1. Introduction

In the last few years strong coupling effects between plasmon resonances and phonons in the mid and far infrared (IR) range have been analyzed in different types of metal/dielectric structures. This includes Au split-ring resonators coupled to SiO₂ layers [1], cross-shaped apertures coupled to PMMA layers [2], accuglass or SiO₂ based perfect absorber structures [3,4,5] and Au nanorods antennas or Au stripes coupled to SiO₂, Silicon-rich oxynitride or PMMA layers [6,7,8,9]. It has been shown that the coupling depends on the intensity of the electromagnetic field of the plasmon resonance at the phonon frequency and its overlap with the dielectric layer, as well as on the strength of the phonon absorption band. Moreover, it alters the optical response of the metal-dielectric system with the appearance of resonances having a mixed plasmon-phonon character, enabling new ways of tuning the optical performance of IR devices.

On the other hand, it is well known that a magnetic field modifies the optical properties of magnetic materials [10]. Recently, several approaches have been proposed to increase the intensity of this magnetic field induced changes by, for example, introducing the magnetic material into optical cavities (magneto-photonic crystals) [11] or by combining it with plasmonic structures (magneto-plasmonics) [12,13,14]. In this context, and due to the magneto refractive effect (MRE) [15,16] exhibited by giant magneto resistance (GMR) metallic multilayers [17,18], magnetic modulation of plasmon resonances has been achieved in the mid and far IR range in a number of spintronic-plasmonic systems [19,20,21,22,23], allowing the development of molecular sensors with enhanced sensitivity [24].

In this work we combine a dielectric material with a well-defined phonon band in the mid IR range, with a spintronic-plasmonic system, whose plasmon resonances are susceptible of magnetic field modulation in the same spectral range. For this purpose, we have deposited layers of silicon nitride (which has an absorption band around 12 µm) of different thickness on top of spintronic plasmonic metasurfaces obtained by engraving slit arrays on GMR Ni₈₁Fe₁₉/Au multilayers. These metasurfaces sustain plasmon resonances, which can be modulated by a magnetic field and whose plasmon frequency can be tuned by changing the slit parameters [21]. By this combination, the resulting system allows studying, not only the effect that a magnetic modulation has on both plasmonic and phononic bands, but also in the plasmon-phonon interaction, opening novel opportunities for magnetic field modulated optical functionalities.

2. Results and discussion

Four 200 × 200 µm² arrays of randomly distributed parallel slits were fabricated by direct Focused Ion Beam milling on a 75 nm thick Ni₈₁Fe₁₉/Au multilayer exhibiting 5.3% GMR. Ni₈₁Fe₁₉/Au multilayers were grown on 1 × 1 cm² CaF₂ substrates as explained in Ref. [25]. The slit length was varied from one array to the other in 1 µm steps from 2 to 5 µm, while the width and slit concentration (area covered by the slits) was the same for all the four arrays: 0.3 µm and 2.1%, respectively.

The reflectivity spectra were obtained using an IR microscope (Bruker Hyperion) equipped with a liquid nitrogen cooled MCT detector, polarizers and a reflecting 15x Schwarzschild objective, which has a working distance of 24 mm and 0.4 numerical aperture. The large working distance of the objective allows the insertion of a small ferrite electromagnet capable of applying an in plane magnetic field large enough to saturate the GMR multilayer. The microscope was coupled to a FTIR spectrometer (Bruker Vertex 70).

First, we revisit the optical and magnetic modulation properties of the elements conforming the considered system, as a first step to understand the most remarkable consequences of their combination. In Fig. 1(a) we first present the reflectivity spectra for light polarized parallel (dotted line) and perpendicular (continuous line) to the slit long axis for the 2 µm slit arrays normalized to the region without slits. In this spectral range, and due to the dimensions of the slits, the plasmon resonances are only excited for light polarized perpendicular to the slits. The spectrum for light polarized parallel to the slit is, therefore, featureless, showing a slightly monotonical decrease of the reflectivity as we decrease the wavelength. On the other hand, for light polarized perpendicular to the slit, the spectrum shows a dip that corresponds to the excitation of the slit plasmon resonance, and that is well known to shift towards longer wavelengths as we increase the slit length [21].

 

Fig. 1. Left hand side, from top to bottom: schema of the uncovered slit array, layer of silicon nitride, and slit array covered with a layer of silicon nitride. (a) Reflectivity spectra of the uncovered 2 µm slit array for light polarized parallel, dotted line, and perpendicular, continuous line, to the slit long axis. (b) Absorbance spectrum of a silicon nitride film deposited by chemical vapor processes. (c) Reflectivity spectra of the 2 µm slit array covered with 200 nm of silicon nitride for light polarized parallel, dotted line, and perpendicular, continuous line, to the slit long axis. (d) Magneto refractive (MRE) spectra of the uncovered 2 µm slit array for light polarized parallel, dotted line, and perpendicular, continuous line, to the slit long axis. (e) MRE spectrum only due to the magnetic modulation of the slit resonance. (f) MRE spectra of the 2 µm slit array covered with 200 nm of silicon nitride for light polarized parallel, dotted line, and perpendicular, continuous line, to the slit long axis. (g) MRE spectrum only due to the magnetic modulation of the resonances.

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As mentioned before, as dielectric we have selected silicon nitride, a material that by its hardness and stability is used in different fields and technological processes. In Fig. 1(b) we present a characteristic absorbance spectrum of silicon nitride films deposited by chemical vapor processes. It shows a broad and intense absorption band around 12 µm linked to vibrations of the Si-N bonds, as well as less intense features around 9 and 5 µm related to vibrations of N-H and Si-H bonds, respectively [26,27], due to the presence of hydrogen in the gases involved in the nitride deposition.

In the present work silicon nitride was deposited by PECVD at 300 °C on top of the slit arrays described before. Atomic force microscopy measurements (not shown) confirm the conformal growth of the silicon nitride on the slits. In the bottom panel of Fig. 1(c) we present the reflectivity spectra for light polarized parallel (dotted lines) and perpendicular (continuous lines) to the slit long axis of the 2 µm slits array covered with 200 nm of silicon nitride. For parallel polarization, the slit resonance is not excited and the spectrum is very similar to that of the clean slits, with weak features related to the presence of silicon nitride, namely to the absorption of the of the Si-H, and N-H and Si-N bonds. On the other hand, when the slit resonance is excited (light polarized perpendicular to the slit) the dip associated with the slit resonance is slightly redshifted with respect to that of the uncovered slits. Additionally, a new dip emerges around 13 µm whose intensity is much higher than the silicon nitride features observed for the parallel spectrum, and whose position is redshifted with respect to the Si-N vibrational band. This new dip arises from the interaction between the slit resonance and Si-N vibration band which increases the optical response of the phonon band and shifts its position to lower energies. On the contrary, the position of the slit resonance results from a competition between the redshift of the resonance induced by the increase of the refractive index of the region around the slit [28,29] and the blueshift induced by the interaction with the vibration band.

The spintronic nature of the Ni₈₁Fe₁₉/Au multilayers, exhibiting GMR, brings as a consequence the before mentioned MRE, and therefore the possibility to magnetically modulate the slit resonances [21]. In our case we measure the MRE as magnetic field induced changes of the reflectivity, ΔR/R = (R_H=Hs − R_H=0)/R_H=0, where H = Hs stands for magnetic saturation of the Ni₈₁Fe₁₉/Au multilayers and therefore low electrical resistivity state, and H=0 stands for no magnetic field applied, and therefore high electrical resistivity state. This defines the two magnetic states that determine the magnetic modulation of the optical properties and as a consequence the MRE in these multilayers [20]. In Fig. 1(d) we show the MRE, ΔR/R, for the clean 2 µm long slits. For light polarized along them, where no slit resonance is excited in the considered spectral region, we observe a monotonic decrease of the MRE in the short wavelength range, then it saturates and starts to increase as we increase the wavelength. This broad modulation band is also very similar to the MRE spectrum of the region of the Ni₈₁Fe₁₉/Au multilayer without slits and corresponds to the MRE response of the continuous part of the array. On the other hand, when plasmon resonances are excited (light polarized perpendicular to the slits), and superimposed to the broad band already discussed, an additional structure appears due to the magnetic modulation of the slit resonance. The contribution of the slit resonance to the MRE spectrum can be isolated by removing the contribution of the continuous part. This continuous part is the same for both polarizations; therefore, the MRE response due only to the magnetic modulation of the slit resonance is (ΔR_⊥ - ΔR_//)/R_⊥. The spectrum thus obtained is presented in Fig. 1(e), with a clear derivative shape and represents the effect of the magnetic modulation on the slit resonance, which can be viewed mainly as a modulation of the energetical position of the resonance, ΔE_slit.

Following the same procedure, we now present the ΔR/R and (ΔR_⊥ - ΔR_//)/R_⊥ spectra for the silicon nitride covered slits. Regarding ΔR/R (Fig. 1(f)), the polarization dependence of the excitation of the slit resonance manifests again, the corresponding slit feature appearing for perpendicular polarization. Interestingly, and even though silicon nitride is not ferromagnetic and therefore does not exhibit MRE, now magnetic modulation appears also in the region where the nitride phonon band is present. This is much more clearly seen in the corresponding (ΔR_⊥ - ΔR_//)/R_⊥ spectrum (Fig. 1(g)), where two modulation features associated to the slit plasmon and the nitride phonon bands are observed at around 7 and 13 µm respectively. This is a clear indication that plasmon-phonon interaction effects are taking place, endorsing the phonon band with a magnetic-active character. Worth to mention, similar effects have previously been observed in the visible range in magneto-plasmonic dimers [30,31], where magneto optical activity is endorsed in pure Au disks via dipole-dipole interaction with nearby ferromagnetic disks, and highlight the relevance of electromagnetic interactions in general in this kind of ferromagnetic/non ferromagnetic hybrid systems.

This endorsed magnetic character that the phonon band acquires via its interaction with the slit plasmon resonance is expected to depend on the intensity of this interaction. With this in mind, we now study these interaction effects as a function of the silicon nitride thickness, for a fixed slit length of 2 µm. In Fig. 2(a) we present the reflectivity spectra for light polarized parallel to the slit of the 2 µm slits array for different thickness of the deposited silicon nitride layer. For clarity, the spectra have been shifted vertically. As we know, for this polarization the slit resonance is not excited, and the spectra are very similar to those of the regions without slits. As we increase the amount of deposited silicon nitride, we observe the appearance of some small features around 5 µm and in the 9-12 µm region, being the shape and position of these features not dependent on the amount of deposited material. These structures arise from the absorption of the of the Si-H, and N-H and Si-N bonds, of the silicon nitride layer, respectively. On the other hand, when the slit resonance is excited (light polarized perpendicular to the slit, Fig. 2(b)) the dip associated with the slit resonance (labelled HE) shifts towards longer wavelengths as we increase the thickness of the silicon nitride layer. As explained before, this shift is the result from a competition between the redshift induced by the increase of the refractive index and the blueshift induced by the interaction. Besides, we also confirm the appearance of an additional dip (labelled LE) near the Si-N phonon band which also red shifts and increases in intensity as we increase the thickness of the silicon nitride layer. This thickness dependence of the position and intensity of the new dip strongly suggests that it originates from the interaction between the slit resonance and the Si-N phonon band, which increases as we increase the amount of silicon nitride. As a consequence of this interaction, the electromagnetic nature of both resonances has now a mixed plasmonic-phononic character, being the HE resonance more plasmon-like, and the LE one more phonon-like. In this context, and due to the mixed character of the resonances, we expect that the MRE activity of the plasmon slit resonance of the uncovered slit array should be shared by both resonances in the covered structures, as anticipated on the results shown in Fig. 1(f), (g). This is better seen in Fig. 2(c), (d), where we present the MRE response (ΔR/R) for light polarization parallel (Fig. 2(c)) and perpendicular (Fig. 2(d)) to the slits, and where all spectra appear vertically shifted for clarity. As it can be seen, as we increase the thickness of the silicon nitride layer for light polarization parallel to the slit, a very small bulging appears around 12 µm. On the other hand, for light polarization perpendicular to the slits, together with the feature around 7 µm related to the slit resonance, we observe the appearance of an additional feature around 13 µm associated to the LE resonance. Finally, in Fig. 2(e) we present the MRE response only due to the resonances ((ΔR_⊥ - ΔR_//)/R_⊥). As it can be observed, as we increase the amount of deposited silicon nitride layer, the derivative-like feature corresponding to the magnetic modulation of the slit resonance (HE resonance) of the uncovered structure shifts towards lower energy and its intensity decreases. On the other hand, as we increase the amount of deposited silicon nitride, we observe the appearance of a dip in the same spectral region of the LE dip observed in the reflectivity spectra, whose intensity increases with silicon nitride thickness.

 

Fig. 2. Reflectivity spectra of the 2 µm slits array for different thickness of the deposited silicon nitride layer for light polarized parallel (a) and perpendicular (b) to the slit long axis. MRE spectra of the 2 µm slits array for different thickness of the deposited silicon nitride layer for light polarized parallel (c) and perpendicular (d) to the slit long axis. (e) MRE spectra only due to the magnetic modulation of the resonances of the 2 µm slits array for different thickness of the deposited silicon nitride layer.

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All the results presented so far show that the interaction between slit resonances and the 12 µm phonon band of the silicon nitride layer can be effectively modified by changing the amount of deposited silicon nitride. On the other hand, the effect of the interaction on the optical and MRE response of the slit array-dielectric layer system may also depend on the energy difference between the slit resonance and the phonon band, which can be controlled by modifying the slit length. We have studied this effect by growing similar silicon nitride layers on slit arrays with 3, 4 and 5 µm long slits. In Fig. 3 we present the corresponding results, now focusing only on the spectra for the reflectivity measured with polarization perpendicular to the slits (Fig. 3(a), (b), (c)) and for the MRE response only due to the resonances (Fig. 3(d), (e), (f)). For all the three arrays we observe that, as we increase the thickness of the silicon nitride layer, the dip associated to the slit resonance gives rise to a low energy dip, labeled LE, and a structured high energy dip, labelled HE. The LE dip red shifts, whereas the convolution of the HE dip blue shifts as we increase the thickness of the deposited silicon nitride layer. On the other hand, the MRE spectra only due to the resonances evolve from a derivative-like shape of the uncovered arrays to a more complex line shape which finally gives rise to a peak in the region of the HE resonance and a derivative-like dip in the region of the LE resonance, being the intensity of the LE structure higher than that of the HE one.

 

Fig. 3. Reflectivity spectra for light polarized perpendicular to the slit long axis of the 3 µm (a), 4 µm (b), and 5 µm (c) slits arrays for different thickness of the deposited silicon nitride layer. MRE spectra only due to the magnetic modulation of the resonances of the 3 µm (d), 4 µm (e), and 5 µm (f) slits arrays for different thickness of the deposited silicon nitride layer.

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Summarizing at this point, the results of the four slit arrays and their thickness dependence can be understood in terms of strong coupling effects between the slit resonances and the silicon nitride phonons. As a result of this interaction the optical and MRE response of the uncovered slit arrays are modified, giving rise to new resonances with MRE activity, whose spectral position and intensity depend on the slit length and the thickness of the silicon nitride layer. On the other hand, the structured nature of the HE dip of the 3, 4 and 5 slit µm arrays and the small shoulder in the HE dip of the spectra of the 100, 150 and 200 nm of silicon nitride on the 2 µm slits array strongly suggest that the interaction between the slit resonance and the silicon nitride phonons is complex and not limited to only one type of Si-N vibration. In particular, as mentioned, a non-homogeneous Si-N environment as well as other vibrations such those arising from the N-H bonds may be involved. Nevertheless, and despite the low energy shoulder observed in the reflectivity of the HE dip of the 2 µm long slits array, we can assume that for this specific case the interaction occurs mainly between the slit plasmon resonance and the 12 µm phonon band. Therefore, in what follows we analyze the structure using a phenomenological model of two coupled oscillators. In this case, the first oscillator corresponds to the Si-N phonon band, whose energy, E_phonon, is the same for all the different thickness of the silicon nitride layer, and the second oscillator is the slit plasmon resonance, whose energy, E_slit(d), depends on the local dielectric environment and changes as we increase the thickness of the silicon nitride layer. On the other hand, the interaction, V(d), between these two oscillators depends on the spatial overlap between the electromagnetic field associated with the plasmon resonance and the silicon nitride layer, and therefore also depends on the thickness of the silicon nitride layer. Within this phenomenological model, the 2 µm system (2 µm array with a silicon nitride layer on top) is described by the following matrix

Their eigen values determine the position of the resonances (E_HE or E_LE) and the eigen vectors the plasmon, C_HE,pl or C_LE,pl, and phonon, C_HE,ph or C_LE,ph, character of each resonance. The thickness dependence of the dielectric shift of the slit resonance, ΔE_slit(d)= E_slit(0)- E_slit(d), and the interaction parameter, V(d), can be obtained from the experimental values of the positions of the resonances as:

These two magnitudes are shown on the inset of Fig. 4(a) and, as expected, both increase as we increase the thickness of the deposited silicon nitride layer. The different thickness dependence between the interaction parameter, V, and the resonance shift, ΔE, could be related to the fact that the interaction parameter depends on the intensity of the plasmon electromagnetic field at the frequency of the phonon band. This electromagnetic field increases as we decrease the difference between the frequency of the plasmon resonance and that of the phonon band. On the contrary, the resonance shift depends on the refractive index of the silicon nitride layer at the frequency of the plasmon resonance. In this spectral range this refractive index decreases as we increase the wavelength, which results in a smaller increase of the resonance shift with the thickness of the deposited layer. On the other hand, and due to the different strength of the light-plasmon and light-phonon interaction, we can assume that only the plasmon fraction, C_HE,pl or C_LE,pl, determines the intensity of the HE and LE resonances. The simulated reflectivity spectra are presented in Fig. 4(a) assuming Lorentzian line shapes for the resonances.

 

Fig. 4. (a) Simulated reflectivity spectra for light polarized perpendicular to the slit long axis of the 2 µm slits array for different thickness of the deposited silicon nitride layer. The inset shows the thickness dependence of the dielectric shift of the slit resonance, ΔE, and the interaction parameter, V. (b) Simulated MRE spectra only due to the magnetic modulation of the resonances of the 2 µm slits array for different thickness of the deposited silicon nitride layer.

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R₀, A, Γ_HE and Γ_LE, were obtained from the 200 nm spectrum and kept constant for all the series. As it can be observed, this simple model reproduces the thickness dependence of the reflectivity spectra. Moreover, within this approach the MRE response of the resonances can be simulated taking into account that the magnetic field modifies both, the slit resonance energy E_slit (d) (due to the magnetic field induced changes of the dielectric constant of the metallic layer), and the interaction parameter V(d) (due to the magnetic modulation the plasmon electromagnetic field [20] and, therefore, of the overlap with the silicon nitride). However, due to its intrinsic nature, the phonon frequency is not affected by the magnetic field.

These magnetic field modifications imply that the energies of the resonances, E_HE,LE and their plasmon fraction, C_HE,LE,Pl, transform into E_HE,LE^Δ and C_HE,LE,Pl^Δ, respectively. Therefore, the spectrum of the contribution to the magnetic modulated reflectivity only due to the resonances can be expressed as:

In Fig. 4(b) we present the spectra thus obtained for the 2 µm system. The magnetic field induced modification of the slit resonance frequency (ΔE_slit(d) = 0.062 meV) and the interaction parameter (ΔV(d)/V(d)=−0.14%), where obtained from the MRE spectrum of the 200 silicon nitride covered slits spectrum and kept constant for all the series. As it can be observed this simple model reproduces the thickness dependence of the MRE spectra. In particular, the difference between the spectral shape of the HE and LE features, derivative-like for the HE feature and dip-like for the LE feature, as well as their intensity evolution, are well reproduced.

This phenomenological description allows us to clarify the magnetic modulation of the resonances in GMR metallic/dielectric structures with strong plasmon-phonon interaction effects, such as the four slits arrays presented here. In these systems, the magnetic field modulation of the resonances results from the combination of three factors: first the mixed plasmon-phonon character of the resonances, second the magnetic modulation of the plasmon resonance, and third the magnetic modulation of the interaction. The first one is intrinsic to the hybrid metal/dielectric structure, whereas the second and third factors result from the magnetic field dependence of the optical properties of the GMR metallic multilayer, leading to a magnetic modulation of the plasmon resonance and its associated electromagnetic field. In consequence, the plasmon like resonance induces a MRE activity into the phonon-like resonance, which in the absence of any interaction has no magnetic character. On the other hand, this behavior of inducing magnetic activity in resonances which have no magnetic nature at all, has also been observed in other systems and for other magneto-optical related effects. For example, it has been shown that the interaction between a plasmonic and a magneto-plasmonic metallic nanodisk leads to the appearance of magneto-optical activity in the purely plasmonic disk induced by the magneto-plasmonic one, opening new ways to tune the magneto-optical response of the system [30,31,32].

3. Conclusions

In summary, a study of the effect that the interaction between plasmons and phonons has on the optical and magneto refractive activity of spintronic-plasmonic/dielectric structures has been presented. These hybrid systems were obtained by depositing silicon nitride layers on top of slits arrays engraved on a GMR Ni₈₁Fe₁₉/Au multilayer. Due to the interaction, the optical and magneto refractive response of the system is modified, with the appearance of resonances with mixed plasmon-phonon character. On the other hand, the intensity of the interaction depends on parameters such as the thickness of the silicon nitride layer and the slit length, opening new ways to control the optical and magneto refractive response of this kind of systems.