Magnetic Field Sensor Based on Magnetic Optical Surface Plasmon Resonance

Surface plasmon resonance with high sensitivity is widely used in molecular dynamics detection. Herein, a magneto‐optic surface plasmon resonance (MOSPR) sensor based on Au/Co/Au thin film for detecting magnetic fields is developed. The strong coupling between the magneto‐optical waveguide mode and the surface plasmon resonance mode is analyzed and the linear relationship between the reflectivity of the MOSPR sensor and the magnetic field is established. The response, response–recovery time, and dispersion relationship for different magnetic fields are also numerically simulated. Additionally, experimental data on the MOSPR sensor's response to magnetic fields at room temperature (25 °C) are obtained. During the experiment, a differential signal in the light path is applied to reduce the noise generated by the environment. The results demonstrate that the MOSPR sensor exhibits high response, ultrafast response time, and long‐term stability. The study provides a promising approach for detecting magnetic fields with high sensitivity and accuracy.


Introduction
Magnetic fields are a common physical phenomenon that constantly influences human health and well-being, playing vital roles in human life, such as magnetic storage, intelligent sensing, and biomedical.3][4][5] Therefore, developing a magnetic field sensor with high sensitivity, lower cost, miniaturization, and real time is urgently essential.
Surface plasmon resonance (SPR) is widely used for detection due to its sensitivity to the surrounding environment (10 À12 RIU), fast response time (femtosecond), and real time.SPR arises from the collective motion of electrons (plasma) at the noble metal-dielectric sensing medium interface when transverse magnetic polarization (TM) is incident on the material.[8] The rotation of polarization from magnetic fields was first proposed by M. Faraday (1845) and J. Kerr (1877). [9,10]he plane of polarization rotation in magnetic optical effect is derived from the difference of electric orbit between left and right circularly polarized light in the medium under a magnetic field.[13][14][15] Recently, the article reported that the Faraday magnetooptical effect is applied to detect magnetic fields.However, the high cost of the detection system and complex light path usually hinder practical application. [16]he optic fiber based on the SPR covered with magneto-fluid (a colloidal liquid consisting of magnetic solid particles, active agent, and medium) is sensitive to the temperature and magnetic field also, which realized two-parameter measurements simultaneously, although the magneto-fluid is unstable, restrained further development. [17]Previous reports on the detection of magnetic fields have suffered from issues such as sensitivity, response time, stability, and applicability.
In this work, we demonstrate the modulation of magnetic fields on the interaction between light and matter and prepare an Au/Co/Au magneto-optic surface plasmon resonance (MOSPR) sensor by electron beam vapor deposition.The magnetic optical surface plasmon resonance sensor based on Au/Co/Au films exhibits high sensitivity, fast response-recovery time, and better signal-to-noise (SNR) ratio toward the magnetic field in both simulation and experiment.Our work provides a promising approach for developing highly sensitive, low-cost, miniaturized, and real-time magnetic field sensors.

Experimental Section
The dielectric constant describes the polarization characteristics of a material to light (electromagnetic waves).Recent research has shown that magnetization can vary the distribution of domains and influence the dielectric constant.The elements in the dielectric constant tensor depend on magnetization, magnetization directions, and the free electron gas dielectric constant (as shown in Note S1, Supporting Information). [18]The magnetization directions parallel or perpendicular to the light propagation surface and material surface are polar, longitudinal, and transversal Kerr effects.In the transversal Kerr effect mode, the dielectric constant tensor becomes [19] ε Q is the Voigt constant and my is the magnetization of cobalt.The sensing properties of simulation and experiment will be discussed subsequently.

Theoretical Derivation
In the magnetic optical surface plasma resonance, the SPP wave vector k sp,x would become [20] where k 0 sp is the SPP wave vector without an applied magnetic field; the modulation term Δk sp represents the effect induced by the transverse Kerr magnetic optical effect because the diagonal part ε Co xy is not zero.Originating from Maxwell's equations, combined with boundary conditions and effective index constants, Δk sp has been described as follows (steps for solving in detail see Note S2, Supporting Information) Here, ε d , ε p , ε d , ε Co , and ε Co xy represent the dielectric constants element of gold, prism, water, and cobalt.The upper gold layer thickness and cobalt layer thickness is denoted by h and t Co , and k 0 is the wave vector of light in vacuum.We can conclude that only the magnetization is unknown.As a result, Δk sp and reflectivity depend linearly on magnetization, as per formula 3 and Fresnel reflective formula (see Note S3, Supporting Information).

Simulation
The commonly used experimental arrangement is the Kretschmann configuration, and the MOSPR simulation was studied by finite-difference time-domain (FDTD).
The prism, Au, Co, water, and the Kerr attributes are all contained within this simulation mode (Figure 1a).The periodic condition of this simulation mode along the x direction is a perfectly matched layer (PML), and along the y direction is Bloch.The Kerr attributes are the most general type of unitary transformation for achieving advanced material features.The three-dimensionality mode of the interaction between the Kerr magnetic optical effect and surface plasmon is shown in Figure 1b, allowing us to visualize the physical process.

Experiment
The MOSPR sensor was fabricated using the Kretschmann configuration (Figure 2).The sensor structure was constructed by electron beam vapor depositing an Au/Co/Au film on a BK7 (quartz) prism.The element distribution of the Au/Co/Au film was obtained by the transmission electron microscope equipped with energy-dispersive spectroscopy.There are Au and Co elements in the film.Moreover, the element distribution of the film in detail and a real-life picture of the sensor are shown in Note S4, Supporting Information.The MOSPR detection device was driven by naturally polarized light (633 nm), generated by a He-Ne laser (25-LHP-991-230, Melles Griat), and modulated by a half-wave piece.A telescope system was utilized to align the light from the helium-neon laser and extend the beam of light available to contribute to surface plasmon resonance and imaging in future work.A drop of water on the surface of the Au/Co/Au film was used as a medium to protect the system from environmental effects and enhance sensitivity.The Au/Co/Au thin film was magnetized by applying an external magnetic field produced by a U-shaped electromagnetic.The s-and p-polarized light was obtained by a polarization beam splitter (CCM5-PBS201/M, Thorlabs) and detected by a photoelectric balance detector (PDB210A/M, Thorlabs).The output voltage was shown on an oscilloscope (MSO56, Tektronix).A differential signal was employed in this system to minimize significant noise caused by  the environment and to ensure that the effective signal was considerably greater than the system noise.The entire system was operated at 25 °C, and the humidity of the environment was 65%.

Results and Discussion
[23] From Figure 3, it reveals that the dispersion curve of surface plasma waves will translate down linearly under 0, 0.3, 0.6, and 0.9 magnetization rates, and the dispersion curve of the light wave in the prism will intersect with the dispersion curve of the plasma wave in different magnetization rate.That indicates that magnetization and Co doping were the primary sources of wave vector modulation.
The sensor's response to the magnetic field was defined as R = ∂B ∂R , where ∂B is the partial differential magnetic field intensity and ∂R is the partial differential reflectivity.Millitesla (mT) and unit one are the magnetic field intensity and reflectivity units.
The consequence of magnetization from 0 to 1 on the resonance angle and reflectivity of different thickness Co layers is shown in Figure 4. We can conclude that the resonance angle of the different Au/Co/Au thin films is approximately 72.5-73°, and the resonance angle shift increases with the thickness of the Co layer in Au/Co/Au thin films with different magnetic fields.There is no noticeable resonance angle shift and reflectivity change in pure Au films because small magneto-optical constants of Au are insufficient to excite the magneto-optical effect (Figure 1a). [24,25]he response of the Au/Co/Au sensor toward the magnetic field with 0, 6, 9, and 12 nm Co layers was 0, 4219.29,[28][29][30] The ultrahigh response is attributed to the strong local electric field on the surface of the Au/Co/Au film  under the surface plasmon resonance (Figure 5). [31,32]The full width at half maxima (FWHM), a pivotal point to evaluate the sensing characteristic of the SPR sensor, of Au/Co/Au magnetic sensor with different thicknesses of Co layer (0, 6, 9, 12 nm) is 0, 8.8, 11.9, 12.4, and 12.6, respectively, which rises with the thickness of Co increase, due to the ohmic loss of Co.The Au/Co/Au sandwich structure, where the top and bottom Au layers are equivalent to a resonant cavity, can tremendously reduce Co's ohmic loss and improve sensitivity and quality factors.The optimal thickness of the bottom and top Au in Au/Co/Au thin films was also simulated by the FDTD, as shown in Note S5, the Supporting Information.
The electric field would reflect after the optical wave incident in the interface without SPR (Figure 5a).In contrast, the electric field distribution would be located on the interface surface with SPR (Figure 5b).This electric field change demonstrates that the electric field distribution would be located on the interface due to SPR.
In Figure 5c, the amplitude of the x-direction electrical field would be enhanced under magnetization because magnetization would alter the polarization state of matter and cause strong coupling between surface plasma and magnetic optical, as shown in formula 4.
As shown in Figure 6a, the pulse width of pure light and the light on the Au/Co/Au-water interface is 2528.04 and 2819.87 fs, respectively.The pulse width of light on the Au/Co/Au surface has an obvious broadening (291.83fs) compared with the pure optic wave due to surface plasma resonance.The broadening (291.83fs) is the response time of surface plasma resonance, demonstrating that the sensor based on the Au/Co/Au thin film possesses ultrafast response time and the capacity to detect rapidly alternating magnetic fields theoretically.
The index refraction resolution of the system based on the Au/ Co/Au system was defined as follows The SNR, S response , and I noise are the device's signal noise ratio, response, and electrical noise, respectively.In this sensor system, the electrical noise is mainly caused by the photonic detector (PDB210A/M, Thorlabs).From the product manual, the electrical noise of the PD is 6.6 Â 10 À4 V, which is larger than the vertical resolution of the oscilloscope (MSO56, Tektronix).When S response ¼ I noise , we consider that the change of refractive index is the refractive index resolution theoretically.The result is 4 Â 10 À8 RIU.That indicates that the sensor system based on Au/Co/Au film can be used to detect the weak magnetic field.
The sensor system is linear and time-invariant.The relationship between the input signal (RF input) and output signal (RF output) satisfies the formula 6. [33] RF input ⊗GðxÞ ¼ RF output (6)   We define G(x) as an impulse response, meaning the system's time response to the input signal.The impulse response result of the Au/Co/Au sensor system is shown in Figure 6b.The time of G(x) approaches 10 ns, which is larger than the consequence of simulation by FDTD (291.83 fs) due to restrictions of the photoelectric balance detector (bandwidth resolution 100 MHZ).
We have demonstrated the sensing properties and feasibility of the Au/Co/Au thin film sensor by simulation, and the optimum thickness of Au/Co/Au thin films for magnetic sensing is 19-6-13 nm.We fabricated the sensor and the detection system based on the parameters obtained and proceeded with further research experiments.
The MOSPR sensor's responses to a 23 mT magnetic field with three cycles are shown in Figure 7a.Due to environmental noise, the MOSPR sensor's baseline is around 0.04-0.06V.The output voltage increases to 0.1-0.13V under the 23 mT magnetic field.The slight perturbation of the output voltage results from some unevenness in the film, as demonstrated in the Note S4, Supporting Information.The MOSPR sensor's output voltage to 8, 16, 24, and 32 mT is 0.08, 0.118, 0.152, and 0.15 V, respectively (Figure 7b).The output voltage tends to stabilize when the magnetic field reaches 24 mT.According to the operating instructions and sensitivity defined in the Note S6, Supporting Information, we can calculate that the MOSPR sensor's response  In summary, the sensing behavior has been improved both in simulation and experiment, which can be attributed to the following reasons: first, the strong coupling between the surface plasmon and magnetic optical enhances the local electric field, improving the sensitivity of surface plasmon resonance.Second, higher magneto-optical constants of Co compared with Au enhance the sensitivity to magnetic fields.Finally, the differential signal reduces noise in the experiment and enhances the sensitivity. [34]

Conclusion
The magnetic optical surface plasmon resonance sensor based on Au/Co/Au thin films was simulated using FDTD and fabricated by electron beam vapor deposition.Unusually, the Au/Co/ Au sensor exhibits higher response, ultrafast response-recovery time, and long-term stability in both simulation and experiment.The excellent sensing properties are attributed to the strong coupling between magnetic optical and surface plasmon resonance, the higher magneto-optical constant of Co compared with precious metals (Au, Ag), the Au/Co/Au thin film structure, and the differential signal to reduce noise in the light path.This work indicates that the Au/Co/Au MOSPR sensor could be the best candidate for applications in detecting magnetic fields, and further expansion can realize multichannel magnetic field imaging.

Experiment Data
The dielectric constant in this article is described as

Figure 1 .
Figure 1.a) The simulated mode of the MOSPR sensor using FDTD.b) 3D mode of the interaction between the Kerr magnetic optical effect and surface plasmon.

Figure 2 .
Figure 2. Schematic optical path diagram for magneto-optical surface plasmon resonance.The laser is a helium-neon laser (633 nm); a pair of plano-convex lenses construct the telescope system; λ/2 WP is a half-wave piece; M1, M2, and M3 are mirrors; PBS is a polarizing beam splitter; PD is an optical balance detection amplifier.

Figure 4 .
Figure 4.The consequence of magnetization from 0 to 1 on resonance angle and reflectivity of different thickness Co layers in Au/Co/Au thin film was simulated by FDTD (the thickness of Co layer from (a) to (d) is 0, 6, 9, and 12 nm, respectively).

Figure 5 .
Figure 5.The electric field distribution simulated by FDTD.a) The distribution of local electric field without surface plasmon resonance.b) The distribution of local electric field with surface plasmon resonance.c) The distribution of local electric fields with different magnetic fields.
is 2837.5 mT reflectivity À1 , consistent with the simulation result in Figure4.The reflectivity of the Au/Co/Au sensor in a 10 MHz frequency alternating magnetic field from 23 to À23 mT is shown in Figure7c.The sensor's alternating period is around 100 ns, indicating its ability to detect ultrafast magnetic fields.The hysteresis loop was obtained by a vibrating-sample magnetometer, as shown in Figure7d.Notably, the easy magnetization of Au/Co/Au thin films ranges from À40 to 40 mT, consistent with the experimental result.

Figure 6 .
Figure 6.The response time of the Au/Co/Au sensor.a) The pulse width of pure light and light on the Au/Co/Au interface simulated by FDTD.b) The impulse response of the Au/Co/Au sensor from the signal system.

Figure 7 .
Figure 7.The experimental consequence of the MOSPR sensor to magnetic fields.a) Response of the MOSPR sensor to a 23 mT magnetic field intensity with three cycles.b) Response of the MOSPR sensor to 0, 8, 16, 24, and 32 mT magnetic fields, respectively.c) The reflectivity of the MOSPR sensor under a 5 mT magnetic field in a 10 MHz frequency.d) The hysteresis loop of Au/Co/Au thin films under room temperature (25 °C).