0018-9464 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TMAG.2017.2714841, IEEE Transactions on Magnetics AS-12 0018-9464 © 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. (Inserted by IEEE.) 1 Dual Tuning of Doubly-Hybridized Spin-Electromagnetic Waves in All-Thin-Film Multiferroic Multilayers Aleksei A. Nikitin 1 , Vitaliy V. Vitko 1 , Andrey A. Nikitin 1,2 , Alexandr V. Kondrashov 1,2 , Alexey B. Ustinov 1,2 , Alexander A. Semenov 1 , and Erkki Lähderanta 2 1 Department of Physical Electronics and Technology, St. Petersburg Electrotechnical University, St. Petersburg, 197376, Russia 2 Department of Mathematics and Physics, Lappeenranta University of Technology, Lappeenranta, 53850, Finland Theoretical investigation of dual (electric and magnetic) tuning of dispersion characteristics has been studied for the doubly- hybridized spin-electromagnetic waves (SEWs) propagating perpendicularly to the direction of static magnetization in tangentially magnetized all-thin-film multiferroic multilayers. The multilayers consisted of two thin ferrite films separated by a thin ferroelectric film. The SEW spectrum was formed due to double hybridization among one electromagnetic mode and two spin-wave modes. Such hybridization took place if the initial dispersion characteristics of these modes were degenerated. The electric tuning was realized owing to changing of the magneto-dipole interaction between the magnetic films caused by a variation of dielectric constant of the ferroelectric film. It was shown that a decrease in permittivity of the ferroelectric film of micrometer thickness by a factor of two induces change of the SEW wavenumber up to tens of radian per centimeter. Index Terms—ferroelectrics, ferrites, multiferroics, spin-electromagnetic waves. I. INTRODUCTION NCREASED demands to frequency-agile materials used for microwave applications has led to appearance of artificial multiferroics [1]. Artificial multiferroics are usually fabricated with a combination of ferrite and ferroelectric layers, so as to obtain micro- and nanostructures [2], [3]. An interaction between the ferromagnetic and ferroelectric phases is realized through electrodynamic coupling of spin and electromagnetic waves. This interaction leads to a formation of spin- electromagnetic waves (SEWs) [4]. Dispersion characteristics of hybrid spin-electromagnetic waves (SEWs) combine features of electromagnetic waves in ferroelectric-based materials and spin waves in ferrites. Therefore, the resulting wave spectrum is dually controllable by the both electric and magnetic fields. The electric tuning is realized through the variation of dielectric permittivity of the ferroelectric layer by changing the applied electric field. The magnetic tuning is provided by a dependence of magnetic permeability of ferrites on the bias magnetic field. As it was shown earlier, degrees of hybridization strongly depend on a overlapping of the dynamics fields of the electromagnetic and spin waves. The overlapping depends on the geometry of the layered structures and parameters of the materials [4]. Until now the high research activity was mainly given to two layered multiferroic structures consisted of one ferrite and one ferroelectric layer [4]-[18]. An effective coupling at microwave frequencies was achieved in multiferroic structures fabricated with a relatively thick (200-500 µm) ferroelectric layers [19]. Such thicknesses of the ferroelectric layer lead to relatively high control voltages (up to 1000 V) needed for an effective electric tuning of the SEW dispersion characteristics. Recently, all-thin-film multiferroic structures based on slot transmission line were suggested in order to decrease the thickness of the ferroelectrics [20], [21]. In the latter work, a decrease in the control voltage and increase in the tuning efficiency were achieved with the reduction of the slot-line gap width. However, in practice such a reduction is limited by increase of losses in metal electrodes. In our opinion, further advances in the dual-tunable multiferroic devices could be achieved with development of the ferrite-ferroelectric-ferrite structures [22], [23]. One of the main advantages of these structures is existence of magneto-dipole interaction between the ferrite films separated with a thin ferroelectric film. It leads to a complication of the SEW spectrum, which is formed due to interaction between two pure spin-wave modes and one electromagnetic mode. Two possible situations are shown in Fig. 1. The first hybridization takes place in the point I between two spin-wave modes shown by dashed lines. The second hybridization with electromagnetic mode could take place in the same point or in the other points (e.g. points II and III) depending on the parameters of the structure. The first situation, in which all dispersion curves cross each other in one point, is called as “double hybridization”. Fig. 1. Qualitative picture of showing possible relative positions of two pure spin-wave modes (dotted lines) and electromagnetic mode (solid line). The purpose of this work is to theoretically investigate the SEW spectra formed due to double hybridization. Such a hybridization provides an effective tuning of the SEW I