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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="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">mireabulletin</journal-id><journal-title-group><journal-title xml:lang="ru">Russian Technological Journal</journal-title><trans-title-group xml:lang="en"><trans-title>Russian Technological Journal</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2782-3210</issn><issn pub-type="epub">2500-316X</issn><publisher><publisher-name>RTU MIREA</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.32362/2500-316X-2022-10-3-85-92</article-id><article-id custom-type="elpub" pub-id-type="custom">mireabulletin-526</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>МИКРО- И НАНОЭЛЕКТРОНИКА. ФИЗИКА КОНДЕНСИРОВАННОГО СОСТОЯНИЯ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>MICRO- AND NANOELECTRONICS. CONDENSED MATTER PHYSICS</subject></subj-group></article-categories><title-group><article-title>Анизотропный магнитоэлектрический эффект в структуре цирконат–титанат свинца / магнитострикционный волоконный композит</article-title><trans-title-group xml:lang="en"><trans-title>Anisotropic magnetoelectric effect in lead zirconate titanate and magnetostrictive fiber composite structures</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-7762-9198</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Савельев</surname><given-names>Д. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Saveliev</surname><given-names>D. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Савельев Дмитрий Владимирович - аспирант кафедры наноэлектроники Института перспективных технологий и индустриального программирования.</p><p>119454, Москва, пр-т Вернадского, д. 78. Scopus Author ID 57196479660, ResearcherID D-8952-2019</p></bio><bio xml:lang="en"><p>Dmitriy V. Saveliev - Postgraduate Student, Department of Nanoelectronics, Institute for Advanced Technologies and Industrial Programming.</p><p>78, Vernadskogo pr., Moscow, 119454. Scopus Author ID 57196479660, ResearcherID D-8952-2019</p></bio><email xlink:type="simple">dimsav94@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/0000-0002-3699-4321</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Фетисов</surname><given-names>Л. Ю.</given-names></name><name name-style="western" xml:lang="en"><surname>Fetisov</surname><given-names>L. Y.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Фетисов Леонид Юрьевич - доктор физико-математических наук, доцент кафедры наноэлектроники Института перспективных технологий и индустриального программирования.</p><p>119454, Москва, пр-т Вернадского, д. 78. Scopus Author ID 26431336600, ResearcherID D-1163-2013</p></bio><bio xml:lang="en"><p>Leonid Y. Fetisov - Dr. Sci. (Phys.–Math.), Associate Professor, Department of Nanoelectronics, Institute for Advanced Technologies and Industrial Programming.</p><p>78, Vernadskogo pr., Moscow, 119454. Scopus Author ID 26431336600, ResearcherID D-1163-2013</p></bio><email xlink:type="simple">fetisovl@yandex.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-2995-8824</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Мусатов</surname><given-names>В. И.</given-names></name><name name-style="western" xml:lang="en"><surname>Musatov</surname><given-names>V. I.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Мусатов Владимир Иванович - студент кафедры наноэлектроники Института перспективных технологий и индустриального программирования.</p><p>119454, Москва, пр-т Вернадского, д. 78. Scopus Author ID 57416814900</p></bio><bio xml:lang="en"><p>Vladimir I. Musatov - Student, Department of Nanoelectronics, Institute for Advanced Technologies and Industrial Programming.</p><p>78, Vernadskogo pr., Moscow, 119454. Scopus Author ID 57416814900</p></bio><email xlink:type="simple">musatov_vovak@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-7714-2742</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Джапаридзе</surname><given-names>М. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Dzhaparidze</surname><given-names>M. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Джапаридзе Михаил Валерьевич - аспирант кафедры наноэлектроники Института перспективных технологий и индустриального программирования.</p><p>119454, Москва, пр-т Вернадского, д. 78. Scopus Author ID 57395288400</p></bio><bio xml:lang="en"><p>Mikhail V. Dzhaparidze - Postgraduate Student, Department of Nanoelectronics Institute for Advanced Technologies and Industrial Programming.</p><p>78, Vernadskogo pr., Moscow, 119454. Scopus Author ID 57395288400</p></bio><email xlink:type="simple">mvd-1997@yandex.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>МИРЭА – Российский технологический университет</institution><country>Россия</country></aff><aff xml:lang="en"><institution>MIREA – Russian Technological University</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2022</year></pub-date><pub-date pub-type="epub"><day>09</day><month>06</month><year>2022</year></pub-date><volume>10</volume><issue>3</issue><fpage>85</fpage><lpage>92</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Савельев Д.В., Фетисов Л.Ю., Мусатов В.И., Джапаридзе М.В., 2022</copyright-statement><copyright-year>2022</copyright-year><copyright-holder xml:lang="ru">Савельев Д.В., Фетисов Л.Ю., Мусатов В.И., Джапаридзе М.В.</copyright-holder><copyright-holder xml:lang="en">Saveliev D.V., Fetisov L.Y., Musatov V.I., Dzhaparidze M.V.</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.rtj-mirea.ru/jour/article/view/526">https://www.rtj-mirea.ru/jour/article/view/526</self-uri><abstract><sec><title>Цели</title><p>Цели. Разработка композитных структур, в которых наблюдается сильно анизотропный магнитоэлектрический (МЭ) эффект, актуальна для создания датчиков, чувствительных к направлению магнитного поля. Такой МЭ эффект может быть обусловлен анизотропией как магнитного, так и пьезоэлектрического слоя. Авторами изготовлен новый анизотропный материал – магнитострикционный волоконный композит (МВК), представляющий собой набор никелевых проволок, расположенных вплотную параллельно друг к другу в один слой и погруженных в полимерную матрицу. Цель работы – исследование линейного МЭ эффекта в композитных структурах со слоями из МВК и керамики цирконата титаната свинца (ЦТС-19).</p></sec><sec><title>Методы</title><p>Методы. Магнитострикция МВК была измерена тензометрическим методом, МЭ эффект – методом низкочастотной модуляции магнитного поля.</p></sec><sec><title>Результаты</title><p>Результаты. Были изготовлены структуры с диаметрами никелевых проволок 100, 150 и 200 мкм. Измерены полевые зависимости магнитострикции МВК, а также частотные, полевые и амплитудные зависимости МЭ напряжения для случая линейного МЭ эффекта при различной величине угла между направлением магнитного поля и проволоками. Показано, что все образцы обладают сильной анизотропией относительно направления магнитного поля. МЭ напряжение уменьшается от максимального значения до нуля при изменении направления магнитного поля с параллельного до перпендикулярного относительно волокон никеля.</p></sec><sec><title>Выводы</title><p>Выводы. Наибольшим по величине МЭ коэффициентом, составляющим 1.71 В/(Э · см), обладает структура, изготовленная на основе МВК с диаметром проволоки 150 мкм. Частота резонанса растет от 3.5 кГц до 6.5 кГц с увеличением диаметра проволок. Величина магнитострикции МВК сопоставима по величине с магнитострикцией пластины никеля такой же толщины.</p></sec></abstract><trans-abstract xml:lang="en"><sec><title>Objectives</title><p>Objectives. The development of composite structures in which a strongly anisotropic magnetoelectric (ME) effect is observed is relevant for the creation of sensors that are sensitive to the direction of the magnetic field. Such an ME effect can arise due to the anisotropy of both the magnetic and the piezoelectric layers. In this work, a new anisotropic material named as a magnetostrictive fiber composite (MFC), comprising a set of nickel wires placed closely parallel to each other in one layer and immersed in a polymer matrix, is manufactured and studied. The study aimed to investigate the linear ME effect in a structure comprising of a new magnetic material, MFC, and lead zirconate titanate (PZT-19).</p></sec><sec><title>Methods</title><p>Methods. The magnetostriction for the MFC structure was measured using the strain-gauge method; the ME effect was determined by low-frequency magnetic field modulation.</p></sec><sec><title>Results</title><p>Results. Structures with nickel wire diameters of 100, 150, and 200 μm were fabricated. The MFC magnetostriction field dependences were determined along with the frequency-, field-, and amplitude dependences of the ME voltage in the case of linear ME effect. Measurements were carried out at various values of the angle between the direction of the magnetic field and the wires. All samples demonstrated strong anisotropy with respect to the direction of the magnetic field. When the magnetic field orientation changes from parallel to perpendicular with respect to the nickel wire axes, the ME voltage decreases from its maximum value to zero.</p></sec><sec><title>Conclusions</title><p>Conclusions. The largest ME coefficient 1.71 V/(Oe · cm) was obtained for a structure made of MFC with a wire diameter of 150 μm. With increasing wire diameter, the resonance frequency increases from 3.5 to 6.5 kHz. The magnetostriction of the MFC is comparable in magnitude to that of a nickel plate having the same thickness.</p></sec></trans-abstract><kwd-group xml:lang="ru"><kwd>магнитоэлектрический эффект</kwd><kwd>магнитострикция</kwd><kwd>волоконные композиты</kwd><kwd>пьезоэффект</kwd><kwd>анизотропия</kwd></kwd-group><kwd-group xml:lang="en"><kwd>magnetoelectric effect</kwd><kwd>magnetostriction</kwd><kwd>fiber composites</kwd><kwd>piezoelectric effect</kwd><kwd>anisotropy</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">Работа выполнена в рамках гранта Российского фонда фундаментальных исследований, грант № 20-32-90-190</funding-statement><funding-statement xml:lang="en">The study was supported by the Russian Foundation for Basic Research, grant No. 20-32-90-190</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">Wang Y., Li J., Viehland D. Magnetoelectrics for magnetic sensor applications: status, challenges and perspectives Mater. Today. 2014;17(269):269–275. https://doi.org/10.1016/j.mattod.2014.05.004</mixed-citation><mixed-citation xml:lang="en">Wang Y., Li J., Viehland D. Magnetoelectrics for magnetic sensor applications: status, challenges and perspectives Mater. Today. 2014;17(269):269–275. https://doi.org/10.1016/j.mattod.2014.05.004</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Liang X., Matyushov A., Hayes P., Schell L., Dong C., Chen H., He Y., Will-Cole A., Quandt E., Martins P., McCord J., Medarde M., Lanceros-Mendez S., van Dijken S., Sun N.X., Sort J. Roadmap on magnetoelectric materials and devices. IEEE Trans. Mag. 2021;57(8).400157. https://doi.org/10.1109/TMAG.2021.3086635</mixed-citation><mixed-citation xml:lang="en">Liang X., Matyushov A., Hayes P., Schell L., Dong C., Chen H., He Y., Will-Cole A., Quandt E., Martins P., McCord J., Medarde M., Lanceros-Mendez S., van Dijken S., Sun N.X., Sort J. Roadmap on magnetoelectric materials and devices. IEEE Trans. Mag. 2021;57(8).400157. https://doi.org/10.1109/TMAG.2021.3086635</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">He Y., Luo B., Sun N.-X. Integrated magnetics and magnetoelectrics for sensing, power, RF, and microwave electronics. IEEE J. Microw. 2021;4:908–929. https://doi.org/10.1109/JMW.2021.3109277</mixed-citation><mixed-citation xml:lang="en">He Y., Luo B., Sun N.-X. Integrated magnetics and magnetoelectrics for sensing, power, RF, and microwave electronics. IEEE J. Microw. 2021;4:908–929. https://doi.org/10.1109/JMW.2021.3109277</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Nan C.-W., Bichurin M.I., Dong S., Viehland D., Srinivasan G. Multiferroic magnetoelectric composites: Historical perspective, status and future directions. J. Appl. Phys. 2008;103(3):031101. https://doi.org/10.1063/1.2836410</mixed-citation><mixed-citation xml:lang="en">Nan C.-W., Bichurin M.I., Dong S., Viehland D., Srinivasan G. Multiferroic magnetoelectric composites: Historical perspective, status and future directions. J. Appl. Phys. 2008;103(3):031101. https://doi.org/10.1063/1.2836410</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Oh Y.S., Crane S., Zheng H., Chu Y.H., Ramesh R., Kim K.H. Quantitative determination of anisotropic magnetoelectric coupling in BiFeO3–CoFe2O4 nanostructures. Appl. Phys. Lett. 2010;97(5):052902. https://doi.org/10.1063/1.3475420</mixed-citation><mixed-citation xml:lang="en">Oh Y.S., Crane S., Zheng H., Chu Y.H., Ramesh R., Kim K.H. Quantitative determination of anisotropic magnetoelectric coupling in BiFeO3–CoFe2O4 nanostructures. Appl. Phys. Lett. 2010;97(5):052902. https://doi.org/10.1063/1.3475420</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Vargas J.M., Gómez J. In-plane anisotropic effect of magnetoelectric coupled PMN-PT/FePt multiferroic heterostructure: Static and microwave properties. APL Mater. 2014;2(10):106105. https://doi.org/10.1063/1.4900815</mixed-citation><mixed-citation xml:lang="en">Vargas J.M., Gómez J. In-plane anisotropic effect of magnetoelectric coupled PMN-PT/FePt multiferroic heterostructure: Static and microwave properties. APL Mater. 2014;2(10):106105. https://doi.org/10.1063/1.4900815</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Vidal J.V., Timopheev A.A., Kholkin A.L., Sobolev N.A. Anisotropy of the magnetoelectric effects in tri-layered composites based on single-crystalline piezoelectrics. Vacuum. 2015;122(B):286–292. https://doi.org/10.1016/j.vacuum.2015.06.022</mixed-citation><mixed-citation xml:lang="en">Vidal J.V., Timopheev A.A., Kholkin A.L., Sobolev N.A. Anisotropy of the magnetoelectric effects in tri-layered composites based on single-crystalline piezoelectrics. Vacuum. 2015;122(B):286–292. https://doi.org/10.1016/j.vacuum.2015.06.022</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Aubert A., Loyau V., Mazaleyrat F., LoBue M. Enhancement of the magnetoelectric effect in multiferroic CoFe2O4/PZT bilayer by induced uniaxial magnetic anisotropy. IEEE Trans. Magn. 2017;53(11):8109405. https://doi.org/10.1109/TMAG.2017.2696162</mixed-citation><mixed-citation xml:lang="en">Aubert A., Loyau V., Mazaleyrat F., LoBue M. Enhancement of the magnetoelectric effect in multiferroic CoFe2O4/PZT bilayer by induced uniaxial magnetic anisotropy. IEEE Trans. Magn. 2017;53(11):8109405. https://doi.org/10.1109/TMAG.2017.2696162</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Bent A.A., Hagood N.W. Piezoelectric fiber composites with interdigitated electrodes. J. Intell. Mater. Syst. Struct. 1997;8(11):903–919. https://doi.org/10.1177/1045389X9700801101</mixed-citation><mixed-citation xml:lang="en">Bent A.A., Hagood N.W. Piezoelectric fiber composites with interdigitated electrodes. J. Intell. Mater. Syst. Struct. 1997;8(11):903–919. https://doi.org/10.1177/1045389X9700801101</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Burdin D., Chashin D., Ekonomov N., Fetisov L., Fetisov Y., Shamonin M. DC magnetic field sensing based on the nonlinear magnetoelectric effect in magnetic heterostructures. J. Phys. D: Appl. Phys. 2016;49(37):375002. https://doi.org/10.1088/0022-3727/49/37/375002</mixed-citation><mixed-citation xml:lang="en">Burdin D., Chashin D., Ekonomov N., Fetisov L., Fetisov Y., Shamonin M. DC magnetic field sensing based on the nonlinear magnetoelectric effect in magnetic heterostructures. J. Phys. D: Appl. Phys. 2016;49(37):375002. https://doi.org/10.1088/0022-3727/49/37/375002</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Amirov A., Baraban I., Panina L., Rodionova V. Direct magnetoelectric effect in a sandwich structure of PZT and magnetostrictive amorphous microwires. Materials. 2020;13(4):916. https://doi.org/10.3390/ma13040916</mixed-citation><mixed-citation xml:lang="en">Amirov A., Baraban I., Panina L., Rodionova V. Direct magnetoelectric effect in a sandwich structure of PZT and magnetostrictive amorphous microwires. Materials. 2020;13(4):916. https://doi.org/10.3390/ma13040916</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Fetisov Y., Chashin D., Saveliev D., Fetisov L., Shamonin M. Anisotropic magnetoelectric effect in a planar heterostructure comprising piezoelectric ceramics and magnetostrictive fibrous composite. Materials. 2019;12(19):3228. https://doi.org/10.3390/ma12193228</mixed-citation><mixed-citation xml:lang="en">Fetisov Y., Chashin D., Saveliev D., Fetisov L., Shamonin M. Anisotropic magnetoelectric effect in a planar heterostructure comprising piezoelectric ceramics and magnetostrictive fibrous composite. Materials. 2019;12(19):3228. https://doi.org/10.3390/ma12193228</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Newnham R.E., Skinner D.P., Cross L.E. Connectivity and piezoelectric-pyroelectric composites. Mater. Res. Bull. 1978;13(5):525–536. https://doi.org/10.1016/00255408(78)90161-7</mixed-citation><mixed-citation xml:lang="en">Newnham R.E., Skinner D.P., Cross L.E. Connectivity and piezoelectric-pyroelectric composites. Mater. Res. Bull. 1978;13(5):525–536. https://doi.org/10.1016/00255408(78)90161-7</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Chashin D.V., Burdin D.A., Fetisov L.Y., Ekonomov N.A., Fetisov Y.K. Precise measurements of magnetostriction of ferromagnetic plates. J. Siberian Federal Univ. Math. &amp; Phys. 2018;11(1):30–34. https://doi.org/10.17516/19971397-2018-11-1-30-34</mixed-citation><mixed-citation xml:lang="en">Chashin D.V., Burdin D.A., Fetisov L.Y., Ekonomov N.A., Fetisov Y.K. Precise measurements of magnetostriction of ferromagnetic plates. J. Siberian Federal Univ. Math. &amp; Phys. 2018;11(1):30–34. https://doi.org/10.17516/19971397-2018-11-1-30-34</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Feng M., Wang J.-J., Hu J.-M., Wang J., Ma J., Li H.-B., Shem Y., Lin Y.-H., Chen L.-Q., Nan C.-W. Optimizing direct magnetoelectric coupling in Pb(Zr,Ti)O3/Ni multiferroic film heterostructures. Appl. Phys. Lett. 2015;106(7):072901. https://doi.org/10.1063/1.4913471</mixed-citation><mixed-citation xml:lang="en">Feng M., Wang J.-J., Hu J.-M., Wang J., Ma J., Li H.-B., Shem Y., Lin Y.-H., Chen L.-Q., Nan C.-W. Optimizing direct magnetoelectric coupling in Pb(Zr,Ti)O3/Ni multiferroic film heterostructures. Appl. Phys. Lett. 2015;106(7):072901. https://doi.org/10.1063/1.4913471</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Greve H., Woltermann E., Quenzer H.J. Wagner B., Quandt E. Giant magnetoelectric coefficients in (Fe90Co10)78Si12B10-AlN thin film composites. Appl. Phys. Lett. 2010;96(18):182501. https://doi.org/10.1063/1.3377908</mixed-citation><mixed-citation xml:lang="en">Greve H., Woltermann E., Quenzer H.J. Wagner B., Quandt E. Giant magnetoelectric coefficients in (Fe90Co10)78Si12B10-AlN thin film composites. Appl. Phys. Lett. 2010;96(18):182501. https://doi.org/10.1063/1.3377908</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Timoshenko S. Vibration Problems in Engineering. New York: D. Van Nostrand Company, Inc.; 1961. 468 p.</mixed-citation><mixed-citation xml:lang="en">Timoshenko S. Vibration Problems in Engineering. New York: D. Van Nostrand Company, Inc.; 1961. 468 p.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Fetisov L.Y., Fetisov Y.K., Sreenivasulu G., Srinivasan G. Nonlinear resonant magnetoelectric interactions and efficient frequency doubling in a ferromagneticferroelectric layered structure. J. Appl. Phys. 2013;113(11):116101. https://doi.org/10.1063/1.4798579</mixed-citation><mixed-citation xml:lang="en">Fetisov L.Y., Fetisov Y.K., Sreenivasulu G., Srinivasan G. Nonlinear resonant magnetoelectric interactions and efficient frequency doubling in a ferromagneticferroelectric layered structure. J. Appl. Phys. 2013;113(11):116101. https://doi.org/10.1063/1.4798579</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Bichurin M.I., Petrov V.M., Srinivasan G. Theory of lowfrequency magnetoelectric coupling in magnetostrictivepiezoelectric bilayers. Phys. Rev. B. 2003;68(5):054402. https://doi.org/10.1103/PhysRevB.68.054402</mixed-citation><mixed-citation xml:lang="en">Bichurin M.I., Petrov V.M., Srinivasan G. Theory of lowfrequency magnetoelectric coupling in magnetostrictivepiezoelectric bilayers. Phys. Rev. B. 2003;68(5):054402. https://doi.org/10.1103/PhysRevB.68.054402</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Joseph R.I., Schlömann E. Demagnetizing field in nonellipsoidal bodies. J. Appl. Phys. 1965;36(5):1579–1593. https://doi.org/10.1063/1.1703091</mixed-citation><mixed-citation xml:lang="en">Joseph R.I., Schlömann E. Demagnetizing field in nonellipsoidal bodies. J. Appl. Phys. 1965;36(5):1579–1593. https://doi.org/10.1063/1.1703091</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>
