1. Introduction

Demand for custom products in medicine, robotics, science, and mechanical engineering makes leaders of the world market supplant classic production techniques towards more technologically complex and competitive manufacturing. One of the modern trends to achieve that is the implementation of an industrial internet of things [1] - a digital platform combining multiple sensors, machine lines, supply chains, and operators into a network, collecting all the data and transforming it into the information about manufacturing efficiency and ways to improve it. Among all the sensors required for such a network, magnetic field sensors are of the main interest since they are used in most industrial, electronic, and automotive devices for signal registering [2], compensation of environmental noise [3], or manipulation control [4].

Depending on the task and operating environment, magnetic field sensors can be of various shapes, linear dimensions, and operating principles [5]. However, the most limiting factor for the implementation of a magnetic field sensor in a manufacturing process is its price. Expensive magnetic field sensors like SQUID or optically-pumped spin relaxation free magnetometers are suitable for specified tasks, like biomedical applications, magnetic field detection in outer space, or in other fields where the use of expensive and highly sensitive detectors is reasonable [6–8]. Relatively inexpensive and ubiquitous magnetic field sensors used in manufacturing are based on Hall, magnetoresistance, magnetoimpedance, and fluxgate effects. Such sensors can be easily implemented in most electronic devices but their linear dimensions reduction results in a subsequent sensitivity and limit of detection decrease.

Existing technologies for the production of such sensors are also suitable for the manufacture of the cost comparable, highly sensitive and local magnetic field sensors based on high magneto-optical activity in monocrystalline bismuth rare-earth iron-garnet films [9] or on magneto-optical effects enhanced with the use of surface plasmon polaritons (SPPs) excitation [10,11]. SPPs are TM electromagnetic waves of light and free electrons collective oscillations at the dielectric/metal interface [12]. As evanescent waves, SPPs propagate along the dielectric/metal boundary and decay into both metal and dielectric layers. SPPs enhance electromagnetic field inside the metal layer resulting in the enhanced magneto-optical activity because magneto-optical effects are proportional to the electromagnetic field inside material [13].

Excitation of SPPs at the dielectric/metal interface is a result of phase-matching conditions fulfillment that is achieved with several experimental schemes: Kretschmann or Otto geometries [14,15], excitation with SNOM probe or diffraction on surface features [16–18]. Due to the developed infrastructure for nanostructured materials fabrication, the most convenient regime of the SPPs excitation is the use of diffraction gratings made of combined noble and ferromagnetic metals, called magnetoplasmonic crystals (MPlCs) [13]. In MPlCs, diffracted light components coinciding with the SPP’s wavevector are coupled to surface plasmons leading to the compliance of phase-matching conditions. Wavevector conversation from light to SPPs appears as a sharp dip in the reflected or transmitted light spectra, called Wood’s anomaly. It is related to the light diffraction and SPPs excitation in the wavelength region defined by the angle of light incidence, structure parameters and refraction indexes of MPlC layers. Consequently, in the same wavelength region, magneto-optical effects are resonantly enhanced [19–23].

MPlCs for magnetic field sensing can be opaque [24,25] or transparent [26,27], depending on the observable magneto-optical effect. Recently, a new approach for magnetic field detection with the use of MPlCs was presented. It is based on the detection of the SPPs enhanced transverse Kerr effect (TKE) of a 100 nm thick Fe film-based MPlC exposed to an external required modulation AC magnetic field. Measuring the AC field dependence in the presence of any DC magnetic field, it is possible to measure the magnitude of the applied DC field with the sensitivity of 10⁻⁶ Oe at a local area of 1 mm² in the modulation AC field of 14.6 Oe [28]. To minimize energy consumption and price of the device, magnetically soft 100 and 130 nm thick permalloy (Py) films were used reducing the AC field magnitude to 7.3 Oe [25]. This value can be decreased even more with the use of thin Py layers without significant losses in the functionality of the MPlC-based magnetic field sensor, thus, allowing to fabricate more energy efficient sensing elements.

In this work, we propose a 5-nm thick Py film-based MPlC with the low coercive force for the reduction of the AC modulating field required for the magnetic field measurements. Before the fabrication of the MPlC, its optical and magneto-optical properties were modeled by the finite-difference time-domain (FDTD) method to define suitable geometrical parameters of the MPlC for further sensing applications. Experimentally measured reflectivity and TKE spectra of the fabricated sample are compared with the modeled dependencies. Magnetic properties of the fabricated sample were measured with the Kerr and vibrating sample magnetometry to estimate local and volume values of the sample’s coercive field. It is shown that the MPlC has twice lower coercive field and measurable field region comparable to previously published results.

2. Materials and methods

Proposed MPlC had a trilayer structure of Ag (250 nm)/Ni₈₀Fe₂₀ (5 nm)/Si₃N₄ (10 nm) layers applied on the surface of a one-dimensional quasi-sinusoidal diffraction grating with the period of 320 nm and diffraction stripes height of 20 nm. The optical and magneto-optical activity of the magnetoplasmonic crystal were modeled with the use of the Lumerical FDTD software package. In simulations the sample was illuminated by a plane wave propagating at a fixed angle of 68°, corresponding to the maximum TKE value for such MPlCs [20]. When an external magnetic field is applied to the sample, the dielectric permittivity tensor ε of Ni₈₀Fe₂₀ becomes anisotropic. Its non-zero off-diagonal elements ε_xy and ε_yx are equal to ± ig, where g is the gyration constant taken from experimental data in Ref. [29]. To model the TKE, reflection spectra were simulated in two opposite directions of the magnetic field. The TKE value was calculated with the formula:

The DC magnetron sputtering method was used to prepare the MPlC with the corresponding layers’ thickness, period, and stripes height on top of the polymer substrate. Sputtering was performed with the ORION-8-UHV magnetron sputtering setup at room temperature in the atmosphere of argon with a flow of 6 ppm. The source power was 75 W and the pressure in a chamber was 3 mTorr. Reference sample with the same composition based on the flat Si (100) substrate was made in the same sputtering cycle. The morphology of the prepared MPlC was studied with the atomic force microscope (AFM) NTEGRA AURA in a semi-contact mode. Magnetic properties of the MPlC in the external magnetic field directed along the easy magnetization axis (EMA) were studied with the NanoMOKE III magneto-optical Kerr magnetometer (MOKE) in the longitudinal Kerr effect geometry and with the vibrating sample magnetometer (VSM) LakeShore 7400. Additionally, a vector magnetometry hysteresis loop along EMA in the transverse geometry of the applied field, corresponding to the hard magnetization axis (HMA), was obtained with the Evico Magnetics magneto-optical Kerr microscope & magnetometer. MPlC reflectivity and TKE spectral dependencies in the visible wavelength region were studied with the optical setup consisting of a halogen lamp, two Glan–Taylor prisms as p-polarizer for the SPPs excitation and analyzer, a system of collimation lenses, Helmholtz coils, an optomechanical chopper, a SR830 Lock-in amplifier and a photomultiplier tube as a detector. The angle of the light incidence was equal to 68° corresponding to the −1^st diffraction order in accordance with the diffraction grating formula. For optical measurements, the light beam was modulated with the optomechanical chopper at the frequency of 298 Hz and for the TKE studies, the sample was exposed to the AC saturating modulation magnetic field with the magnitude of 250 Oe and frequency of 68 Hz. To calculate the TKE value from the experimentally obtained spectra, the following equation was used:

3. Results and discussion

The studied MPlC shown in Fig. 1(a) has a geometry-driven anisotropy of magnetic properties formed by the diffraction grating [31]. The easy magnetization axis (EMA) of the MPlC is directed along the stripes and the hard magnetization axis (HMA) is perpendicular to them. Because application of a magnetic field along the diffraction stripes corresponds to the case of the SPPs enhanced TKE, hysteresis loops along the EMA are of particular interest [19]. The MPlC remagnetization along the EMA is mostly driven by the domain wall movement leading to high squareness ratio of the hysteresis loop independent of the measurement method. This can be seen from the measured hysteresis loops shown in Fig. 1(b).

 

Fig. 1. (a) Atomic force microscopy image of the magnetoplasmonic crystal. Arrows correspond to the easy (EMA) and hard (HMA) magnetization axes of the sample. (b) Hysteresis loops of the magnetoplasmonic measured along the EMA with the magneto-optical Kerr magnetometer (MOKE, red line with circles) and vibrating sample magnetometer (VSM, black line with rectangles). (c) The vector magnetometry hysteresis loop along EMA in the magnetic field applied along HMA.

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The shape difference between loops is due to the MOKE and VSM methods’ features. The MOKE is sensitive to the magnetic moment in a small volume at the MPlC center area and the VSM is sensitive to the magnetic moment of the whole sample including its edge defects. The coercive field H_C of the MPlC was 7.7 Oe and 5.2 Oe according to the MOKE and VSM magnetometry, respectively. A higher coercive field in the case of MOKE magnetometry is a result of the MPlC center magnetization switching in larger magnetic fields, which can be observed for similar structures [31].

To verify the absence of magnetic interactions between MPlC stripes and the discontinuity of the sputtered Py layer, we obtained the vector magnetometry hysteresis loop, shown in Fig. 1(с). The measured magnetic moment is proportional to the projection of the magnetic moment of the sample along the EMA while the external magnetic field is aligned along the HMA. In absence of the applied magnetic field, most magnetization vectors are aligned along the EMA that is in accordance with the MOKE and VSM results. With the increase of the applied magnetic field, magnetization vectors start following the external magnetic field until the magnetization along the EMA reaches almost zero. Absence of any additional phases in this process is a result of the coherent rotation of magnetization vectors indicating no magnetic interactions between structure parts and continuity of the sputtered Py layer [32]. Kerr rotation in high magnetic fields and the magnetic moment along the EMA, respectively, does not vanish due to a small misalignment of the external magnetic field and the HMA direction, which can be explained by the domain splitting phase in the remagnetization process [33].

Results of the reflectivity and TKE preliminary modeling for the fabricated MPlC are shown in Fig. 2(a, b). Modeled reflectivity spectra (Fig. 2(a), dashed black line) possess an asymmetric Fano-shape profile consisting of the peak and following sharp dip. The peak is related to the diffracted light propagation along the MPlC surface, called the Rayleigh anomaly, and the dip is related to the fulfillment of the phase-matching of the incident light and surface plasmon polaritons, called the Wood anomaly. Spectral positions of the Rayleigh and Wood anomalies were λ=616 nm and λ=631 nm, respectively. Shape, width, and amplitude of the Wood anomaly depend on the sample’s profile parameters and composition [34], as well as on the angle of light incidence [16]. Spectral position of the Rayleigh anomaly is defined by the diffraction grating formula and the Wood anomaly is associated with the excitation of the SPPs in a narrow spectral range [35]. Both resonant features depend on the MPlC composition and can undergo a spectral shift depending on the sample’s functional layers’ thicknesses [36] and profile parameters [22,37–39]. In the same wavelength region of the TKE spectrum (Fig. 2(b), red dashed line), a Fano-shape resonance, being a result of the SPP wave vector modulation by the external magnetic field, was observed. The TKE is significantly enhanced up to 1.2% at the resonant wavelength λ = 640 nm with respect to the reference sample based on a flat Si substrate with the same composition as the studied MPlC. Both optical and magneto-optical resonant features in preliminary modeled spectra were detected in the experimentally obtained reflectivity (open black circles) and TKE (red open circles) spectra shown in Fig. 2(a, b). The spectral position of the Rayleigh anomaly in the reflectivity spectra was the same as for the modeled result, but the spectral position of the Wood anomaly was shifted to λ=640 nm. Because the TKE resonance’s spectral position is defined by the Wood anomaly, it was also shifted to the higher wavelength region in comparison to the modeled result. Amplitudes of both resonant features were also slightly different for modeled and experimental spectra due to the difference between materials’ permittivity in the modeled and fabricated MPlC or due to a slightly different thicknesses of MPlC’s functional layers formed by the magnetron sputtering method. A better resemblance between experimental results and numerical simulations of the reflectivity and TKE spectra was obtained with the modified model where the thicknesses of the Py and silica nitride layers in the model were changed to 4 nm and 12 nm, respectively. Results of the simulated reflectivity (solid black line) and TKE (red solid line) spectral dependences are shown in Fig. 2(a) and Fig. 2(b), respectively. In such a model, spectral position and width of the reflectivity minima coincided with the experimentally obtained dependence while the Fano-shape resonance in the TKE spectra was 5 nm shifted in the region of smaller wavelengths with respect to the experimentally obtained data. It should be noted that the simulated spectral dependence of TKE and the maximal TKE value are similar for both simulation models. These spectral dependence’s shape and values are in good agreement with experimental TKE spectra. Therefore, a slight change of the Py layer thickness on 1 or 2 nm during the MPlC fabrication process does not significantly modify TKE spectral dependence, maximal TKE value and MPlC performance for sensing applications. However, further deviation of the layers’ thicknesses in the simulation model can significantly change the reflectance spectrum and TKE values in the MPlC. To verify the SPPs excitation, near-field simulations were performed for the modified MPlC model. Figure 2(c) demonstrates |E|² distribution at λ=640 nm corresponding to the simulated TKE maximum (solid line in Fig. 2(b)). Electric field is strongly enhanced near the MPlC interface due to the SPP excitation. It provides higher sensitivity of the MPlC to the external magnetic field in comparison with nonstructured films that do not support SPP [40].

 

Fig. 2. Experimental results (blank circles), preliminary model (dash line), and modified model (solid line) of MPlC (a) reflectivity and (b) TKE spectra. Solid lines with circles correspond to the reference sample spectral dependencies of reflectivity (black) and TKE (red). (c) Simulation of the ${|E |^2}$ near-field distribution at the metal/dielectric interface of the MPlC.

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The working principle of the proposed sensing element is based on the measurement of a magnetic field-dependent magneto-optical signal change caused by the addition of a DC magnetic field to the MPlC exposed to the constantly applied AC modulation field with the H_MOD magnitude [28]. This type of dependences is measured at a resonant wavelength resulting in the magneto-optical activity enhancement [40] that can be expressed in terms of the SNR shown in Fig. 3.

 

Fig. 3. SNR_AC dependence (black line) where H_MOD is the center of the dependence slope and ΔH is a measurable field region. H_MOD and ΔH were calculated according to the maximum and FWHM of the SNR_AC first derivative (red solid line), respectively.

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The measurable field region and ΔSNR_AC is proportional to the detectable signal. Values were calculated according to the FWHM of the dependence first derivative. The center of the dependence’s slope, calculated from its first derivative maximum, denotes the working point of the sensing element, and the required value of the modulation magnetic field H_MOD that was 5.1 Oe for the proposed sample. The sensitivity of the assembled setup to the applied DC magnetic field was limited by the signal deviation from the H_MOD, equal to 7.5 mOe.

4. Conclusions

To conclude, magnetic, optical, and magneto-optical properties of the one-dimensional magnetoplasmonic crystal based on a thin permalloy film were experimentally and numerically studied. Numerical simulations of the reflectivity and the transversal Kerr effect spectra are in good accordance with experimental results and provide the geometrical parameters for the fabrication of magnetoplasmonic crystals with different compositions for sensing applications. Demonstrated parameters H_MOD, ΔH, and ΔSNR_AC allow the use of the fabricated sample for magnetic field detection without losses in functional properties. The use of a magnetically soft thin permalloy layer led to the two-fold reduction of ΔH_MOD and value of the required modulation field as well as one order decrease of ΔSNR_AC in comparison with previously shown data. Reduction of the modulation field value allows one to use smaller and less energy consuming electromagnets to produce cheaper, more energy efficient and size-minimized magnetic field sensors based on magnetoplasmonic crystals.