<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.3 20210610//EN" "JATS-journalpublishing1-3.dtd">
<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">mrisel</journal-id><journal-title-group><journal-title xml:lang="en">Magnetic Resonance in Solids</journal-title><trans-title-group xml:lang="ru"><trans-title>Magnetic Resonance in Solids</trans-title></trans-title-group></journal-title-group><issn pub-type="epub">2072-5981</issn><publisher><publisher-name>Kazan Federal University</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.26907/mrsej-24111</article-id><article-id custom-type="elpub" pub-id-type="custom">mrisel-250</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="ru"><subject>Статьи</subject></subj-group></article-categories><title-group><article-title>Comparison of several methods for determining the critical temperature of a superconducting transition in ferromagnet/superconductor heterostructures</article-title><trans-title-group xml:lang="ru"><trans-title></trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="western" xml:lang="en"><surname>Tumanov</surname><given-names>V. A.</given-names></name></name-alternatives><bio xml:lang="en"><p>Kazan 420008</p></bio><email xlink:type="simple">tumanvadim@yandex.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="western" xml:lang="en"><surname>Proshin</surname><given-names>Yu. N.</given-names></name></name-alternatives><bio xml:lang="en"><p>Kazan 420008</p></bio><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff xml:lang="en" id="aff-1"><institution>Kazan Federal University</institution><country>Russian Federation</country></aff><pub-date pub-type="collection"><year>2024</year></pub-date><pub-date pub-type="epub"><day>19</day><month>04</month><year>2024</year></pub-date><volume>26</volume><issue>1</issue><issue-title>SPECIAL ISSUE dedicated to Boris I. Kochelaev's 90th birthday</issue-title><elocation-id>24111 (9 pp.)</elocation-id><permissions><copyright-statement>Copyright &amp;#x00A9; Tumanov V.A., Proshin Y.N., 2024</copyright-statement><copyright-year>2024</copyright-year><copyright-holder xml:lang="ru">Tumanov V.A., Proshin Y.N.</copyright-holder><copyright-holder xml:lang="en">Tumanov V.A., Proshin Y.N.</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://www.mrsej.ru/jour/article/view/250">https://www.mrsej.ru/jour/article/view/250</self-uri><abstract><p>Two methods for calculating the superconducting transition critical temperature of superconductor / ferromagnetic metal heterostructures in the dirty limit are compared. The first method relies on an approximation where the order parameter is assumed to be constant within each superconducting layer. The second method does not use any approximations and involves a numerical iterative process where the critical temperature and the order parameter distribution are jointly searched for in each iteration. Using these methods, we study various heterostructures involving a ferromagnetic and superconducting layers, including case where the ferromagnetic layer is split into domains.</p></abstract><kwd-group xml:lang="en"><kwd>superconductivity</kwd><kwd>ferromagnetism</kwd><kwd>proximity effect</kwd><kwd>critical temperature</kwd><kwd>order parameter</kwd></kwd-group><funding-group><funding-statement xml:lang="en">This paper has been supported by the Kazan Federal University Strategic Academic Leadership Program.</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">Buzdin A. I., Reviews Of Modern Physics 77, 935 (2005)</mixed-citation><mixed-citation xml:lang="en">Buzdin A. I., Reviews Of Modern Physics 77, 935 (2005)</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Efetov K. B., Garifullin I. A., Volkov A. F., Westerholt K., in Magnetic Heterostructures: Advances and Perspectives in Spinstructures and Spintransport (Springer, 2008) pp. 251–290</mixed-citation><mixed-citation xml:lang="en">Efetov K. B., Garifullin I. A., Volkov A. F., Westerholt K., in Magnetic Heterostructures: Advances and Perspectives in Spinstructures and Spintransport (Springer, 2008) pp. 251–290</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Izyumov Y. A., Proshin Y. N., Khusainov M. G., Physics-Uspekhi 45, 109 (2002)</mixed-citation><mixed-citation xml:lang="en">Izyumov Y. A., Proshin Y. N., Khusainov M. G., Physics-Uspekhi 45, 109 (2002)</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Oh S., Youm D., Beasley M., Applied Physics Letters 71, 2376 (1997)</mixed-citation><mixed-citation xml:lang="en">Oh S., Youm D., Beasley M., Applied Physics Letters 71, 2376 (1997)</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Tagirov L. R., Physical Review Letters 83, 2058 (1999)</mixed-citation><mixed-citation xml:lang="en">Tagirov L. R., Physical Review Letters 83, 2058 (1999)</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Buzdin A. I., Vedyayev A. V., Ryzhanova N. V., Europhysics Letters 48, 686 (1999)</mixed-citation><mixed-citation xml:lang="en">Buzdin A. I., Vedyayev A. V., Ryzhanova N. V., Europhysics Letters 48, 686 (1999)</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Proshin Y. N., Zimin A., Fazleev N. G., Khusainov M. G., Physical Review B 73, 184514 (2006)</mixed-citation><mixed-citation xml:lang="en">Proshin Y. N., Zimin A., Fazleev N. G., Khusainov M. G., Physical Review B 73, 184514 (2006)</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Tumanov V. A., Goryunov Y. V., Proshin Y. N., JETP Letters 107, 426 (2018)</mixed-citation><mixed-citation xml:lang="en">Tumanov V. A., Goryunov Y. V., Proshin Y. N., JETP Letters 107, 426 (2018)</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Krunavakarn B., Physics Letters A 383, 1341 (2019)</mixed-citation><mixed-citation xml:lang="en">Krunavakarn B., Physics Letters A 383, 1341 (2019)</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Borisova O. N., Tumanov V. A., Proshin Y. N., Physics of Metals and Metallography 121, 434 (2020)</mixed-citation><mixed-citation xml:lang="en">Borisova O. N., Tumanov V. A., Proshin Y. N., Physics of Metals and Metallography 121, 434 (2020)</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Khusainov M. G., Izyumov Y. A., Proshin Y. N., Physica B: Condensed Matter 284, 503 (2000)</mixed-citation><mixed-citation xml:lang="en">Khusainov M. G., Izyumov Y. A., Proshin Y. N., Physica B: Condensed Matter 284, 503 (2000)</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Ryazanov V., Oboznov V., Rusanov A. Y., Veretennikov A., Golubov A. A., Aarts J., Physical Review Letters 86, 2427 (2001)</mixed-citation><mixed-citation xml:lang="en">Ryazanov V., Oboznov V., Rusanov A. Y., Veretennikov A., Golubov A. A., Aarts J., Physical Review Letters 86, 2427 (2001)</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Karabassov T., Stolyarov V., Golubov A., Silkin V., Bayazitov V., Lvov B., Vasenko A., Physical Review B 100, 104502 (2019)</mixed-citation><mixed-citation xml:lang="en">Karabassov T., Stolyarov V., Golubov A., Silkin V., Bayazitov V., Lvov B., Vasenko A., Physical Review B 100, 104502 (2019)</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Houzet M., Buzdin A. I., Physical Review B 76, 060504 (2007)</mixed-citation><mixed-citation xml:lang="en">Houzet M., Buzdin A. I., Physical Review B 76, 060504 (2007)</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Houzet M., Buzdin A. I., Physical Review B 74, 214507 (2006)</mixed-citation><mixed-citation xml:lang="en">Houzet M., Buzdin A. I., Physical Review B 74, 214507 (2006)</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Tumanov V. A., Proshin Y. N., Journal of Low Temperature Physics 185, 460 (2016)</mixed-citation><mixed-citation xml:lang="en">Tumanov V. A., Proshin Y. N., Journal of Low Temperature Physics 185, 460 (2016)</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Tumanov V. A., Proshin Y. N., Physics of Metals and Metallography 125, 237 (2024)</mixed-citation><mixed-citation xml:lang="en">Tumanov V. A., Proshin Y. N., Physics of Metals and Metallography 125, 237 (2024)</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Bakurskiy S. V., Golubov A. A., Klenov N. V., Kupriyanov M. Y., Soloviev I., JETP Letters 101, 765 (2015)</mixed-citation><mixed-citation xml:lang="en">Bakurskiy S. V., Golubov A. A., Klenov N. V., Kupriyanov M. Y., Soloviev I., JETP Letters 101, 765 (2015)</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Andriyakhina E. S., Burmistrov I. S., Physical Review B 103, 174519 (2021)</mixed-citation><mixed-citation xml:lang="en">Andriyakhina E. S., Burmistrov I. S., Physical Review B 103, 174519 (2021)</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Baumard J., Cayssol J., Bergeret F. S., Buzdin A., Physical Review B 99, 014511 (2019)</mixed-citation><mixed-citation xml:lang="en">Baumard J., Cayssol J., Bergeret F. S., Buzdin A., Physical Review B 99, 014511 (2019)</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Avdeev M., Proshin Y. N., JETP 117, 1101 (2013)</mixed-citation><mixed-citation xml:lang="en">Avdeev M., Proshin Y. N., JETP 117, 1101 (2013)</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Avdeev M. V., Proshin Y. N., JETP Letters 102, 96 (2015)</mixed-citation><mixed-citation xml:lang="en">Avdeev M. V., Proshin Y. N., JETP Letters 102, 96 (2015)</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Fominov Y. V., Chtchelkatchev N., Golubov A., Physical Review B 66, 014507 (2002)</mixed-citation><mixed-citation xml:lang="en">Fominov Y. V., Chtchelkatchev N., Golubov A., Physical Review B 66, 014507 (2002)</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Pugach N., Safonchik M., Champel T., Zhitomirsky M., Lahderanta E., Eschrig M., Lacroix C., Applied Physics Letters 111, 162601 (2017)</mixed-citation><mixed-citation xml:lang="en">Pugach N., Safonchik M., Champel T., Zhitomirsky M., Lahderanta E., Eschrig M., Lacroix C., Applied Physics Letters 111, 162601 (2017)</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">Garifullin I. A., Tikhonov D. A., Garif’yanov N. N., Lazar L., Goryunov Y. V., Khlebnikov S. Y., Tagirov L. R., Westerholt K., Zabel H., Physical Review B 66, 020505 (2002)</mixed-citation><mixed-citation xml:lang="en">Garifullin I. A., Tikhonov D. A., Garif’yanov N. N., Lazar L., Goryunov Y. V., Khlebnikov S. Y., Tagirov L. R., Westerholt K., Zabel H., Physical Review B 66, 020505 (2002)</mixed-citation></citation-alternatives></ref><ref id="cit26"><label>26</label><citation-alternatives><mixed-citation xml:lang="ru">Andriyakhina E. S., Apostoloff S., Burmistrov I. S., JETP Letters 116, 825 (2022)</mixed-citation><mixed-citation xml:lang="en">Andriyakhina E. S., Apostoloff S., Burmistrov I. S., JETP Letters 116, 825 (2022)</mixed-citation></citation-alternatives></ref><ref id="cit27"><label>27</label><citation-alternatives><mixed-citation xml:lang="ru">Bergeret F., Efetov K., Larkin A., Physical Review B 62, 11872 (2000)</mixed-citation><mixed-citation xml:lang="en">Bergeret F., Efetov K., Larkin A., Physical Review B 62, 11872 (2000)</mixed-citation></citation-alternatives></ref><ref id="cit28"><label>28</label><citation-alternatives><mixed-citation xml:lang="ru">Bergeret F. S., Volkov A. F., Efetov K. B., Reviews Of Modern Physics 77, 1321 (2005)</mixed-citation><mixed-citation xml:lang="en">Bergeret F. S., Volkov A. F., Efetov K. B., Reviews Of Modern Physics 77, 1321 (2005)</mixed-citation></citation-alternatives></ref><ref id="cit29"><label>29</label><citation-alternatives><mixed-citation xml:lang="ru">Fominov Y. V., Volkov A. F., Efetov K. B., Physical Review B 75, 104509 (2007)</mixed-citation><mixed-citation xml:lang="en">Fominov Y. V., Volkov A. F., Efetov K. B., Physical Review B 75, 104509 (2007)</mixed-citation></citation-alternatives></ref><ref id="cit30"><label>30</label><citation-alternatives><mixed-citation xml:lang="ru">Demler E. A., Arnold G., Beasley M., Physical Review B 55, 15174 (1997)</mixed-citation><mixed-citation xml:lang="en">Demler E. A., Arnold G., Beasley M., Physical Review B 55, 15174 (1997)</mixed-citation></citation-alternatives></ref><ref id="cit31"><label>31</label><citation-alternatives><mixed-citation xml:lang="ru">Khusainov M. G., Khusainov M. M., Ivanov N., Proshin Y. N., JETP Letters 90, 359 (2009)</mixed-citation><mixed-citation xml:lang="en">Khusainov M. G., Khusainov M. M., Ivanov N., Proshin Y. N., JETP Letters 90, 359 (2009)</mixed-citation></citation-alternatives></ref><ref id="cit32"><label>32</label><citation-alternatives><mixed-citation xml:lang="ru">Kuprianov M. Y., Lukichev V. F., JETP 94, 149 (1988)</mixed-citation><mixed-citation xml:lang="en">Kuprianov M. Y., Lukichev V. F., JETP 94, 149 (1988)</mixed-citation></citation-alternatives></ref><ref id="cit33"><label>33</label><citation-alternatives><mixed-citation xml:lang="ru">Khusainov M. G., Sov. Phys. JETP Letters 53, 579 (1991)</mixed-citation><mixed-citation xml:lang="en">Khusainov M. G., Sov. Phys. JETP Letters 53, 579 (1991)</mixed-citation></citation-alternatives></ref><ref id="cit34"><label>34</label><citation-alternatives><mixed-citation xml:lang="ru">Hubert A., Schafer R., Magnetic domains: the analysis of magnetic microstructures (Springer Science &amp; Business Media, 1998)</mixed-citation><mixed-citation xml:lang="en">Hubert A., Schafer R., Magnetic domains: the analysis of magnetic microstructures (Springer Science &amp; Business Media, 1998)</mixed-citation></citation-alternatives></ref><ref id="cit35"><label>35</label><citation-alternatives><mixed-citation xml:lang="ru">Tumanov V. A., Zaitseva V. E., Proshin Y. N., JETP Letters 116, 449 (2022)</mixed-citation><mixed-citation xml:lang="en">Tumanov V. A., Zaitseva V. E., Proshin Y. N., JETP Letters 116, 449 (2022)</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>
