Artificial multiferroic materials

effective length of the electric field strength line.

The features of BST ferroelectrics mentioned above enable them to be implemented in a set of microwave applications including tunable filters (Nath, 2005), switches (Karmanenko, 2004), parametric generators (Vendik, 1999), and other voltage-controlled devices. In comparison with magnetic tuning, the advantages of the electric tuning of microwave devices based on ferroelectrics are operation speed, power consumption, and the size of the control system, but such devices lose on a range of this tuning.

2.3

Increased demands in frequency-agile materials used for microwave applications have led to the appearance of composite materials known as multiferroic structures. Endowed with both ferromagnetic and ferroelectric features they are potentially capable of enhancing the functionality of microwave devices by adding the advantages of electric tuning to spin-wave elements. However, the key issue inherent to applications of multiferroics is associated with the strength of the magneto-electric coupling.

In general, multiferroics may be divided into two major categories, the first of which is single-phase homogeneous media ordered in a certain range of temperatures, both ferroelectrically and ferromagnetically (e.g., BiFeO3). However, such natural multiferroics show a limited potential for real microwave devices due to extremely low values of magneto-electric coefficients. In order to overcome this limitation, a second category of multiferroics has been proposed. Usually, these multiferroics are fabricated by a thin-film deposition in the form of layered (composite or monolithic) materials, where the coupling interactions between different phases are realised [Sun, 2012]. Such composite structures are widely known as artificial or extrinsic multiferroics.

The interaction between different layers of composite structures exhibiting ferromagnetic and ferroelectric nature may be due to two effects. The first explores the

magneto-elastic properties of most ferromagnetic materials combined with ferroelectrics that are usually excellent piezoelectrics (e.g., lead zirconate titanate). The general idea of the magnetoelectric interaction is that an external electric field is applied to a piezoelectric produces mechanical strain. This strain leads to a variation of the internal static magnetic field and consequently to a shift of a spin-wave spectrum. The theory of this effect was developed by Shastry et al. (Shastry, 2004).

A second effect utilises the electrodynamic interaction between microwave electromagnetic and spin waves in the layered ferrite-ferroelectric structures. This interaction leads to a formation of hybrid spin-electromagnetic waves (SEW) (Anfinogenov, 1989; Demidov, 2002a). Dispersion characteristics of hybrid SEW combine features of electromagnetic waves in ferroelectric-based materials and spin waves in ferrites. Therefore, the resulting wave spectrum is dually controllable by both electric and magnetic fields. The electric tuning is realised through a variation of the dielectric permittivity of a ferroelectric layer by changing an applied electric field, while the magnetic tuning is provided by a dependence of the magnetic permeability of ferrites on a bias magnetic field.

The general dipole-exchange theory of SEW spectra in layered multiferroic structures consisting of ferrite-ferroelectric bilayer structure was developed in 2002 (Demidov, 2002a). The theory predicted that only relatively thick ferroelectric layers (on the order of hundreds of micrometres) provide effective hybridisation of spin waves and electromagnetic waves at microwave frequencies and, consequently, an effective electric field tuning of the SEW dispersion (see Figure 2.5). These findings were also confirmed by experiments (Fetisov, 2005). In later research, the electrodynamic theory of SEW spectra was extended to an arbitrary number of ferrite and ferroelectric layers (Grigorieva, 2009). These theories were developed with a tensorial Green’s function method taking into account electromagnetic retardation. However, an application of the extended theory for the investigation of SEW modes in complex multilayered structures consisting of two or more magnetic layers has not yet been published. This is obviously due to computational difficulties with finding the zeroes of an infinite matrix determinant, which represents the dispersion equation within the Green’s function method.

One of the main trends in the development of modern physics and electronics is associated with the development of miniature microwave devices and electronically tunable devices with a high performance, small size, and low power consumption.

These features may be achieved by utilising multiferroic structures containing ferroelectric and ferrite films. As seen in the literature, the multiferroic structures had a great success in the development of microwave devices. Among them are the delay lines (Fetisov, 2005), the tunable microwave resonators (Ustinov, 2006), and the ferromagnetic resonance phase shifters (Leach, 2010).

A further development of microwave multiferroic devices for general computing and microwave signal processing is connected with thin-film structures (Zhu, 2017). In

particular, thin-film ferrite-ferroelectric structures provide an opportunity to reduce the control voltage that is desirable for exploiting of the tunable devices based on them.

Therefore, from a practical point of view, it would be beneficial to investigate novel thin-film heterostructures exploiting the spin-electromagnetic waves for enhanced logic control as well as for tunable microwave devices.

Until now, high research activity has mainly given to two-layered multiferroic structures consisting of one ferrite and one ferroelectric layers. As previously mentioned, there is an essential disadvantage in this configuration. An effective coupling at microwave frequencies was achieved in multiferroic structures fabricated with a relatively thick (200–500 μm) ferroelectric layer. Such thicknesses of the ferroelectric layer lead to relatively high control voltages (up to 1000 V) required for an effective electric tuning of the SEW dispersion characteristics.

Figure 2.5: (a) Spectrum of the hybrid SEW formed due to an electrodynamic interaction between fundamental mode of a surface SW and electromagnetic mode TE1; (b) Electric field tuning of the dispersion characteristic. Adapted from (Demidov, 2002a); (c) Wavenumber variation as a function of the absolute value of the wavenumber when dielectric permittivity varies between 1000 and 500 for different dielectric layer thicknesses: 50 µm, 100 µm, and 200 µm. Adapted from (Demidov, 1999).

In order to increase the energy efficiency of microwave devices based on layered multiferroic structures, Semenov et al. proposed to use thin-film ferrite-ferroelectric structures combined with a slot line (Semenov, 2008). In this case, the SEW are originated from an electrodynamic coupling of the EMW propagating in a slot transmission line with the SW existing in a ferrite film. Moreover, the obtained results were validated by both experimental measurements and theoretical analysis (Nikitin, 2014; Nikitin, 2015b). However, other thin-film ferrite-ferroelectric structures exhibiting an effective hybridisation of waves in the range of microwave frequencies have not been proposed until now. Thus, theoretical and experimental investigations of wave dynamics in novel all-thin-film ferrite-ferroelectric structures will be presented in this thesis.