang="en">Corte-Le´on P., Gonzalez-Legarreta L., Zhukova V., Ipatov M., Blanco J.M., Churyukanova M., Taskaev S. and Zhukov A. Controlling the domain wall dynamics in Fe-, Ni- and Co- based magnetic microwires. J. Alloys Compound., 2020. 834, P. 155170.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Tejo F., Fernandez-Roldan J.A.F., Guslienko K., Otxoa R.M. and Chubykalo-Fesenko O. Giant supermagnonic Bloch point velocities in cylindrical ferromagnetic nanowires. Nanoscale, 2024, Advance Article</mixed-citation><mixed-citation xml:lang="en">Tejo F., Fernandez-Roldan J.A.F., Guslienko K., Otxoa R.M. and Chubykalo-Fesenko O. Giant supermagnonic Bloch point velocities in cylindrical ferromagnetic nanowires. Nanoscale, 2024, Advance Article</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Alam J., et.al. Cylindrical micro and nanowires: Fabrication, properties and applications. J. Magn. Magn. Mater., 2020, 513, P. 167074.</mixed-citation><mixed-citation xml:lang="en">Alam J., et.al. Cylindrical micro and nanowires: Fabrication, properties and applications. J. Magn. Magn. Mater., 2020, 513, P. 167074.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Yan M. Beating the Walker limit with massless domain walls in cylindrical nanowires. Phys. Rev. Lett., 2010. 104, P. 057201.</mixed-citation><mixed-citation xml:lang="en">Yan M. Beating the Walker limit with massless domain walls in cylindrical nanowires. Phys. Rev. Lett., 2010. 104, P. 057201.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Zhukova V., Corte-Leon P., Gonz´alez-Legarreta, L., Talaat, A., Blanco, J.M., Ipatov, M., Olivera, J. and Zhukov, A. Review of domain wall dynamics engineering in magnetic microwires. Nanomaterials, 2020. 10(12), P. 2407.</mixed-citation><mixed-citation xml:lang="en">Zhukova V., Corte-Leon P., Gonz´alez-Legarreta, L., Talaat, A., Blanco, J.M., Ipatov, M., Olivera, J. and Zhukov, A. Review of domain wall dynamics engineering in magnetic microwires. Nanomaterials, 2020. 10(12), P. 2407.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Chiriac H., Ovari T., Zhukov A. Magnetoelastic anisotropy of amorphous microwires. J. Magn. Magn. Mater., 2003. 496, P. 254–255.</mixed-citation><mixed-citation xml:lang="en">Chiriac H., Ovari T., Zhukov A. Magnetoelastic anisotropy of amorphous microwires. J. Magn. Magn. Mater., 2003. 496, P. 254–255.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Zhukova V., Blanco J.M., Ipatov M., Zhukov A. Magnetoelastic contribution in domain wall dynamics of amorphous microwires. Physica B, 2012, 407, P. 1450–1454.</mixed-citation><mixed-citation xml:lang="en">Zhukova V., Blanco J.M., Ipatov M., Zhukov A. Magnetoelastic contribution in domain wall dynamics of amorphous microwires. Physica B, 2012, 407, P. 1450–1454.</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Chichay K., et. al.Tunable domain wall dynamics in amorphous ferromagnetic microwires. J. Alloys Compound., 2020. 835, P. 154843.</mixed-citation><mixed-citation xml:lang="en">Chichay K., et. al.Tunable domain wall dynamics in amorphous ferromagnetic microwires. J. Alloys Compound., 2020. 835, P. 154843.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Gudoshnikov S.A., Grebenshchikov Yu.B., Ljubimov B.Ya., Palvanov P.S., Usov N.A., Ipatov M., Zhukov A., Gonzalez J. Ground state magnetization distribution and characteristic width of head to head domain wall in Fe-rich amorphous microwire. Phys. Stat. Sol. A, 2009, 206(4), P. 613–617.</mixed-citation><mixed-citation xml:lang="en">Gudoshnikov S.A., Grebenshchikov Yu.B., Ljubimov B.Ya., Palvanov P.S., Usov N.A., Ipatov M., Zhukov A., Gonzalez J. Ground state magnetization distribution and characteristic width of head to head domain wall in Fe-rich amorphous microwire. Phys. Stat. Sol. A, 2009, 206(4), P. 613–617.</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Chichay K.A., Lobanov I.S. Uzdin V.M. The structure of magnetic domain walls in cylindrical nano- and microwires with in- homogeneous anisotropy. Nanosystems: Phys. Chem. Math., 2023. 15, P. 55–59.</mixed-citation><mixed-citation xml:lang="en">Chichay K.A., Lobanov I.S. Uzdin V.M. The structure of magnetic domain walls in cylindrical nano- and microwires with in- homogeneous anisotropy. Nanosystems: Phys. Chem. Math., 2023. 15, P. 55–59.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Lobanov I.S., Potkina M.N., Uzdin V.M. Stability and Lifetimes of Magnetic States of Nano- and Microstructures (Brief Review). JETP Letters, 2021. 113, 12, P. 801–813.</mixed-citation><mixed-citation xml:lang="en">Lobanov I.S., Potkina M.N., Uzdin V.M. Stability and Lifetimes of Magnetic States of Nano- and Microstructures (Brief Review). JETP Letters, 2021. 113, 12, P. 801–813.</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Lobanov I.S., Uzdin V.M. The lifetime of micron scale topological chiral magnetic states with atomic resolution. Comp. Phys. Commun., 2021, 269, P. 108136.</mixed-citation><mixed-citation xml:lang="en">Lobanov I.S., Uzdin V.M. The lifetime of micron scale topological chiral magnetic states with atomic resolution. Comp. Phys. Commun., 2021, 269, P. 108136.</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Vansteenkiste A., Leliaert J., Dvornik M., Helsen M., Garsia-Sanchez F., B. Van Waeyenberge F. The design and verification of MuMax3. AIP Advances, 2014, 4, P. 107133.</mixed-citation><mixed-citation xml:lang="en">Vansteenkiste A., Leliaert J., Dvornik M., Helsen M., Garsia-Sanchez F., B. Van Waeyenberge F. The design and verification of MuMax3. AIP Advances, 2014, 4, P. 107133.</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Fischbacher T., Franchin M., Bordignon G., and Fangohr H. A Systematic Approach to Multiphysics Extensions of Finite-Element-Based Micromagnetic Simulations: Nmag, IEEE Transactions on Magnetics, 2007, 43(6), P. 2896–2898.</mixed-citation><mixed-citation xml:lang="en">Fischbacher T., Franchin M., Bordignon G., and Fangohr H. A Systematic Approach to Multiphysics Extensions of Finite-Element-Based Micromagnetic Simulations: Nmag, IEEE Transactions on Magnetics, 2007, 43(6), P. 2896–2898.</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Abert C., Exl L., Bruckner F., Drews A., Suess D. magnum. fe: A micromagnetic finite-element simulation code based on FEniCS. Journal of Magnetism and Magnetic Materials, 2013, 345, P. 29–35.</mixed-citation><mixed-citation xml:lang="en">Abert C., Exl L., Bruckner F., Drews A., Suess D. magnum. fe: A micromagnetic finite-element simulation code based on FEniCS. Journal of Magnetism and Magnetic Materials, 2013, 345, P. 29–35.</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Chiriac H., Ovari T.A., Pop Gh. Internal stress distribution in glass-covered amorphous magnetic wires. Phys. Rev. B., 1995, 52(14), P. 10104.</mixed-citation><mixed-citation xml:lang="en">Chiriac H., Ovari T.A., Pop Gh. Internal stress distribution in glass-covered amorphous magnetic wires. Phys. Rev. B., 1995, 52(14), P. 10104.</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
