Enhanced Sensitivity of Magneto-Optical Surface Plasmon Resonance in the FeCu Superlattices

We demonstrated the sensitivity enhancement for magneto-optical surface plasmon resonance (MOSPR) using noble/ferromagnetic metals multilayers. The proposed structure is based on the Kretschmann configuration in the transverse magneto-optical Kerr effect (TMOKE) methods with the FeCu superlattices (SLs) as magneto-plasmonic materials and gelatin as biomolecules analyte. The dielectric constants of the FeCu SLs are taken from first principles calculation, which is performed by using a full-potential linearized augmented plane wave (FLAPW) method. The important role of the hybridization process in optical transitions has been identified, and it can be modulated by adjusting the thickness of superlattices. The dependence of the reflectivity on the dielectric constant is performed by 4×4 transfer matrix methods. It is found that the minimum reflectivity directly influences the slope of angular spectra, with a maximum slope of TMOKE signal is 12.23/degree. The change in the gelatin’s refractive index results in TMOKE signal response, then the enhancement of the sensitivity of the MOSPR system can be shown.


Introduction
Surface plasmon resonance (SPR) devices as biosensors are interesting to study due to their high sensitivity and great potential in many areas.SPR sensor is based on the surface plasmon polaritons (SPP), which can be excited by light at the metal-dielectric interface.The high sensitivity of SPR biosensors is achieved due to a significant shift in SPR angle even at small changes of the refractive index in the close vicinity of the sensing layer.However, several studies have been proposed to improve the sensitivity of the conventional SPR, especially in detecting the biomolecules.The hybrid magneto-plasmonic (MP) materials combining noble and magnetic metals have been explored for enhanced SPR, so-called magneto-optical SPR (MOSPR) [1].MOSPR sensors utilizing the transverse magneto-optical Kerr effect (TMOKE) have been exploited to date [2][3][4][5][6].The TMOKE has the capability to adjust the intensity in reflected light when the applied magnetic field is oriented perpendicular to the plane of incident light.Therefore, the TMOKE can be utilized to monitor the changes in the refractive index of the dielectric.
The investigation of optical loss parameters in materials holds significance in the comprehensive understanding of MP structures.This parameter can determine the strength of SPP excitation and the magneto-optical (MO) activity, namely the modification of the optical response induced by magnetization.The optical losses in materials arise from the interband transition, encompassing both optical and MO absorption.Tuning hybridization in the superlattice system can control the interband transition at the desired frequency spectrum.
In this work, we present a study on the influence of optical losses of ferromagnetic/noble metal SL, i.e., FeCu SLs, on the sensitivity of the sensor.The highest sensitivity of FeCu SLs in the MOSPR system is due mainly to the highest TMOKE signal, indicating a promising potential device for biosensing application.The structure of the paper is as follows.Sec.II describes the computational methods and the MOSPR simulations.Sec.III describes the investigation of the interband transitions responsible in the optical losses of the superlattices and proposed a MP structure to enhance the sensitivity of the MOSPR system.

Computational methods
We studied the FexCux SLs with x = 1, 2, and 3 in unit of monolayer, which are constructed stacking along [001] direction with the magnetization direction along (100) axis; the diagram shown in figure 1(a).The case where x equals 1 corresponds to an L10-type ordered structure of Fe1Cu1 SLs.The lattice constants in both the in-plane (a) and out-of-plane (c) directions were fully optimized through a total energy minimization process.Calculations were performed utilizing a full-potential linearized augmented plane wave (FLAPW) method, incorporating the generalized gradient approximation (GGA) for the exchange-correlation potential [7,8].A k-point mesh of 51×51×51 for the Brillouin zone (BZ) integration was used for all SLs.The details of the computational method can be found in our previous paper [9].We take into account both interband and intraband contributions to the optical conductivity tensor .In the case of the interband contribution, the Kubo formula of the linear response theory [10,11] is employed to derive , considering the interband transition parameter γ = 0.5 eV.The Drude model has been used to combine the intraband contribution to the diagonal component of .In contrast, its contribution to the off-diagonal component is usually neglected.The dielectric tensor ε is connected to  through: where ω is photon energy, and δαβ is Kronecker delta.Regarding the small quadratic contribution of the dielectric tensor and simplification, the dielectric tensor in the TMOKE configuration is assumed in the form: [12]   = ( where yz = iqm.Here, q represents the MO constant of the material, and it is proportional to the magnitude of the applied magnetic fields or magnetization.The parameter m, taking values of ±1, accounts for whether the field or magnetization aligns parallel or antiparallel to the x-axis. We analyze the [prism/FexCux/Au/gelatin] structures as MOSPR systems in the Kretschmann configuration at a fixed light wavelength of λ = 632.8nm, shown in figure 1(b).In the calculations, the incident medium is a half-cylindrical prism (BK7, n = 1.515) and the external medium is gelatin (nd = 1.341).The crystal orientation of the FexCux SLs in the MOSPR system is similar to the Cartesian coordinate system used in the calculations.The Au film (d = 1 nm) prevents the FexCux SLs oxidation with the dielectric constant at λ = 632.8nm is −11.740+1.2611i[13].The dielectric constant of the FexCux SLs is obtained from the calculation as shown in table 1.Only the ordinary index of the diagonal of dielectric constant (  =   ) is used in calculating the reflection coefficient for ppolarized light.
Table 1.The diagonal and the off-diagonal of dielectric constant (  and   ) of FexCux SLs at λ = 632.8nm. Superlattices Simulation of the reflectivity (R) and the TMOKE signals (R/R) were conducted using the 4 × 4 transfer-matrix methods [14].The magnitude of R/R is expressed as: [15] where Rpp(−M) and Rpp(+M) denote the reflectivities of the p-polarized light for negative and positive magnetization, respectively.

Electronic, optical and magneto-optical properties
The calculated structural properties of the FexCux SLs are presented in table 2. The Fe1Cu1 SLs is usually considered as the L10 structure with a ratio of c/a is 1.04, agreed with that in the previous calculation [16].As shown in table 2, the value of Fe-Cu interlayer spacing along the z-axis in the Fe2Cu2 and Fe3Cu3 SLs increased compared to Fe1Cu1 SLs, as well as Fe-Fe interlayer spacing along the z-axis in Fe3Cu3 SLs compared to Fe2Cu2 SLs.The out-plane distance between the nearest neighboring of Fe in the Fe2Cu2 and Fe3Cu3 SLs is half that in the Fe1Cu1 SLs, while the in-plane distance decreases with an increasing number of x.The spin-polarized partial densities of states (PDOS) of the FexCux SLs are presented in figure 2. Since the total DOS on each atom for in-plane (100) and out-of-plane (001) magnetization are the same but differ only in projections, we present PDOS in (100) magnetization for convenience.Qualitatively, we observe a shift in the peak of PDOS in the Fe-minority unoccupied state as the increases in x.The PDOS peaks are related to the hybridization of Fe atoms.In the Fe1Cu1 SLs, as shown in figure 2(a), the peaks around the Fermi level (EF) are from    =0 (=   2 − 2 ) orbitals due to out-of-plane dd hybridization in the next nearest neighboring Fe atoms, while the DOS peak at 1.2 eV above is dominant from    =±1 (= dxz,yz) orbitals due to an Fe-Cu dd hybridization, indicated by the small magnetics moment of Cu of 0.09 B.Furthermore, the robust in-plane dd hybridization between the neighboring in-plane Fe atoms leads to a large dispersion of    =±2 (=  , 2 − 2 ) [9].
In the Fe2Cu2 SLs, as shown in figure 2(b), there are two peaks at 0.7 and 2.0 eV contributed by originating    =±1 and    =±2 orbitals due to an Fe-Fe dd hybridization.Although the interlayer distance of Fe-Cu is slightly shorter than that of Fe-Fe, Fe-Cu dd hybridization is smaller than dd hybridization in the nearest neighboring Fe atoms, which is indicated by a smaller magnetics moment of Cu of 0.05 B compared to the Fe1Cu1 SLs.Therefore, the double peaks of DOS in the Fe2Cu2 SLs are a blue shift to the DOS peak in the Fe1Cu1 SLs with a reduced magnitude due to the hybridization process.In the Fe3Cu3 SLs, as shown in figure 2  The absorptive part of optical conductivities of the FexCux SLs is summarized in figure 3.At the low energy, the significant peak of the real part of the diagonal component of the optical conductivity, 1xx, is observed at around 1.5, 2.4 and 2.0 eV for x =1, 2, and 3, respectively, as depicted in figure 3(a).This peak is attributed to the interband transition of Fe atoms.For the Fe1Cu1 SLs, the first peak at 1.5 eV mainly contributed from Fe d→p orbitals at minority states correspond to the in-plane Fe-Fe dd hybridization [9].It indicates that the interband transition is influenced by the hybridization process [17].Therefore, we can estimate that the broad peaks of 1xx in the Fe2Cu2 SLs correspond to double peaks DOS of Fe minority state at around 0.8 and 2.0 eV above EF.The spectrum peak of about 2.4 eV is a blue shift to around 1.5 eV of the Fe1Cu1 SLs.Meanwhile, the broad peaks of 1xx in the Fe3Cu3 SLs around 2.0 eV were contributed by interband transitions in the interface and interior of Fe atoms, namely Fe1 (=Fe3) and Fe2, respectively.The Fe interface contributes broad peaks of 1xx around 1.0 to 2.5 eV, while the interior Fe contributes narrower broad peaks around 2.0 to 3.0 eV.These two contributions give a red-shift of peaks of the Fe3Cu3 SLs towards the Fe2Cu2 SLs.

Sensitivity of magneto-optical surface plasmon resonance
First, we calculated the optimum thickness of the FexCux SLs as a function of incident angle in order to obtain the reflectivity minimum (Rmin), where SPP excitation occurs.Under these conditions, the R/R curve can exhibit the maximum slope; therefore, the angular spectra are also maximized.Reflectivity of [prism/FexCux/Au/gelatin] system versus both incident angle and thickness of Fe3Cu3 SLs assumed to be in contact with gelatin is shown in figure 5(a).With reasonable approximation, a drastic decrease in reflectivity around the incident angle of 75 is observed.For improved clarity, the locations of Rmin are annotated with a white plus sign (+) at the center of the blue zone.Reflectivity calculations indicate that the optimal thickness for Fe3Cu3 SLs is 19.7 nm, while for Fe2Cu2 and Fe1Cu1 SLs, it is 20.3 and 20.8 nm, respectively.In the simulation, we utilized a thickness of 19.7 nm to explore the IOP Publishing doi:10.1088/1742-6596/2696/1/0120076 sensitivity of the MOSPR system.It is worth noting again that the decrease in reflectivity is the result of strong SPP excitation in the FexCux SLs which is related to optical absorption.
The reflectivity and TMOKE signal spectra of the FexCux SLs versus the incident angle are depicted in figure 5(b).In comparison to pure noble metals, the FexCux SLs do not exhibit a deep and sharp reflectivity minimum, primarily due to their higher value of 1xx.The spectra exhibit a reflectivity minimum at around 75, which corresponds to SPP excitation in the FexCux SLs.These values closely align with the experimental of the conventional SPR for gelatin, which was 75.4 [18].
Around SPR, there is a significant enhancement in R/R.Moreover, there is a significant decrease in the magnitude of R/R as the incident angle increases away from SPR.The maximum slope of reflectivity spectra of 0.13, 0.13 and 0.14 /degree and the TMOKE signal spectra is 0.31, 1.00, and 12.23 /degree for x = 1, 2, and 3, respectively.These results indicate a two-order magnitude increase in the slope of the TMOKE signal when compared to reflectivity spectra for the Fe3Cu3 SLs.The robust R/R observed under SPP excitation can be attributed to a dual effect: the concurrent decrease in the reflectivity and the amplification of the electromagnetic field at the MO active layer [1,19].The MOSPR system in the high sensitivity for biosensing is the main issue in this study.Sensitivity is defined as the change in the sensor's response per unit change in the analyte refractive index nd, quantified in terms of degrees per refractive index unit (RIU).In general, sensitivity can be expressed as: [20,21] where S corresponds to Rpp detection (in the case of conventional SPR measurement) or R/R (in the case of MOSPR) and A represents the angle of incidence.Therefore, achieving the highest sensitivity involves a double optimization: ensuring a high slope in the measured resonance angular curve and a significant shift of the resonance angle with changes in the analyte refractive index.
In figure 6(a), we calculate a variation in the TMOKE signal when the refractive index of gelatin increases.We assumed that the refractive index increases from 1.341 to 1.347 by intervals of 0.001.With increasing the refractive index, the TMOKE signal spectra gradually shift toward higher angles, attributed to the larger SPP excitation.The sensitivity, as indicated in Eq. 4, is depicted for the MOSPR system in figure 6(b).The FexCux SLs show good linearity as a function of the analyte refractive index.The highest sensitivity of 600 RIU -1 is observed in the Fe3Cu3 SLs, while lower sensitivity values of 54 RIU -1 and 19 RIU -1 , respectively, are observed in the Fe2Cu2 and Fe1Cu1 SLs, indicating a decrease in the sensitivity due to the smaller slope of TMOKE signal.The sharp behavior of the TMOKE signal under resonant conditions leads to increased sensitivity.The higher sensitivity of the MOSPR system at Fe3Cu3 SLs implies that even small changes in the refractive index can be distinctly detected.Additionally, we performed sensitivity calculations for conventional SPR, and the findings are illustrated in figure 6(c).In the SPR system, the sensitivity for FexCux SLs with x = 1, 2, and 3 exhibits an equivalent value of 9 RIU -1 , indicating a lower sensitivity compared to the MOSPR system.Due to the ultranarrow characteristics of the TMOKE signal versus angle at the resonance condition, the TMOKE signal can exhibit better sensitivity to changes in the refractive index compared to conventional reflection measurements.It can be note that the shift of SPR, resulting from changes in nd, is consistent between conventional SPR and MOSPR systems.Thus, we can infer that the magnitude of the sensitivity is primarily attributed to the slope of angular spectra.
There are several ways to analyze the sensitivity of the MOSPR system.For example, Lu et al., [22] and Rizal et al., [23] defines sensitivity as the change in the output signal (S) at fixed incident angle m when nd changes.However, this analysis can only be applied to a lower slope of R/R.In another analysis, sensitivity is calculated as the ratio of the TMOKE peaks changes to the nd changes [5,24,25].However, we observe that in the Fe3Cu3 SL, the change in the TMOKE peaks of the MOSPR system is almost the same as the change in the resonance angle of the SPR system when the nd changes.

Conclusions
In summary, we have shown that the FexCux SLs can be used for the MP structure.The electronic and optical properties are calculated by performing the FLAPW method.Our conclusion is that the hybridization process, which influences optical losses through interband transitions, can be controlled by adjusting the thickness of the superlattices.We illustrated the refractive index sensing in the gelatin in the reflectivity and TMOKE signal spectra.Our study shows that the sensitivity of the MOSPR system is strongly related to the optical and MO properties of MP materials.Then, the enhanced sensitivity of the MOSPR system based on the FexCux SLs is useful for a biosensing platform.

Figure 1 .
Figure 1.(a) The unit cells employed for FexCux SLs.Fe atoms are represented by blue spheres, while Cu atoms are depicted by brown spheres.(b) Schematic diagram of the MOSPR structure in the Kretschmann configuration.
(c), the absence of a DOS peak at the interface Fe above EF indicates weak dispersion of d orbitals; however, the Fe    =0 orbitals with the out-of-plane dd bonding and antibonding states are observed to cross EF.Meanwhile, the two DOS peaks of the interior Fe at 0.5 and 2.0 eV indicate more localized electrons due to the Fe dd hybridization of    =±1 and    =±2 orbitals.

Figure 3 .
Figure 3.The optical conductivity: (a) the real parts of diagonal component, and (b) the imaginary parts of off-diagonal component.The imaginary parts of the off-diagonal components of the optical conductivity, 2yz, which describes magneto-optical absorption, are shown in figure 3(b).The prominent peaks at low energy are located around 1.7, 1.9, and 1.4 eV for x = 1, 2, and 3, respectively.The spectrum of 2yz behaves complicatedly though on the Fe1Cu1 SLs due to suppression in the band-by-band decomposition compared to 2xy spectrum [9].Both interband and intraband transition contributions are taken into account in the dielectric constant, and the real part of the diagonal component is depicted in figure 4(a).The metallic properties of FexCux SLs is indicated by the negative value of ε1xx, reflecting a high plasma frequency (p > 6 eV).The absolute of the off-diagonal component ε1yz of the Fe2Cu2 and Fe3Cu3 SLs is nearly identical and more significant than that of the Fe1Cu1 SLs, as presented in figure 4(b).The minor peaks around 2.0 for the Fe2Cu2 SLs and 1.4 eV for Fe3Cu3 SLs correspond to blue-and red shift in the peaks of 2yz spectrum.

Figure 4 .
Figure 4. Dielectric tensor of FexCux SLs: (a) the real parts of diagonal component, (b) the imaginary parts of off-diagonal component.
on Modern Optics and Its Applications Journal of Physics: Conference Series 2696 (2024) 012007

Figure 5 .
Figure 5. (a) Reflectivity versus both incident angle and thickness of Fe3Cu3 SLs.(b) Simulation of R and ∆  ⁄ of FexCux SLs as a function of incident angle.

Figure 6 .
Figure 6.(a) Comparison of R/R of Fe3Cu3 SLs as a function of nd, (b) and (c) show the dependence of output signal S on the variation of refractive index for MOSPR and SPR systems, respectively.

Table 2 .
The structural properties of the FexCux SLs.