Thickness dependent enhancement of the polar magneto-optic Kerr effect in Co magnetoplasmonic nanostructures

Large surface plasmon polariton assisted enhancement of the magneto-optical activity has been observed in the past, through spectral measurements of the polar Kerr rotation in Co hexagonal antidot arrays. Here, we report a strong thickness dependence, which is unexpected given that the Kerr effect is considered a surface sensitive phenomena. The maximum Kerr rotation was found to be -0.66 degrees for a 100 nm thick sample. This thickness is far above the typical optical penetration depth of a continuous Co film, demonstrating that in the presence of plasmons the critical lengthscales are dramatically altered, and in this case extended. We therefore establish that the plasmon enhanced Kerr effect does not only depend on the in-plane structuring of the sample, but also on the out-of-plane geometrical parameters, which is an important consideration in magnetoplasmonic device design.


I. INTRODUCTION
Magnetoplasmonics is an emergent research field that aims to strongly modify the magneto-optic response in the presence of surface plasmons and to control plasmonic resonances with magnetic field [1,2]. The enhancement of the magneto-optical effects especially of the polar and transversal Kerr effect (PMOKE-TMOKE) due to the presence of surface plasmons has been shown in many different nanostructures. Examples are hybrid nanostructures of noble metal/ferromagnetic metal (or dielectric) like Co/Au, YIG/Au [3], in Au/Co/Au trilayers [4] and multilayers [5], as well as in patterned pure magnetic films [6][7][8][9][10][11][12]. The enhancement has been reported for both types of plasmonic excitations for localized (LSPs)and for propagating (SPPs) surface plasmons. The mechanism for the increased magneto-optical values is the enhancement of the electric field provided by the excitation of either localized plasmons or propagating plasmons as very recently shown by correlating near-and far field optical-and magneto-optical response [13].
Despite the numerous studies on materials combinations and geometrical considerations little attention has been given to the parameter of the thickness of the magnetic layer. In Au/Co/Co trilayers [14] an optimum Co thickness for the redistribution of the electromagnetic field in the magnetic layer has been observed at around 8 nm when plasmon excitation is occurring at the Au/air interface. However, there is no such study for the case of pure magnetic nanostructures. In this paper we use hexagonal arrays of holes perforated in Co films of different thicknesses. We use optical reflectivity and polar magneto-optical Kerr effects together with simulations characterise the thickness dependence of the magnetic layer to magneto-optic enhancement in magnetoplasmonic structures. Our study is focused in relatively * papaio@rhrk.uni-kl.de thick metal films with the film thickness, t, being smaller than the wavelength of the incident light λ, and larger than the skin depth δ of the metal, i.e. δ ≤ t < λ. We show that the thickness constitute another way to strongly manipulate the enhancement of the PMOKE signal.
Three Co films were patterned by the use of selforganization of colloidal polystyrene beads on Si substrates as shadow masks [7]. The final layout of the samples, is presented in Fig. 1. There is a hexagonal hole structure with a periodicity of a 0 = 470(15) nm and with hole sizes of d = 260(10)nm. A very thin buffer layer of Ti was initially deposited for better adhesion of the Co on the Si and Co layers with different thickness were grown on the seeding layer. To prevent oxidation of the Co surface, a capping layer of 2 nm Au was deposited. The final form of the samples were: Au (2 nm)/Co (X nm)/Ti (2nm)/Si(111), with X being either 20, 60, or 100 nm. Continuous thin films of the same composition were prepared at the same time, as reference samples.
There are two characteristic main directions that are relevant for plasmon excitation and they are the nearest neighbour (ΓK, [10]) and the second nearest neighbour (ΓM, [11]) directions that are aligned parallel to the scattering plane. In our work we have performed measurements aligning the plane of incidence to the ΓK, [10] direction, as shown in Fig. 1.
For the PMOKE measurements a white light source of a mercury lamp is used to obtain a broadband light spectrum.The light is guided into a monochromator with 600 lines/mm gratings. After the monochromator, the light is guided first through a highpass filter to suppress the effects from higher harmonics and thereafter through a set of beam-shaping and focusing lenses to maximise the intensity reaching the sample. To minimise the noise, the light is modulated with either a chopper or Faraday cell. Before being reflected, the light is focused onto the sample with an angle of incidence of 4 degrees through a hole in the magnetic core of the ferromagnetic coils. The maximum magnetic field strength is 2.2 T. Finally the light goes through the automated polariser before being focused onto the photo-detector or photo-multiplier tube. The modulated signal is measured through either a photo-detector or a photo-multiplier tube connected to a lock-in amplifier. For the spectral reflectivity the same setup like the PMOKE measurements is used adjusted for reflectivity measurements by guiding the reflected light through a lens into a photo-multiplier tube (PMT) or photo detector. The configuration of the setup allows for measuring low light intensities, although as all light will not be collected the reflectivity has arbitrary units. The polar Kerr rotation is measured in absolute values (degrees), as it is measured through magnetically saturating the sample in the two polar directions and comparing the polarisation rotation difference, by scanning the polariser for the point of light extinction.
Reflectivity and polar Kerr-rotation measurements were performed at an energy range from 1 to 4.2 eV. Polar Kerr-rotation spectra were measured at samples' saturation state (maximum applied magnetic field B = 1.1 T), while the samples were oriented with the ΓK-direction of the hexagonal array parallel to the plane of incidence. Figure 2 (a) shows the calculated reflectivity, (c) the experimental reflectivity, (b) the calculated magnetooptical spectra for the three antidot samples, and (d) the MOKE spectra of the patterned samples in comparison with their corresponding continuous films. The reflectivity curves were obtained with p-polarized light and measured relative to the intensity of the direct beam. Figure 2 (b) shows that below 3 eV the main feature is the trough in reflectivity at ≈ 2.81 eV for the 60 nm sample and at ≈ 2.69 for the 100 nm. The trough is present but hardly visible for the sample with 20 nm Co thickness, however can be estimated around ≈ 2.9. The continuous reference films exhibit a typical metallic be-haviour. A second broad and intense dip is appearing for energies ≈ 3.75 eV and ≈ 4.0 eV for the 100 nm and 60 nm respectively. Figure 2 (a) presents the calculated reflectivity curves for the three samples. Apart from the 20 nm sample where the reflectivity of the Si substrate dominates, the calculation captures well the reflectivity behaviour of the samples. The observed minima in reflectivity for all the Co samples are the result of the resonant coupling of light to SPPs excitations at the Co / air patterned interfaces as it can numerically calculated by using the scattering matrix approach [15] and shown in Fig. 2 (a). The simulation is close to the experiment as indicative shown with the vertical lines, showing reduced reflectivity where SPPs are excited. An additional feature is appearing in the calculation at ≈ 3.1 eV that originates from the splitting of the plasmonic excitation in different directions as we move away from the normal incidence. Experimentally we hardly see these dips in the reflectivity curves due to their lower relative intensity in combination with the smaller resolving power of our reflectivity setup.
From Fig. 2 we see that the reflectance minima exhibit a red shift in energies as we change the thickness from 20 to 100 nm. For example, the three minima of reflectivity for the sample of 60 nm are located at ≈ 2.81, ≈ 3.2 (calculation) and ≈ 4.0. On the contrary the three minima of reflectivity for the sample of 100 nm are at ≈ 2.69, at ≈ 3.1 and ≈ 3.75 all of them red shifted compared to the thinner 60 nm sample. By holding constant the size of the holes at 260 nm the critical parameter here becomes the ratio of the thickness with respect to the period of the pattern h/a [16]. By increasing the thickness from to 60 nm to 100 nm sample and the corresponding ratio from h/a = 0, 13 to h/a = 0, 21, we cause a redshift of the reflectivity minima. Similar redshift of transmission maxima with the thickness in the presence of plasmonic excitations has been observed in antidot structures composed of Ag, and Au [16]. The presence of an absorbing magnetic metal does not alter this behaviour revealing that the driving force of the reflection minima or transmission maxima are the excitation of surface plasmons polaritons.
The experimental Kerr rotation spectra of the three patterned and the three reference Co samples, with different thicknesses, are presented in Fig. 2 (d). The magneto-optic response depends on the minima of reflectivity. The thinnest sample of 20 nm that presents a very small signature of SPPs signature in its reflectivity curve, does not exhibit a significant difference in the Kerr spectrum with respect to its continuous counterpart. However, the other two patterned samples show strong changes as compared to the continuous films, with extraordinary enhancement of the Kerr rotation. At the energies where SPP modes are involved the Kerr rotation θ K is enhanced. θ K is maximized at ≈ 2.69, and at ≈ 2.81 for the 100 and 60 nm respectively. A second important feature appears at energies ples. Another surprising characteristic is the behaviour above 3.5 eV. For the 60 nm sample, the enhancement around 4 eV is strong, 3 times higher that its continuous counterpart. Furthermore, the broad trough in reflectivity for the 100 nm sample around ≈ 3.75 eV gives rise to a surprising nine fold enhancement of the Kerr rotation, as compare to the continuous film at the same energy. The size of the enhancement is one of the biggest ever reported (Ref [2] and references therein). The extraordinary enhancement is correlated to the third broader and deep trough in reflectivity that appears in the energy region ≈ 3.8 − 4.0 eV for the 2 thicker samples. Reduced reflectivity at the beginning of the ultraviolet region is also a typical property of the continuous films. The impressive enhancement of the Kerr rotation depends on the plasmonic excitations and moreover it can be controlled by the thickness. Figure 2 nicely shows that the feature of enhancement does not only depend on the in-plane structuring of the sample but also on the outof-plane geometrical parameters such as the thickness.
The excited SPPs are correlated to the thickness through their field penetration depth. As it has been shown the penetration depth of SPPs, δ skin , in a metals is usually of the order of 10 nm in the visible and infrared [17]. Furthermore, in our case the absorbing ferromagnetic materials introduces significant losses (large intrinsic absorption). The role of overlapping SPPs field in the magnetic layer has been previously observed in symmetric structures of Au/Co/Au [14,18] and in Ptcapped Ag/Co/Ag structures [19]. They have revealed an optimum enhancement of the MO activity for specific Co thickness being around 7-10 nm where the excitation of the SPP in the Au layer maximises the electromagnetic field distribution in the MO Co layer for that thickness. So one would expect that our samples with much higher thickness should have higher optical absorption and dominant damping preventing an optimal SPP excitation, and therefore a reduction in the observed MO signal. Instead, the experiment shows a maximum enhancement for the 100 nm sample. Here, we must mention that the aforementioned SP penetration depth is referred to continuous trilayers and they are not to be compared and confused with our antidot structures. The antidot structure and the presence of holes render the thickness parameter a very important factor for the behaviour of SPPs. As we have shown in Ref. [13] the excitations of surface plasmon polaritons in thick magnetic films leads to remarkable electric field intensity patterns that are responsible for the magneto-optic enhancement. The enhancement of electric field of the excited SPPs that is sufficiently strong in order to interact within the magnetic Co layer together with the multiplicity of the excited plasmonic modes leads the large enhancement of the Kerr rotation at energies above ≈ 3.5 eV. Although the calculation in Fig. 2 (b) captures well the size and the shape of magneto-optic enhancement in the whole spectral region it can not reproduce the very big enhancement above ≈ 3.75. The experiment shows an impressive enhancement. The reason for this is the almost zero reflectivity that is experimentally measured while in the theory the samples obtain a significant percentage of reflectivity. Accordingly, the experimentally measured θ K depends not only in the polarization conversion due the SPPs excitations but also on the reflectivity [13]. When the reflectivity goes to zero the Kerr rotation is diverging since the optical reflection coefficient is in the denominator [13]. The very low measured reflectivity that strongly depends on the thickness of the antidot samples significantly contributes to the very large enhancement of Kerr rotation.
In conclusion we have shown a new way to manipulate the magneto-optic response of magnetoplasmonic structures by taking advantage of the thickness of the magnetic layer. We have used patterned Co hexagonal an-tidot lattices with different thickness to generate a large enhancement of P-MOKE signal close to SPP resonances. We have revealed that not only the in-plane structural parameter that defined the excitation condition for SPPs is important for the PMOKE enhancement but also the out of plane direction represented by the thickness of the magnetic layer is crucial. We have shown that the thickness can control the magneto-optic Kerr enhancement by SPPs excitation and very low reflectivity values. Consequently, new routes for tailoring the functionality of patterned structures can emerge, when the influence of the thickness on the magneto-optic activity is taken into account.