{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,13]],"date-time":"2026-04-13T08:34:59Z","timestamp":1776069299548,"version":"3.50.1"},"reference-count":56,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2019,4,12]],"date-time":"2019-04-12T00:00:00Z","timestamp":1555027200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100006769","name":"Russian Science Foundation","doi-asserted-by":"publisher","award":["18-19-00090"],"award-info":[{"award-number":["18-19-00090"]}],"id":[{"id":"10.13039\/501100006769","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Intensive studies of the magnetoimpedance (MI) effect in nanostructured multilayers provide a good phenomenological basis and theoretical description for the symmetric case when top and bottom layers of ferromagnet\/conductor\/ferromagnet structure have the same thickness and consist of one magnetic layer each. At the same time, there is no model to describe the MI response in multilayered films. Here, we propose the corresponding model and analyze the influence of the multilayer parameters on the field and frequency dependences of the MI. The approach is based on the calculation of the field distribution within the multilayer by means of a solution of lineralizied Maxwell equations together with the Landau\u2013Lifshitz equation for the magnetization motion. The theoretical model developed allows one to explain qualitatively the main features of the MI effect in multilayers and could be useful for optimization of the film parameters. It might also be useful as a model case for the development of MI magnetic biosensors for magnetic biomarker detection.<\/jats:p>","DOI":"10.3390\/s19081761","type":"journal-article","created":{"date-parts":[[2019,4,12]],"date-time":"2019-04-12T12:55:04Z","timestamp":1555073704000},"page":"1761","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":24,"title":["Magnetoimpedance in Symmetric and Non-Symmetric Nanostructured Multilayers: A Theoretical Study"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3719-5692","authenticated-orcid":false,"given":"Nikita A.","family":"Buznikov","sequence":"first","affiliation":[{"name":"Scientific and Research Institute of Natural Gases and Gas Technologies\u2014Gazprom VNIIGAZ, Razvilka, Leninsky District, Moscow Region 142717, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3712-1637","authenticated-orcid":false,"given":"Galina V.","family":"Kurlyandskaya","sequence":"additional","affiliation":[{"name":"Department of Magnetism and Magnetic Nanomaterials, Institute of Natural Sciences and Mathematics, Ural Federal University, Ekaterinburg 620002, Russia"},{"name":"Department of Electricity and Electronics, Basque Country University UPV\/EHU, 48940 Leioa, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,4,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"961","DOI":"10.1038\/135961a0","article-title":"Electrical properties of wires of high permeability","volume":"135","author":"Harrison","year":"1935","journal-title":"Nature"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"759","DOI":"10.1016\/0924-4247(91)87083-F","article-title":"Magnetic field sensors based on amorphous ribbons","volume":"27","author":"Makhotkin","year":"1991","journal-title":"Sens. Actuators A"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"3652","DOI":"10.1063\/1.111170","article-title":"Giant magnetic field dependent impedance of amorphous FeCoSiB wire","volume":"64","author":"Beach","year":"1994","journal-title":"Appl. Phys. Lett."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1189","DOI":"10.1063\/1.112104","article-title":"Magneto-impedance effect in amorphous wires","volume":"65","author":"Panina","year":"1994","journal-title":"Appl. Phys. Lett."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"6563","DOI":"10.1063\/1.356919","article-title":"Giant ac magnetoresistance in the soft ferromagnet Co70.4Fe4.6Si15B10","volume":"75","author":"Machado","year":"1994","journal-title":"J. Appl. Phys."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"6204","DOI":"10.1063\/1.358536","article-title":"Very Large magneto-impedance in amorphous soft ferromagnetic wires","volume":"76","author":"Rao","year":"1994","journal-title":"J. Appl. Phys."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1016\/j.bios.2011.05.041","article-title":"Pulse-driven magnetoimpedance sensor detection of biomagnetic fields in musculatures with spontaneous electric activity","volume":"27","author":"Nakayama","year":"2011","journal-title":"Bios. Bioelectr."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3833","DOI":"10.1109\/TMAG.2012.2198627","article-title":"Recent advances of pico-Tesla resolution magnetoimpedance sensor based on amorphous wire CMOS IC MI Sensor","volume":"48","author":"Uchiyama","year":"2012","journal-title":"IEEE Trans. Magn."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"3346","DOI":"10.1063\/1.115242","article-title":"Longitudinal and transverse magneto-impedance in amorphous Fe73.5Cu1Nb3Si13.5B9 films","volume":"67","author":"Sommer","year":"1995","journal-title":"Appl. Phys. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"5734","DOI":"10.1103\/PhysRevB.61.5734","article-title":"Giant magnetoimpedance and domain structure in FeCuNbSiB films and sandwiched films","volume":"61","author":"Xiao","year":"2000","journal-title":"Phys. Rev. B"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"4594","DOI":"10.1109\/20.539090","article-title":"Magneto-impedance in sandwich film for magnetic sensor heads","volume":"32","author":"Hika","year":"1996","journal-title":"IEEE Trans. Magn."},{"key":"ref_12","first-page":"612","article-title":"Giant magnetoimpedance in amorphous and nanocrystalline multilayers","volume":"83","author":"Antonov","year":"1997","journal-title":"Phys. Met. Metallogr."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"4367","DOI":"10.1109\/20.620448","article-title":"Giant magneto-impedance effect in layered thin films","volume":"33","author":"Morikawa","year":"1997","journal-title":"IEEE Trans. Magn."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/S0924-4247(99)00089-8","article-title":"Magneto-impedance in multilayer films","volume":"81","author":"Panina","year":"2000","journal-title":"Sens. Actuators A"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"4760","DOI":"10.1109\/TMAG.2009.2030590","article-title":"Review of on-chip inductor structures with magnetic films","volume":"45","author":"Gardner","year":"2009","journal-title":"IEEE Trans. Magn."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1063\/1.1754924","article-title":"Critical thickness and perpendicular anisotropy of evaporated permalloy films with stripe domains","volume":"10","author":"Sugita","year":"1967","journal-title":"Appl. Phys. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"868","DOI":"10.1134\/1.1778860","article-title":"Modification of the \u201ctranscritical\u201d state in NiFeCuMo films produced by RF sputtering","volume":"49","author":"Svalov","year":"2004","journal-title":"Tech. Phys."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"806","DOI":"10.1016\/j.jmmm.2008.11.072","article-title":"Magnetic properties of FeSiB thin films displaying stripe domains","volume":"321","author":"Vinai","year":"2009","journal-title":"J. Magn. Magn. Mater."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1109\/TMAG.2009.2032519","article-title":"Structure and magnetic properties of thin permalloy films near the \u201ctranscritical\u201d state","volume":"46","author":"Svalov","year":"2010","journal-title":"IEEE Trans. Magn."},{"key":"ref_20","first-page":"6561","article-title":"Domain structure and magnetization process of a giant magnetoimpedance geometry FeNi\/Cu\/FeNi(Cu)FeNi\/Cu\/FeNi sensitive element","volume":"16","author":"Kurlyandskaya","year":"2004","journal-title":"J. Phys.: Condens. Matter"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1016\/j.physb.2006.05.214","article-title":"GMI in FeCuNbSiB\\Cu multilayers","volume":"384","author":"Correa","year":"2006","journal-title":"Physica B"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"295004","DOI":"10.1088\/0022-3727\/43\/29\/295004","article-title":"Tailoring the magnetoimpedance effect of NiFe\/Ag multilayer","volume":"43","author":"Correa","year":"2010","journal-title":"J. Phys. D: Appl. Phys."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"09C502","DOI":"10.1063\/1.3355473","article-title":"FeNi-based magnetic layered nanostructures: Magnetic properties and giant magnetoimpedance","volume":"107","author":"Kurlyandskaya","year":"2010","journal-title":"J. Appl. Phys."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"3328","DOI":"10.1109\/TMAG.2011.2157896","article-title":"Magnetic properties and giant magnetoimpedance of FeNi-based nanostructured multilayers with variable thickness of the central Cu lead","volume":"47","author":"Volchkov","year":"2011","journal-title":"IEEE Trans. Magn."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1375","DOI":"10.1109\/TMAG.2011.2171330","article-title":"Nanostructured magnetoimpedance multilayers","volume":"48","author":"Kurlyandskaya","year":"2012","journal-title":"IEEE Trans. Magn."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1134\/S1063784213010222","article-title":"Nanostructuring effects in soft magnetic films and film elements with magnetic impedance","volume":"58","author":"Savin","year":"2013","journal-title":"Tech. Phys."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1016\/j.jmmm.2015.07.107","article-title":"Thin-film magneto-impedance structures with very large sensitivity","volume":"400","author":"Svalov","year":"2016","journal-title":"J. Magn. Magn. Mater."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1016\/j.jmmm.2017.12.087","article-title":"Manipulating the magnetic anisotropy and magnetization dynamics by stress: Numerical calculation and experiment","volume":"453","author":"Correa","year":"2018","journal-title":"J. Magn. Magn. Mater."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"193702","DOI":"10.1063\/1.4921224","article-title":"Giant magnetoimpedance biosensor for ferrogel detection: Model system to evaluate properties of natural tissue","volume":"106","author":"Kurlyandskaya","year":"2015","journal-title":"Appl. Phys. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"418","DOI":"10.1016\/j.bios.2016.10.031","article-title":"Magnetic impedance biosensor: A review","volume":"90","author":"Wang","year":"2017","journal-title":"Biosens. Bioelectron."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"342","DOI":"10.4028\/www.scientific.net\/SSP.215.342","article-title":"Nanostructured magnetoimpedance multilayers with different thickness of FeNi components","volume":"215","author":"Chlenova","year":"2014","journal-title":"Solid State Phenom."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"220","DOI":"10.1016\/j.jmmm.2014.10.129","article-title":"FeNi-based flat magnetoimpedance nanostructures with open magnetic flux: New topological approaches","volume":"383","author":"Kurlyandskaya","year":"2015","journal-title":"J. Magn. Magn. Mater."},{"key":"ref_33","first-page":"2000605","article-title":"Thin-film magnetoimpedance structures onto flexible substrates as deformation sensors","volume":"53","author":"Combarro","year":"2017","journal-title":"IEEE Trans. Magn."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1038\/nmat803","article-title":"Magnetic domain-wall dynamics in a submicrometre ferromagnetic structure","volume":"2","author":"Atkinson","year":"2003","journal-title":"Nat. Mater."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"10699","DOI":"10.1103\/PhysRevB.57.10699","article-title":"Magnetoimpedance of metallic ferromagnetic wires","volume":"57","author":"Chen","year":"1998","journal-title":"Phys. Rev. B"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/S0924-4247(99)00093-X","article-title":"Size effect on magneto-impedance in layered films","volume":"81","author":"Makhnovskiy","year":"2000","journal-title":"Sens. Actuators A"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"775","DOI":"10.1063\/1.1330763","article-title":"Impedance of a ferromagnetic sandwich strip","volume":"89","author":"Sukstanskii","year":"2001","journal-title":"J. Appl. Phys."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"7221","DOI":"10.1063\/1.1361048","article-title":"Two-dimensional analysis of magnetoimpedance in magnetic\/metallic multilayers","volume":"89","author":"Panina","year":"2001","journal-title":"J. Appl. Phys."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"354","DOI":"10.1016\/S0304-8853(98)00746-X","article-title":"The theoretical limits of giant magneto-impedance","volume":"196\u2013197","author":"Kraus","year":"1999","journal-title":"J. Magn. Magn. Mater."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1063\/1.373671","article-title":"Theory of longitudinal magnetoimpedance in wires","volume":"88","author":"Yelon","year":"2000","journal-title":"J. Appl. Phys."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1249","DOI":"10.1109\/20.364815","article-title":"Giant magneto-impedance in Co-rich amorphous wires and films","volume":"31","author":"Panina","year":"1995","journal-title":"IEEE Trans. Magn."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"5202","DOI":"10.1063\/1.369124","article-title":"Analysis of current distribution in magnetic film inductors","volume":"85","author":"Gromov","year":"1999","journal-title":"J. Appl. Phys."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1109\/TMAG.2012.2218221","article-title":"GMI in nanostructured FeNi\/Ti multilayers with different thicknesses of the magnetic layers","volume":"49","author":"Svalov","year":"2013","journal-title":"IEEE Trans. Magn."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/j.jmmm.2016.01.035","article-title":"Magnetoimpedance of FeNi-based asymmetric sensitive elements","volume":"415","author":"Chlenova","year":"2016","journal-title":"J. Magn. Magn. Mater."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1958","DOI":"10.1134\/1.1130208","article-title":"Multilevel interaction between layers in layered film structures","volume":"39","author":"Savin","year":"1997","journal-title":"Phys. Solid State"},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Handrich, K., and Kobe, S. (1980). Amorphe Ferro- und Ferrimagnetika (Amorphous Ferro- and Ferrimagnets), Akademie-Verlag.","DOI":"10.1515\/9783112528884"},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Chikazumi, S. (1997). Physics of Magnetism, John Wiley. [2nd ed.].","DOI":"10.1093\/oso\/9780198517764.001.0001"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"162410","DOI":"10.1063\/1.4704984","article-title":"FeNi-based magnetoimpedance multilayers: Tailoring of the softness by magnetic spacers","volume":"100","author":"Svalov","year":"2012","journal-title":"Appl. Phys. Lett."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"639","DOI":"10.1002\/pssa.200881251","article-title":"Biomagnetic field detection using very high sensitivity magnetoimpedance sensors for medical applications","volume":"206","author":"Uchiyama","year":"2009","journal-title":"Phys. Status Solidi A"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"10005","DOI":"10.1051\/epjconf\/201818510005","article-title":"Modelling of thin film magnetoimpedance sensitive element designed for biodetection","volume":"185","author":"Volchkov","year":"2018","journal-title":"EPJ Web Conf."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1016\/j.jmmm.2008.08.104","article-title":"Cytotoxicity and GMI bio-sensor detection of maghemite nanoparticles internalized into cells","volume":"321","author":"Nabily","year":"2009","journal-title":"J. Magn. Magn. Mater."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"731","DOI":"10.1016\/S0956-5663(98)00037-2","article-title":"A biosensor based on magnetoresistance technology","volume":"13","author":"Baselt","year":"1998","journal-title":"Biosens. Bioelectron."},{"key":"ref_53","doi-asserted-by":"crossref","unstructured":"Darton, N.J., Ionescu, A., and Llandro, J. (2019). Magnetic Nanoparticles in Biosensing and Medicine, Cambridge University Press.","DOI":"10.1017\/9781139381222"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"702","DOI":"10.1016\/j.jmmm.2005.02.046","article-title":"Magnetic biochips: A new option for sensitive diagnostics","volume":"293","author":"Megens","year":"2005","journal-title":"J. Magn. Magn. Mater."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"163901","DOI":"10.1063\/1.4981536","article-title":"Magnetic nanoparticle detection method employing non-linear magnetoimpedance effects","volume":"121","year":"2017","journal-title":"J. Appl. Phys."},{"key":"ref_56","doi-asserted-by":"crossref","unstructured":"Yang, Z., Wang, H., Guo, P., Ding, Y., Lei, C., and Luo, Y. (2018). A multi-region magnetoimpedance-based bio-analytical system for ultrasensitive simultaneous determination of cardiac biomarkers myoglobin and C-reactive protein. Sensors, 18.","DOI":"10.3390\/s18061765"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/8\/1761\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:45:01Z","timestamp":1760186701000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/8\/1761"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,4,12]]},"references-count":56,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2019,4]]}},"alternative-id":["s19081761"],"URL":"https:\/\/doi.org\/10.3390\/s19081761","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,4,12]]}}}