Evaluation of coplanar line type thin film magnetic field sensor with narrow slits

In recent years, magnetic field sensors have been applied to biological application and nondestructive testing. And numerous studies have been conducted all over the world to improve their sensitivity. Magnetic field sensors include the superconducting quantum interference device (SQUID)¹ and the optical pumping method.² The former requires the liquid nitrogen to cool the sensor head and it is costly because of the complicated maintenance. The latter requires a shielded room for high-sensitivity operation. Therefore, both methods have several objectives. On the other hand, the high-sensitivity magnetic field sensors working at the room temperature have been proposed such as MI,^3–6 GMI,⁷ fluxgate,⁸ and TMR⁹ sensors working in GHz bands. However, there are few discussions about the design method of the sensor element to improve the sensitivity in viewpoint of the impedance matching.

We have developed the sensor using the skin effect and the ferromagnetic resonance in the GHz band by employing the transmission line using a magnetic thin film. In addition, the multipoint measurement of cardiac magnetic fields without a magnetic shield have been succeeded.¹⁰ However, the signal-to-noise (SN) ratio of the sensor is poor in ferromagnetic resonance frequencies (several GHz band). To overcome the obstacle, we have fabricated a thin-film magnetic field sensor consisting of amorphous and dielectric thin-films and a linear coplanar line. Comparing the results of the calculation on finite element method (FEM) and experiment, we have indicated that the impedance mismatching causes the deteriorated SN ratio.¹² 

The most important challenge for the magnetic sensors is to have both the impedance matching and the high sensitivity. In this paper, we have proposed the constructure of the sensor element that can overcome the challenge. And we conducted the valuable discussion that the impedance matching was realized by employing the slit in the magnetic thin film. In the FEM analysis and the measurement, we explored the relationship between the slit width and the S parameters of the transmission coefficient (S₂₁) and the reflection coefficient (S₁₁). In addition, the characteristic impedance and the sensitivity of the sensors were considered. Then we finally confirmed the possibility that the sensitivity was improved by more than 10 times.

Figures 1 and 2 show the principal operation¹¹ and the cross-section view of the sensors. In the measurement of the magnetic field, the DC magnetic field is applied to the longitudinal direction of the sensor. The RF magnetic field is excited to the wide direction of the sensor by applying the high-frequency current on the signal line. The sensor can measure the incident magnetic field for the hard axis by changing the angle between the easy axis and the magnetization, and it can obtain the large change of the carrier signal by the skin effect and the ferromagnetic resonance.

The characteristic impedance of the sensor is very low because the capacitance is distributed between the magnetic thin film and the signal line such as C_mg and C_sm.¹² On the other hand, in the proposed structure, the characteristic impedance increased because of the decrease of C_mm, which is the capacitance distributing on the slit in the magnetic thin film. Therefore, the sensor will be improved by realizing the impedance matching to employ the slit of the appropriate width where the characteristic impedance is 50 Ω.

Figure 3 shows the calculation model of the coplanar thin-film magnetic field sensor in FEM analysis. The FEM simulation was performed by HFSS (ANSYS Electronics Desktop 2020R1). The analysis frequency was set to be 10 determined from the calculated impedance matrix by HFSS. Figure 4 shows the calculated capacitance and characteristic GHz, and the relative permittivity of the SrTiO and the relative permeablity of CoNbZr were set as the constant to be 20 + j0 and 100 + j0, respectively. The slit widths were changed until 50 μm. The narrowest slit width was 6 μm because of the technical limitation of our photolitho process. The capacitance and the characteristic impedance of the sensors were impedance of the sensors versus slit width. As the wide width, the characteristic impedance increased by decreasing the capacitance. And the characteristic impedance converged until 50 μm in the calculation. Figure 5 shows the comparison of the measured and calculated S₁₁ and S₂₁ versus slit width. The DC magnetic field and the frequency of the measured results are 0 Oe and 2.7 GHz. Decreasing S₁₁ and increasing S₂₁ by increasing the slit width indicated that the impedance matching was realized, and the tendency was the same in both results. The calculation results indicated that the impedance matching could be realized by employing the slit.

Figure 6 shows the fabricated coplanar thin-film magnetic field sensors. The sensors having 6.0, 10, 26, 36, 50 μm slits in the magnetic thin film were fabricated. The linear coplanar line was located above the CoNbZr thin film because the magnetic anisotropy of CoNbZr could be control in the low magnetic field and the anisotropic dispersion was small.^10,13

A linear coplanar line (length 19 mm, width 450 μm, gap 50 μm, thickness 1.4 μm) of Cu thin film was formed by a lift-off process on the SrTiO thin film (thickness 3.0 μm). The SrTiO film was deposited by heating the substrate to 140 °C, and a Cr film (0.2 μm thickness) was layered between the SrTiO and Cu films. The CoNbZr was annealed in a rotating magnetic field (350 °C, 2 hours) and in a static magnetic field (250 °C, 0.5 hours) to be the easy axis of the magnetization for the width direction of the sensor. The sensors were evaluated by measuring the S-parameters using a network analyzer (Advantest, R3767CG). In the measurement, S₁₁ and S₂₁ were measured when the DC magnetic field was applied to the wide direction of the coplanar by a Helmholtz coil and the strength was changed from 0 to 20 Oe.

Figure 7 shows the change of S₂₁ versus frequency. Where the change by the magnetic field is defined as the difference between the maximum and the minimum amplitudes of S₂₁. The change without slit was the largest. Those with slits peaked at around 2.7 GHz and it decreased since then. However actually, the signal strength was too low in the sensor without slit because of the impedance mismatching.

Figure 8 show the maximum S₂₁ amplitudes versus the largest changes of the amplitude by the magnetic fields, and each point deals with the frequency. It was improved by more than ten times for the sensors having the slits. The amplitude didn’t decrease rapidly in lower frequency by employing the slit. The change of the amplitude of S₂₁ was large as the narrow slit. Although the change of became small, the amplitude was large by spreading the slit width since the impedance matching was realized.

From the Eq. (1), the sensitivity of the sensor was evaluated by assuming it to be proportional as the product of the phase and the amplitude gradients of S₂₁ for the magnetic field and the carrier signal strength.¹⁴ This formula was given from the sideband strength of the AM modulated signal. The sensitivity was evaluated by assuming the carrier signal on the coplanar line as the AM modulation.

Where J is the carrier’s signal strength of the current, K is the constant defined as the whole resistance of the measurement setup, and ΔS₂₁/ΔH is the S₂₁ gradients as the magnetic field. The maximum gradients of the amplitude and the phase of S₂₁ as the magnetic field was determined by the measurement results on each slit width. And as shown in Fig. 9, the sensitivities of the sensors were evaluated by producing the maximum gradients and the amplitude of S₂₁. Where the amplitude is the same as the carrier signal strength and it was produced at the maximum gradient. Both the amplitude and the phase sensitivities peaked at around 10 μm because the whole capacitance with the 6 μm width was too large and that with over 10 μm width was too small for the ideal capacitance. Therefore, the appropriate slit width was around 10 μm.

In this paper, the coplanar thin-film magnetic field sensor with the slit in the magnetic thin film was proposed to improve the impedance matching and the effectiveness of the slit was investigated in both the calculation and the experiment. There is the trade-off relationship between the sensitivity of the sensor and the impedance matching. From the measurement results, the appropriate slit width was around 10 μm because the characteristic impedance seems to be the closest for 50 Ω then.

This work was supported in part by Adaptable and Seamless Technology Transfer Program (A-STEP) from Japan Science and Technology Agency (JST), Ministry of Internal Affairs and Communications, Japan, and WISE Program for AI Electronics by Tohoku University.

The authors have no conflicts to disclose.

Masaya Sakamoto: Data curation (equal); Writing – original draft (lead). Ryota Suzuki: Data curation (equal). Tomoya Ishihara: Formal analysis (lead); Methodology (equal). Junichi Honda: Data curation (equal); Validation (equal). Shin Yabukami: Conceptualization (equal); Methodology (equal); Project administration (lead); Supervision (lead); Writing – review & editing (lead).

The data that support the findings of this study are available from the corresponding author upon reasonable request.