In-plane direct current probing for spin orbit torque-driven effective fields in perpendicularly magnetized heavy metal/ferromagnet/oxide frames

Electrical manipulation of magnetization states has been the subject of intense focus as it is a long-standing goal in the emerging field of spintronics. In particular, torque generated by an in-plane current with a strong spin-orbit interaction shows promise for control of the adjacent ferromagnetic state in heavy-metal/ferromagnet/oxide frames. Thus, the ability to unlock precise spin orbit torque-driven effective fields represents one of the key approaches in this work. Here, we address an in-plane direct current measurement approach as a generic alternative tool to identify spin orbit torque-driven effective fields in a full polar angle range without adopting the commonly used harmonic analyses. Our experimental results exhibited a strongly polar angular dependency of the spin orbit torque-driven effective fields observed from Ta or W/CoFeM/MgO frames.

Recently, intentional manipulation of magnetization dynamics through the electric fields and current continues to be of significant interest from a fundamental perspective and for spintronic technologies. In particular, the in-plane current-driven spin orbit interaction (SOI) phenomenon, which is the so called spin-orbit torque (SOT), has garnered considerable interest for controlling magnetization in the adjacent ferromagnet. Electric currents in large SOI materials can induce a non-zero spin current or spin accumulation in a direction perpendicular to the charge flow via a conversion between electron spin and linear momentum, which can exert torque on the magnetization in the adjacent ferromagnets. A variety of works have been published on the nature of the SOT-related magnetic dynamics including magnetization switching [1][2][3][4] , logic operations 5 , and domain-wall motion 6,7 by considering two dominant mechanisms. One is the spin Hall Effect (SHE) arising from bulk materials with a large SOI (heavy metal layer) 8 , and the other is the Rashba effect, which occurs at the interface between the heavy metal (HM) layer and ferromagnetic (FM) layer 9,10 . However, while both dynamics can provide two effective magnetic torques, which are commonly called the field-like torque (~M f f Τ Τ σ → × → ) and the damping-like torque × × →ˆˆ, the relative magnitude and direction of T f and T d vary strongly depending on the stack configuration, the choice of HM, and oxidation degree 1,11 . In addition, previous studies have shown that the T f is mainly induced by the Rashba effect, while the T d is mostly governed by the spin Hall effect 12 .
To date, numerous studies have also reported the successful determination of each effective magnetic field by means of diverse analysis approaches, such as field-current equivalence 13 and harmonic analysis 11,12,14 . However, the experimentally observed torque components (T f and T d ) evaluated even in the same structural frames exhibited distinct measurement or analysis dependence. For instance, Chen et al. 15 reported that the T f is nearly three times larger than the T d , while Liu et al. 3 presented a large SHE-induced torque in Ta/CoFeB/MgO with a perpendicular magnetic anisotropy (PMA) feature. Furthermore, the suggested two underlying physics for spin-orbit torque (that is, the Rashba effect and SHE) cannot explain several reported phenomena, such as the influence of oxygen bonding state 1 and polar angle of magnetization 15 . Thus, the ability to identify each individual torque Figure 1a shows an optical microscope image of the fabricated Hall device with a 10 μm width. A more detailed description of the fabrication process is given in the Methods section. The sample stacks used have the structure of Si/SiO 2 (200)/HM (5)/CoFeB (1.2)/MgO (1)/Ta (3) (thicknesses in nanometers) and were post-annealed at a moderate temperature, where two different annealing temperatures are chosen for 250 °C for Ta and 350 °C for W HMs. Hereafter, the Ta-based sample is referred to as 'Sample A, ' and the W-based sample is 'Sample B' . All samples exhibit typical PMA features due to the presence of interface anisotropy at CoFeB/MgO that is attributed to the hybridization of Fe 3d and O 2p orbitals 18 after the annealing process (see Supplementary Information 3). Figure 1b and c illustrate the DC source-driven SOT effective magnetic fields in the presence of an applied magnetic field (H ext ), along with the definition of the coordinate system. The current-induced effective magnetic fields have two components: the field-like effective field (H f ) and the damping-like effective field (H d ), which are defined

Results and Discussion
Two separate measurement schemes were introduced with the enlarged figures (right figures). One is the parallel measurement scheme (left of Fig. 1b), and the other is the perpendicular measurement scheme (left of Fig. 1c). In both schemes, the H ext with a tilting angle θ = 85° from vertical is swept in a wide range to maintain a single domain state during magnetization switching. In the parallel scheme, DC current (I dc ) with a magnitude of ±0.5 mA was injected along the x-axis and H ext were applied in the x-z plane with θ H = 85°, while the H ext was applied in the y-z plane with θ H = 85° with the current flow along the x-axis for the perpendicular scheme. The enlarged figures (rights) of Fig. 1b and c also depict the key concept of magnetization tilting upon application of positive and negative ±I dc in both schemes. For zero current (I dc = 0), the direction of a magnetization vector (M → ) in an FM layer is placed at the equilibrium position (θ 0 , ϕ 0 ) and is parallel to the sum of only two magnetic fields: where the anisotropic field ( → H an ) and external field (..). Both magnetic parameters can be determined experimentally. When the I dc is applied through either an HM layer or an FM layer, the current-induced torque will allow for magnetization tilting of the FM layer toward the new equilibrium position (θ, ϕ) from the equilibrium position (θ 0 , ϕ 0 ). That is, an I dc sign with a finite amplitude leads to relative magnetization tilting with an amplitude of Δθ from the equilibrium state. Note that, in this analysis, the variations in the polar and azimuthal angles of magnetizations ( , Δθ Δϕ) mainly originate from the SOTs induced by the application of I dc because of the relatively small magnitude of the current-generated Oersted magnetic field (0.314 Oe, See Supplementary Information 9). In this regard, an I dc -induced variation in magnetization establishes the experimental difference in the total Hall signal (R H ) observed in both schemes. Thus, tailoring the and Δθ Δϕ upon application of I dc is a crucial step for determining the individual current-induced effective magnetic fields. Here, two measurement schemes are chosen to separately determine each individual → H f and → H d . In the two schemes, the injection of an identical current (x-axis) is supposed to create the same direction of H f → (always along the y-axis) with the same magnitude due to the presence of the same spin polarization ( σ → ), which is one parameter for the exchange interaction with the magnetization (M → ) under the Rashba effect-related torque. That is, the is independent of the direction of magnetization. However, as the H d → may arise mainly from the spin current created by the SHE through the spin transfer torque (STT) phenomenon, the → relies on the initial magnetization direction. Thus, our work is hereafter discussed based on the simplest assumption in which the Δθ in a parallel scheme is only given by the H d → in the x-z plane, and the Δθ in a perpendicular scheme is only governed by the H f → in the y-z plane. That is, the separate determination of Δθ in the two schemes serves to determine the strengths of each → H f and H d → . This is a key concept in the application of ±I dc without adopting the commonly used harmonic analyses.
Considering the above concept, Fig. 2a where θ is the polar angle, ϕ is the azimuthal angle of the magnetization, and R AHE and R PHE are the anomalous Hall effect (AHE) and planar Hall effect (PHE) resistances, respectively. Note that a linear background (first term of Equation (1)) generated from the ordinary Hall effect (R OHE ) is excluded due to its negligible magnitude in this analysis. To separate the total observed R H into a pristine Hall signal (R H0 ) upon zero current and a variation in the Hall resistance ( R H Δ ) upon the injection of I dc with a certain magnitude, the R H of Equation (1) was approximated using a Taylor expansion only to the first order as follows: where the Hall resistance in the absence of I dc is denoted by , and the variation of R H by the I DC is ΔR H . The R H0 and R H Δ upon ±I dc can be obtained by Similarly, the two AHE-and PHE-associated terms with respect to ±H ext in the presence of I dc can be determined by the resulting expressions: where detailed equations are given in Supplementary Fig. 2b,c suggests that R PHE is small (i.e., a factor of 10 2 and 10 less than values of R AHE for Samples A and B, respectively), reflecting a slight contribution to the rotational variance around the ϕ upon I dc application. Thus, the magnitude of R PHE can be used to determine current-induced effective fields only by means of the ΔR AHE estimated for both schemes because the contribution of R PHE to the R H is negligible in our work. Similarly, the R H , R AHE , and R PHE trends of Sample B are similar to the observations of Sample A. More detailed plots for Sample B are presented in Fig. S2 of the Supporting Information. We believe that the determined R AHE and R PHE are primarily the consequence of magnetization tilting induced by the application of I dc , as depicted in Fig. 1b,c.  (A15) of β-W, while the α-phase W with a BCC structure is expected to have a smaller SHA value. Thus, the use of the β-phase W buffer layer in Sample B corresponds to the presence of a large SOT in our work (see the XRD analysis given in Supplementary Information 4 and the determined resistivity 172 μΩ•cm, 139 μΩ•cm for Ta and W, respectively). Secondly, it is widely believed that three main mechanisms have a significant impact on the SHE dynamics: an intrinsic mechanism, skew scattering, and side-jump scattering. The last two scattering terms are the so-called extrinsic mechanism, where the scattering sources are likely to arise from impurities or defects generated mainly in the HMs. In general, post annealing is a generic approach for the formation of well-aligned crystalline regions through boron out-diffusion from the CoFeB FM layer. This process ensures that the interface PMA features operate reliably to meet the demand of PMA-based devices. Thus, thermal annealing of Samples A and B lets thermally-activated B ions diffuse toward the HM layer or thermally-activated Ta or W ions migrate toward the FM layer, causing atomic intermixing of the layers 22 . According to recent work 23 , a heavy metal dopant on the ferromagnet resulted in an enhancement in SOI. In this regard, annealing results in suitable atomic mixing with Co, Fe, B, HM, or oxygen atoms in an FM or HM layer, reflecting the presence of an enhanced SOI-driven SHA in Sample B. Third, the different crystalline states observed within the two Ta and W buffer layers are also related to the SOI features. The Ta buffer layer exhibits a nearly β-phase structure, while the W buffer layer reveals a A15 crystalline structure after annealing (See XRD analysis given in Supplementary Information 4 and the determined resistivity of 172 μΩ•cm, 139 μΩ•cm for Ta and W, respectively). Therefore, HM and FM can include different defects or impurities after annealing. Finally, the affinity of B for the Ta and W buffer layers can likely help reduce the amount of defects or impurities within the HMs since B diffusion is different even at the same annealing temperature 24 . Figure 3a,c also show that a relatively large R H Δ occurs at around 3 kOe for Sample A and 6 kOe for Sample B, in which fields of 3 and 6 kOe are very close to the anisotropy fields (H k ) of Samples A and B, respectively (see Supplementary Information 3). Similarly, Fig. 3b,d show the change in magnetization polar angle (Δθ) induced by the positive current (+0.5 mA) injection, which is determined from the two separated AHE signals (I = 0, +0.5 mA) for Samples A and B. A relatively large Δθ in both samples also becomes obvious in the vicinity of the s H k . Thus, the similarities in peaks of R H Δ and Δθ in the vicinity of the s H k implies that their natures are similar regardless of whether the Ta or W buffer layer is used. However, the peak behavior in the vicinity of the s H k for Samples A and B is not clearly understood at present. Differences in Δθs are commonly caused by variations in the magnitudes of H f and H d , which are separately determined from the parallel and perpendicular schemes. As displayed in Fig. 3b,d, the H ext -dependency of Δθ implies that the magnitude of the current-induced torques is not constant with regard to H ext or θ. In this sense, the specific dependence of θ on the magnitudes of H f and H d can be obtained from the observed Δθ traces to further explore the nature for the SOTs in the FM layer. Thus, to derive the magnitude of each H f and H d from the observed θ, the total magnetic energy of a perpendicularly magnetized system with the injected current can be expressed as . A more detailed description of the above equations is given in Supplementary Information 1. Figure 4 exhibits the θ-dependence of H d and H f for Samples A (Fig. 4a,b) and B (Fig. 4c,d) under positive (black) and negative (red)I dc . Plots of Sample A present the typical behaviors in sign and magnitude observed from the previously reported works 11,12,26 , where the representatively reported average magnitudes of H d and H f for Sample A are ~20 Oe/MA•cm −2 , which corresponds to the obtained values from the typical harmonic analysis for Sample A (blue spheres). As harmonic signal-based analysis cannot be applied to W-based samples 27  , ultimately reflecting larger H d and H f values for Sample B even at the same current injection. In addition, the presence of relatively higher resistance in W buffer layer may be associated with the particularly enhanced Hf component of Sample B. The recent theoretical work 28 has suggested that the field-like torque can significantly be affected by the current flowing inside an FM layer with a 2D Rashba model or SHE model. In this sense, the W buffer layer that can absorb more boron and oxygen atoms during growth or annealing possibly creates a higher resistance than that of the Ta layer (See Supplementary Information S9) Fig. 4. However, questions remain regarding why there is an abnormal angular dependence of both components over the full θ range. In addition, the experimental observations cannot be completely described by either the SHE or Rashba model. The unclear θ-dependent phenomena observed in the full θ range are likely linked to a combination of two apparent dynamics, along with unknown additional structural contributions. Recent theoretical works 12,14,15,29 addressed the θ-dependent behaviors of spin-orbit torque without identifying their origins. For example, the bulk SHE-based theories combined with the Boltzmann equation and a simpler drift-diffusion approach 30 predicted no angular dependence of either Hf or Hd. On the other hand, the interfacial Rashba-based theories in a strong Rashba effect regime (compared to the exchange coupling strength 31 ) showed a strong angular dependence of Hd through the anisotropy of the spin relaxation. However, Hf remains almost constant even after introduction of spin relaxation anisotropy. Thus, the θ dependence of diverse Hd and Hf reported by numerous studies 12,14,15,29 (including our work) showed less agreement with the currently available theoretical models. Thus, attaining a firm understanding of the physical nature of these systems is still a major challenge that must be addressed to extend their use. Overall, a clearer model for the origin of current-induced effective fields observed in the samples must be developed.   (Fig. 5a) and H d (Fig. 5b) of Samples A (black line) and B (red line) as a function of θ to emphasize the difference in magnitude of the current-induced effective fields. Experiments showed that the magnitude of H d and H f for Sample B was about 10 times (H f ) and 2 times (H d ) larger over the whole θ region. This increase in H d and H f magnitude for Sample B can be ascribed to the enhanced bulk-SHE or the current in an FM layer, as explained in Fig. 4  ) are comparable with To give rough estimates for the strong θ-dependent SHA, a brief interfacial spin-dependent scattering concept in a particular high θ regime is provided as proof of the possible nature. Zhang et al. 32 have addressed that the interfacial transparency of spin current can be associated with the spin-mixing conductance, which is a function of magnetic damping constant. In addition, W. Kim et al. 33 reported the angle-dependent magnetic damping constant possibly induced by the spin pumping effect. This paper pointed out the decrease in damping constant as the θ increased. Thus, the decreased damping constant can reduce the transparency of spin current at the interface when the following equation is used where G ↑↓ is the spin-mixing conductance, λ is the spin diffusion length, σ HM is the conductivity of heavy metals, h HM is Planck's constant and d HM is the thickness of heavy metals. This models may explain the reduction in the effective SHA and the corresponding H d as the θ increases. In addition, using Zhang's initial transparency concept, another feasible scenario for the transparency could be as follows: if the injected spin current pointing along the y-axis exchanges with a total angular momentum ( → J ) in d orbitals of an adjacent FM, the spin current transparency at the interface is also affected by the θ of FM when the θ-dependent barrier height is present at the interface. In this scenario, the H d in a parallel scheme is not relevant to the θ dependence since the spin current injected along the y-axis is always perpendicular to the magnetization direction in a parallel scheme. The corresponding exchange interaction is equal for all magnetization polar angles. However, the H f in a perpendicular scheme also has θ dependence due to the presence of M J ex σ −  → ⋅ → , where σ → is directed along the y-axis. Thus, since movement toward the high θ regime allows the magnetization direction to primarily be close to the y-axis, the electron in the spin current will experience fewer scattering events due to the further reduced energy barrier. Such an event results in a spin current with large transparency, which facilitates injection of spin current. As a result, the H f is enhanced with an increase in θ, as seen in the high θ region of Fig. 4a,c. The angular dependence of H f in the high θ region can be expressed by the transparency concept. However, the abnormal decrease in higher θ (>°75 ) and the behavior in the middle range (20 60 ) θ°∼° of both samples still remains a challenge so that a new physics beyond the currently available models should be established.

Conclusions
In summary, in-plane DC measurements of spin-orbit torque components in Ta-and W-based CoFeB/MgO frames are employed as an independent analysis tool to examine the in-plane current-induced magnetization switching. The observed spin-orbit torque components for the two frames reveal a strong dependence on the magnetization of the polar angles. In particular, relatively larger Rashba and spin Hall dynamics are the dominant contributions to Samples A and B, respectively. Identifying the underlying nature of these phenomena remains a key challenge toward extending the use of these materials. One possible nature is the interfacial spin-dependent scattering arising from the exchange interactions between the angular momentum of d electrons in the CoFeB layer and the spin state of conduction electrons in the heavy metal layer. We anticipate that the study of this simple DC approach will open a suitable path to explore new physical phenomena and provide low power and high speed spin-orbit torque-based spintronic devices.

Methods
The stacks used in this work were deposited on thermally oxidized Si substrates utilizing magnetron sputtering with a base pressure <2 × 10 −8 Torr at room temperature. Species were as follows: [Si/SiO 2 (200)] substrate/heavy metals (5)/Co 20 Fe 60 B 20 (t CFB )/MgO (1)/Ta (2), where the numbers in parentheses refer to the layer thickness in nanometers, and the heavy metals are Ta (Sample A) and W (Sample B). To promote perpendicular magnetic anisotropy (PMA) features, a post-annealing process was carried out at 250 °C (Sample A) and 300 °C (Sample B) for 1 hour under vacuum conditions below ~1 × 10 −6 Torr with a 3 Tesla perpendicular magnetic field for all samples investigated here. The deposited stacks were spin-coated with AZ5214E image reversal photoresist and patterned into 10 μm width Hall bars by photolithography and Ar ion milling. Acetone was used to lift off the photo resist. Oxygen plasma etching was carried out for 2 minutes with 50 Watt RF power to remove residual photoresist hardened during the ion-milling process. The Hall channel contacts were defined by photolithography followed by the deposition of W (50 nm) and were connected to the Hall bars. Devices were wire-bonded to the sample holder using indium balls and were installed in a home-made electrical probing system with a ~1 Tesla electromagnet using a Keithley 236 source measure unit and Hewlett Packard 34401A multi-meter devices 34 .