# Low-Frequency Noise of Magnetic Sensors Based on the Anomalous Hall Effect in Fe–Pt Alloys

^{*}

## Abstract

**:**

_{x}Pt

_{100-x}system with various thin film thicknesses and Fe concentrations. The noise source consisted of 1/f and Johnson noise. A large current density increased the 1/f noise but not the Johnson noise. We found that the field detectability of the optimized Fe–Pt thin film offers much better low-frequency performance than a highly sensitive commercial semiconductor Hall sensor. Anomalous Hall effect sensors are, therefore, good candidates for magnetic sensing applications.

## 1. Introduction

_{x}Pt

_{100-x}thin-film alloys with various thicknesses and Fe atomic concentrations.

## 2. Materials and Methods

_{x}Pt

_{100-x}thin films using the high vacuum magnetron sputtering technique which is detailed in [10]. We patterned the films into Hall bars with a single step lift-off photo-lithography process. All measurements were performed at room temperature. We used the standard four-probe method to measure AHE resistivity under an out-of-plane magnetic field [11]. We measured the noise spectra from the Hall leads using the two-channel time cross-correlation method [17]. All noise measurement was performed over a broad frequency range from 1 Hz to 5 kHz. From the measured field sensitivity and noise spectrum, we calculated the field detectability (${S}_{T}$, in unit of ${T}^{2}/Hz$), defined as the noise spectral density (${S}_{V}$, in unit of ${V}^{2}/Hz$) divided by sensitivity, under a specific input (or measuring) current into the AHE sensor.

## 3. Results and Discussion

_{x}Pt

_{100-x}thin-film samples were found to be linear in the magnetic field up to the saturation fields (4πM

_{s}, where M

_{s}is the saturation magnetization). The results were presented in our previous work [3,10,11]. We also found that both intrinsic (Berry phase) mechanism and extrinsic side-jump mechanism contribute to the AHE, regardless of Fe concentration [10]. We first investigated the effect of Fe concentration x in the Fe

_{x}Pt

_{100-x}thin film. As shown in Figure 1a, x = 29 gives a much higher Hall slope than other Fe concentrations. As for thickness dependence, we obtained the highest Hall slope of $16.6\text{}\mu \Omega \xb7\mathrm{cm}/T$ in the 20 nm thick Fe

_{29}Pt

_{71}sample at room temperature. Correspondingly, the best field sensitivity reaches $23.6\text{}V/A\text{}T$, which is smaller than the field sensitivity of traditional semiconductor Hall sensors [14,16]. Another important parameter is the output resistance of our Hall sensor, which is the resistance between the two Hall leads. As discussed later, the output resistance defines the noise floor at high frequency. Additionally, low output resistance is required for radio-frequency application. Figure 1b shows output resistance for the Fe

_{29}Pt

_{71}samples with various thicknesses. The output resistance follows a power-law relationship as $R~{t}^{-1.1}$ (the exponent is close to 1, as would be expected).

_{29}Pt

_{71}thin-film sample under various input currents from 0 to 1.5 mA. At high frequency, the white Johnson noise dominates and shows no dependence on the input current. On the other hand, the low-frequency 1/f noise tends to increase as the input current rises above 0.1 mA. The knee frequency ${f}_{knee}$ can be defined as the crossover point between 1/f noise and white noise, where 1/f noise equals Johnson noise. Spectra of the field detectability are shown in Figure 2b. At high frequency, a larger input current leads to better detectability. The effect of input current becomes complicated at low frequency. At relatively small input current, a larger input current improves field detectability. At a large input current, low-frequency field detectability becomes almost independent of input current.

_{29}Pt

_{71}sample under a broad range of input currents (0.01 to 8.9 mA). As shown in Figure 3a, high-frequency noise is independent of input current, and its value can be well explained by Johnson noise. As long as the input current is not large enough to significantly heat up the thin film, high-frequency white noise is unchanged. Since high-frequency white noise is unchanged, we can use knee frequency to characterize low-frequency noise. Figure 3b shows ${f}_{knee}$ at different input currents for the 5 nm thick Fe

_{29}Pt

_{71}sample. When the input current is less than 1 mA, ${f}_{knee}$ is nearly constant. However, beyond 1 mA, ${f}_{knee}$ increases quadratically with input current. The transition point between low and high input current is defined as the critical current. Figure 3c shows the low-frequency noise at 10 Hz of the Fe

_{29}Pt

_{71}samples with different thicknesses below each sample’s critical current. 1/f noise is commonly believed to be the thermal fluctuation of discrete fluctuators. The noise power of 1/f noise is inversely proportional to the number of fluctuators. Therefore, the power-law relationship (${S}_{v}^{1/2}~{t}^{-0.5}$) is expected, assuming that the density of fluctuators has no dependence on film thickness. Figure 3d shows the relationship between critical current and sample cross-section area. As expected, a linear relationship is observed, and the slope gives a critical current density (J

_{c}) of $1.7\times {10}^{6}\text{}\mathrm{A}/{\mathrm{cm}}^{3}$. This number is an intrinsic value of the AHE sensor at a particular Fe concentration x. Deviation of the data from the fitting line is mainly due to uncertainty in determining the critical current. In addition, a small offset on the x-axis can be observed, which can be attributed to the surface dead layer effect [18]. The desired input current is slightly higher than the critical current. Thus, low-frequency detectability is optimized and power consumption of the AHE sensor is not too large.

_{x}Pt

_{100-x}samples at high and low frequencies. For the fixed sample thickness, the Fe

_{29}Pt

_{71}alloy has the largest Hall slope and the best detectability value. At both high and low frequencies, field detectability follows a power-law relationship with film thickness, with the exponent close to −0.5. The best detectability is achieved in the 30 nm thick Fe

_{29}Pt

_{71}sample ($50\text{}nT/\sqrt{Hz}$ at 1 kHz and $7\mu T/\sqrt{Hz}$ at 1 Hz).

## 4. Conclusions

_{x}Pt

_{100-x}thin-film alloys with variable thicknesses and Fe concentration x. In the Fe

_{x}Pt

_{100-x}system, the field detectability depends on sample thickness, Fe concentration x, Hall slope, and input (measuring) current density. Fe

_{29}Pt

_{71}thin films offer the best field detectability, that is, $50\text{}nT/\sqrt{Hz}$ at 1 kHz and $7\text{}\mu T/\sqrt{Hz}$ at 1 Hz. The Fe

_{29}Pt

_{71}AHE sensor outperforms a highly sensitive commercial Hall sensor in the frequency range of 31–500 Hz. The AHE sensor is metal based and can be easily fabricated. Its low-frequency magnetic sensing performance makes it a promising magnetic sensor candidate. Further optimization in AHE sensors may make AHE sensors rival the best semiconductor Hall sensors.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**(

**a**) Hall slopes versus film thickness and Fe concentration x. (

**b**) Output resistance of Fe

_{29}Pt

_{71}Hall-bar samples with various film thicknesses. The red dashed line is the linear fitting line in the log–log plot, which gives $R~{t}^{-1.1}$.

**Figure 2.**(

**a**) Noise spectra and (

**b**) field detectability spectra of the 4 nm thick Fe

_{29}Pt

_{71}thin-film sample under various input currents.

**Figure 3.**(

**a**) High-frequency noise of the 20 nm thick Fe

_{29}Pt

_{71}sample under various input currents. The red dashed line shows the theoretical prediction of Johnson noise $\sqrt{4{k}_{B}RT}$. (

**b**) Knee frequency of the Fe

_{29}Pt

_{71}sample under various input currents. Above critical current (~1 mA), knee frequency increases quadratically with input current. (

**c**) Low-frequency noise of the Fe

_{29}Pt

_{71}sample with different thicknesses. Input current is kept below critical current. The red dashed line shows the linear fitting in the log–log plot, which gives ${S}_{v}^{1/2}~{t}^{-0.5}$. (

**d**) Critical current of the Fe

_{29}Pt

_{71}sample with different cross-section areas (width of the Hall bar is 20 μm). The slope of the red dashed line gives the critical current density of $1.7\times {10}^{6}\text{}\mathrm{A}/{\mathrm{cm}}^{2}$.

**Figure 4.**Field detectability of different Fe

_{x}Pt

_{100-x}sensors at (

**a**) 1 Hz and (

**b**) 1 kHz. Both low-frequency and high-frequency detectabilities show the power-law relationship with film thickness, with the exponent close to −0.5.

**Figure 5.**Comparison of the (

**a**) voltage noise spectra and (

**b**) field detectability spectra between the 30 nm thick Fe

_{29}Pt

_{71}anomalous Hall effect (AHE) sensor and a commercial semiconductor Hall sensor.

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**MDPI and ACS Style**

Zhang, Y.; Hao, Q.; Xiao, G.
Low-Frequency Noise of Magnetic Sensors Based on the Anomalous Hall Effect in Fe–Pt Alloys. *Sensors* **2019**, *19*, 3537.
https://doi.org/10.3390/s19163537

**AMA Style**

Zhang Y, Hao Q, Xiao G.
Low-Frequency Noise of Magnetic Sensors Based on the Anomalous Hall Effect in Fe–Pt Alloys. *Sensors*. 2019; 19(16):3537.
https://doi.org/10.3390/s19163537

**Chicago/Turabian Style**

Zhang, Yiou, Qiang Hao, and Gang Xiao.
2019. "Low-Frequency Noise of Magnetic Sensors Based on the Anomalous Hall Effect in Fe–Pt Alloys" *Sensors* 19, no. 16: 3537.
https://doi.org/10.3390/s19163537