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## Creator

[Murali Krishnan Manikketh](https://orcid.org/0000-0002-6445-1121), [Prabhanjan D. Kulkarni](https://orcid.org/0000-0002-4605-5256), [Tomoya Nakatani](https://orcid.org/0000-0001-9590-216X), [Hirofumi Suto](https://orcid.org/0000-0003-4387-5862), [Yuya Sakuraba](https://orcid.org/0000-0003-4618-9550)

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Copyright 2024 Author(s). This article is distributed under a Creative Commons Attribution (CC BY) License.[Creative Commons BY Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0/)

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[Effects of layer thickness and annealing process on low-frequency noise and detectivity in tunnel magnetoresistive sensors with CoFeSiB soft magnetic layers](https://mdr.nims.go.jp/datasets/94e6fd89-a8dc-429c-a953-b1e4c3e00f82)

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Microsoft Word - TMR-resubmission_revision1-CLEAN.docx1  Effects of layer thickness and annealing process on low-frequency noise and detectivity in tunnel magnetoresistive sensors with CoFeSiB soft magnetic layers  Murali Krishnan Manikketh, Prabhanjan D. Kulkarni,* Tomoya Nakatani,** Hirofumi Suto, and Yuya Sakuraba  Research Center for Magnetic and Spintronic Materials, National Institute for Materials Science, 1-2-1, Sengen, Tsukuba, Ibaraki 305-0047, Japan,   * Present address: Centre for Sensors Vision Technology and IT, Central Manufacturing Technology Institute, Bengaluru, Karnataka, India. ** Corresponding author. Email: nakatani.tomoya@nims.go.jp  ABSTRACTWe investigated the effects of the CoFeSiB soft magnetic layer thickness and annealing process on the magnetic field sensing and low-frequency 1/f noise characteristics of tunnel magnetoresistive (TMR) sensors. A thicker CoFeSiB layer improved the soft magnetic properties of the free layer, and the process order of device fabrication and annealing significantly influenced the 1/f noise characteristics of the TMR sensors. A magnetic field detectivity of 0.8 nT/Hz0.5 at 10 Hz was achieved in a single device TMR sensor annealed after the device fabrication, which suppressed both electrical and magnetic 1/f noise compared to the annealing performed before device fabrication. The spectral density of the 1/f noise voltage scaled linearly with the sensitivity of the sensor; thus, the detectivity showed an approximately constant value regardless of the change in sensitivity.  2  I. INTRODUCTION Tunnel magnetoresistance (TMR) magnetic devices are promising for magnetic sensors in various fields owing to their high sensitivity, low power consumption, wide frequency response, small size, and room temperature operation advantages.1–6 In particular, the development of TMR magnetometers for detecting very small magnetic fields is attracting considerable research attention, with promising applications in biomagnetic field sensing and nondestructive testing.7–9 However, these applications require reduction of sensor noise at low frequencies, which is dominated by 1/f noise.10,11 Previous studies have shown that the 1/f noise in TMR and giant magnetoresistive (GMR) sensors can be classified into two types of origin.11–15 One is electrical 1/f noise, which is primarily due to lattice defects in the tunnel barrier. The other is magnetic 1/f noise, believed to be due to thermal fluctuations of the magnetization and magnetic domains. The magnetic field-equivalent noise level of magnetic sensors, often referred to as the detectivity (D), is defined as  𝐷 =  𝑆 /(𝑆 ∙ 𝑉 ),       (1) where 𝑆  is the spectral density of the noise voltage (unit: V/Hz0.5), S is the sensitivity of the sensor defined by ∙ , and Vb is the bias voltage applied to the sensor. The power spectral density (𝑆   in V2/Hz) of the 1/f noise in TMR devices is known to follow the empirical relationship of 𝑆 = 𝛼  , where 𝛼   is the Hooge’s noise parameter representing the magnitude of the 1/f noise of the material system and A is the area of the tunnel barrier.10 Therefore,  𝐷 =  √𝛼 /( 𝐴𝑓 ∙ 𝑆).      (2) Note that 𝛼  is correlated with S. Based on the fluctuation-dissipation theorem, 𝛼  is expected to be linearly proportional to S.12,13 From Eq. (2), an increase in S results in a decrease in D, 3  which is desirable for magnetic sensors. Although the scaling relationship of 𝛼 ∝ 𝑆 has been confirmed in experiments,11,15–18 another type of scaling of 𝛼 ∝ 𝑆  has also been observed.19–21 For 𝛼 ∝ 𝑆  , from Eq. (2), D is independent of S. Therefore, an increase in S does not decrease D. The 𝛼 -S scaling is thought to be governed by the magnetization process of the free layer (FL), the coherent magnetization rotation, or by the motion of magnetic domains.15 However, a systematic study of the 𝛼  -S dependence for highly sensitive TMR sensors is insufficient. Therefore, studying the 𝛼 -S scaling in TMR and other spintronic magnetic sensor devices22 is important from both practical and fundamental perspectives.   The soft magnetic properties of the FL are critical for magnetic sensors. The anisotropy field (Hk) of the FL determines S by MR/2Hk, where MR is the magnetoresistance ratio. The coercivity (Hc) of the FL often leads to noise and error in magnetic field sensing. Although the CoFeB/MgO/CoFeB magnetic tunnel junctions23,24 show large TMR ratios, the CoFeB FL does not exhibit sufficient soft magnetic properties for magnetic sensors because the amorphous CoFeB crystallizes to a bcc-CoFe with a relatively large Hc. Therefore, composite FL structures composed of a CoFeB layer and a soft magnetic layer have been widely used in TMR magnetic sensors. For example, NiFe/CoFeB and NiFe/Ru/CoFeB composite FLs have been developed.25,26 However, the TMR ratio with these FLs tends to be lower than that with the CoFeB FL without NiFe. This is because the fcc-NiFe layer with the 〈111〉-oriented out-of-plane texture tends to degrade the crystallization of CoFeB into bcc-CoFe with the highly 〈100〉-oriented out-of-plane texture.24 In subsequent studies, composite FLs with amorphous soft magnetic layers, such as CoFeSiB, CoFeBTa, and CoFeSiBTa, were developed with improved TMR ratios.27–29 These amorphous soft magnetic materials are stable at 300–400 °C,28–30 and the adjacent CoFeB layer does not receive a crystallization template effect from the amorphous soft magnetic layers.  4  To induce Hk in composite FLs and achieve magnetic sensor operation without an external bias magnetic field, the so-called two-step annealing process is often employed.26,31 This process induces a magnetic easy axis of the FL that is orthogonal to the pinning direction of the pinned layer and the reference layer (RL). The thickness of the soft magnetic layer of the FL and the annealing process are known to significantly influence the TMR ratio and the magnetic properties of the FLs;26–29,31,32 however, their effects on 1/f noise are not sufficiently understood, which is critical for developing TMR sensors with high sensitivity and low noise. In this study, we investigated the effects of the thickness of CoFeSiB soft magnetic layers27,33 and the two-step annealing conditions on the magnetic and noise properties of TMR sensors with a CoFeSiB/Ta/CoFeB composite FL. We found that the annealing temperature, and the device fabrication and annealing process order significantly affect the value of D. The difference in the 1/f noise properties of the TMR sensors with different CoFeSiB thicknesses and annealing conditions is discussed.  II. EXPERIMENTAL PROCEDURES The TMR sensor stacks with the following layer structure were deposited by magnetron sputtering: thermally oxidized Si substrate/bottom electrode/Ta (5)/Co70Fe5Si15B10 (tCFSB)/Ta (0.3)/Co40Fe40B20 (3)/MgO (1.8)/ Co40Fe40B20 (2.5)/Ta (0.3)/ Co40Fe40B20 (0.5)/ Co50Fe50 (1)/Ru (0.8)/ Co50Fe50 (3)/ Ir20Mn80 (8)/Ru (8) (thickness in nm and alloy composition in at. %), as shown in Fig. 1(a). The bottom electrode comprised a Ta (5)/Cu (100)/Ta (10)/Ru (10) structure, and the surface of the Ta (10) layer was planarized via chemical mechanical polishing. Devices with four different CoFeSiB FL thicknesses [tCFSB(nm) = 10, 20, 40, and 80] were fabricated. The films were patterned using optical lithography and Ar ion milling. MTJ pillars with 60-µm diameters were milled down to the surface of the FL. The FL was patterned to a rectangular shape of 440×180 µm. 5  As shown in Fig. 1(b), we performed a two-step annealing process either before or after device fabrication process. This paper refers to the annealing process performed before device fabrication as pre-fabrication annealing and that performed after device fabrication as post-fabrication annealing. In both cases, the first annealing was performed at T1 = 350 °C for 1 h under an external magnetic field of 0.7 T in the +x direction. A subsequent second annealing was performed for 1 h at T2 = 180−250 °C under 0.7 T in the +y direction. T2 for the pre- and post-fabrication annealing are referred to as 𝑇  and 𝑇 , respectively. The first annealing induces uniaxial magnetic anisotropy along the FL in the x-axis, and the second annealing pins the magnetization of the CoFe pinned layer next to the IrMn antiferromagnetic layer in the +y direction. The magnetization of the RL is pinned in the −y direction owing to the antiferromagnetic interlayer exchange coupling through the Ru (0.8 nm) layer. Consequently, the FL magnetization is stabilized in the direction orthogonal to that of the RL, technically termed as crossed anisotropy, and the TMR device obtains a sensitivity axis on the y-axis. The R-H curves and noise characteristics of the TMR devices were measured in a triple-walled permalloy magnetic shielding box using the DC four-probe technique. An external magnetic field (H) was applied along the magnetic hard axis of the FL (y-axis). Figure 2 shows the circuit diagram for the noise measurement. Bias voltage (Vb) was applied to a TMR device using a 1.5 V dry cell. By adjusting the resistance of the ballast resistor (potentiometer), the bias voltage across the TMR device was set to Vb0 = 30 mV at H = 0. This supplies an approximately constant bias current to the device. When H is applied, the device resistance, R, changes; therefore, Vb follows 𝑉 = 𝑅(𝐻)/𝑅 ∙ 𝑉 . The noise across the TMR device was amplified to 40 dB using a low-noise preamplifier (NF Corporation, SA-200F3) and recorded using a 24-bit digitizer (NI, PCI-4461). 6    FIG. 1. Schematics of (a) layer structure, (b) annealing process, and (c) top view of the TMR device and the magnetization easy axis of the reference layer (RL) and free layer (FL).   FIG. 2. Circuit diagram for the noise measurement.  III. RESULTS A. Second annealing temperature dependence First, we investigated the effect of the second annealing temperature of the pre-fabrication annealing process ( 𝑇  ) for the devices with tCFSB = 20 nm. Figure 3(a) shows the magnetization–magnetic field (M–H) curves of the unpatterned TMR films annealed at different 𝑇 . The plateau of the M–H curve observed between μ0H = 0 mT and ~40 mT for 𝑇  = 180–Ballast resistor(potentiometer)1.5 Vdry cellTMRdevice24-bitdigitizerPre-amp.40 dBV7  250 °C corresponds to the antiparallel (AP) magnetization state between the FL and RL. The kink in the M–H curve at μ0H ~40 mT indicates the effective pinning field for the RL. The film for 𝑇  = 150 °C did not show a clear AP magnetization state, indicating insufficient exchange bias pinning for the RL. Figure 3(b) shows the TMR (ΔR/Rmin) curves of the devices. The resistance–magnetic field (R–H) curves are shown in Fig. S1 in the supplementary material. The resistance-area product values in the P-state (RAP) were in the 25–120 kΩ µm2 range depending on 𝑇  with a trend of increased RAP at 𝑇  ≥ 225 °C. For 𝑇  = 150 °C, the TMR ratio was only ~88% owing to insufficient pinning, which was also evident from the increase in R as H became more negative, indicating RL magnetization rotation. The TMR ratios were >160% for 𝑇  ≥ 180 °C, indicating that 𝑇  ≥180 °C was required to obtain a sufficient pinning of the RL and a high TMR ratio. The TMR curves in Fig. 3(b) show a gradual change in the resistance between the parallel (P) and AP magnetization states because of the crossed anisotropy induced by the two-step annealing process. The anisotropy field (Hk) of the FL was defined as (H95%–H5%)/2, where H95% and H5% are the magnetic fields at which ΔR/Rmin reached the 95% and 5% of the maximum value, respectively. Hk exhibited systematic decrease as 𝑇  increased, as shown in Fig. 3(c). This leads to an increase in the magnetic field sensitivity (S) of the TMR sensor at higher 𝑇 . However, the devices with 𝑇  = 225 and 250 °C showed large hysteresis. Similar behaviors of decreasing Hk and increasing hysteresis with increased T2 were also observed for CoFeBTa/Ta/CoFeB composite FLs, and their origins were explained by additional magnetic anisotropy in the FL induced by the second annealing process.28  Figures 3(d) and (e) show the noise spectra of the TMR devices in the P magnetization state (μ0H = −3 mT) and the intermediate magnetization state with the highest S (e.g., at μ0H = 1.0 and 0.6 mT for 𝑇   = 180 and 250 °C, respectively). Because these devices exhibited magnetic hysteresis, we first saturated the magnetization configuration in the AP state and 8  reduced H to achieve the intermediate state. In both the P and intermediate states, all the devices exhibited 1/f noise spectra, which is typical for TMR devices. However, the magnitude of the 1/f noise in the intermediate magnetization state was much larger than that in the P state owing to the 1/f noise with magnetic origin. This resulted in a significant increase in the corner frequency of the 1/f noise, defined as the frequency at which the 1/f noise spectral density becomes equal to the thermal white noise, from the order of 103 Hz in the P state to the order of 104 Hz in the intermediate state. Figure 3(f) shows the spectra of D in the intermediate state, showing comparable values of D at low frequencies for the devices annealed at 𝑇  = 180–250 °C.    FIG. 3. (a) M–H and (b) ΔR/Rmin–H curves of the TMR devices with tCFSB = 20 nm processed at different second pre-fabrication annealing temperatures (𝑇 ). (c) 𝑇 dependence of the anisotropy field (Hk) and sensitivity (S). (d) Noise spectra in the parallel magnetization state at μ0H = −3 mT.  Spectra of (e) noise and (f) detectivity in the intermediate magnetization states -200 -100 0 100 200-40-2002040m 0M t (T nm)m0H (mT)Tpre2  (°C) 150 180 200 225 250Effective pinning field-5.0 -2.5 0.0 2.5 5.0050100150200Tpre2  (°C) 150 180 200 225 250DR/Rmin (%)m0H (mT)(a) (b) (c)100 101 102 103 104 10510-910-810-7P-state (m0H = -3 mT)f (Hz)(d) (e)140 160 180 200 220 240 2600.51.01.52.0Tpre2  (°C)Hk (mT)20406080100120S (%/mT)100 101 102 103 104 10510-910-810-710-6f (Hz)(f)Intermediate state100 101 102 103 104 10510-1010-910-8D (T/Hz0.5)f (Hz)Tpre2  (°C) 150 180 200 225 250Vb (mV)R (Ω)T2pre(°C)37.722.615043.219.018046.016.720042.846.122542.867.5250Vb (mV)R (Ω)T2pre(°C)31.018.615025.711.318024.28.7820023.925.722526.942.4250µ 0Hk(mT)9  with the highest S. For (d)–(f), the roll-off below 5 Hz was caused by the cutoff of the AC input of the analyzer, and the peaks observed above 10 kHz were caused by external noise.   B. CoFeSiB thickness dependence  Next, the dependence of the sensitivity, noise, and detectivity on tCFSB was investigated. For the devices with tCFSB = 20 nm, 𝑇  = 180 °C provided sufficient pinning, a high TMR ratio of 160%, a small coercivity, and the lowest noise, as shown in Fig. 3. Thus, we used 𝑇  = 180 °C for the tCFSB dependence study. The device with tCFSB = 10 nm showed RAP = 78.6 kΩ µm2, and those with tCFSB = 20–80 nm showed similar values of RAP of ~35 kΩ µm2 (see the supplementary material.). Figure 4(a) shows the TMR curves for tCFSB = 10–80 nm. The TMR ratio for tCFSB = 10 nm (134%) was significantly lower than those for tCFSB = 20–80 nm (~155%). In addition, the magnetic hysteresis for tCFSB = 10 nm was much larger than those for the other values of tCFSB. The device with tCFSB = 80 nm exhibited the best soft magnetic properties in terms of small hysteresis and Hk, resulting in the highest S of 93.4 %/mT as shown in Fig. 4(b). The improvements in the soft magnetic properties and S for thicker FLs are consistent with previous reports on NiFe-based26,31 and CoFeSiB-based27 composite FLs.   Figure 4(c) shows the noise spectra of the TMR devices with different tCFSB values under a constant bias magnetic field of +1 mT. The devices all showed similar 1/f noise levels despite the large variation of S; 𝑆  = 81.4 and 96.1 nV/Hz0.5 at 10 Hz, and S = 49.3 and 93.4 %/mT for tCFSB = 20 and 80 nm, respectively, as shown in Figs. 4(b) and 4(d). A minimum value of D at 10 Hz of 2.1 nT/Hz0.5 was obtained for tCFSB = 80 nm.   10   FIG. 4. (a) ΔR/Rmin–H curves of the devices with tCFSB = 20–80 nm and 𝑇  = 180 °C. (b) The tCFSB dependences of Hk and S. Noise voltage spectral densities in the (c) P-state and (d) intermediate state. Spectral densities of the (d) noise voltage and (e) detectivity in the intermediate states. The inset in (e) shows the tCFSB dependencies of the spectral densities of the voltage density and detectivity at f = 10 Hz.    C. Effect of post-fabrication annealing To discuss the effect of the process order of the device fabrication and annealing on the TMR and the noise properties, we compared the properties of the TMR devices for tCFSB = 80 nm with pre-fabrication annealing at 𝑇  = 180 and 225 °C and post-fabrication annealing at 𝑇  = 225 °C, as shown in Fig. 5(a). Compared to the device for 𝑇  = 180 °C, the device for 𝑇  = 225 °C showed a higher TMR ratio and a lower Hk, resulting in a maximum S of 164 %/mT, which is consistent with the results for tCFSB = 20 nm (Fig. 3(b)). However, unlike in the case of tCFSB = 20 nm, a higher 𝑇  did not significantly increase the hysteresis of the TMR curve for tCFSB = 80 nm because of the improved magnetic softness of the thicker CoFeSiB film. The TMR ratio and S were further enhanced to 209% and 168 %/mT, respectively, by post--5.0 -2.5 0.0 2.5 5.004080120160DR/Rmin (%)m0H (mT)tCFSB (nm) 10 20 40 80(a)100 101 102 103 104 10510-910-810-710-6f (Hz)Intermediate state, m0H = 1 mT (d)0 10 20 30 40 50 60 70 80 900.51.01.52.0tCFSB (nm)m 0Hk (mT)(b)406080100S (%/mT)100 101 102 103 104 10510-1110-1010-910-810-7D (T/Hz0.5)f (Hz)tCFSB (nm) 10  20  40  80 0 20 40 60 8080100120140tCFSB (nm)f = 10 Hz2468100 101 102 103 104 10510-910-810-710-6f (Hz)(c)(e)P-stateVb(mV)R (Ω)tCFSB(nm)40.843.31043.219.02051.124.84050.223.180Vb(mV)R (Ω)tCFSB(nm)26.227.81025.711.32025.412.34025.011.58011  fabrication annealing at 𝑇  = 225 °C. The values of RAP were 32.5, 45.1, and 7.2 kΩ µm2 for 𝑇  = 180 and 225 °C and 𝑇  = 225 °C, respectively, (see the supplementary material). Figures 5(b) and (c) show the noise spectra of the devices in the P and intermediate magnetization states, respectively. In the P state, the device with 𝑇   = 225 °C showed a significantly reduced 1/f noise compared to those with 𝑇   = 180 and 225 °C. The corresponding 𝛼  values were 1.7×10-10 μm2 for 𝑇   = 225 °C, and 5.6×10-9 and 4.4×10-9 μm2 for 𝑇  = 180 and 225 °C, respectively. Because the 1/f noise observed in the P state is considered to be of purely electrical origin, the suppressed 1/f noise for 𝑇  = 225 °C may be due to reduced lattice defects in the MgO barrier or at the CoFeB/MgO interface. The post-fabrication annealing process may recover lattice defects, such as those induced during Ar ion milling. In the intermediate magnetization state, as shown in Fig. 5(c), the device processed at 𝑇  = 225 °C showed a lower 1/f noise than the other devices. The corresponding 𝛼  values for 𝑇   = 225 °C, 𝑇   = 180 and 225 °C, were 3.5×10-8, 1.7×10-7, and 1.1×10-7 μm2, respectively. Figure 5(d) shows the magnetic field dependence of 𝛼  of these devices. The device for 𝑇  = 225 °C showed a lower 𝛼  compared to the other devices in the P state and in the intermediate magnetization state. The variations in the magnetic 1/f noise of these three devices are discussed in Sec. IV. Figure 5(e) shows the magnetic field dependence of D at f = 10 Hz. D was calculated with the values of 𝑆 , S from the TMR curve, and Vb at each value of H. Interestingly, in the intermediate magnetization state (−0.6 mT ≤ H ≤ +0.8 mT), where the devices exhibited non-zero S, D showed an approximately constant value for each device: D = 2.6±0.5, 1.7±0.5, and 0.8±0.2 nT/Hz0.5 at f = 10 Hz for 𝑇  = 180 and 225 °C, and 𝑇  = 225 °C, respectively.  12  We plotted the noise voltage density 𝑆 , for sensitivity in terms of  in Fig. 5(f) to understand this behavior. The reason for plotting 𝑆  versus  instead of the commonly used sensitivity defined by 𝑆 = ∙   is as follows. As mentioned in II. EXPERIMENTAL PROCEDURES, Vb is H-dependent in our noise measurement, following 𝑉 = 𝑅(𝐻)/𝑅 ∙𝑉  . Therefore, from Eq. (1), 𝐷 = 𝑆 /( ∙ ) , indicating that the 𝑆  –   relationship determines the H-dependence of D. As shown in Fig. 5(f), 𝑆   scales linearly with  , therefore, D showed approximately constant values in the intermediate magnetization state, despite the change in sensitivity. Note that such a linear scaling relationship between 𝑆  and  or S has been observed experimentally in TMR devices.19–21   FIG. 5. (a) ΔR/Rmin–H curves and noise voltage ( 𝑆 ) spectra in (b) the P state and (c) the intermediate magnetization state of the devices with different T2 conditions. The inset in (c)  shows the detectivity spectra in the intermediate state. Magnetic field dependence of (d) Hooge’s noise parameter (𝛼 ) and (e) D at f = 10 Hz. (f) Dependence of 𝑆  at f = 10 Hz on 100 101 102 103 104 10510-1010-910-810-710-6f (Hz)100 101 102 103 104 10510-910-810-7f (Hz)(b) (c)(d) (e)-3 -2 -1 0 1 2 30.010.1110a H (´10-8mm2)m0H (mT)T2 (°C) 180 (pre) 225 (pre) 225 (post)-3 -2 -1 0 1 2 3100101102103104D (nT/Hz0.5 )m0H (mT)T2 (°C) 180 (pre) 225 (pre) 225 (post)IntermediatestateP-state100 10110-910-810-7dR/dH (W/mT)T2 (°C) 180 (pre) 225 (pre) 225 (post)(f)100 101 102 103 104 10510-1110-1010-910-8D (T/Hz0.5)f (Hz)Vb(mV)R (Ω)T2 (°C)50.223.1180 (pre)43.828.3225 (pre)54.95.6225 (post)Vb(mV)R (Ω)T2 (°C)25.011.5180 (pre)24.615.9225 (pre)24.82.5225 (post)-3 -2 -1 0 1 2 3050100150200250T2 (°C) 180 (pre) 225 (pre) 225 (post)m0H (mT)DR/Rmin (%)(a)13  . The dashed lines show 𝑆 = 𝑎 , where a is a constant and n = 0.5 and 1.  tCFSB = 80 nm for all devices   Table 1 summarizes the properties of the present and previously reported TMR sensor devices with different FL materials. Because 𝑆  and D are inversely proportional to √𝐴 (Eq. (2)), αH and √𝐴 ∙ 𝐷 are the appropriate parameters to compare the magnitude of 1/f noise and D, respectively, of the TMR devices with different A. Compared with the TMR device with the amorphous CoFeBTa-based FL,28 the present device with the CoFeSiB-based FL exhibited improved S and comparable αH, resulting in a smaller √𝐴 ∙ 𝐷. Using a 150-nm-thick CoFeSiB-based FL, Oogane et al.8 reported D ~0.03 nT/Hz0.5 at 10 Hz for a TMR sensor comprising 74 MTJs connected in series. The corresponding √𝐴 ∙ 𝐷 of 13 µm∙nT/Hz0.5 is the lowest value ever reported. They achieved D < 0.3 pT/Hz0.5 at 10 Hz using magnetic flux concentrators.  Table 1. Comparison of the properties of the reported and present TMR sensor devices with NiFe, CoFeBTa, and CoFeSiB soft magnetic layers.  Ref 34 Ref 28 Ref 8 Ref 33 Present study  FL material NiFe CoFeBTa CoFeSiB T2 (°C) 300 200 225 250 225 FL thickness (nm) 70 20 140 30 80 Device structure single device single device 74 MTJs array single device single device MTJ area, A (µm2) 3,200 1,962 185,000 300 2,826 TMR ratio (%) 140 155 >200 200 209 Hk (mT) 0.3 1.2 0.1 1.63 1.1 S (%/mT) 250 70 1150 n/a 168 14  single MTJ 𝑆  at 10 Hz (V/Hz0.5) n/a 4.6×10-8 n/a 4.3×10-8 5.1×10-8 αH (µm2) 3.3×10-7 P-state 4×10-8 1.2×10-9 P-state 4×10-9 3.5×10-8  D at 10 Hz (nT/Hz0.5) n/a 2.2 ~0.03 4.5 0.8 √𝐴 ∙ 𝐷  (µm∙nT/Hz0.5) n/a 97 ~13 78 43   IV. DISCUSSION This section discusses the variations in the magnetic 1/f noise in the three devices with tCFSB = 80 nm and the different annealing processes described in Sec. III. C. As shown in Figs. 5(b) and (d), the device with 𝑇  = 225 °C exhibited significantly reduced electrical 1/f noise in the P state compared with the other devices processed with pre-fabrication annealing. In the intermediate magnetization state with high S, all devices exhibited a higher 1/f noise than those in the P state. However, the device with 𝑇  = 225 °C again showed a lower 1/f noise than the other devices. Electrical and magnetic 1/f noises are generally assumed to be independent,14 and the power spectrum of 1/f noise is expressed as the sum of those of the electrical and magnetic 1/f noise: 𝑆 = 𝑆 + 𝑆  . Similarly, 𝛼 = 𝛼 + 𝛼  . Figure 6(a) shows the 𝑆  spectra of the devices obtained by subtracting 𝑆  measured in the P state (Fig. 5(b)) from 𝑆  in the intermediate state (Fig. 5(d)). The device with 𝑇  = 225 °C showed a lower 𝑆  spectrum. In the fluctuation-dissipation theorem, assuming a uniform FL magnetization in thermal equilibrium,13,15 the Hooge’s parameter of the magnetic 1/f noise, 𝛼 , is expressed as 𝛼 = 𝜀(𝑓, 𝐻) ,    (3) 15  where 𝜀(𝑓, 𝐻) is the phase lag of the resistance response to an AC magnetic field (𝜀(𝑓, 𝐻) ≡𝜒"  /𝜒 ), 𝜒"  and 𝜒  are the imaginary and real parts of the resistance susceptibility, respectively, 𝑘  is the Boltzmann constant, T is the temperature, 𝜇  is the vacuum permeability, Ms is the saturation magnetization, and ΔR = RAP−RP. Note that  is not the full TMR ratio (= ΔR/RP) but is ΔR divided by R at each sensor operating point.  is called the magnetoresistance-sensitivity product (MSP).  Figure 6(b) shows the αH vs. MSP of the three devices from the P state to the maximum MSP, showing nonlinear curves despite the linear dependence of 𝛼  on MSP by Eq. (3). For all types of devices, αH showed approximately constant values below the threshold values of MSP, e.g., MSP ~0.3, 0.7, and 0.8 mT−1 for 𝑇   = 180, 225 °C, and 𝑇   = 225 °C, respectively. Above the threshold values of MSP, αH increased significantly with increasing MSP. Figures 6(c) and (d) show the H dependence of MSP and αH of 𝑇  = 180 °C and 𝑇  = 225 °C devices, respectively. The R-H curves are shown in the insets. The shaded regions indicate the states showing a large increase in αH when MSP is increased. Both devices showed non-zero S and MSP at approximately H = 0, where the αH values were close to those in the P states. A rapid increase in αH was observed as S and MSP increased. The nonlinear αH−MSP curves of the present TMR devices suggest that the magnetic 1/f noise is not only due to the thermal fluctuation of uniform magnetization, which is expressed by Eq. (3). Note that the FL with uniaxial magnetic anisotropy is demagnetized with the multi-domain structure under zero H. Therefore, when an external H is applied to the hard axis, the FL is magnetized through a magnetic domain wall motion, and the magnetization is saturated at above Hk. Therefore, the large increase in αH in the high-S state may be related to the motion of magnetic domain walls and their pinning and depinning at defect sites, i.e., Barkhausen-type domain motion. 16  We also analyzed the H dependences of Hc in the R–H curves of the three devices with variations in the annealing condition, as shown in Fig. S2 in the supplementary materials. The largest 1/f noise was observed at µ0H ~1 mT for all the devices, where the values of Hc were relatively small. Therefore, we observed no clear correlation between Hc and the magnetic 1/f noise. In addition, we measured the phase lag for the devices with 𝑇  = 225 °C, and 𝑇  = 225 °C; however, we did not observe a clear difference in the phase lag values between these two devices.  These results demonstrate that post-fabrication annealing increases the TMR ratio and S and decreases both the electrical and magnetic 1/f noises, which is significantly beneficial for the development of TMR sensors with fine magnetic field resolutions. The increased TMR ratio and decreased electrical 1/f noise may be related to the recovery of lattice defects by post-fabrication annealing, such as those caused by the Ar ion milling during device fabrication. We also conducted experimental investigations to understand the relationship between reduced magnetic 1/f noise and improved soft magnetic properties obtained by post-fabrication annealing, such as the magnetic damping of the patterned FLs. However, no reasonable correlation has been observed. Therefore, further studies are required to understand the mechanism of the suppressed magnetic 1/f noise due to post-fabrication annealing.  Furthermore, to deepen the understanding of the mechanism that determines the scaling between noise spectral density and sensitivity (or MSP), investigations of the noise properties in TMR devices with different soft magnetic materials and/or different methods of the FL magnetization stabilization, such as by the soft-pinning by exchange bias18,25,35 and external magnetic field, are important.  17    FIG. 6. (a) Spectra of the magnetic 1/f noise at the highest S states for the devices annealed at 𝑇  = 180 and 225 °C, and 𝑇 = 225 °C. (b) αH vs. magnetoresistance-sensitivity product (MSP).  Magnetic field dependence of the αH and MSP of the devices annealed at (c) 𝑇  = 180 °C and (d) 𝑇 = 225 °C. The insets in (c) and (d) are the ΔR/Rmin–H curves of the devices.  V. CONCLUSIONS The TMR and 1/f noise characteristics of CoFeB/MgO/CoFeB-MTJ-based sensor devices using a composite FL with an amorphous CoFeSiB soft magnetic layer were investigated. A two-step annealing process at temperatures of T1 = 350 °C and T2 = 180–250 °C was employed to obtain a uniaxial magnetic anisotropy of FL and an R-H response with low coercivity. Consistent with previous studies, the soft magnetic properties of the CoFeSiB-based 1 10 100 1000 10000 10000010-1010-910-810-710-6T2 (°C) 180 (pre) 225 (pre) 225 (post)f (Hz)0.0 0.5 1.0 1.50.05.0x10-81.0x10-71.5x10-72.0x10-7a H (mm2)MSP (mT-1)T2 (°C) 180 (pre) 225 (pre) 225 (post)(a) (b)-3 -2 -1 0 1 2 30.00.51.0 MSP aHMSP (mT-1)m0H (mT)05101520a H (´10-8 mm2 )-3 -2 -1 0 1 2 30.00.51.01.52.0MSP (mT-1)m0H (mT)02468a H (´10-8 mm2 ) MSP aH-2 -1 0 1 2050100150DR/Rmin (%)m0H (mT)-2 -1 0 1 2050100150200DR/Rmin (%)m0H (mT)(c) (d)= 180 °CP state= 225 °C18  composite FL improved with thickness, and we obtained a high sensitivity of up to 168 %/mT (ΔR/Rmin = 209% and Hk = 1.1 mT) by using an 80-nm-thick CoFeSiB and optimizing the annealing condition. This sensor with an MTJ area of 2,826 µm2 achieved a magnetic field detectivity of D = 0.8 nT/Hz0.5 at f = 10 Hz, which is the lowest value ever reported for a single TMR device without magnetic flux concentrators. We found that the annealing process performed after device fabrication (post-fabrication annealing) significantly improved the TMR ratio and decreased both the electrical and magnetic 1/f noises, which is beneficial for the development of TMR sensors with ultra-fine D. However, the mechanism for 1/f noise reduction is an open question. In addition, the magnetic 1/f noise voltage density scales linearly with sensitivity. Therefore, D has an approximately constant value in the intermediate magnetization state, despite the sensitivity variation.  Acknowledgements  This work was partly supported by JSPS KAKENHI (Grant No. 24K00932).  Supplementary material See the supplementary material for additional data on the R-H curves, Hc, and resistance susceptibility including the phase lag.    Author Declarations The authors have no conflicts to disclose.  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