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## Creator

[Prabhanjan D. Kulkarni](https://orcid.org/0000-0002-4605-5256), [Tomoya Nakatani](https://orcid.org/0000-0001-9590-216X)

## 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 Prabhanjan D. Kulkarni, Tomoya Nakatani; Tunnel magnetoresistive sensors with non-hysteretic resistance–magnetic field curves using noncollinear interlayer exchange coupling through RuFe spacers. Appl. Phys. Lett. 14 October 2024; 125 (16): 162405, and may be found at https://doi.org/10.1063/5.0231451.[In Copyright](http://rightsstatements.org/vocab/InC/1.0/)

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[Tunnel magnetoresistive sensors with non-hysteretic resistance-magnetic field curves using noncollinear interlayer exchange coupling through RuFe spacers](https://mdr.nims.go.jp/datasets/79a14d49-3d8d-4d7e-bc80-bacf2749f756)

## Fulltext

Microsoft Word - RuFe noncolli-IEC_FINAL.docx1  Tunnel magnetoresistive sensors with non-hysteretic resistance-magnetic field curves using noncollinear interlayer exchange coupling through RuFe spacers  Prabhanjan D. Kulkarni*, and Tomoya Nakatani**  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: nakatani.tomoya@nims.go.jp  ABSTRACT Magnetic stabilization of the ferromagnetic layers of magnetoresistive elements is a key technological requirement for highly sensitive and accurate magnetic sensors. Here, we report on a tunnel magnetoresistive (TMR) sensor wherein the free layer (FL) magnetization is stabilized by combining exchange bias, noncollinear interlayer exchange coupling through a RuFe spacer, and orange-peel ferromagnetic coupling. This method facilitates the stabilization of the FL magnetization over a wide range of noncollinear angles with respect to the pinning direction by controlling the composition of the RuFe spacer. Moreover, the uniaxial anisotropy induced in the FL by annealing plays an important role in the resistance–magnetic field (R–H) curve, which was studied both experimentally and through simulation. The TMR devices exhibited negligible hysteresis even in the major R–H loops, which is promising for magnetic field-sensing applications. 2  Controlling and stabilizing the magnetization directions of ferromagnetic (FM) layers are important for spintronic devices, such as magnetic memories and sensors. Exchange bias, interlayer exchange coupling (IEC), and magnetic anisotropy are key tools for achieving this function. The unidirectional exchange bias obtained in an antiferromagnet (AFM)/FM bilayer structure is used to pin the magnetization of the FM layer, referred to as the spin-valve structure.1 IEC oscillates between AFM and FM couplings depending on the thickness of the nonmagnetic spacer for various materials, such as Cr, Cu, and Ru.2–5 The AFM-IEC through Cu and Ru spacers is particularly important for giant magnetoresistance devices and synthetic antiferromagnet structure,6 respectively. Further, the recently reported noncollinear IEC in Co/RuFe/Co, Co/RuCo/Co, and Co/IrFe/Co trilayer structures facilitates the control of the magnetization configuration of the Co layers at arbitrary angles by changing the composition and thickness of the RuFe, RuCo, and IrFe spacers.7–10 Magnetization stabilization is critical for tunnel magnetoresistance (TMR) magnetic sensors, which have recently attracted much attention because of their expanding applications and markets. For many applications, TMR sensors must exhibit an output voltage proportional to the strength of the magnetic field. This can be achieved by stabilizing the magnetization of the free layer (FL) along one direction (easy axis) and sensing the magnetic field along the orthogonal direction (hard axis); consequently TMR devices exhibit pseudo linear resistance–magnetic field (R–H) response curves.11–14 Various methods have been developed to induce magnetic anisotropy in FL, such as shape anisotropy,15 external bias magnetic field,11 perpendicular magnetic anisotropy,16,17 annealing-induced uniaxial anisotropy,18,19 and exchange bias.12,13,20,21  Uniaxial anisotropy orthogonal to the pinning direction is induced by two-step annealing at two different temperatures under magnetic fields along orthogonal directions. 3  Because the typical anisotropy field of annealing-induced uniaxial anisotropy is a few mT or smaller, soft-magnetic FLs with uniaxial anisotropy are often used for high-sensitivity TMR sensors.19,22 However, as pointed out by Wang et al.,12 FLs with only uniaxial anisotropy are demagnetized into a multi-domain structure under a zero magnetic field. Consequently, the R–H curves of the TMR devices exhibit magnetic hysteresis, which is undesirable for magnetic sensors. Another sensor design where the FL is stabilized by unidirectional anisotropy (exchange bias) results in a single-domain state of FL magnetization, causing a considerably smaller magnetic hysteresis.12,13,20,21 These sensors achieve an orthogonal magnetization configuration between the FL and reference layer (RL) using two AFM layers with different blocking temperatures processed by two-step annealing. This study developed a TMR sensor stack where the FL magnetization is stabilized in the single domain state along a noncollinear direction with respect to the pinning direction. This was achieved by transferring the exchange bias through the noncollinear IEC via a RuFe spacer. By controlling the directions of the noncollinear IEC and annealing-induced uniaxial anisotropy, TMR sensors with linear R–H curves and negligible magnetic hysteresis can be obtained, which are considered to be suitable for magnetic sensing applications. The core component of the present study is two Co layers magnetically coupled in a noncollinear configuration through a RuFe spacer. Nunn et al.7 reported that the noncollinear IEC between the Co layers can be controlled by the composition and thickness of the RuFe spacer. For simplicity, the RuFe thickness was fixed at 1 nm, whereas the RuFe composition was varied by co-sputtering deposition from Ru and Fe targets. The composition of the RuFe film was measured using X-ray fluorescence spectroscopy.  First, to measure the magnetization angle between two Co layers separated by a RuFe spacer, we fabricated current-in-plane giant magnetoresistance (CIP-GMR) spin-valve 4  structures of thermally oxidized Si substrate/Ta (2)/Ru (2)/IrMn (6)/Co50Fe50 (1)/Co (2)/Ru100-xFex (1)/Co (3)/Cu (3)/Co90Fe10 (5)/Ru (4) (thickness in nm), as shown in Fig. 1(a). The CIP-GMR films were annealed at 350 °C for 1 h under a magnetic field of 0.7 T to pin the magnetization direction of the Co50Fe50 (1)/Co (2) pinned layer (PL). The magnetization configuration diagram in Fig. 1(a) shows that the magnetization of the Co (3) RL was fixed at an angle of θIEC with respect to the PL magnetization by the noncollinear IEC through the RuFe spacer. The FL magnetization was saturated by an external magnetic field (H) of 5 mT applied at θ angle with respect to the PL magnetization. Figure 1(b) shows the θ dependence of the GMR ratio, defined as (𝑅 − 𝑅 )/𝑅  (𝑅 : minimum resistance), of the spin-valve films with three different RuFe compositions. θ at (GMR ratio) = 0 corresponds to θIEC, which was 132°, 101°, and 77° for x = 57, 63, and 67 at. %, respectively. As shown in Fig. 1(c), θIEC varied as 50°–130° by changing x.  The noncollinear IEC can be phenomenologically described by bilinear and biquadratic IEC components, whose energies are expressed by J1 and J2, respectively. J1 and J2 are obtained by fitting the magnetization (M) vs. H curves (e.g., for the Ru40Fe60 spacer in the inset of Fig. 1(d)) by minimizing the total magnetic energy with Zeeman, IEC and exchange bias energies. 𝐸 =  𝐸 + 𝐸 + +𝐸 ,      (1) where 𝐸 = −𝐻(𝑀 𝑡 cos 𝜑 + 𝑀 𝑡 cos 𝜑 + 𝑀 𝑡 cos 𝜑 ),  (2) 𝐸 = −𝐽 cos( 𝜑 − 𝜑 ) − 𝐽 cos ( 𝜑 − 𝜑 ),         (3) 𝐸 = − 𝐽 cos 𝜑 ,       (4) where M and t are the saturation magnetization and film thickness, respectively, φ is the angle 5  between M and H, and  𝐽  is the exchange bias energy between the PL and the IrMn AFM layer. As shown in Fig. 1(d), J2 exhibited similar values of –0.3 mJ/m2 for x ranging as 54–70 at. %, whereas J1 varied between negative and positive values, corresponding to AFM and FM bilinear IECs, respectively. As previously reported,23,24 θIEC is determined using J1 and J2 as 𝜃 =cos (−𝐽 /2𝐽 ) when −2 ≤ 𝐽 /𝐽 ≤ 2. The calculated θIEC were consistent with the directly measured values [Fig. 1(c)].   FIG.1. (a) Schematic layer structure and magnetization configuration of the CIP-GMR spin-valves with a noncollinear IEC between PL and RL through the Ru100-xFex spacers. External magnetic field (5 mT) was applied at θ angle with respect to the PL magnetization (mPL). (b) GMR ratio vs. θ curves for x = 57, 63, and 67 at. %. The θ value at GMR ratio = 0 corresponds 54 57 60 63 66 69 72-0.4-0.3-0.2-0.10.00.10.20.30.4J 1, J2 (mJ/m2)x in Ru100-xFex (at. %) J1 J20 90 180 270 36001234567GMR ratio (%)q (deg.)x in Ru100-xFex (at. %) 57 63 6754 57 60 63 66 69 720306090120150180 Measured from GMR ratio vs q Calculated by qIEC = cos-1(-J1/2J2)q IEC (deg.)x in Ru100-xFex (at. %)Ru (4)Co (3)Ru (2)Co (2)SiOx sub.Co50Fe50 (1)IrMn (6)FLCu (3)Co90Fe10 (5)RLspacerPLRuFe (1)Ta (2)(a) (b)(c) (d)mPLmRLH, mFLθIECθnoncollinearIEC-400 -200 0 200 400-101M/Msm0H (mT) Exp. FitRu40Fe606  to θIEC. x dependences of (c) θIEC and (d) J1 and J2. The inset of (d) shows the M–H curve for x = 60 at. % and its fitting curve.   Subsequently, we fabricated TMR spin-valve devices with a layer structure of thermally oxidized Si substrate/Cu bottom electrode/Ta (2)/Ru (2)/IrMn (6)/CoFe (1)/Co (2)/Ru100-xFex (1)/Co (3)/AgSn (2.5)/CoFe (1)/CoFeBTa (30)/Ta (0.3)/CoFeB (3)/MgO (1.8)/CoFeB (2.5)/Ta (0.15)/CoFeB (0.5)/CoFe (1)/Ru (0.8)/CoFe (3)/IrMn (8)/Ru (8) (thickness in nm) with variations in the Fe concentration of the RuFe spacer including pure Ru, as shown in Fig. 2(a). The nominal compositions of the alloy layers were Ir20Mn80, Co50Fe50, Ag90Sn10, Co38Fe38B19Ta5, and Co40Fe40B20. The magnetization of the Co (2) PL2 was pinned along the noncollinear direction with respect to that of CoFe (1)/Co (2) PL1. The CoFe (1)/CoFeBTa (30)/Ta (0.3)/CoFeB (3) layers functioned as FL through strong FM coupling between the CoFeBTa amorphous soft magnetic layer and the CoFeB electrode via the thin Ta layer, which was inserted to promote the crystallization of CoFeB during annealing. The AgSn spacer was inserted to weakly ferromagnetically couple the magnetizations of PL2 and FL via orange-peel coupling.25,26 Thus, the direction and strength of the unidirectional stabilization field to the FL were controlled by the RuFe composition and AgSn thickness, respectively. The layers above the MgO barrier were patterned to a circular shape with a diameter of 40 μm, whereas the layers below the MgO barrier were patterned to a circular shape with a diameter of 180 μm. Circular shapes were selected to avoid the in-plane shape anisotropy. The patterned devices were annealed at 350 °C for 1 h under a magnetic field of 0.7 T. The resistance-area product values in the parallel magnetization configuration (RAp) of the devices were 20–200 kΩ µm2 (A = 1,256 µm2). Despite the variation in the RAp value, which was due to batch-to-7  batch variation and non-uniformity within the substrate of the MgO thickness and quality, the TMR ratio was approximately constant at 180%.  Figure 2(b) shows the expected magnetization (m) configuration of the FM layers of the TMR device under zero external magnetic field (H). mPL2 was pinned at an angle of θIEC from mPL1, and mFL was stabilized along the same direction as mPL2. H was applied along the x direction. Figure 2(c) shows the TMR curves of these devices. For the pure Ru spacer, the TMR ratio was 0 at Hx = 0, indicating a parallel configuration between the mFL and mRL. Thus, the type of the IEC through the pure Ru spacer was AFM. Rotation of mFL was observed at µ0Hx of approximately 8 mT, which is the strength of the orange-peel FM coupling through the AgSn spacer. The TMR ratio at Hx = 0 changed for different Fe concentrations in the RuFe spacer. Thus, the magnetization angle between the FL and RL was controlled by the noncollinear IEC through the RuFe spacer. However, these devices exhibited pronounced magnetic hysteresis, rendering them unsuitable for magnetic sensor applications. The coercivity (Hc) of the TMR curve for the Ru37Fe63 spacer was 0.23 mT.  8   FIG. 2. (a) TMR spin-valve structure with FL whose magnetization direction is stabilized along a noncollinear direction with respect to the pinning direction by the noncollinear IEC through the RuFe spacer. (b) Magnetization (m) configuration of the FM layers of the spin-valve under a zero external magnetic field (H). (c) TMR curves of the devices with variation in Fe concentration in the RuFe spacer. H was applied along the x direction.   Note that annealing process under a magnetic field induces uniaxial magnetic anisotropy in FM layers. Therefore, in the present spin-valve devices, the magnetization process of FL is governed by three factors: unidirectional anisotropy, uniaxial anisotropy, and external H. Trial and error of the annealing process revealed that the uniaxial anisotropy induced in the tilted angle from the direction of H significantly reduced the magnetic hysteresis of the TMR Ru capCo (3)Ta (2)Co (2)RuFe (1)CoFe (1)IrMn (6)FLAgSn (2.5)CoFeBTa (30)PL2PL1MgORu (0.8)CoFe(3)IrMn (8)CoFeB (3)CoFeB/CoFeCoFeB (2.5)CoFe (1)Ta (0.3)Ta (0.3)PL3RL mPL1, PL3mPL2, FLθIECat H = 0mRL(a) (b)-12 -9 -6 -3 0 3 6 9 12050100150200TMR ratio (%)m0Hx (mT)x in Ru100-xFex (at. %) 0 63 75(c)xyRu (2)Cu electrodeorange-peel FM couplingnoncollinearIEC9  curves. The reason for this has not yet been elucidated. Further, the shape of the TMR curve was highly dependent on the direction of the uniaxial anisotropy. To understand this behavior, we performed numerical simulations of the TMR curve in the single magnetic domain regime using the Stoner-Wohlfarth model.  Figure 3(a) shows the configuration of the in-plane magnetization of the FM layers and the directions of the magnetic anisotropies of the FL. The unidirectional and uniaxial anisotropies were induced at angles of θud and θua, respectively, with respect to mPL1 which was pinned along the +x direction. This configuration of the two types of magnetic anisotropies was achieved by the annealing process shown in Fig. 3(b). First, the devices were annealed at 350 °C under a magnetic field at θua, which induced a uniaxial anisotropy parallel to this direction and also crystallized the CoFeB/MgO interfaces. Thereafter, the temperature was lowered to 220 °C, which was above the blocking temperature of the IrMn layer (approximately 200 °C). The magnetic field direction was then changed to the +x direction (θ = 0°), and the temperature was lowered to room temperature, which pinned mPL1 and mPL3 along this direction. In addition, the unidirectional anisotropy of the FL has two equivalent directions at θud clockwise and counterclockwise from mPL1, as shown in Fig. 3(a). The FL magnetization state realized depends on the history of application of external H to the device. For simplicity, we considered only the unidirectional anisotropy counterclockwise from mPL1, which can be selected by applying H along the +y direction, hereafter referred to as a “set field”, prior to the TMR measurement with sweeping Hx. The angle (θFL) between the FL magnetization and Hx was calculated by minimizing the total magnetic energy, considering the Zeeman energy, exchange bias, annealing-induced uniaxial anisotropy, AFM and noncollinear IEC through the Ru and RuFe spacers, respectively, and the orange-peel FM coupling through the AgSn spacer. The calculation details are provided in the Supplementary Material. 10  Figure 3(c) shows the simulated TMR curves for a constant θud of 120° and θua = 0–120°. The TMR curve shape was strongly dependent on θua, and the highest value of sensitivity, defined by , at Hx = 0 was obtained for θua = 30°. Figure 3(d) shows the contour plot of the sensitivity at Hx = 0 for θud and θua, providing the choice of the values of θud and θua to obtain high sensitivity. Figures 3(e) and (f) show the experimental TMR curves for the 1-nm-thick Ru40Fe60 and Ru35Fe65 spacers, respectively. The angles of the magnetic anisotropies were θud ~130° and θua = 40° for the Ru40Fe60 spacer, and θud ~120° and θua = 120° for the Ru35Fe65 spacer. θud was estimated by fitting the M–H curves (not shown here), and θua was controlled by the annealing process. Compared to the device with θua = 0, which exhibited µ0Hc = 0.23 mT [Fig. 2(c)], these device with θua ≠ 0 showed significantly reduced hysteresis: µ0Hc ~ 0.02 mT for the Ru40Fe60 spacer and µ0Hc ~ 0 mT for the Ru35Fe65 spacer [the insets of Figs. 3(e) and (f), respectively], indicating that a single magnetic domain structure was obtained for θua ≠ 0. For the Ru40Fe60 spacer, the highest sensitivity state (21 %/mT) was obtained at Hx = 0, which is preferred for magnetic sensor applications. On the other hand, the device with the Ru35Fe65 spacer exhibited a relatively low sensitivity at Hx = 0 (14 %/mT). The trend of the sensitivity at Hx = 0 of these devices was consistent with the simulated results shown in Fig. 3(d). However, magnetic hysteresis cannot be simulated in the single-domain regime. Thus, the reason why tilting the uniaxial anisotropy axis of FL away from the pinning and H directions significantly reduced the hysteresis of the R–H curve is an open question.    11   FIG. 3. (a) Configuration of the magnetizations (m) of the FM layers of the spin-valve device. The unidirectional anisotropy has two equivalent directions with respect to mPL1, indicated as the dashed arrows labeled as “ud”. θua and θud are the angles between the easy axes of the uniaxial and unidirectional anisotropies, respectively, and mPL1. (b) Annealing process to obtain the anisotropy configuration in (a). (c) Simulated TMR curves for θud = 120° and θua = 0–120°. The inset shows the sensitivity curve for θua = 30°. (d) Contour plot of sensitivity at Hx = 0 for θua and θud. (e) and (f) Experimental TMR and sensitivity curves with 1-nm-thick Ru40Fe60 and Ru35Fe65 spacers, respectively. The insets show the same TMR curves in a small field range.  Next, we discuss the effects of the two possible directions of unidirectional anisotropy on the shape of the TMR curve. Figure 4(a) shows the magnetization configuration diagram. After applying a set field of Hy > 0, mFL stabilizes to the state indicated by the blue counterclockwise arrow from mPL1 owing to the balance of the uniaxial and unidirectional anisotropies. Similarly, after Hy < 0 is applied, mFL stabilizes to the state indicated by the red arrow. The shape of the TMR curve changes depending on the direction of the set field, as (a)T = 350 °C, 1 hH = 0.7 T at θuaθuaHDecrease Tto 220 °CChange H angleto 0° and decrease T to RTHsubstrate(b)(c)-10 -5 0 5 10050100150200TMR ratio (%)m0Hx (mT)02040Sensitivity (%/mT)-10 -5 0 5 1005010015020002040TMR ratio (%)m0Hx (mT)Sensitivity (%/mT)(e) Ru40Fe60 (f) Ru35Fe65H sweepdirectionmRLymPL1, PL3mFLθFLHxθuaθududxθududmPL20 30 60 90 120 150 1800306090120150180q ud (°)qua (°)−0612182430364248sensitivity (%/mT)at Hx = 0(d)−10 −5 0 5 10050100150200TMR ratio (%)m0Hx (mT)qua (°) 0 30 60 90 120−10 0 1002040Sensitivity (%/mT)m0Hx (mT)qua = 30°θud = 120°device in (f)device in (e)-0.2 0.0 0.220253035TMR ratio (%)m0Hx (mT) -0.2 0.0 0.2152025TMR ratio (%)m0Hx (mT)12  confirmed experimentally and shown in Fig. 4(b). This device was fabricated with a Ru35Fe65 (1 nm) spacer with θud ~±120° and θua = 60°. First, we applied a positive set field Hy and measured the R–Hx curve for Hy = 0. The TMR curve plotted in blue in Fig. 4(b) exhibited the highest sensitivity and relatively good linearity at Hx = 0, indicating that the angle between mFL and mRL at Hx = 0 was approximately 90°. After negative Hy was applied, the TMR curve changed its shape, as shown in red, because mFL was stabilized along a different direction from that of positive Hy, as shown schematically depicted in Fig. 4(a). When positive Hy was applied again, the TMR curve shown by the dashed green curve was identical to that following the first positive Hy (blue). Therefore, the stabilization of mFL along two directions by unidirectional anisotropy and the TMR curve are reversible. For magnetic sensors, TMR curves with a high sensitivity at Hx = 0 and good linearity are preferred, which is the case for the positive set field for this device. However, the presence of another magnetization energy minimum requires care not to expose the sensor device to an unexpectedly large magnetic field along the y direction. The present devices achieve essentially the same function as the sensors with soft-pinned FLs,12,13,20,21 in terms of linear R–H curves with negligible hysteresis. The soft-pinned FL sensors obtain unidirectional FL anisotropy orthogonal to the RL magnetization by two-step annealing for two AFM layers with different blocking temperatures, e.g., PtMn and IrMn layers. The strength of the FL anisotropy field is controlled by the thickness of the ultrathin dusting layer, typically with Ru, inserted between the AFM layer and the FL. On the other hand, the present devices achieve a noncollinear magnetization configuration between the FL and RL by exchange bias transferred via a noncollinear IEC through the RuFe spacer. The FL anisotropy field is controlled by the strength of the orange-peel FM coupling through the thickness of the AgSn nonmagnetic spacer. These two types of sensor designs may have different advantages and challenges depending on the required sensor characteristics such as sensitivity and dynamic 13  range. Therefore, for specific applications, various technical and economic aspects such as sensing characteristics, reliability, manufacturability, and cost must be evaluated. In summary, we have developed a TMR sensor structure wherein the magnetization of the FL is stabilized in the single-domain regime in an arbitrary direction by a noncollinear IEC through a RuFe spacer. The strength of the magnetic stabilization field of the FL is controlled by orange-peel FM coupling through a nonmagnetic spacer, such as AgSn. Further, the uniaxial magnetic anisotropy induced by magnetic field annealing facilitate the determination of the shape of the TMR curve and its magnetic hysteresis. By controlling the directions of the noncollinear IEC and uniaxial magnetic anisotropy, TMR sensor devices with high sensitivity under a zero magnetic bias field and negligible magnetic hysteresis can be obtained, which are promising for various magnetic sensing applications.   14   FIG. 4. (a) Magnetization configuration depending on the direction of set field (Hy). The blue and red arrows indicate mFL at Hx = 0 after applying positive and negative Hy, respectively. (b) Experimental TMR curves along two directions of set field (θud ~ ±120° and θua = 60°).    -10 -5 0 5 10050100150200Set field Hy direction positive negative positive (repeated)TMR ratio (%)m0Hx (mT)(b)(a)HxθuaθudθudmPL1mFL (Hx = 0)mFL (Hx = 0)xyset fieldHyudud-10 0 10020406080Sensitivity (%/mT)m0Hx (mT)15  Acknowledgement We thank Hiroshi Imamura (National Institute of Advanced Industrial Science and Technology) for valuable discussions.  Supplementary material  Refer to the supplementary material for details of the R-H curve simulations and the hysteresis of the device shown in Fig. 4(b).  Data Availability Statement The data supporting the findings of this study are available from the corresponding author upon reasonable request.  Conflict of interest The authors have no conflict of interest regarding the publication of this article.    16  References 1 B. Dieny, V.S. Speriosu, S.S.P. Parkin, B.A. Gurney, D.R. Wilhoit, and D. Mauri, Phys. Rev. B 43, 1297 (1991). 2 S.S.P. Parkin, N. More, and K.P. Roche, Phys. Rev. Lett. 64, 2304 (1990). 3 S.S.P. Parkin, R. Bhadra, and K.P. Roche, Phys. Rev. Lett. 66, 2152 (1991). 4 S.S.P. Parkin, Phys. Rev. Lett. 67, 3598 (1991). 5 S.S.P. Parkin and D. Mauri, Phys. Rev. B 44, 7131 (1991). 6 R.S. Beach, M. Pinarbasi, and M.J. Carey, J. Appl. Phys. 87, 5723 (2000). 7 Z.R. Nunn, C. Abert, D. Suess, and E. Girt, Sci. Adv. 6, eabd8861 (2020). 8 Z.R. Nunn, J. Lisik, P. Omelchenko, S. Koraltan, C. Abert, D. Suess, and E. Girt, J. Appl. Phys. 133, 123901 (2023). 9 C. Abert, S. Koraltan, F. Bruckner, F. Slanovc, J. Lisik, P. Omelchenko, E. Girt, and D. Suess, Phys. Rev. B 106, 054401 (2022). 10 J. Besler, S. Myrtle, and E. Girt, J. Magn. Magn. Mater. 585, 171109 (2023). 11 X. Liu, C. Ren, and G. Xiao, J. Appl. Phys. 92, 4722 (2002). 12 D. Wang, J. Daughton, C. Nordman, P. Eames, and J. Fink, J. Appl. Phys. 99, 08H703 (2006). 13 B. Negulescu, D. Lacour, F. Montaigne, A. Gerken, J. Paul, V. Spetter, J. Marien, C. Duret, and M. Hehn, Appl. Phys. Lett. 95, 112502 (2009). 14 A. V. Silva, D.C. Leitao, J. Valadeiro, J. Amaral, P.P. Freitas, and S. Cardoso, EPJ Appl. Phys. 72, 10601 (2015). 15 Y. Lu, R.A. Altman, A. Marley, S.A. Rishton, P.L. Trouilloud, G. Xiao, W.J. Gallagher, and S.S.P. Parkin, Appl. Phys. Lett. 70, 2610 (1997). 16 P. Wisniowski, J. Wrona, T. Stobiecki, S. Cardoso, and P.P. Freitas, IEEE Trans. Magn. 48, 3840 (2012). 17  17 P. Wisniowski, M. Dabek, J. Wrona, S. Cardoso, and P.P. Freitas, J. Appl. Phys. 122, (2017). 18 K. Fujiwara, M. Oogane, S. Yokota, T. Nishikawa, H. Naganuma, and Y. Ando, J. Appl. Phys. 111, 07C710 (2012). 19 D. Kato, M. Oogane, K. Fujiwara, T. Nishikawa, H. Naganuma, and Y. Ando, Appl. Phys. Express 6, 103004 (2013). 20 R. Ferreira, E. Paz, P.P. Freitas, J. Wang, and S. Xue, IEEE Trans. Magn. 48, 3719 (2012). 21 J.Y. Chen, J.F. Feng, and J.M.D. Coey, Appl. Phys. Lett. 100, 142407 (2012). 22 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). 23 E.E. Fullerton and S.D. Bader, Phys. Rev. B 53, 5112 (1996). 24 P.D. Kulkarni, T. Nakatani, T. Sasaki, and Y. Sakuraba, J. Appl. Phys. 129, 213901 (2021). 25 J.C.S. Kools, W. Kula, D. Mauri, and T. Lin, J. Appl. Phys. 85, 4466 (1999). 26 T. Nakatani, H. Suto, P.D. Kulkarni, H. Iwasaki, and Y. Sakuraba, Appl. Phys. Lett. 121, 192406 (2022).