Study of Spin-Orbit Interactions and Interlayer Ferromagnetic Coupling in Co/Pt/Co Trilayers in a Wide Range of Heavy-Metal Thickness

Study of Spin−Orbit Interactions and Interlayer Ferromagnetic Coupling in Co/Pt/Co Trilayers in a Wide Range of Heavy-Metal Thickness Piotr Ogrodnik,*Krzysztof Grochot, Łukasz Karwacki, Jarosław Kanak, MichałProkop, Jakub Checinski, Witold Skowronski, Sławomir Zietek, and Tomasz Stobiecki Cite This: ACS Appl. Mater. Interfaces 2021, 13, 47019−47032 Read Online ACCESS Metrics & More Article Recommendations * sıSupporting Information ABSTRACT: The spin−orbit torque, a torque induced by a charge current flowing through the heavy-metal-conducting layer with strong spin−orbit interactions, provides an efficient way to control the magnetization direction in heavy-metal/ferromagnet nanostructures, required for applications in the emergent magnetic technologies like random access memories, high-frequency nanooscillators, or bioinspired neuromorphic computations. We study the interface properties, magnetization dynamics, magnetostatic features, and spin−orbit interactions within the multilayer system Ti(2)/Co(1)/Pt(0−4)/Co(1)/MgO(2)/Ti(2) (thicknesses in nanometers) patterned by optical lithography on micrometer-sized bars. In the investigated devices, Pt is used as a source of the spin current and as a nonmagnetic spacer with variable thickness, which enables the magnitude of the interlayer ferromagnetic exchange coupling to be effectively tuned. We also find the Pt thickness-dependent changes in magnetic anisotropies, magnetoresistances, effective Hall angles, and, eventually, spin−orbit torque fields at interfaces. The experimental findings are supported by the relevant interface structure-related simulations, micromagnetic, macrospin, as well as the spin drift-diffusion models. Finally, the contribution of the spin−orbital Edelstein−Rashba interfacial fields is also briefly discussed in the analysis. KEYWORDS: ferromagnetic resonance, spin Hall effect, magnetoresistance, spin−orbit torques, Rashba−Edelstein effect 1. INTRODUCTION The magnetic multilayer structures consisting of thin ferromagnetic (F) layers and nonmagnetic spacers are known to exhibit plenty of phenomena, among which one can find those extensively studied for the last decades like anisotropic, giant and tunneling magnetoresistance or spin-transfer torque effect (STT), 1,2 and recently, current-driven spin−orbit torque (SOT) magnetization switching. 3 These effects are widely exploited in the spintronic devices, magnetic random access memories (MRAM) like STT-MRAM and SOT-MRAM, 4−7 as well as may be exploited in magnetic sensors (including magnetic nanoparticles) and nano-oscillators. 8,9 Such devices include nonmagnetic layers that are crucial for their features and performance. These layers may be both insulating (e.g., MgO in magnetic tunnel junctions) and metallic (e.g., Cu, Au in GMR devices). 9 Recently, the nonmagnetic layers made of heavy metallic (HM) elements (W, Ta, Pt, and their alloys 10−12 ) are extensively studied because of their large spin−orbit coupling (SOC). 13 Such layers combined with ferromagnetic ones (typically Co, CoFeB) are expected to have new spin transport properties related to the SOC, e.g., spin Hall effect (SHE) and Rashba−Edelstein effect (REE). 14,15 Although the SHE occurs in a single HM layer, 16 it is detectable in heterostructures with ferromagnets only, such as F/HM bi17 and F/HM/F trilayers. 18,19 In these structures, the spin-polarized electrons can accumulate at the HM/F interfaces and then may be efficiently injected into the F Received: June 22, 2021 Accepted: September 14, 2021 Published: September 24, 2021 Research Articlewww.acsami.org © 2021 The Authors. Published by American Chemical Society 47019 https://doi.org/10.1021/acsami.1c11675 ACS Appl. Mater. Interfaces 2021, 13, 47019−47032 Downloaded via CSIC on March 31, 2022 at 12:17:24 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles. layer exerting the spin−orbit torque (SOT) on its magnetic moment. This effect has been predicted theoretically 20−22 and reported in many experimental works on SOT-induced magnetic dynamics 23 and magnetic switching. 19,24−26 Especially for the F layers with a magnetic perpendicular anisotropy, the SOT enables a promising way to design efficient, ultralow power consumption spintronic devices. Apart from the SHE and related spin accumulation, the other pure interfacial effects, like charge-spin conversion REE at interfaces, contribute to the SOT. 27−29 Particularly, in multilayer systems with the symmetry-breaking axis along the direction of the current flow, the REE enables field-free magnetization switching. 30,31 Similar effect was also found in the magnetic multilayers in the presence of spin current gradients. 32,33 Therefore, interface engineering and quantifying the REE become significant for the optimization of SOT-based devices. 34−36 The spin currents injected into the F layer and SOTs may be examined by electric measurements through its magnetoresistance 37−39 and the anomalous Hall effect (AHE). 40 The change of the resistance of the hybrid structure caused by the above effects is referred to as spin Hall magnetoresistance (SMR). 41 Up to date, the specific multilayer structures (biand trilayers) were studied in detail. Among them, we find CoFeB-based structures like W/i-CoFeB/Pt 42 and p-CoFeB/Ta, as well as the Co-based multilayers like 43 pCo/Pt/i-Co, 19 p-Co/Pt, 44−46 i-Co/Ta, 46 Ta/i-Co/Pt, 47 Ru/pCo/Ru, and Ru/p-Co/Ru/W, 48 where p(i) stands for perpendicular(in-plane) anisotropy. Also, the recent studies on Pt/Co/Ru/Co/Pt showed that the RKKY interlayer exchange coupling (IEC) could tailor the properties of the multilayers. 49 In this paper, we present the detailed studies of the Co/Pt/ Co system with the use of the electrically detected FMR (ferromagnetic resonance), as well as low-frequency harmonic Hall voltage and static magnetotransport measurements. Here, the Pt layer plays a double role in the considered structure, first as a source of substantial spin currents and second as an essential element of the exchange ferromagnetic coupling mechanism. Therefore, the Pt thickness can be varied to control the spin currents and interlayer coupling, both essential for designing SOT-MRAM and high-frequency spintronic devices. We provide the results on the resonance frequencies and the SOT effective fields depending on the Pt thickness. Also, we analyze the magnetic parameters of the system like anisotropies, saturation magnetizations, and the IEC. We show that anisotropies and the IEC strongly depend on the Pt thickness, particularly for Pt layer thicknesses less than 2 nm. For such a thin Pt, the transition from the effective in-plane Co anisotropy to the perpendicular one may occur. We account for the features by providing reliable theoretical macrospin models of magnetization dynamics, magnetoresistance, and the effective spin Hall effect angle. 2. EXPERIMENTAL SECTION 2.1. Multilayer Stack. Multilayers are deposited on thermally oxidized Si substrates using magnetron sputtering at room temperature. We study the Co/Pt/Co trilayer within the Ti(2)/Co(1)/ Pt(0−4)/Co(1)/MgO(2)/Ti(2) structure shown in Figure 1 (the numbers in parentheses indicate the nominal thickness of the individual layers in nanometers). The Co/Pt/Co trilayer was designed so that it allows us to study the influence of the Pt thickness on the magnetic anisotropy of bottom and top Co layers, the IEC between Co layers through the Pt spacer, magnetization dynamics, and SHEdriven SOT acting on the F layers. For this purpose, both bottom and top thin Co layers should have small anisotropy (differing by interfaces Ti/Co and Co/MgO), with values close to the transition from in-plane to perpendicular. The Ti underlayer improves subsequent layers’adhesion and smoothens the substrate surface. Moreover, as shown in ref 50, the Ti/Co interface is alloyed due to mixing during magnetron deposition, while the Co/MgO interface is sharp. 51 Therefore, the top Co layer is characterized by a higher interface perpendicular anisotropy. 2.2. Structural Characterization. High-resolution X’Pert−MPD diffractometer with a Cu anode was used for X-ray diffraction (XRD) characterization. Figure 2 shows the XRD θ−2θprofiles of the Si/ SiO2/Ti/Co(1)/Pt(0−4)/Co(1)/MgO/Ti multilayer measured at different positions of the Pt wedge. The θ−2θmeasurements show the preferred growth of the Pt/Co in the [111] direction of the fcc structure. The peak of the Co layers is invisible because of their tiny thicknesses (tCo ≈1 nm). The arrows indicate the Co (111) peak position present in the thick Co layer case (see the Supplemental Figure 1. (a) Experimental multilayer stack with a wedge of Pt. The red thick (thin) wavy arrows indicate strong (weak) IEC, whereas the gray arrows show the change in the magnetization alignment with the Pt thickness; (b) the patterned device for a certain thickness of Pt the arrows indicate the direction of the current flow (jc ) and associated spin current (js  ) due to SHE. The short arrows depicted in the Co layers denote their magnetization vectors for a given Pt thickness at remanence; and (c) the polar and azimuthal angles describing the magnetization direction within the Co layers. Figure 2. XRD θ−2θprofiles of a Si/SiO2/Ti/Co(1)/Pt(0−4)/Co/ MgO/Ti measured at different positions of the Pt wedge. The arrow indicates the 2θposition of the structural Co (111) peak visible in the reference sample with 8 nm of Co and 4 nm of the Pt layer thickness (inset). ACS Applied Materials & Interfaces www.acsami.org Research Article https://doi.org/10.1021/acsami.1c11675 ACS Appl. Mater. Interfaces 2021, 13, 47019−47032 47020 Material in refs 19,52). The peak on the right side of the Pt(111) is a Laue satellite 19 that confirms the asymmetry in top Pt/Co and bottom Co/Pt interfaces. The intensity of the profiles depends on the number of Pt atoms. Therefore, in the case of very thin (0.2 nm) Pt layers, the Laue peaks are out of detection of the experimental method. However, one can see that the Pt peak slightly shifts to the right for thin Pt layers. It suggests that most of the Pt layer becomes mixed with Co atoms, making a rather Co−Pt compound than a wellseparated layer. Figure 3a shows the profile measured for the Si/SiO2/Ti(2)/ Co(1)/Pt(4)/Co(1)/MgO(2)/Ti(2) at a Pt thickness of ≈4 nm, together with the profile calculated using the simulated 52 structure (Figure 3b). An excellent agreement between the experimental and theoretical profiles is achieved. The structure was simulated with the assumption of Pt and Co mixing at the interfaces. The simulations represent the columnar grains in the Pt and Co layers and a transition area with the Pt−Co mixed interface. Mixing of the Pt and Co atoms at the interface causes decreasing Pt lattice plane spacing compared to that of pure Pt. The simulation assumes more significant mixing at the bottom side of the Pt than at the top one. In the former case, the heavy Pt atoms can penetrate the Co layer more easily than in the latter case. Moreover, for Pt within Co, the interfacial enthalpy is −33 kJ/(mole of atoms), whereas, for Co in Pt, the interfacial enthalpy is −26 kJ/ (mole of atoms). Higher negative enthalpy results in easier mixing at the bottom Co/Pt interface. 3. THEORY 3.1. Resonance Model. This subsection presents the macrospin model that allows us to calculate resonance frequencies of the considered Co/Pt/Co structure. Since the Co layers may be either coupled or uncoupled, we employ the approach that has been already presented in detail and successfully applied in our previous work. 53 We describe magnetic moments of each layer by spherical angles (polar θi and azimuthal ϕi) M Msin cos , sin sin , cos iSi i iiii,θϕ θϕ θ=[ ] (1) where i= 1(2) is referred to as the top(bottom) cobalt layer. The magnetization dynamics of the system is described by two coupled Landau−Lifshitz−Gilbert (LLG) equations MMH M Md dt M d dt () i ii i e g Si eDL i FL i eff,i , ,, ττ γα γ =− × + × ++ (2) where 1.760859644 10 e 11 rad sT γ ≈× is the gyromagnetic ratio, and αgis the Gilbert damping parameter for each layer. The terms τDL =HDL(mi×mi×ey) and τFL =HFL(mi×ey) stand for SOT damping-like (DL) and field-like(FL) components with the unit vector mM 12 M () S 12() ,1(2) =and the amplitudes HDL and HFL, respectively. The effective field (Heff) can be expressed as a functional derivative of the following total magnetic energy of the system MH MH MM UKt K tt J (cos sin sin sin cos ) (cos (cos cos sin sin sin ) cos sin sin ) ( cos sin sin ) iiij i iCo iiii i ii iiii iiiii i Co Co dem i 1 2 , 2 i 2 , 222 ext , i ii ∑βθϕ βθ δθβ θϕβ ϕθδ θ θ ϕ =[ − + ++− −]++− −·− · −· = ⊥ (3) The complex expression for the anisotropies originates from the rotation of the easy axes around x and y directions with the use of the relevant Euler rotation matrices. The angles βand δ have been introduced to account for a small deviation of the perpendicular anisotropies (K⊥,i) from the perpendicular (z) direction (δ,β≪π/2). The perpendicular anisotropy terms simplify into a well-known form K⊥,isin2θiwhen δi,βi=0. Also, we have added a small in-plane contribution K∥≪K⊥ along the ydirection. As long as they are small, they slightly improve the fitting of the macrospin model to the experimental data. In eq 3,tCo,i,Hext,Hdem,i, and Jstand for magnetic layer thickness, external magnetic field, demagnetizing field, and IEC, respectively. The LLG equation (eq 2) in polar coordinates can be written in the general form v(, ) ii T α θϕ =(4) where αand vare the vectors containing the spherical angles (θ1,2,ϕ1,2), time-derivatives, and the right-hand side (RHS) of the LLG equation, respectively. After linearization of vwith respect to small deviations in θiand ϕifrom their stationary values, one can write eq 4 in the form Xt() α Γ =(5) where Xis a 4 ×4 matrix consisting of the derivatives of the RHS of eq 4 with respect to the angles θi,ϕi(i.e., X kj vk j ≡α ∂ ∂), while Γ(t)=(δα1(t), ..., δα 4(t))Tis a vector containing timedependent angle differentials, i.e., δα1(t)≡δθ 1(t), δα2(t)≡δ ϕ1(t), etc. When small oscillations are assumed and in the absence of the external driving force (i.e., SOT or Oersted field), eq 5 can be rewritten as an eigenvalue problem of the matrix X XI 0 ω | −|= (6) The solution of the problem provides the complex eigenvalues ωidetermining two distinct natural resonance angular frequencies of the system, ωR,i=Reωi. Figure 3. Measured and calculated XRD θ−2θprofiles (a). The assumed thicknesses of the Pt and Co layers and transition area with the Pt−Co mixed interfaces (inset). A snapshot of the Monte Carlo simulation of the interface structure in Co/Pt/Co (b). ACS Applied Materials & Interfaces www.acsami.org Research Article https://doi.org/10.1021/acsami.1c11675 ACS Appl. Mater. Interfaces 2021, 13, 47019−47032 47021 3.2. Diffusive Model of the Magnetoresistance. The average longitudinal resistance of our trilayer stack is, in general, dependent on the orientation of magnetizations m1(2) in both ferromagnetic layers and reads Ä Ç Å Å Å Å Å Å Å Å Å Å Å Å É Ö Ñ Ñ Ñ Ñ Ñ Ñ Ñ Ñ Ñ Ñ Ñ Ñ mm R L wE t dzj z() 11 (, ) xx xcx 12 12() ,() 1 ∫ ∑ =∑χχχχ χ − (7) where Exis the electric field in the xdirection, Lis the length, wis the width, and tχis the thickness of layer χ=HM,F1, F2, and ∫χdenotes the integral with limits corresponding to the position of layer χin the stack. For Pt, i.e., for χ=HM, the charge current density reads m m j zE e z z (, ) 1 2 (, ) cx HM HM x SH HM sy HM 12 12 ,() ,() ρ θ ρ μ =−∂ ∂(8) where ρHM is the resistivity of the Pt layer, θSH is the spin Hall angle defined as the charge-to-spin current conversion efficiency at a very thick HM layer limit, and μs,y HM(z,m1(2)) is the spin accumulation, while for the ferromagnetic layers, i.e., χ=F1(χ=F2) mmx j zE(, ) 1() cx FF AMR FF x12 12 , 1( 2) () () 2 1( 2) θ ρ =[− · ] (9) where ρF1(F2) is the resistivity of the corresponding ferromagnetic layer, θAMR is the AMR in the thick ferromagnetic limit (assumed for simplicity the same in both ferromagnetic layers). For more details, see, e.g., ref 37. To obtain spin accumulation in the Pt layer, we consider the spin current density flowing in Pt Figure 4. Experimental versus theoretical relations of dispersion for samples from regions I (a, b), II (c, d), III (e, f), and IV (g, h). Left column: the sets of theoretical (lines) and experimental (points) dependencies for each region. Right column: the experimental VDC spectra shown as color map (color is the magnitude of the SD signal) and the source raw spectra measured at the frequency ranging from 2 to 20 GHz (light color lines), with the corresponding theoretical f(H) dependencies (solid black lines). The macrospin simulation magnetic parameters are the same as presented in Figure 5a−d. ACS Applied Materials & Interfaces www.acsami.org Research Article https://doi.org/10.1021/acsami.1c11675 ACS Appl. Mater. Interfaces 2021, 13, 47019−47032 47022 my m zE e z z j(, ) 11 2 (, ) s HM SH HM x HM s HM 12 12 () () μ θρρ =− +∂ ∂ (10) along with the boundary conditions mmtjq(,) () s HM H11 1 −= (11a) mmjq(0, ) ( ) s HM 22 2 =− (11b) j tt() 0 s F HM F 1 1 −− = (11c) m j tmq() () s F HM 1 1 11 −=· (11d) m j mq(0) ( ) s F 2 2 22 =· (11e) j t() 0 s F F 2 2=(11f) where the spin current in ferromagnetic metals assumes the following form j ze z z () (1 ) 2 () s FF FF FF s FF 1( 2) 1( 2) 2 1( 2) 1( 2) β ρ μ =−∂ ∂(12) and the interfacial spin currents qm m m m mm mm Gt t Gt Gt m () ( ) ( , ) (,) (,) ss F HM s HM HM rs HM HM is HM HM 11121 112 112 1 (1) 1 () (1) 1() (1) () μ μ μ μ=[− −· − ] +××− +×− (13a) qm m m m mm m mm G G G () (0) (0, ) (0, ) (0, ) ss F s HM rs HM is HM 22122 22 12 212 2 (2) 2 () (2) () (2) () μ μ μ μ=[ −· ] +×× +× (13b) where Gs(1) and Gs(2) are spin conductances and Gr(i)(1) and Gr(i)(2) are the real (imaginary) parts of spin-mixing conductances for interfaces 1 (F1/HM) and 2 (HM/F2), respectively. Moreover, the effective fields, HDL and HFL (cf. Section 3.1), due to SHE and spin accumulation at the interfaces can be expressed as follows H eMt xm q 2 1() DL SFF 1(2) 2 0,1(2) 1( 2) 1(2) 1(2) μ =−ℏ·× (14) and H eMt ym q 2 1() FL SFF 1(2) 2 0,1(2) 1( 2) 1(2) 1(2) μ =−ℏ·× (15) To fit the appropriate magnetoresistance relations obtained from eq 7, we use the following parameters: 37,54−56 ρHM =59 μΩcm, ρF1(F2) = 72.5 μΩcm, λHM = 1.8 nm, λF1=λF2= 7 nm, θSH = 8%, θAMR = 0.15%, β1=β2= 0.3, Gs(1) =Gs(2) =Gr(1) = Gi(1) =10 15 Ω−1m−2, and Gr(2) =Gi(2) = 0.4 Gr(1). The parameters were also used to calculate SOT effective fields that turn out to be pivotal in the interpretation of the experimental data presented in Section 4.3. 4. RESULTS 4.1. FMR and Interlayer Coupling. First, we measured the magnetization dynamics of the Co/Pt/Co sample in a wide range of Pt thickness from strong through moderate coupling to completely decoupled Co layers. The dynamics was investigated using the electrically detected FMR through the spin diode effect, 57 as described in Section 6.3. We observed the dispersion relations changing once the Pt thickness reaches boundary values. Thus, we could point out the distinct regions where the system behaves differently. This feature is illustrated in Figure 4. On the right panel of Figure 4, one can see the color FMR spectral line shapes. On the left panel, points correspond to the experimental resonance frequencies. On both sides of this figure, we show that for thin Pt spacer (below 1 nm), the dispersion relations are typical Kittel-like dependencies and move toward lower frequencies when the Figure 5. Magnetic parameters of the Co layers as a function of the Pt layer thickness derived from the macrospin simulations of the spin diode FMR spectra: perpendicular and effective anisotropies (a, b), magnetization saturation (c), and interlayer coupling (d). ACS Applied Materials & Interfaces www.acsami.org Research Article https://doi.org/10.1021/acsami.1c11675 ACS Appl. Mater. Interfaces 2021, 13, 47019−47032 47023 tPt is growing. Next, for tPt >1nm, the f(Hr) changes their slopes. Also, their branches part from each other, especially at low frequencies when a sort of resonance mode gaps in experimental data occurs. The increase of the Pt thickness (tPt > 2 nm) provides the Kittel-like dependencies again. However, for thick Pt (tPt > 3 nm), the experimental f(Hr) practically does not change anymore with the Pt thickness. To understand the f(Hr) dependence on the Pt thickness, we performed the macrospin simulations and a vast number of fittings for the whole range of the Pt thickness, i.e., from 0.09 to 4.04 nm (Figure 4). Varying the anisotropies (K⊥(∥),1(2)), perpendicular easy-axis deviation angles (β1(2),δ1(2)), magnetization saturations (MS1(2)), and the interlayer coupling strength (J) from eq 3, we reproduced the difference in the dynamical behavior of the structure and were able to identify the boundaries between different regions of Pt thickness where these behaviors occur, namely, regions I (thin Pt), II (medium Pt), III (intermediate Pt), and IV (thick Pt). Despite the similarity of f(Hr) in regions III and IV, we refer to the former as the intermediate since the differences occur in magnetoresistance results discussed in the further part of the paper. The presence of the additional modes (especially in regions III and IV) that were not registered in the experiment can be explained in a couple of ways. First, the theoretical results based on the model presented in Section 3.1 come from the solution of the eigenvalue problem, i.e., the model predicts all possible steady-state modes, regardless of the source of their excitations. On the other hand, the different way of forcing the excitation (by SOTs or Oersted field) is inherent. The resonance modes are not always excited, depending on the force amplitude and its origin. Second, these additional modes are related to the independent dynamics of two magnetizations of F1 and F2 layers due to weak interlayer coupling in regions III and IV. In contrast to regions I and II, there are no collective oscillations and therefore the mode with the large amplitude originates from the in-plane, whereas all other modes come from the perpendicular magnetization dynamics. However, the magnetization oscillations in the latter case do not contribute to the SD signal because of the significant effective damping caused by spin-pumping. 58 The macrospin parameters are summarized in Figure 5. The vertical dashed lines indicate the boundaries between regions I, II, III, and IV. Figure 5a−d presents perpendicular anisotropies K⊥,1,2, saturation magnetization MS,1,2, as well as the strength of the interlayer coupling. We also depicted the effective anisotropies KK M eff S,1,2 ,1,2 2,1,2 2 0 ≡− μ ⊥. The in-plane anisotropies (see the Supporting Information) have small values that have the importance in reproducing subtle Rxx (Hz) dependencies for the thinnest Pt layers only (e.g., see in Figure 6a). On the other hand, the anisotropy deviation angles (less than 30°) had to be introduced so that we could find a set of magnetic parameters reproducing both the static (magnetoresistance, AHE) and dynamic (FMR) characteristics simultaneously. One can see that the Co layer (indexed as 1) covered by the MgO layer exhibits a larger perpendicular anisotropy than that adjacent to the Ti layer (indexed as 2), similarly as in the system Si/SiO2/Ti(2)/Co(3)/Pt(tPt)/Co(1)/MgO(2)/ Ti(2) examined in our previous work. 19 Moreover, on the basis of magnetization measurements in an external perpendicular field, using vibrating sample magnetometer (VSM), we showed that the sample Pt(4)/Co(1)/MgO(2)/Ti(2) has a smaller effective anisotropy field (HK,eff = 1.3 kOe) than Ti(2)/ Co(1)/Pt(4) (HK,eff = 1.65 kOe). In Figure 5a,b, we show that the effective anisotropy Keff,1 changes its sign, while the Keff,2 is negative for all Pt thicknesses. The change in the sign of the effective anisotropy is related to the boundary between regions I and II. Furthermore, one can see that K⊥,1 increases with the Pt thickness up to tPt = 2 nm, whereas the value of K⊥,2 is growing just up to 1 nm. Above this thickness, K⊥,2 is rather Figure 6. Magnetoresistances Rxx and Rxy (inset) as a function of the magnetic field in the samples with Pt thickness: (a) 0.52 nm as an example from region I, (b) 1.74 nm from region II, (c) 2.63 nm from region III, and (d) 3.76 nm from region IV: Rxx experimental data measured at the magnetic field applied in x(blue triangles), y(green circles), and z(gray squares) directions. The depicted diagrams for all regions indicate the direction of magnetizations of magnetic layers at remanence. The macrospin (black solid and dashed lines) and micromagnetic (dashed red and blue lines) simulations of Rxx(Hy). Micromagnetic simulations for tPt = 3.76 nm were performed using the same parameters (cf. Figure 5) as derived from the macrospin model (red-dashed line), as well as for a K1anisotropy increased by 0.17 MJ/m3(blue dashed line). ACS Applied Materials & Interfaces www.acsami.org Research Article https://doi.org/10.1021/acsami.1c11675 ACS Appl. Mater. Interfaces 2021, 13, 47019−47032 47024 stable, and its values are more or less 0.2 MJ/m3. The K⊥,1 reaches its highest value at tPt ≈2 nm when it drops to the level of about 0.75 MJ/m3. We relate the different values of K⊥,1 than those of K⊥,2 to the much more efficient perpendicular anisotropy at Co/MgO than at the Co/Ti interface. On the other hand, the mean value magnetization saturation averaged over the whole range of the Pt thickness is about 1.07 T for both Co layers. The actual value for a given tPt differs by ±10 %. The abrupt decrease in MSfor the very thin Pt layer (0.09 nm) is caused by the quality of the interfaces and related intermixing of Pt and Co atoms. The last but not least, the parameter derived from the macrospin is the interlayer coupling energy J. The polarization of the Pt is the mechanism of the interaction between two magnetic moments in Co layers. Such an interaction is ferromagnetic by its very nature, 59 whereas the dipolar coupling (neglected here) is antiferromagnetic. The indirect way to probe the coupling (and the polarization of the Pt) by electrical detection is to measure FMR by rectification of radiofrequency current. 60−62 We derived the coupling (J) from the macrospin simulations, similarly to magnetizations and anisotropies. The coupling dependence on Pt thickness is shown in Figure 5d. However, we could estimate Jdown to a Pt thickness of 1.36 nm, at which J= 5.5 mJ/m2. Below this thickness, the coupling has no effect on the resonance fields at frequencies experimentally accessible (<25 GHz). The strong coupling causes both Co layers to rotate in the same manner, and they can be treated as one layer rather than two separate layers. In addition, two magnetizations of Co layers oscillate in phase (acoustic mode). It is seen in the experiment as the observed low-frequency mode. 53 On the contrary, the magnetization oscillations with opposite phases correspond to the high-frequency optical mode (>30 GHz), not achievable in the experimental method due to large losses in the power of the microwave current injected into the sample. 62 For this reason, although the exact value of Jis undeterminable for tPt < 1.36 nm, we just kept the value J= 5.5 mJ/m2for simulations. This Jmagnitude is marked as a horizontal dashed line in Figure 5d. Its real value may reach any point from the hatched region,andparticularly,itmayfollowtheexponential dependence, as predicted in ref 59 and shown in Figure 5d too. For the thicker Pt (tPt ≥1.36 nm), the fitting procedure to the Pt polarization model returned the Pt polarization depth parameter ξ≈0.47 nm, which is 1.5 times greater than ξ reported for the Py/Pt/Py structure. 59 Summarizing, we emphasize that the coupling strength correlates with the regions from I to IV. The constant value of Jwithin region I corresponds to large and undetectable coupling, whereas in region II, Jis still significant and measurable. The intermediate region III is characterized by weak coupling, while samples within region IV are practically decoupled. Having the magnetic parameters derived from the macrospin simulations of the spin diode FMR dynamics, we calculated longitudinal static magnetoresistance (Rxx) dependencies on the external magnetic field in Hx,Hy, and Hzdirections. We also modeled the anomalous Hall resistance (Rxy) when the external magnetic field is applied in the zdirection. 4.2. Magnetoresistance and Anomalous Hall Effect. The Pt-based magnetic multilayers are expected to exhibit a large spin magnetoresistance due to substantial spin−orbit interaction within the HM layer. These interactions cause the relatively large spin currents to be generated and injected into the ferromagnetic layers. The spin currents and spin accumulations at the Co/Pt interfaces influence the magnetoresistance of the sample, as predicted by the theoretical model presented in Section 3.2. Here, we focus on the spin−orbit interactions that are reflected in SMR. The SMR is defined as the difference in the longitudinal resistance measured in the saturated magnetization of Co layers under the external magnetic field applied in the yand zdirections, i.e., SMR = Rxx(Hy)−Rxx(Hz), while the AMR is defined similarly as in Section 3.2 as AMR = Rxx(Hx)−Rxx(Hz). 41 Also, we measured the AHE configuration (Rxy) in the field applied in the z direction. All magnetoresistance and AHE measurements were performed by the DC current method sweeping the external magnetic field up to 10 kOe. Then, we modeled the magnetoresistance dependencies with the use of the macrospin model. We used the parameters derived previously by fitting the model to the FMR experimental results (shown in Figure 5). For the sake of simplicity, we treat the considered sample as doubled bilayers: Co/Pt and Pt/Co. It allows us to calculate the resistance of the Co/Pt/Co structure as the equivalent resistance of layers connected in parallel: R xx RR RR 12 12 =· +where composite layer resistances are described by Rxx1(2) =R0,1(2) +ΔRAMRmx1(2)2+ ΔRSMRmy1(2)2. 41 The AHE-related resistances are given by Rxy = ΔRAHEmz1(2). 41 In Figure 6, we show the typical MR curves for samples from regions I to IV. For tPt = 0.52 nm, the macrospin qualitatively reproduces a narrow peak in MR. It also accounts for a more complicated dependence of Rxx(Hz) (see Figure 6a). The AHE curve does not exhibit a hysteresis and its shape is typical for the hard-axis rotation of both Co layers magnetized in-plane in the remanent state. The hysteresis in Rxx(Hz) is due to a competition between different anisotropies: in-plane and perpendicular that affect how the magnetizations rotate. Moreover, as one can see in Figure 7b, the AMR effect dominates in region I with the thinnest Pt layers. On the contrary, in region II, the SMR is the highest as predicted by the spin-diffusive model and macrospin simulations (cf. Figure 7a). The representative sample from region II (tPt = 1.74 nm) exhibits a parabolic-like R(Hy) dependence. It means that two Co layers are magnetized perpendicularly to the sample plane in the remanent state. Therefore, the AHE reveals a clear switching-like shape (see the inset in Figure 6b). Both, simulation and experimental results, show negligible contribution of the AMR. For the sample from region III (tPt = 2.63 nm), the R(Hy)is rather convex-shaped than parabolic. On the other hand, the AHE curve still exhibits a switching-like behavior. It suggests that the magnetization of layer 2 is tilted away from the perpendicular toward the in-plane direction. For the thickest Pt layer (e.g., tpt = 3.76 nm in Figure 6d) when the Co layers are weakly coupled (region IV), one can see Rxx(Hy) having a parabolic-like shape in high magnetic fields. This part of the curve is due to the rotation of the perpendicularly magnetized Co layer from the zto ydirection. On the contrary, at low fields, there is a characteristic sharp peak related to the rotation of the in-plane magnetized Co layer from its remanent state direction to the y direction. The dependence was well reproduced by the macrospin model (black solid line in Figure 6d). The same macrospin parameters provide the satisfactory agreement of AHE magnetoresistance with experimental points (see the inset in ACS Applied Materials & Interfaces www.acsami.org Research Article https://doi.org/10.1021/acsami.1c11675 ACS Appl. Mater. Interfaces 2021, 13, 47019−47032 47025 the same figure). The AHE curve exhibits a smooth-edged shape hysteresis, characteristic for the simultaneous rotation of the bottom Co layer magnetization (M  2) in its hard direction and switching of the top Co layer between two states: ±M  1,z. We supported the macrospin model with micromagnetic simulations in the case of the almost decoupled Co layers. The relevant calculations were performed with MUMAX3, 63 where the LLG equation was integrated numerically for each simulation cell. Due to memory and time usage limits, the simulated area was nominally restricted to 5 ×20 μm2. However, we also utilized periodic boundary conditions along the xdirection to produce a demagnetization tensor matching the actual experimental conditions. To optimize simulation performance, the cell size was chosen as 4.88 ×4.88 ×0.87 nm3for tPt = 1.74 nm and as 4.88 ×4.88 ×0.94 nm3for tPt = 3.76 nm. In both cases, the external magnetic field Hywas increased with a 500 Oe step, and the magnetization of Co layers was allowed to relax fully before moving to the next step. Then, the averaged magnetization vector for each layer was registered and used as an input for further resistance calculations. The micromagnetics revealed the same shapes of Rxx curves as the macrospin model, for the same parameters (or very close), as shown in Figure 5 (see the caption of Figure 6for details). The agreement between macrospin and micromagnetic simulations confirmed that the macrospin parameters are reliable. For the sake of completeness, in Figure 7, we show the ΔRAMR and ΔRSMR that were derived in the whole range of the Pt thickness from experiment and predicted by the spindiffusive model described in Section 3.2.Theobtained amplitudes agree to a satisfactory extent. As one can see from eqs 8 and 9, the SMR and AMR depend on the charge current flowing in HM and F layers, respectively. However, the currents in the HM layer are also influenced by spin accumulation at interfaces of this layer due to inverse SHE. The spin accumulation is mainly determined by the mean spin diffusion length (λHM) and spin Hall angle (θSH). The negative value of the SMR reaches its maximum at tPt ≈1.5 nm and decreases for thicker Pt layers, for which the spin decoherence affects the spin current, which, in turn, reduces the effective spin accumulation at the F/HM interface. On the contrary, the positive value of the AMR rapidly and monotonically decreases with HM thickness since the average charge current density flowing into the F layer decreases for the thicker Pt layer. Figure 7. (a) SMR and (b) AMR amplitudes derived directly from the measurements (empty gray triangles) and calculated within the diffusive model (red-dashed lines) as a function of the Pt thickness. Figure 8. Experimental harmonic voltages Vωand V2ωfor the representative samples from regions (a, b) II (tPt = 1.74 nm) and (c, d) III (tPt = 2.63 nm), both measured at the in-plane magnetic fields (Hxand Hy) swept from −1.5 to +1.5 kOe (cf. eq 16). The fitted linear and quadric functions correspond to the field-sweeping method (see ref 65). ACS Applied Materials & Interfaces www.acsami.org Research Article https://doi.org/10.1021/acsami.1c11675 ACS Appl. Mater. Interfaces 2021, 13, 47019−47032 47026 Discrepancies between the experimental and theoretical MR dependencies in region I result from strongly mixed and alloyed interfaces for small thicknesses of Pt. 4.3. Spin Hall Angle and Spin−Orbit Torques. To quantitatively characterize the spin−orbit interactions in the Co/Pt/Co trilayers, we performed the harmonic measurements briefly described in Section 6.4. For the samples for which both or one of the Co layers is magnetized in-plane (regions I and IV) in the remanent state, we applied the angular harmonic voltage measurement method. 11,64 On the contrary, in the case of the Co layers that magnetizations are perpendicularly oriented (regions II and III), we measured the field dependence of the relevant harmonic voltages. 65 In the latter method, the damping-like (DL) and field-like (FL) components of SOT fields are determined using the following formula HBB 22 14 DL FL xy yx () () () 2 ξ ξ Δ =− ± −(16) where B/ xy V H V H () xy xy 2 () 2 () 2 ≡∂ ∂ ∂ ∂ ωω and Hx(y)stands for the in-plane external magnetic field applied in the x(y) direction (cf. Figure 1). The parameter R R PHE AHE ξ =Δ Δis planar to the anomalous Hall effect ratio. The first and second harmonic voltages (Vωand V2ω) measured as a function of the applied magnetic fields (Hx and Hy) are plotted in Figure 8. The results shown in Figure 8 are representative of the samples from regions II (tPt = 1.74 nm) and III (tPt = 2.63 nm). Next, we could use eq 16 and follow the method described in ref 65 to calculate SOT effective fields ΔHDL(FL)in samples from regions II and III. Nevertheless, the above method turns out to be ineffective in the case of samples with one or both layers magnetized inplane. In this case, to determine ΔHDL(FL), we measured the angular dependence of V2ωon the magnetic field applied in the sample plane. Such a dependence may be expressed as follows 11,64 VH HRH HR I (cos2 1 2) cos FL ext PHE H DL eff AHE H 20 ϕα ϕ =− Δ−Δ+ ω (17) where ϕHstands for the in-plane angle of the magnetic field. The term α0is the anomalous Nernst effect (ANE) coefficient due to thermal gradients within the samples induced by the Joule heating. 64 The experimental angular dependencies V2ω(ϕH) for the samples with tPt = 0.52 nm (region I) and tPt = 3.76 nm (region IV) are shown in Figure 9a,b. As one can see, the damping-like SOT effective field (ΔHDL) is proportional to the cosϕH, whereas the field-like one (ΔHFL)is proportional to the cosϕHcos 2ϕH.Moreover,the H H eff ext K M 2eff S =− , where Keff (defined as in Section 4.1) and MSare the parameters of the Co layers magnetized in-plane. As long as we knew the magnetic parameters (summarized in Figure 5) of the layers, we could fiteq 17 to the experimental data and consequently determine both field-like and dampinglike SOT components. In addition, by plotting the terms proportional to ΔHDL as a function of 1/Hext, we could estimate the contribution of the ANE. One should note that the offset of linear fit (at 1/Hext = 0) visible in Figure 10a,b is the ANE contribution α0I0.We show the relevant plots for two samples (tPt = 0.52 and 3.76 nm). The small offsets of fitted lines (≈−0.3μV) and (≈ −0.15μV) corresponding to the ANE-related electric fields EANE ≈−0.03V/mand EANE ≈−0.015V/m, respectively, are much smaller than the values in the Co/Pt systems present in the literature, e.g., in ref 64. Therefore, it suggests that the ANE contribution is negligible in our devices with thin and thick Pt layers. It is worthy to notice that the dependencies shown in Figure 10 can be used to examine the applicability of eq 17. At low magnetic fields, the dependencies deviate from Figure 9. Experimental harmonic voltages V2ωfor the representative samples from regions (a) I (tPt = 0.52 nm) and (b) IV (tPt = 3.76 nm), both measured using the angular harmonic voltage method (cf. eq 17). The fitted trigonometric functions follow eq 17. Figure 10. Amplitude of eq 17 plotted as a function of the magnetic field 1/Hext measured in the samples with Pt thicknesses 0.52 nm (a) and 3.76 nm (b) at angle ϕH=45°. The interceptions with the yaxis indicate the ANE contribution. ACS Applied Materials & Interfaces www.acsami.org Research Article https://doi.org/10.1021/acsami.1c11675 ACS Appl. Mater. Interfaces 2021, 13, 47019−47032 47027