2. Investigation of spin-electromagnetic waves spectra in multilayered
2.2. Investigation of spin-electromagnetic waves spectra in thin-film
The theoretical model described above can be used to determine the spectra of the
SEWs in structures that consist of two ferrite films separated by relatively thin
ferroelectric layer. Let’s begin the investigation from the simplest case. Consider
now two ferrite layers separated by free space. It will give an opportunity to explain
complex cases.
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Investigated structures that are consisted of two ferrite films on the dielectric substrates are shown in the figure 2.2.
Figure 2.2. Two layered ferrite structure.
As it was discussed in the first chapter one of the most popular thin film ferrite structures for the MW application is a single crystal YIG film on a gadolinium gallium garnet (GGG) substrate. Therefore, usual parameters for such materials were used in the calculations.
Dispersion characteristics of surface SW were considered in the two cases. The first one is structure composed of the ferrite films with equal parameters (a2=a4= 20 m, M2=M4= 1750 G). The second one is the structure based on the films with different thicknesses and saturation magnetizations. The most interesting case is intersection of dispersion characteristics of the surface SW in different films. In order to satisfy this condition following parameters a2= 20 m, M2 = 1750 G, a4=6 m, M4= 1790 G were chosen.
Dispersion characteristics of the SW in the first case at different distance between ferrite films (a3) are shown in the figure 2.3.
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Figure 2.3. Dispersion characteristics of the surface SWs in the two ferrite films with equal parameters separated by free space a3.
As it can be seen from this figure if the distance has devoted to an infinity then SWs propagate independently and dispersion curves coincide (black solid line). If the distance has decreased then waves interact and dispersion curves repulse (red dash line). As would be expected, interaction attenuates with the decrease of wavelength. Interaction between SWs and repulsion of the dispersion curves increases at the decrease of the distance (blue dash dot line). Finally, dispersion curve corresponds with dispersion characteristic of the SWs in the ferrite film with double thickness (green dot line).
The same calculations were repeated for the second case of the different ferrite parameters (figure 2.4). Like in the previous case, SWs are not interacting and propagating independently at the infinity apart from each other. Therefore, dispersion curves intersect each other (black solid line). And again if the distance between the films has decreased then waves interact near intersection point (red dash line). As it was mentioned above, interaction increases with approach of the films (blue dash dot line). Dispersion curve at a3=0 is shown in the figure 2.4 by green dot line.
100 200 300 400
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Figure 2.4. Dispersion characteristics of the surface SWs in the two ferrite films with different parameters separated by free space.
It can be concluded that that two ferrite layers placement leads to the splitting of the fundamental mode into two branches. Besides interaction between SWs in different ferrite layers repulses these branches. Insertion of the ferroelectric layer between ferrites leads to complication of the spectra, because it is formed by several hybridizations. Due to this fact the spectra have three dispersion branches. In order to investigate the SEWs spectra features in such structure, following layer parameters were chosen. Two ferrite layers with thickness a2= 20 m, permittivity 2= 14, magnetization M2 = 1750 G, thickness a4=6 m, permittivity4= 14, magnetization M4= 1790 G separated by ferroelectric with thickness a3= 25 m and permeability 3= 1500. These are shown in the figure 2.5. The external field H0 was 1500 Oe.
30 60 90 120
6.1 6.2 6.3 6.4
a2= 20 m; M2= 1750 G;
a4= 6 m; M4= 1790 G;
a3=
a3= 200 m a3= 25m a3= 1 m
Frequency, GHz
Wave numbers (cm-1 )
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Figure 2.5. Two ferrite layers separated by ferroelectric.
Dispersion characteristics of SWs in two ferrite layers with distance a3= 25 m are shown in figure 2.6 by red dash lines. It is well known that surface SWs are not reciprocal. It means that SWs field distributions depend on the propagating direction at fixed external magnetic field direction. If the wave propagates along x axis, then the maximum of the field distribution is on the top surfaces of the ferrites. In the opposite direction it corresponds to the bottom ferrite surfaces.
20 40 60 80 100 120 -120 -100 -80 -60 -40 -20
6.1 6.2 6.3 6.4
SEW
SW SEW
EMW EMW
SW
Frequency, GHz
Wavenumber, cm-1
Figure 2.6. Spectra of SEWs in the multilayered ferrite-ferroelectric structures with thin ferroelectric layer between ferrites. Black dot line is EMW, red dash line is SW and blue
solid line is SEW spectra.
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Thus it was shown that SWs interact in the intersection point of dispersion characteristics. It leads to the changing of the SWs spectra. Dispersion characteristics of the SWs in the independent ferrite layers (a3=, 3=1) and in the two ferrite layers at the distance a3= 200 m and a3= 25 m are shown in the figure 2.7 (a, b) by black short dot lines and red dash lines, respectively.
As shown in figure 2.7, the dispersion characteristic of EMW (black dot line) intersects both SW dispersion characteristics. If the EMW propagates along x axis then due to field configuration SW in the thick ferrite (a2) interacts with the EMW that is located in the
Figure 2.7. Spectra of SEWs in the multilayered ferrite-ferroelectric structures with (a) thick a3= 200 m and (b) thin a3= 25 m ferroelectric layers between ferrites
(Calculation parameters are shown in the figure 2.5)
b)
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ferroelectric layer (a3). It leads to the formation of the SEW dispersion characteristics. This is shown by the green dashed lines in the figure 2.7. Note that such spectrum was calculated for the structure that contains only one thick ferrite. It is seen that the lower dispersion SEW branch intersects dispersion characteristic of the SW in the thin ferrite layer. It leads to wave interaction in two ferrite layers separated by the ferroelectrics layer and formation of a new type of hybrid SEW spectrum that consists of the three dispersion branches (blue solid lines). In case of the opposite propagation direction interaction between the EMW and SW in the thin ferrite layer (a4) is stronger than in the previous case. Therefore, SEW spectra in the structure that contains only thin ferrite layer were calculated (green dashed lines). In this case the lower SEW dispersion branch approaches to the SW dispersion characteristic in thin ferrite layer. Thus spectrum of the SEW in the two ferrite layers separated by ferroelectric layer in all propagation directions consists of three dispersion branches.
As mentioned above, surface SWs are not reciprocal. It means that SEWs propagating in different directions have different behavior (figure 2.7). Namely, influence of the ferroelectric layer permittivity on the intermediate SEW dispersion branch in the case of wave propagation opposite to the x-axis direction is much weaker than in the direction along the x-axis. Further increase in the number of ferrite layers makes SEW spectrum more complicated but gives additional features. These features can be used in the novel MW devices.
In order to illustrate features of these spectra in both propagation directions, ferroelectric layer permittivity 3 was changed. Influence of the ferroelectric layer permittivity on dispersion characteristics is shown in figure 2.8. It is worth noting that ferroelectric permittivity 3 was change from 1500 to 1000.
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As it was shown above, decrease of ferroelectric layer thickness leads to decrease of interaction between the EMW and SW. Finally these waves have a weak interaction at the thickness on the order of several micrometers. It can be considered that these waves propagate independently. On the other hand, in the case of ferrite-free space-ferrite structure interaction between SW in the different ferrites depends on the distance between them. Thus it can be concluded that presence of a thin ferroelectric film between the ferrite layers gives possibility to electric tuning of dispersion characteristics, because the changing of the ferroelectric layer permittivity influences on spin wave interaction (figure 2.8.).
To sum up, the dispersion relation strongly depends on the parameters of the structure. In order to investigate this influence to the wave’s interaction the values of wave number
Figure 2.8. Electric tunability of dispersion characteristic of SEW in the multilayered ferrite-ferroelectric structure thick a3= 200 m and (b) thin a3= 25 m ferroelectric
layers between ferrites (Calculation parameters are shown in the figure 2.5).
a)
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variation k with changing of the ferroelectric layer permittivity from 1500 to 1000 were calculated. The wave number variations for the investigated structure with different ferroelectric layer thicknesses from 10 to 30 m are shown in figure 2.9. It should be noted that wave number variations were calculated only for the middle and bottom SEW dispersion branches since number variations are much bigger for them.
It is seen from the figure that decrease of ferroelectric layer thickness in the FF structure leads to decrease of interaction between the EMW and the SW. Finally, at the thickness on the order of several micrometers this interaction can be relatively small especially for middle dispersion branch. One can see the wave number variation for the bottom branch amounts to higher values than for the middle branch. Therefore influence of the ferroelectric permittivity is stronger and electric tunability of SEW on the bottom dispersion branch is higher. Besides the electric tuning interval increases with the increase of the ferroelectric layer thickness.
Figure 2.9. Dependencies of the wave number variation on a frequency of (a) middle and (b) bottom SEW dispersion branches in the FF structure with different thicknesses of the
ferroelectric layer thicknesses a3= 10 m … 30 m.
6.12 6.15 6.18 6.21 6.24 6.27 6.30
0
6.23 6.24 6.25 6.26 6.27 6.28 6.29 6.30 0.0
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The influences of the thicknesses of both ferrite layers also were investigated. Thicknesses of the bottom ferrite layer were changing in the range from 6 to 20 m. Dependencies of the wave number variations on a frequency are shown in Figure 2.10. Thicknesses of the upper ferrite layer were change in the same ranging and dependencies are shown in Figure 2.11.
It is seen from the figure that increasing of the thickness of the bottom ferrite layer leads to decreasing of interaction between SWs. Therefore the value of the wave number variation decreases for the middle dispersion branch and increases for the bottom one. In this case the frequency of the wave number variation maximum shifts to the lower values. It should be underlined that wave number variation for the middle branch has different behavior then for the bottom branch. The wave number variation has a peak near the frequency of wave interaction for the bottom branch and growth with the frequency increasing for the middle branch.
Figure 2.10. Dependencies of the wave number variation on a frequency of (a) middle and (b) bottom SEW dispersion branches in the FF structure with different thicknesses of the
bottom ferrite layer a2= 6 m … 20 m.
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It can be seen from this figure that increasing of thickness of the upper ferrite layer leads to stronger interaction between waves. Frequency of the wave number variation maximum shifts to the higher frequencies values. It should be noted that including of thick ferrite layers leads to stronger interaction between SWs and EMW. Therefore the electrical tuning of the SEW in this case can be much higher.
As soon as SWs could be easily tuned be the external magnetic field, magnetic tunability of SEWs spectra were also investigated (figure 2.12).
Figure 2.11. Dependencies of the wave number variation on a frequency of (a) middle and (b) bottom SEW dispersion branches in structure with different thicknesses of the
upper ferrite layer a4= 6 m … 20 m.
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Figure 2.12. Dependencies of the wave number shift on a frequency of middle (a) and bottom (b) SEW dispersion branches in the FF structure at different external magnetic field
from 1490 Oe to 1510 Oe.
It is seen from this figure that the advantage of the magnetic tunability is to control the dispersion of SEWs in relatively wide ranges of frequencies. It means that a small change of the external magnetic field can effectively tune the spectrum of SEW.
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Conclusions on the second chapter:
Spectra of spin-electromagnetic waves in thin-film ferrite-ferroelectric structures consisting of two ferrite layers separated by ferroelectric layer were investigated. Electric and magnetic tuning of spin-electromagnetic waves spectra were demonstrated. Influences of the different parameters (such as thickness of ferroelectric/ferrite layered, external magnetic field value) were investigated and analyzed. Based on these results, it can be concluded that the advantages of electric fields tuning are high speed of operation and low power consumption. On the other hand, magnetic field tuning of spin-electromagnetic waves spectra have a relatively wide tuning range.
It was demonstrated in this chapter that:
1. the distance between the ferrite layers influences of the a spin-electromagnetic wave spectrum. Namely SEWs propagate separately and do not interact at wavelengths much shorter than the distance between the ferrites;
2. electrical tunability of a spin-electromagnetic wave spectrum in multiferroic structures is still possible in the case of thin ferroelectric layer at microwave frequencies due to interaction of the spin waves in the two ferrite layers;
3. surface spin-electromagnetic waves are not reciprocal. It means that wave properties of the ferrite-ferroelectric structure depend on the direction of propagation;
4. variation of the thickness of the ferrite layer leads to a significant change in the SEW spectrum. The frequency of maximum value of electric tuning can be shifted by hundreds of MHz.
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3. INVESTIGATION OF SPIN-ELECTROMAGNETIC WAVES