# Fileset

[Final version for MDR upload.pdf](https://mdr.nims.go.jp/filesets/94fcfb04-48e2-4bdb-84cb-63d18885776b/download)

## Creator

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

## Rights

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article
appeared in Tomoya Nakatani. Appl. Phys. 134, 213904 (2023) and
may be found at https://doi.org/10.1063/5.0180812[In Copyright](http://rightsstatements.org/vocab/InC/1.0/)

## Other metadata

[Improvement of magnetic field detectivity in electrical 1/f noise-dominated tunnel magnetoresistive sensors by AC magnetic field modulation technique](https://mdr.nims.go.jp/datasets/3b6fb13b-9c3d-41c8-9bff-c568ddb075ac)

## Fulltext

Microsoft Word - Final vesion for MDR.docx1  Improvement of magnetic field detectivity in electrical 1/f noise-dominated tunnel magnetoresistive sensors by AC magnetic field modulation technique  Tomoya Nakatani,* Hirofumi Suto, Prabhanjan D. Kulkarni, Hitoshi Iwasaki, and Yuya Sakuraba  Research Center for Magnetic and Spintronic Materials, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki, 305-0047, Japan *  Corresponding author: nakatani.tomoya@nims.go.jp  Abstract Suppression of 1/f noise in tunnel magnetoresistance (TMR) sensors is a central issue in the realization of magnetic field sensors with ultrafine magnetic field detectivity. Although AC modulation with an external magnetic field has been proposed as a method to shift the operating frequency of a sensor to a high frequency and substantially suppress 1/f noise, its effects on the two types of 1/f noise, that is, magnetic and electrical 1/f noise, are not well understood. In this study, we investigated the noise characteristics and signal detection performance of TMR sensors with an even-function resistance-magnetic field curve operated by the AC modulation method. For one TMR device in which the magnetic 1/f noise was dominant, AC modulation degraded the magnetic field detectivity owing to the additional noise induced by the AC modulation field. However, in another TMR device, in which the electrical 1/f noise was artificially enhanced by introducing lattice defects in the MgO tunnel barrier, AC modulation effectively suppressed the 1/f noise and improved the magnetic field detectivity by one order. 2  This demonstrates that the AC modulation method using an external magnetic field is effective for magnetic field sensors in which electrical 1/f noise is dominant.   I. Introduction Magnetoresistive (MR) sensors, such as giant magnetoresistance (GMR) and tunnel magnetoresistance (TMR) sensors, offer various magnetic field-sensing applications. One of the most challenging applications is the detection of ultra-small magnetic fields such as biomagnetic fields for magnetocardiogram and magnetoencephalogram, which are sub-pT-level AC magnetic fields at low frequencies (typically 0.1-100 Hz).1–5 For these applications, obtaining MR sensors with small magnetic field detectivities (D) is critical, where D is defined by 𝐷 = 𝑆 /  , where 𝑆   is the noise voltage density, and   is the output voltage sensitivity of the sensor. D indicates the magnetic field-equivalent noise level of the sensor. At low frequencies, the noise of the MR sensors is dominated by 1/f noise, which has both electrical and magnetic origins.6–8 The electrical 1/f noise originates from lattice defects, and the quality of the tunnel barrier greatly affects the electrical 1/f noise in TMR sensors.9,10 On the other hand, the magnetic 1/f noise is attributed to the thermal fluctuations of the magnetization and the magnetic domain wall.6,7,11,12 Reducing the 1/f noise in MR devices has been the central issue for magnetic sensors, and has been achieved in various ways; e.g., by selecting appropriate ferromagnetic materials,13–15 using an MgO tunnel barrier or optimizing its fabrication process,4,9,10,16 connecting many individual MR devices,17–19 chopping techniques,20,21 and AC modulation techniques.22–25  The typical AC modulation method using movable magnetic flux concentrators fabricated by microelectromechanical systems modulates the frequency of the signal field to 3  the sidebands of the carrier frequency of the AC modulation (fac), by which we can avoid the low-frequency regime where the 1/f noise is dominant. Therefore, we can effectively suppress the noise of the MR sensor.22,23 However, the major challenge in applying this AC modulation method is the large output signal of the AC modulation at fac, which makes it difficult to detect the weak magnetic fields whose signals appear in the sidebands of fac. Recently, another AC modulation method using an external AC magnetic field was proposed.26,27 This method uses GMR or TMR devices with symmetric changes in resistance (R) with respect to the sign of the magnetic field (H), that is, even-function R-H response curves. An AC modulation field with fac in the kHz range is applied along the sensing axis of the sensor. The output signal of a sensing field at a frequency of fsen is modulated to fac±fsen, whereas the output signal of the modulation field appears at 2fac due to the even-function R-H curve, thus the output signals of the sensing field and the modulation field are sufficiently separated in frequency. Therefore, this method is expected to improve (decrease) the D value of the MR sensors. Note that the improvement of D is due to the transfer of the output signal of the sensing field to a higher frequency, thus the 1/f noise is not intrinsically suppressed. However, from the user's point of view, the noise of the sensor appears to be effectively suppressed. Therefore, in this study, we often use the expression “suppression” for the effect of the AC modulation method on the 1/f noise. We recently reported that magnetic 1/f noise is also transferred by the AC modulation field; therefore, magnetic 1/f noise cannot be avoided by this method.28 This is because the virtual magnetic field that causes the thermal fluctuation of magnetization is indistinguishable from the actual magnetic field to be detected. This implies that the 1/f noise of electrical origin, which has no susceptibility to magnetic field, can be avoided (or effectively suppressed) by this AC modulation method; however, quantitative investigations have not been reported. Therefore, the main purpose of this study is to investigate whether the electrical 1/f noise at low frequencies 4  is avoided by the AC modulation using an external magnetic field. Using a TMR sensor device in which the electrical 1/f noise was artificially enhanced, we demonstrated that the electrical 1/f noise was avoided by the AC modulation method and that the magnetic field detectivity was improved.  II. Experimental procedures The TMR sensor devices used in this study are composed of the soft-pinned free layer (FL) structure, where the FL is weakly pinned unidirectionally.28–30 Figure 1(a) shows the structure of the TMR sensors used in this study. We sputter-deposited bottom electrode/Ta (2)/Ru (2)/IrMn (6)/CoFe (2)/AgSn spacer (2.8)/CoFe (1)/CoFeBTa (20)/Ta (0.3)/CoFeB (3)/MgO (2)/CoFeB (2.5)/Ta (0.3)/CoFeB (0.5)/CoFe (1)/Ru (0.8)/CoFe (3)/IrMn (8)/Ru (8) cap (thickness in nm). The nominal compositions of the alloy layers were Ir20Mn80, Co50Fe50, Ag90Sn10, Co38Fe38B19Ta5, and Co40Fe40B20 (at. %). The CoFe/CoFeBTa/Ta/CoFeB layers below the MgO barrier act as a soft-pinned FL whose pinning strength is adjusted by the ferromagnetic orange-peel coupling through the AgSn spacer.28 We fabricated two types of samples (devices A and B) with a difference in the magnitude of the electrical 1/f noise. For device B, we artificially introduced lattice defects into the MgO barrier by exposing it to Ar plasma before depositing the subsequent layers. On the other hand, device A as a control sample was fabricated without the Ar plasma exposure. The details of this process are described in the Supplementary materials. The TMR films were patterned into 40-μm diameter devices down to the MgO tunnel barrier, whereas the FL was patterned into a 400×180 μm rectangular shape. After completion of the microfabrication process, the devices were annealed at 350 °C for 1 h under a magnetic field of 0.5 T. As shown in Fig. 1(a), the magnetization directions of the reference layer and FL 5  point in opposite directions in the x direction at zero external magnetic field, and the device has a magnetic hard axis (HA) in the y direction, which is the sensing axis. The R-H curves of the TMR devices were measured using the four-terminal method with a constant bias current of 0.1-1.0 mA using a source measure unit. An AC modulation field was applied along the HA using a coil fabricated on a printed circuit board, on which the substrate of the TMR device was placed. The Joule heating of the coil limited the maximum amplitude of the AC field (Hac) to ~1 mTrms. Noise measurements were performed using the four-terminal method in a permalloy magnetic shield box, and the TMR devices were electrically biased using a dry cell and a ballast resistor. The bias voltage (Vb) was set to Vb0 = 40 mV at H = 0, where the sensor resistance (R) was maximized (Rmax). Because R changes with H, Vb follows Vb = R/Rmax·Vb0. Details of the sample properties, processes, and measurements are described in our previous publication.28  III. Results and discussion A. TMR properties Figures 1(b) and (c) show the R-H curves of the TMR sensors without (device A) and with (device B) Ar plasma exposure process to the MgO barrier, respectively. When H was applied in the easy axis (EA) in the x direction, device A showed a TMR ratio of 218% and a resistance-area product in the parallel magnetization state (RAP) of ~72 kΩ μm2. The shift of the R-Hx curve from H = 0 corresponds to the soft-pinning strength (Hsp) of the FL of 0.9 mT, and the soft-pinned FL showed an EA coercivity (𝐻 ) of 0.9 mT. For H in the HA, the R-Hy curve showed an even-function curve with negligible magnetic hysteresis. Device B showed similar Hsp of 1.2 mT and 𝐻  of 0.9 mT in the EA, but with a much lower TMR ratio of 71% (RAP ~9 kΩ μm2). Nevertheless, device B exhibits a non-hysteretic even-function R-Hy curve. Because both devices showed similar Hsp and 𝐻 , the Ar plasma was considered to introduce 6  lattice defects in the MgO barrier. The soft-pinned FL was practically intact, which was also suggested by the additional experimental observations described in the supplementary materials.    FIG. 1. (a) Schematic structure of the TMR devices with a soft-pinned FL. The bottom and top electrodes and the SiO2 insulating layer around the pillar are not shown. The arrows drawn on the ferromagnetic layers are their magnetization directions at H = 0. (b) and (c) show R-H curves of devices A (control sample) and B (MgO barrier exposed to Ar plasma), respectively, for EA and HA. (d) and (e) show HA and EA sensitivity (SHA and SEA) curves of device A and B, respectively.  Ru (2)Ta (2)IrMn (6)seed layerCoFe (2) pinned layerAgSn (2.8) spacer layerCoFeB (3)Ta (0.3)CoFeBTa (20)CoFe(1)soft-pinnedfree layerMgO (2) barrierreferencelayerCoFe (1)CoFeB (0.5)Ta (0.3)CoFeB(2.5)Ru (0.8)IrMn (8)Ru cap40 μm dia.easy axis (x)CoFe (3) pinned layer400 180 μm(a)-10 -5 0 5 1005101520 HA EASensitivity (%/mT)m0Hy (mT)-10 -5 0 5 1050100150200 EA HAR (W)m0H (mT)-10 -5 0 5 1068101214 EA HAR (W)m0H (mT)TMR = 218% TMR = 71%(b) device A (c) device B-10 -5 0 5 1001020304050 HA EASensitivity (%/mT) m0Hy (mT)(d) device A(e) device Bμ0Hsp = 0.9 mTμ0Hc = 0.9 mTμ0Hsp = 1.2 mTμ0Hc = 0.9 mT7  Figures 1(d) and (e) show the sensitivity curves of devices A and B, respectively. The HA sensitivity (SHA) is the numerical derivative of the R-Hy curve normalized by R, i.e., 𝑆 =∙  , which determines the output voltage (Vout) as 𝑉 = 𝑆 𝑉 𝐻  , where 𝐻   is the amplitude of an AC signal field. On the other hand, the EA sensitivity (SEA), which is not a derivative of the R-Hx curve, was measured by the change in the R-Hy curve under a small bias magnetic field in the EA (x direction). SEA gives the intensity of the noise caused by magnetization fluctuation, which was described in detail in our previous publication.28 For both samples, SHA and SEA showed maximum value at |μ0Hy| = 1.5 and 2.5 mT, respectively.  B. Noise properties We characterized the noise and signal field detection characteristics of devices A and B in two types of sensor operation modes. The first one was under a static bias field Hy, where the devices gained non-zero sensitivity (Figs. 1(d) and (e)). The other was under an AC modulation field at fac = 1−30 kHz applied to the HA; no static bias field was applied. We applied AC signal fields at 30 Hz with amplitudes of 31 nTrms and 93 nTrms to devices A and B, respectively. The choice of 30 Hz was arbitrary. The larger amplitude of the signal field for device B was because this device was too noisy to detect the 31 nTrms field. The signal-to-noise ratio (SNR) was defined as SNR = 20log ( 𝑆 / 𝑆 ), where 𝑆  and 𝑆  are the voltage densities ( 𝑆 ) of the signal and noise at 30 Hz, respectively.  (i) Device A fabricated without Ar plasma exposure to MgO barrier  Figure 2(a) shows the 𝑆   spectra of device A under the bias fields in HA (Hy). Because the SHA of this device was zero at Hy = 0, as shown in Fig. 1(d), the 𝑆  spectrum at 8  Hy = 0 exhibited only noise with a 1/f characteristic without a signal peak at 30 Hz. When Hy was applied, the device obtained a non-zero SHA, and the 31 nTrms signal field was detected, as indicated by the peaks at 30 Hz. Simultaneously, the intensity of the 1/f noise increased with increasing Hy owing to the contribution of the magnetic 1/f noise. The 𝑆  spectra were fitted by 𝑆 = 𝑆 + 𝛼 𝑉 𝐴 𝑓/, where 𝑆  is the power spectral density of the white noise, 𝛼  is the Hooge parameter of 1/f noise, A is the area of the MTJ, and β is the exponent of f. As shown in Fig. 2(b), 𝛼  increased with increasing Hy, except for the noisy spot at μ0Hy = 1.7 mT, which was characteristic of this particular device. The inset of Fig. 2(b) shows a linear dependence of 𝛼  on SEA, consistent with the fluctuation-dissipation relation for magnetic 1/f noise.6 However, the slope of the 𝛼  vs. SEA dependence changes at SEA ~ 10 %/mT, whose origin remains unclear. Figure 2(c) shows the Hy-dependencies of the signal and noise amplitudes at 30 Hz. The noise amplitude at 30 Hz was extrapolated from the values at 25-29 and 31-35 Hz, as shown in the inset of Fig. 2(a). The signal amplitude is saturated at μ0Hy ~1.5 mT, which is consistent with the saturation of the SHA at μ0Hy ~1.5 mT (Fig. 1(d)). Consequently, the SNR for the 31 nTrms signal field is saturated to ~17 dB at μ0Hy ~1.5 mT. From the relationship of SNR = 20 log (Sig/D), where Sig is the spectral density of the signal field (31 nT/Hz0.5 in this case) and D is the detectivity, the minimum D of device A at 30 Hz was 4.4 nT/Hz0.5, which is close to the value of D (4.0 nT/Hz0.5 at 30 Hz) calculated from the noise amplitude and SHA by the definition of 𝐷 = 𝑆 /(𝑆 ∙ 𝑉 ).   This device with an area A of 1256 μm2 showed a smaller D compared to the TMR device with a CoFeB (2)/Ta (0.21)/NiFe (4) FL with A =  2463 μm2 showing D = 8.6 nV/Hz0.5 (30 Hz).31 However, TMR devices with CoFeSiB-based FLs have been reported to show superior performance of D. Huang et al.14 reported D = 4.5 nT/Hz0.5 (10 Hz) using a single TMR sensor  device (A = 300 μm2) with a CoFe (3)/Ru (0.2)/CoFeSiB (30) FL. Oogane et al.4 9  reported D ~ 10 pT/Hz0.5 (30 Hz) using an array of 74 TMR devices (A of each device was 250 μm2) with a CoFeB (3)/Ru (0.4)/CoFeSiB (140) FL.  Thus, the application of the amorphous CoFeSiB soft magnetic layer may further reduce the D of our TMR sensors.   FIG. 2. (a) Voltage density spectra of device A under static bias magnetic fields in HA (Hy). The output signals of the 31 nTrms field are observed at 30 Hz (b) Hooge parameter (αH) vs. Hy. The inset shows a linear relationship between αH and SEA. (c) Dependences of the signal and noise at 30 Hz and signal-to-noise ratio (SNR) on Hy.   Next, the signal detection of device A using AC modulation (fac = 1−30 kHz) was tested. The even-function R-H curves of the TMR sensors can be approximated by quadratic functions for small 𝐻 . Therefore,  𝑅 = 𝑎𝐻 + 𝑅 ,       (1) where a (< 0) is a coefficient and 𝑅  is the maximum resistance of the sensor at Hy = 0. When an AC modulation field and an AC signal field, i.e., 𝐻 = 𝐻 sin 𝜔 𝑡 + 𝐻 sin 𝜔 𝑡, are applied, the voltage across the sensor is expressed as: 𝑉 = 𝐼 𝑅 = 𝐼 𝑎 − cos 2𝜔 𝑡 − 𝐻 𝐻 cos 𝜔 + 𝜔 𝑡 − cos 𝜔 − 𝜔 𝑡 −0.0 0.5 1.0 1.5 2.00.05.0x10-81.0x10-7a H (mm2 )m0Hy (mT)1 10 100 1000 1000010-910-810-7m0Hy (mT) 0.0 0.5 1.0 1.5 2.0f (Hz)25 30 3510-810-70.0 0.5 1.0 1.5 2.00100200300NoiseSignalm0Hy (mT)SNR05101520SNR (dB)(c) (b) (a) noise at 30 Hz0 10 20 30 400.05.0x10-81.0x10-7a H (mm2 )SEA (%/mT)μ0Hy = 1.5 mTf (Hz)30 Hz10  cos 2𝜔 𝑡 + 𝑉  ,      (2) where 𝐼   is the bias current, and 𝑉 = 𝐻 + 𝐻 + 𝐼 𝑅  . The second and third terms in Eq. (2) are the signal components in the sidebands of fac, which are re-written as 𝑉 = −𝑉𝑅∙𝑑𝑅𝑑𝐻12𝐻∙ 𝐻 𝐻 cos 𝜔 + 𝜔 𝑡 − cos 𝜔 − 𝜔 𝑡  = − ∙ 𝑆 (𝐻 ) ∙ 𝐻 cos 𝜔 + 𝜔 𝑡 − cos 𝜔 − 𝜔 𝑡 ,  (3) where we used the relations of 𝐼 =  , 𝑎 =   (from Eq. (1)), and 𝑆 (𝐻 ) =  . Therefore, the output voltage of the signal field is proportional to the product of 𝑆 (𝐻 ) and 𝐻 . Figure 3(a) shows the 𝑆  spectra for different Hac values at fac = 10 kHz. The 30 Hz signal field is modulated to (fac±30) Hz. As shown in Fig. 3(b), the signal amplitude at (fac±30) Hz increased with increasing Hac due to the increasing SHA in the range of Hy (Fig. 1(d)). As Hac increases, the noise level also increases with two types of characteristics, as reported previously.28 One is noise with a flat spectrum, as observed at f < fac shown in Fig. 3(a), which is attributed to random telegraph noise (RTN) caused by the creation and annihilation of small magnetic domains under an AC modulation field. The other is observed as a skirt-like spectrum in the sideband of the fac peak (see the inset of Fig. 3(a)), which is attributed to the transfer of magnetic 1/f noise to fac. Due to these types of additional noises, the noise level at (fac±30) Hz showed a linear increase with increasing Hac. Consequently, as shown in Fig. 3(c), the SNR was approximately constant at ~11 dB, much lower than the 17 dB measured under a bias Hy of ~1.5 mT. Therefore, D at 30 Hz under the AC modulation was 8.7 nT/Hz0.5, which was higher than the D of 4.4 nT/Hz0.5 under the bias Hy. Therefore, for the regular TMR devices, where the magnetic 1/f noise is dominant, the AC modulation by an external magnetic field degrades D. 11    FIG. 3. (a) Voltage density spectra of device A under AC modulation fields at fac = 10 kHz. The inset shows the spectra around fac. The peaks marked with an asterisk (*) indicate the modulated signals of the 30 Hz, 31 nTrms field and those marked with a dagger (†) are 50 Hz noise from the power line. The Hac-dependences of (b) the signal and noise at (fac±30) Hz, and (c) the SNR of the signal field.  (ii) Device B with artificially induced lattice defects in MgO barrier We performed the same tests for device B, in which the MgO barrier was exposed to Ar plasma. Figure 4(a) shows the 𝑆  spectra under static Hy, which exhibits 1/f noise up to 100 kHz. As shown in Fig. 4(b), αH of device B was ~5×10-6 μm2, two orders of magnitude larger than that of device A (Fig. 2(b)). Because the FLs of devices A and B have similar magnetic properties, that is, Hsp and 𝐻  , as shown in Figs. 1(b) and (c), respectively, the magnetic 1/f noises in these two devices are expected to be similar. Thus, the larger noise in device B is attributed to the electrical 1/f noise induced by the Ar plasma damage in the MgO barrier. This is also consistent with the observation that αH did not increase with increasing SEA (the inset of Fig. 4(b)). Although αH decreases with increasing Hy, the origin is unclear at present. This may be related to the decrease in device resistance with increasing Hy. As shown in Fig. 4(a), the 93 nTrms signal field was detected only for μ0Hy ≥ 0.8 mT, indicating D > 93 nT/Hz0.5 0.0 0.2 0.4 0.6 0.8 1.0 1.2051015fac (kHz) 1 5 10 20 30SNR (dB)m0Hac (mTrms)10 100 1000 1000010-910-810-710-610-510-410-3m0Hac (mTrms) 0.00 0.35 0.70 0.99f (Hz)fac2fac9900 10000 1010010-910-810-710-610-5fac* *† †0.0 0.2 0.4 0.6 0.8 1.0 1.2050100150Noise extrapolated to (fac±30) Hzfac (kHz) 1 5 10 20 30m0Hac (mTrms)Signal at (fac±30) Hz(b) (c) (a) 12  at 30 Hz for μ0Hy < 0.8 mT. Fig. 4(c) shows the Hy-dependence of the SNR for the 93 nTrms signal field. The maximum SNR was ~6 dB at μ0Hy ~ 1.5 mT; therefore, the minimum D was ~50 nT/Hz0.5 at 30 Hz, which was approximately ten times larger than that of device A. Figure 4(c) shows the values of D calculated by 𝐷 = 𝑆 /(𝑆 ∙ 𝑉 )  and similar values to those calculated from the SNR of the signal field.   FIG. 4. (a) Voltage density spectra of device B under static bias magnetic fields (Hy), and (b) the Hy-dependence of αH. The inset of (b) shows αH plotted for SEA. (c) The Hy-dependences of SNR for 30 Hz, 93 nT signal field, and D. (d) Voltage density spectra of device B under AC modulation field at fac = 10 kHz with various amplitudes (Hac). The peaks marked with an asterisk (*) and a dagger (†) in the inset figure are the modulated signal and 50 Hz noise, respectively. The Hac-dependences of (e) the signal and noise at (fac±30) Hz, and (f) the SNR of the signal field. The inset of (e) shows the noise voltage density at (fac±30) Hz on the logarithmic scale.  The results of the AC modulation experiments for device B are shown in Figs. 4(d)-(f). 1 10 100 1000 10000 10000010-910-810-710-6m0Hy (mT) 0.0 0.5 1.0 1.5 2.0f (Hz)(a) (c) 0.0 0.5 1.0 1.5 2.00246810SNR (dB)m0Hy (mT)050100150200Detectivity (D) calculated by SNR HA sensitivity and noiseD (nT/Hz0.5 )0.0 0.5 1.005101520fac (kHz) 1 5 10 20 30SNR (dB)m0Hac (mTrms)10 100 1000 10000 10000010-910-810-710-610-510-410-3m0Hac(mTrms) 0.00 0.32 0.64 0.90f (Hz)9900 10000 1010010-810-710-610-510-4fac2facfac† †* *(d) (f) 25 30 3510-710-6m0Hy (mT) 0.8 1.50.0 0.5 1.0 1.5 2.02.0x10-64.0x10-66.0x10-68.0x10-61.0x10-5a H (mm2 )m0Hy (mT)0 5 10 152.0x10-64.0x10-66.0x10-68.0x10-6a H (mm2 )SEA (%/mT)(b) 30 Hzf (Hz)0.0 0.5 1.0050100150200Noisefac (kHz) 1 5 10 20 30m0Hac (mTrms)Signal(e) 0.0 0.5 1.010-810-7Noise on log scale13  Compared to device A, the overall noise characteristics of device B did not significantly change when applying the AC modulation fields. This indicates that the electrical 1/f noise induced by the Ar plasma damage dominates the total noise of this device and that the RTN under the AC modulation field has a comparatively small contribution. The signal peaks were observed at (fac±30) Hz, as shown by the asterisks in the inset of Fig. 4(d), demonstrating that the AC magnetic field modulation technique can effectively reduce electrical 1/f noise by transferring the output signal to the sidebands of fac. Figures 4(e) and (f) show the Hac-dependences of the signal and noise amplitudes at (fac±30) Hz and SNR, respectively. The signal and noise amplitudes increased linearly with increasing Hac because SHA and SEA increased approximately linearly with increasing Hy in this range, as shown in Fig. 1(e). Compared to device A (Fig. 3(b)), device B showed a smaller increase in the noise amplitude with Hac. This is explained by both smaller SEA of device B (Figs. 1(d) and (e)) and smaller contribution of RTN in device B. For a given value of Hac, a higher fac decreases the noise amplitude at (fac±30) Hz, approximately following the 𝑆 ∝ 1/𝑓   relationship. Therefore, the SNR improved more significantly at higher fac values, as shown in Fig. 4(f). The maximum SNR for the 93 nTrms signal field within these measurements was 19.3 dB for μ0Hac = 0.7 mTrms; therefore, D = 10 nT/Hz0.5 at 30 Hz. Compared to the D value of ~ 100 nT/Hz0.5 obtained by applying a static bias field of μ0Hy = 0.7 mT (Fig. 4(b)), the AC modulation method reduced D by a factor of ten. Although in these experiments the fac and Hac were limited by the impedance and Joule heating of the coil to generate the AC modulation field, AC modulations with higher fac and larger Hac could further improve the SNR and D.  IV. Conclusions We have investigated the effects of AC magnetic field modulation on the electrical and 14  magnetic 1/f noise and magnetic field detection performance of TMR sensors with even-function R-H curves. In a regular TMR sensor, the low-frequency noise is dominated by the magnetic 1/f noise, for which no improvement in the magnetic field detectivity is obtained by the AC modulation method. This is due to the RTN and the transfer of the magnetic 1/f noise by the AC modulation field. However, in a TMR device in which the electrical 1/f noise is artificially enhanced by exposing the MgO barrier to Ar plasma, the electrical 1/f noise is effectively suppressed by transferring the output signal to high frequencies by the AC magnetic field modulation, which improves the magnetic field detectivity of the sensor. Since the noise in TMR devices with superparamagnetic FLs has been reported to be dominated by electrical 1/f noise,32–34 the superparamagnetic granular TMR devices with even-function R-H curves35 are worthy of further investigation in combination with the AC modulation method.   Supplementary material  Refer to the supplementary materials for the details of the Ar plasma exposure process and additional data on its effect on the TMR ratio and noise characteristics.  Acknowledgments This work was partly supported by JSPS KAKENHI (grant number 20K04588). We thank Satoshi Shirotori, Yoshihiro Higashi, and Akira Kikitsu (Toshiba Corporation R&D Center) for fruitful discussions.   Author Declarations The authors have no conflicts to disclose. 15  Data Availability Statement The data supporting the findings of this study are available from the corresponding author upon reasonable request.  References 1 M. Pannetier, C. Fermon, G. Le Goff, J. Simola, and E. Kerr, Science (80-. ). 304, 1648 (2004). 2 R.C. Chaves, P.P. Freitas, B. Ocker, and W. Maass, Appl. Phys. Lett. 91, 102504 (2007). 3 K. Fujiwara, M. Oogane, A. Kanno, M. Imada, J. Jono, T. Terauchi, T. Okuno, Y. Aritomi, M. Morikawa, M. Tsuchida, N. Nakasato, and Y. Ando, Appl. Phys. Express 11, 023001 (2018). 4 M. Oogane, K. Fujiwara, A. Kanno, T. Nakano, H. Wagatsuma, T. Arimoto, S. Mizukami, S. Kumagai, H. Matsuzaki, N. Nakasato, and Y. Ando, Appl. Phys. Express 14, 123002 (2021). 5 A. Kanno, N. Nakasato, M. Oogane, K. Fujiwara, T. Nakano, T. Arimoto, H. Matsuzaki, and Y. Ando, Sci. Rep. 12, 6106 (2022). 6 H.T. Hardner, M.B. Weissman, M.B. Salamon, and S.S.P. Parkin, Phys. Rev. B 48, 16156 (1993). 7 N. Smith, A.M. Zeltser, D.L. Yang, and P. V. Koeppe, IEEE Trans. Magn. 33, 3385 (1997). 8 W.F. Egelhoff, P.W.T. Pong, J. Unguris, R.D. McMichael, E.R. Nowak, A.S. Edelstein, J.E. Burnette, and G.A. Fischer, Sensors Actuators A Phys. 155, 217 (2009). 9 A. Gokce, E.R. Nowak, S.H. Yang, and S.S.P. Parkin, J. Appl. Phys. 99, 08A906 (2006). 10 A.F. Md Nor, T. Kato, S.J. Ahn, T. Daibou, K. Ono, M. Oogane, Y. Ando, and T. Miyazaki, J. Appl. Phys. 99, 08T306 (2006). 16  11 S. Ingvarsson, G. Xiao, S.S.P. Parkin, W.J. Gallagher, G. Grinstein, and R.H. Koch, Phys. Rev. Lett. 85, 3289 (2000). 12 A. Ozbay, A. Gokce, T. Flanagan, R.A. Stearrett, E.R. Nowak, and C. Nordman, Appl. Phys. Lett. 94, 202506 (2009). 13 D. Kato, M. Oogane, K. Fujiwara, T. Nishikawa, H. Naganuma, and Y. Ando, Appl. Phys. Express 6, 103004 (2013). 14 L. Huang, Z.H. Yuan, B.S. Tao, C.H. Wan, P. Guo, Q.T. Zhang, L. Yin, J.F. Feng, T. Nakano, H. Naganuma, H.F. Liu, Y. Yan, and X.F. Han, J. Appl. Phys. 122, 113903 (2017). 15 M. Rasly, T. Nakatani, J. Li, H. Sepehri-Amin, H. Sukegawa, and Y. Sakuraba, J. Phys. D. Appl. Phys. 54, 095002 (2021). 16 J. Scola, H. Polovy, C. Fermon, M. Pannetier-Lecœur, G. Feng, K. Fahy, and J.M.D. Coey, Appl. Phys. Lett. 90, 252501 (2007). 17 R. Guerrero, M. Pannetier-Lecoeur, C. Fermon, S. Cardoso, R. Ferreira, and P.P. Freitas, J. Appl. Phys. 105, 113922 (2009). 18 W. Zhang, Q. Hao, and G. Xiao, Phys. Rev. B 84, 094446 (2011). 19 K. Fujiwara, M. Oogane, T. Nishikawa, H. Naganuma, and Y. Ando, Jpn. J. Appl. Phys. 52, 04CM07 (2013). 20 A. Jander, C.A. Nordman, A. V. Pohm, and J.M. Anderson, J. Appl. Phys. 93, 8382 (2003). 21 V.-S. Luong, C.-H. Chang, J.-T. Jeng, C.-C. Lu, J.-H. Hsu, and C.-R. Chang, IEEE Trans. Magn. 50, 4005904 (2014). 22 A.S. Edelstein and G.A. Fischer, J. Appl. Phys. 91, 7795 (2002). 23 A.S. Edelstein, G.A. Fischer, M. Pedersen, E.R. Nowak, S.F. Cheng, and C.A. Nordman, J. Appl. Phys. 99, 08B317 (2006). 24 J. Hu, Q. Du, J. Zhang, M. Pan, K. Sun, H. Luo, X. Zhang, and Y. Yu, AIP Adv. 12, 17  025318 (2022). 25 W. Zhao, X. Tao, C. Ye, and Y. Tao, Sensors 22, 1021 (2022). 26 A. Bocheux, C. Cavoit, M. Mouchel, C. Ducruet, R. Fons, P. Sabon, I.L. Prejbeanu, and C. Baraduc, 2016 IEEE Sensors Appl. Symp. 1 (2016). 27 S. Shirotori, A. Kikitsu, Y. Higashi, Y. Kurosaki, and H. Iwasaki, IEEE Trans. Magn. 57, 4000305 (2021). 28 T. Nakatani, H. Suto, P.D. Kulkarni, H. Iwasaki, and Y. Sakuraba, Appl. Phys. Lett. 121, 192406 (2022). 29 R. Ferreira, E. Paz, P.P. Freitas, J. Wang, and S. Xue, IEEE Trans. Magn. 48, 3719 (2012). 30 J.Y. Chen, J.F. Feng, and J.M.D. Coey, Appl. Phys. Lett. 100, 142407 (2012). 31 J.P. Valadeiro, J. Amaral, D.C. Leitao, R. Ferreira, S.F. Cardoso, and P.J.P. Freitas, IEEE Trans. Magn. 51, 4400204 (2015). 32 P. Wisniowski, J.M. Almeida, and P.P. Freitas, IEEE Trans. Magn. 44, 2551 (2008). 33 K. Ishikawa, M. Oogane, K. Fujiwara, J. Jono, M. Tsuchida, and Y. Ando, Jpn. J. Appl. Phys. 55, 123001 (2016). 34 Y. Zhang, G. He, X. Zhang, and G. Xiao, Appl. Phys. Lett. 115, 022402 (2019). 35 N. Kobayashi, S. Ohnuma, S. Murakami, T. Masumoto, S. Mitani, and H. Fujimori, J. Magn. Magn. Mater. 188, 30 (1998).    18  Supplementary materials  1. Ar plasma damage in MgO tunnel barrier In the present work, we artificially induced lattice defects in the MgO tunnel barrier of the TMR device to manipulate the intensity of the electrical 1/f nose. This was achieved by exposing the MgO barrier (2 nm) to an Ar plasma. The Ar plasma was generated by an RF reserve-sputtering stage of our sputter deposition system. In the deposition system, there is a significant leakage of the RF power to the ground, thus the exact RF power density on the sample surface is not known. However, we have confirmed that the physical etching rate for MgO by the Ar plasma is negligibly small. From the following experimental observations, we consider that the Ar plasma exposure process creates lattice defects only in the surface of the MgO barrier and the property of the soft-pinned FL remains unchanged.  First, we compare the TMR characteristics of two devices, device B and C, which are prepared differently as shown in the flowchart of Fig. S1(a). Device B is the same as in this paper, where the MgO barrier (2 nm) was exposed to the Ar plasma for 30 s. Device C was fabricated similarly, but the Ar plasma exposure for 30 s was placed after the deposition of half of the MgO barrier, i.e., 1 nm, followed by another deposition of 1 nm of MgO. Both devices were annealed at 350 °C for 1 h under a magnetic field of 0.5 T after the device fabrication. Figures S1(b) and (c) show the distributions of RA in the parallel magnetization state vs. TMR ratio of the devices fabricated on the substrates of device B and C, respectively. Device B showed large distributions of RA and TMR ratio among the nominally identical devices, suggesting that the degree of damage caused by the Ar plasma exposure differed from device to device. The TMR ratio of device B was at most 100%, much lower than the TMR ratio of 218% for device A fabricated without Ar plasma exposure (see Fig. 1(b)). On the other hand, 19  device C showed an almost constant TMR ratio of 214%. For this device, the observed RA distribution was as usual for our deposition system, which was due to the non-uniformity of the MgO thickness. The inset of Fig. S1(c) shows the R-H curves of a 40-μm diameter device C, showing a soft-pinning field (Hsp) of 1.1 mT and a coercivity (Hc) of 0.9 mT, very close to those of devices A and B (see Figs. 1(b) and (c)).    FIG. S1. (a) Flowchart of the Ar plasma exposure process to the MgO barrier. (b) and (c) Distribution of RA in the parallel magnetization state (RAP) and TMR ratio of the individual devices with diameters of 20−60 μm of devices B and C, respectively.   Deposition up to CoFeB FLDeposition of MgO (2 nm) barrierDeposition of MgO (1 nm)Ar plasma exposure for 30 sDeposition of CoFeB reference layer and the rest of the layerDeposition of another MgO (1 nm)Device fabricationAnnealing at 350 °CR-H and noise measurementsDevice B Device C0 5 10 15050100Diameter (mm) 20 40 60TMR ratio (%)RAP (W mm2)0 5 10 15 20050100150200250Diameter (mm) 20 40 60TMR ratio (%)RAP (W mm2)(a)(b) Device B(c) Device C-10 -5 0 5 1010203040R (W)m0H (mT)EAHA20  Next, we compare the 1/f noise levels of the devices including device A. Figure S2(a) shows the noise spectra of these devices at Hy = 0, where the magnetizations of the soft-pinned FL and reference layer are in the antiparallel (AP) configuration. Sample B showed a very high 1/f noise level with a Hooge parameter of αH = 4.6×10−6 μm2, due to the electrical 1/f noise caused by the lattice defects induced by the Ar plasma. On the other hand, sample C showed much lower 1/f noise with αH = 1.6×10−8 μm2, comparable to that of sample A, αH = 1.8×10−8 μm2. Figure 2(b) shows the Hy-dependence of αH of devices A and C, both of which shows an increase in αH with increasing Hy. Thus, the 1/f noise of device C is dominated by the magnetic 1/f noise as well as device A. These results indicate that the Ar plasma damage induced in the lower half of the MgO barrier in sample C was healed by the deposition of another half of the MgO barrier, although the mechanism is not clear at present. Possibly, the lattice defects on the MgO surface caused by the Ar plasma, such as oxygen vacancies, are recovered by another MgO deposition. On the other hand, since device C showed a similar 1/f noise level as that of device A, the Ar plasma damage to the soft-pinned FL is considered to be negligible. Therefore, we believe that the Ar plasma exposure process to the MgO barrier induces lattice defects only on the MgO surface, which enhances the intensity of the electrical 1/f noise.  21    FIG. S2. (a) Noise spectra of devices A, B, and C at Hy = 0. The higher white noise level of device A than that of device C is due to the higher resistance of device A (RAP = 182.5 Ω) than that of device C (RAP = 37.6 Ω). (b) Dependence of the Hooge parameter (αH) on the bias field Hy for devices A and C. 1 10 100 1000 1000010-910-810-710-610-5Device A B Cf (Hz)0.0 0.5 1.0 1.5 2.00.05.0x10-81.0x10-7Device A Ca H (mm2 )m0Hy (mT)(a) (b)Hy = 0 (AP state)