# Fileset

[Supplementary_Murali-Krishnan.pdf](https://mdr.nims.go.jp/filesets/69cfe046-0fb5-4935-bed9-5f440a961f14/download)

## 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)

## Rights

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/)

## Other metadata

[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)

## Fulltext

Microsoft Word - Supplementary_v2.docx1  Supplementary material  Effects of layer thickness and annealing process on low-frequency noise and detectivity in tunnel magnetoresistive sensors with CoFeSiB soft magnetic layers  Murali Krishnan M., 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,   * Corresponding author. Email: nakatani.tomoya@nims.go.jp  1. Resistance–magnetic field (R–H) curves Figure S1 shows the R–H curves of the TMR devices used in this study. The device size was 60 µm in diameter. The values of resistance-area product in the P-state (RAP) are given in the table of each figure. Note that the variations in RAP of these devices were not only due to the annealing process and tCFSB variations but also due to the non-uniformity of the thickness of the MgO tunnel barrier on each device, which was unavoidable in our deposition apparatus. Therefore, we do not have a sufficient experimental precision to discuss the relationships between RAP and the annealing process/tCFSB.    FIG. S1. R–H curves of the TMR devices with variations in (a) the temperature of the second pre-fabrication annealing (𝑇 ) for with tCFSB = 20 nm, (b) tCFSB for 𝑇  = 180 °C, and (c) T2 condition for tCFSB = 80 nm. (a), (b), and (c) correspond to Figs. 2, 3, and 4, respectively. -5.0 -2.5 0.0 2.5 5.0020406080100120R (W)m0H (mT)-5.0 -2.5 0.0 2.5 5.0020406080R (W)m0H (mT)-3.0 -1.5 0.0 1.5 3.0010203040R (W)m0H (mT)RAP(kΩ µm2)T2pre (°C)52.615032.018024.820072.8225119.8250RAP(kΩ µm2)tCFSB (nm)78.61032.02034.94032.580RAP(kΩ µm2)T2 (°C)32.5180 (pre)45.1225 (pre)7.2225 (post)(a) (b) (c)2  2. Coercivity and noise  In Figure S2, we show the H dependence of the coercivity (Hc) of the R-H curve, the noise voltage spectral densities at f = 10 Hz, and the sensitivity for the TMR devices annealed at 𝑇  = 180 and 225 °C and 𝑇  = 225 °C. For all devices, the maximum Hc was observed at µ0H ~ 0 mT, whereas the noise showed a peak at µ0H ~ 1 mT. Therefore, Hc and the noise did not show a clear correlation. On the other hand, the noise showed a clear correlation with the sensitivity as discussed in the main text of this paper.    FIG. S2. H-dependences of (a), (c), and (e) coercivity (Hc) of the R-H curves and the noise voltage spectral densities ( 𝑆  ) at f = 10 Hz and (b), (d), and (f) sensitivities of the TMR samples processed at 𝑇  = 180 and 225 °C and 𝑇  = 225 °C, respectively. The large 𝑆  at µ0H = 0.8 mT in (c) was by a low frequency random telegraph noise as shown in the inset.   3. Resistance-susceptibility measurements  Figure S3 shows the schematic block diagram for the resistance susceptibility (𝜒 ) measurement. The TMR device under test was mounted on a concentric six-turn coil fabricated on a printed circuit board (PCB). A constant current of 100 µA was applied to the TMR device using a Keithley 2450 source measure unit. The output voltage of the TMR device was measured by a phase-sensitive detection technique using a lock-in amplifier (Stanford Research Systems, SR830). The voltage across a 0.1 Ω resistor, connected in series between the bipolar 0.000.050.100.150.200.25 Hc ÖSvm 0Hc (mT)080160240320400-3 -2 -1 0 1 2 304080120160m0H (mT)1/R(dR/dH) (%/mT)0.000.050.100.150.200.25 Hc ÖSvm 0Hc (mT)080160240320400480560-3 -2 -1 0 1 2 304080120160m0H (mT)1/R(dR/dH) (%/mT)0.000.050.100.150.200.25 Hc ÖSvm 0Hc (mT)080160240320400-3 -2 -1 0 1 2 304080120160m0H (mT)1/R(dR/dH) (%/mT)(a) (b) (c) (d) (e) (f) 100 101 102 103 104 10510-910-810-710-6ÖSV (V/Hz0.5)f (Hz)µ0H = 0.8 mT3  power supply and the coil, was used as the reference signal for the lock-in amplifier. An external DC magnetic field was applied along the hard axis of the free layer magnetization. An AC modulation field was generated by the six-turn coil and applied along the hard axis of the free layer. The amplitude of the modulation field was calibrated by measuring the shift in the R-H curves when a constant DC current was applied to the coil. A current of 1 A generated a 0.7 mT field at the position of the TMR device.    FIG. S3. Schematic block diagram for resistance susceptibility measurements.  Figures S4(a) and (b) show the H dependence of the sensitivity of the TMR devices annealed at 𝑇   = 225 °C and 𝑇   = 225 °C, respectively. We compared the sensitivity measured by two types of methods: (1) the first derivative of the R-H curve normalized by R  and (2) the sensitivity obtained by the lock-in measurement with a modulation field of 0.03 mT at a frequency of 103 Hz, defined as the magnetoresistance susceptibility (𝜒 /R). R is the resistance of the device, and 𝜒  is the resultant of the 𝜒  and 𝜒"   by the resistance-susceptibility measurement. The 𝜒 /𝑅 value deviated from the  value at the µ0H range at approximately 0.8 mT, which can be explained as follows. In the R-H full loop measurement, a Barkhausen-type jump of the magnetic domains may occur at the transition between the P and AP states. In contrast, in the 𝜒   measurement with a small modulation field, the free layer magnetization responds to the modulation field in magnetization rotation regime without TMR deviceBipolar power supplySMUBias currentLock-in ampCoil currentTMR device outputVoltage controlPower amplifier modeHelmholtz coilDC power supply0.1 Ω series resistorLock-in reference (Vref)Coil on PCBfor HmodHmodH4  causing a magnetic domain jump, resulting in < . For the device with 𝑇  = 225 °C, the highest value of 𝜒 /R was 60.7% of that of . For 𝑇  = 225 °C, the highest value of 𝜒 /R was 44.1% of that of . This indicates that the device with 𝑇  = 225 °C has a more Barkhausen domain jump than that with 𝑇   = 225 °C. Further studies are needed to understand the origin of the reduced magnetic 1/f noise by post-fabrication annealing.           FIG. S4 (a) and (b) Sensitivity curves of the TMR devices annealed at 𝑇  = 225 °C and 𝑇  = 225 °C, respectively, obtained from the R-H full loop measurements ( ) and the locking measurements with a modulation field amplitude of 0.03 mT and a frequency of 103 Hz. (c) and (d) Real (in-phase) and imaginary (out-of-phase) resistance susceptibilities for 𝑇   = 225 °C and 𝑇  = 225 °C, respectively.  -3 -2 -1 0 1 2 3-505101520253035  real imaginarym0H (mT)c R' (W/mT) (c) T2pre = 225 °C-0.50.00.51.01.52.02.53.03.5c R" (W/mT)-3 -2 -1 0 1 2 30510 real imaginarym0H (mT)c R' (W/mT) (d) T2post = 225 °C0.00.51.0c R" (W/mT)-3 -2 -1 0 1 2 30306090120150180Sensitivity (%/mT)m0H  (mT) 1/R×dR/dH cR/R(a) T2pre = 225 °C-3 -2 -1 0 1 2 30306090120150180Sensitivity (%/mT)m0H (mT) 1/R×dR/dH cR/R(b) T2post = 225 °C5  Figures S4(c) and (d) show the in-phase (real part, 𝜒 ) and out-of-phase (imaginary part, 𝜒" ) components of the resistance susceptibility. The values of 𝜒   were approximately ten times larger than those of 𝜒"  in the H range where the device exhibited nonzero sensitivity. In addition, 𝜒  and 𝜒"  showed a similar H dependence. Figure S5 shows the H dependence of the phase lag, 𝜀 = tan−1(𝜒 /𝜒" ) at 103 Hz. The phase shift caused by the electrical cables and the electronic components was corrected from the data obtained for the TMR devices. No significant variation in the phase lag was be observed between these devices in the H range where 𝛼  exhibited a nonlinear dependence with the magnetoresistance-sensitivity product (MSP) (Fig. 5(b)). Furthermore, no clear correlation between Hc of the R-H curve and 𝜀 can be observed when comparing Fig. S2(c, e) and Fig. 5,    FIG. S5. Magnetic field dependence of phase lag for TMR devices annealed at 𝑇  = 225 °C and 𝑇  = 225 °C.   -1.0 -0.5 0.0 0.5 1.0-6-4-202Phase lag (deg.)m0H (mT) T pre 2  = 225 °C T post 2  = 225 °C