## Introduction

Development of magnetic field sensors primarily works on improving the sensor’s design and its characteristics - sensitivity, resolution, locality and reliability as well as on extending the sensor’s operating temperature range or conditions of applicability (like harsh environments)1,2,3,4. One of the cutting-edge topics today is using the magnetic field sensors in medical applications such as magnetocardiography5,6 and magnetotomography7, which require precise measurements of magnetic field with the magnitude reaching 1 μOe. Nowadays the most reliable techniques are based on SQUIDs5,8, induction coil sensors9,10 and Hall-effect sensors11,12. These methods have several limitations connected with the decrease of sensitivity in small volumes13,14, the low temperatures requirement or moving the sensor probe for changing the sensing area. The alternative approach utilizes magneto-optical effects in transmission or reflection configurations, which allow one to preserve sensitivity at a local point and to scan the certain volume without moving the sensing element15,16,17. In this case the locality depends only on the optical beam size and the penetration depth of optical radiation in the medium, while the sensitivity is proportional to magnetization of the medium and the scanning volume can be changed by moving the optical spot.

One of the possible ways to increase the sensitivity of magneto-optical sensors is to get surface plasmon-polaritons (SPPs) excited on the metal-dielectric interface. SPPs induce the resonant magneto-optical effects appearing18,19,20,21,22. They increase the polarization plane rotation or modulation of the reflected (transmitted) light intensity utilizing the nonreciprocity of magneto-optical effects. The surface plasmons, being the electromagnetic excitations at the metal surface consisting of polaritons and electronic gas oscillations, require fulfilling the phase-matching conditions applying various experimental schemes, such as Kretchman, Otto and grating configurations23. Magneto-optical effects can be enhanced by SPPs in magnetoplasmonic crystals fabricated of noble metal and magnetic layers with one- or two-dimensional subwavelength grating20,24,25,26,27. There are several examples of using the magnetoplasmonic excitations in magneto-optical sensors of biomolecules15,28, chemical solutions29,30 and gases31 through detecting the ultralow refractive index changes32. Another promising direction is using the localized surface plasmons excited in metallic and hybrid nanoantennas17,33,34.

In this Letter, we show how the magnetoplasmonic crystal can operate as a highly sensitive local sensor of DC magnetic field. The use of controllable AC magnetic field allows one to choose the certain region at the magneto-optical response curve with the strongest dependence of the signal on the magnetic field magnitude. The sensor measures the DC magnetic field component parallel to the AC magnetic field while the shift of optical beam reveals the magnetic field distribution in the desired volume. The enhanced TMOKE, achieved due to excitation of SPPs, allows us to detect the magnetic field with sensitivity reaching 10−6 Oe.

## Results and Discussions

### Sample characteristics and geometry

Magnetoplasmonic crystals were fabricated by ion-beam deposition of noble (silver) and ferromagnetic (iron) metal layers onto the surface with quasi-sinusoidal subwavelength polymeric grating. Before the fabrication the chamber was vacuumed down to 8 · 10−7 Torr. During the fabrication process the argon flow of 6 ccm and ion source MPC-3000HC with working current of 30 mA and voltage of 1000 V were used. All the substrates were rotating during the fabrication process to avoid the shadowing effect. The period and profile height of the grating were equal to 320 and 20 nm, respectively35,36. Surface of magnetoplasmonic crystals was passivated by a thin transparent layer of dielectric (silica nitride) to prevent oxidation of the iron layer. Thicknesses of functional layers were varied to estimate the contributions of magnetic and plasmonic properties into the enhancement of TMOKE and sensitivity of DC magnetic field sensor based on MPlCs. The samples with thickness of iron layer above 50 nm can be considered as pure ferromagnetic gratings where magnetic contribution is dominant, while in the other samples the contribution of silver layer starts to play an important role in forming the magneto-optical response due to the increase of SPPs free mean path and extending the interaction of light with ferromagnetic material. The thickness parameters of functional layers of magnetoplasmonic crystals are listed in Table 1.

The surface profile and deposited layer thickness were examined by atomic force microscope (AFM) and scanning electron microscope (SEM), the magnetic properties were measured by vibrating sample magnetometer (VSM). Optical and magneto-optical properties were studied by a setup made up of the halogen lamp with a monochromator serving as a light source, Glan-Taylor prism as polarizer, a photomultiplier tube (model H10722-20 by Hamamatsu) with a lock-in amplifier as a detector accompanied by an optical chopper that controls the frequency of an optomechanical modulation or a system of electromagnets which allowed us to control the magnitudes of AC and DC magnetic field.

The setup schematics and the sample’s design were optimal to be measured in TMOKE geometry according two reasons: (i) the magnetic field was applied in-plane along the easy magnetization axis, and gave the highest ratio of the magnetic moment modulation in fields with magnitude below 50 Oe36; (ii) the useful signal (relative magnitude of intensity changes on photodetector) on in magneto-optic measuring schemes for TMOKE is commonly more in comparison with LMOKE. For maximisation of the TMOKE signal measurements were carried out in the p-polarized light with the incidence angle fixed to Θ = 68°35, frequencies of optomechanical and AC magnetic field, HAC, modulations were chosen to be 233 and 317 Hz, respectively. The illuminated spot sizes were 12 mm2 and 1 mm2. Figure 1 shows the schematic view of the sensing element, the spatial profile of magnetoplasmonic crystal obtained by AFM and the SEM cross-section imaging.

### Experimental demonstration

The TMOKE value is defined as δ = (R+H + RH)/R0, where R0 is the reflection amplitude without magnetic field, which was detected with optomechanical modulation of the incident light, R+H and RH denote the field dependent reflection amplitudes. Measurements of spectral dependencies of reflectivity and TMOKE were carried out in saturation AC magnetic field of 50 Oe. Reflection and TMOKE spectra for Sample 1 are shown in Fig. 1d.

The minimum of the specular reflectivity and the maximum of the TMOKE signal are clearly observed at the resonant wavelength of 618 nm and related to strong coupling of plasmon oscillations and the light diffracted into the -1st order23. The excited SPPs tightly localize the electric field of the incident electromagnetic wave at the Fe/Si3N4 interface that leads to efficient light-matter interaction and results into the resonant enhancement of TMOKE.

Figure 2a shows the set of minor hysteresis loops measured by VSM from the saturation magnetic field of Hsat = 50 Oe: the field magnitude was gradually decreased by a small step value of Hstep for measuring the hysteresis loop in magnetic field down to Hn = Hsat − n · Hstep, where n is a step number. By this way the sample was demagnetized and values of $$\Delta M({H}_{n})=M(\,+\,{H}_{n})-M(\,-\,{H}_{n})$$ were obtained (Fig. 3a, solid red curve). The ΔH value shown by dashed lines corresponds to the region of rapidly decreasing ΔM(H) and denotes the field region of hysteresis loop collapse.

The noise of the sensor prototype is measured at the resonant wavelength and saturation magnetic field as the time dependence of PMT voltage output for 500 points with 3 seconds per point. Then, the standard deviation $$\sigma =\sqrt{{({x}_{N}-\bar{x})}^{2}/(N-1)}$$, where N is a number of acquisition points, is used to calculate the signal-to-noise ratio $$SN{R}_{AC}=({R}_{+H}-{R}_{-H})/\sigma$$, where (R+H − RH) value were accumulated for 3 seconds at a given magnetic field and sensitivity ΔSNRH, where ΔSNR is the difference of maximum and minimum SNR values in selected ΔH range.

Figure 2b shows the dependences of the signal-to-noise ratio SNRAC on AC magnetic field for all samples. The SNRAC dependences have a step-like behaviour: in AC magnetic field with an amplitude of the saturation field, SNRAC has the maximum value and starts to decrease to zero with decrease of the magnetic field. The width of the step for the Sample 1 is ΔH = 2.8 Oe and shown by the dashed lines which corresponds the field region of hysteresis loop collapse shown in Fig. 2a.

The SNR(HDC) dependence was obtained by (i) setting of HAC value to the maximum of the derivative $$\partial SN{R}_{AC}/\partial {H}_{AC}$$ that allows one to get the point in the center of the observed slope of SNR(HAC) dependence and (ii) application of additional magnetic field HDC with the magnitude of ±0.18 Oe. This way SNR(HDC) was measured for all samples and compared with the relative changes of iron layer magnetic moment ΔM obtained by demagnetizing the sample using VSM. The shape of magneto-optical response dependence on magnetic field correlates with the relative changes in magnetic moment of iron layer which can be written as $$\delta =({R}_{+H}+{R}_{-H})/{R}_{0}\sim \Delta M={M}_{+H}-{M}_{-H}$$. Typical dependences of SNR(HAC), SNR(HDC) and ΔM(H) are presented in Fig. 3a.

SNRAC and SNRDC dependences show that the magneto-optical response depends on a sum of magnitudes of AC and DC magnetic fields affecting the magnetoplasmonic crystal in the direction perpendicular to the plane of light incidence and proportional to a magnetic moment of ferromagnetic layer. It is possible to use the SNRDC dependence as a calibration curve for estimating the reliable and precise correlation between the field dependent magneto-optical response and the external field magnitude.

Two functions are considered to reveal the dependence of magnetic field sensors sensitivity on the iron layer thickness in magnetoplasmonic crystals. The first one, δH, is shown in Fig. 3b and depends both on the maximum modulation of optical reflectance by magnetic field at the wavelengths corresponding to excitation of SPPs and on the width of the step in SNRAC dependence. The second dependence, Max(SNRAC), describes the dependence of SNRAC at saturation magnetic field on the thickness of the iron layer in magnetoplasmonic crystals. Variation of the iron layer thickness allows one to tune the sensitivity by changing optical and magnetic properties of magnetoplasmonic crystals. Magnetic moment and optical losses monotonously increase with the iron layer thickness, while the shape of the δH dependence is mostly determined by non-monotonic changes of the coercive force and ΔH value36. The shape of Max(SNRAC) strongly depends on the iron layer magnetization and monotonously increases with the growing iron layer thickness. The sensitivities of DC magnetic field sensor prototypes based on magnetoplasmonic crystals are estimated to be 3.7 · 10−6, 3.2 · 10−5, 3.4 · 10−5 and 3.8 · 10−5 Oe at a room temperature for iron layer thickness of 100, 50, 20 and 5 nm, respectively. Thus, it is shown that sensing capabilities are stronger correlated with the value of magnetic moment, than with the plasmonic properties and value of optical losses. The highest sensitivity is achieved for the sample with the iron layer thickness of 100 nm.

Further increase of the TMOKE value is achieved by optimizing the illuminated spot size. For Sample 1 the SNRAC value at saturation magnetic field is changed from 2.7 · 105 to 3.2 · 105 with decreasing the spot size from 12 mm2 to 1 mm2 due to the difference in magnetization processes: using a small region in the center of magnetoplasmonic crystal allows one to increase the steepness of the magnetization curve by neglecting the edge effects which lead to domain nucleation with opposite magnetization direction in lower magnetic field. With the decrease of the spot size the value of sensitivity changes from 3.7 · 10−6 to 3.1 · 10−6. The minimal optical spot size to use the magnetoplasmonic crystal as a magnetic field sensor is determined by the following parameters: diffraction limit, wavelength of SPPs excitation and fulfilling the diffraction conditions and is estimated to be as small as 5 μm2. The theoretical limit of sensitivity of 10−7 Oe is estimated as a sum of four noise sources, namely, of thermal $${i}_{th}=\sqrt{4kTR\Delta f}$$, flicker $${i}_{fl}=1/{f}^{\gamma }$$, shot $${i}_{sh}=\sqrt{(2{q}_{e}I\Delta f)}$$, and avalanche $${i}_{av}=\sqrt{(2{q}_{e}I/2\pi )}$$ noises and did not exceed the value of 6 · 10−9 that was by two orders smaller than the measured noise value. Table 2 compares the sensitivity and locality of various magnetic field sensors and reveals the advantages of the designed sensing element. The sensor based on magnetoplasmonic crystal as a probe provides high sensitivity at small spot size which makes it sufficient and promising for biomedical applications and allows one to scan the surface area without moving the probe element.

## Conclusions

Summarizing, here we demonstrate DC magnetic field sensors based on magnetoplasmonic crystals made of noble and ferromagnetic metals deposited on one-dimensional subwavelength grating utilizing TMOKE enhanced by excitation of SPPs. The correlation between magneto-optical and magnetic properties reveals the possibility to tune the sensitivity of the sensor by changing the ferromagnetic layer thickness. The sensitivity of the sensor prototype based on the magnetoplasmonic crystal was found to be 3 · 10−6 Oe with the spot size of 1 mm2 and can be further improved by optimizing the sensing element and the sensor’s setup overall design.