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Anomalous spin Hall magnetoresistance in Pt/Co bilayers

We have studied the spin Hall magnetoresistance (SMR), the magnetoresistance within the plane transverse to the current flow, of Pt/Co bilayers. We find that the SMR increases with increasing Co thickness: the effective spin Hall angle for bilayers with thick Co exceeds the reported values of Pt when a conventional drift-diffusion model is used. An extended model including spin transport within the Co layer cannot account for the large SMR. To identify its origin, contributions from other sources are studied. For most bilayers, the SMR increases with decreasing temperature and increasing magnetic field, indicating that magnon-related effects in the Co layer play little role. Without the Pt layer, we do not observe the large SMR found for the Pt/Co bilayers with thick Co. Implementing the effect of the so-called interface magnetoresistance and the textured induced anisotropic scattering cannot account for the Co thickness dependent SMR. Since the large SMR is present for W/Co but its magnitude reduces in W/CoFeB, we infer its origin is associated with a particular property of Co.

The spin Hall effect 1-3 of heavy metals allows generation of spin current large enough to control the magnetization direction of a neighboring magnetic layer. The amount of spin current generated via the spin Hall effect is determined by the spin Hall angle and can vary depending on the strength of the spin orbit interaction, band filling and Berry curvature of particular orbitals, and the number of impurities that can cause spin dependent scattering. Significant effort has been made to study the spin Hall effect in heavy metal (HM)/ferromagnetic metal (FM) bilayer system as the spin current generated within the HM layer can induce magnetization switching and coherent precession, domain nucleation and domain wall motion in the FM layer.
The spin current generated by the spin Hall effect can in turn influence the charge current 4 . In particular, the resistance of bilayers consisting of a HM layer and a ferromagnetic insulator (FI) or FM layer changes depending on the magnetization direction of the FI or FM layer [5][6][7][8] . The effect, known as the spin Hall magnetoresistance (SMR), scales with the square of the spin Hall angle of the HM layer. Importantly, the way the resistance depends on the magnetization direction is distinct from that of the anisotropic magnetoresistance (AMR) that takes place in the FM layer. These features allow one to use the SMR as a convenient means to extract the magnitude of spin Hall angle of the HM layer: the spin Hall angle obtained through SMR seem to agree with that estimated by other methods 9 . Recently, studies on SMR related effects have been increasing 10 ; an unidirectional component of the SMR is found in HM/FM bilayers 11 , SMR has been observed in systems with antiferromagnets [12][13][14][15] , the observation of the spin Nernst effect is based on the SMR theory [16][17][18] and the SMR analogue of the Rashba-Edelstein effect 19,20 has been found in Bi based structures 21 .
The magnetoresistance (MR) of heterostructures that include Pt/Co bilayer has been under focus recently. A MR that scales with the inverse of the Co layer thickness has been reported in Pt/Co/Pt trilayers [22][23][24] . Such interfacial contribution to the MR was found to be anisotropic: the MR is different when the (in-plane) magnetization points along or when it is orthogonal to the current flow. Similarly proximity induced magnetic moments of the Pt layer can contribute to the MR via AMR 25 Although not specific to the Pt/Co systems, it has been reported that texture induced anisotropic scattering can influence the MR 26-28 .
Here we report on a systematic study of the MR in Pt/Co bilayers. We show that an anomalously large SMR emerges in Pt/Co bilayers: the SMR increases with increasing Co thickness and the extracted effective spin Hall angle for such structures exceeds the expected value of Pt. An extended drift diffusion model that includes spin current generation and diffusion in the Co layer cannot account for the anomalous SMR. The SMR increases with decreasing temperature and increasing magnetic field for thick Co bilayers, suggesting that magnon-related effects in the Co layer has little influence on the enhancement of the SMR. The large SMR diminishes for films without the Pt layer; it is also found for W/Co but the effect is reduced for W/CoFeB. We thus infer that there is a process in Co that causes the SMR to increase with increasing Co thickness.
Samples are grown on silicon substrates coated with 100 nm thick oxide using RF magnetron sputtering. The film structure is sub.|0.5 Ta|d N Pt|t F Co|2 MgO|1 Ta (units of the thickness is nm). D N and t F represent the thickness of the HM and FM layers, respectively. A 0.5 nm thick Ta layer is used as a seed layer for the growth of the Pt layer. The MgO|Ta is used as a capping layer. Hall bars are created via shadow masking the deposition. The width of the Hall bars is ~0.4 mm and the distance between the voltage probes to measure the resistance is ~1.2-1.5 mm. Transport measurements are carried out in He-filled cryostat (Quantum Design, Physical Properties Measurement System).
The inset of Fig. 1(a) shows a schematic of the film structure together with the definition of the coordinate system. Current is passed along the x-direction. The Pt and Co thickness dependence of the resistivity is plotted in Figs. 1(a) and 1(b), respectively. The resistivity is obtained by measuring the layer thickness dependence of the sheet conductance (G XX ). The fluctuation in the resistivity for thin Pt and/or Co layer films arises since the resistivity is estimated from the thickness derivative of the sheet conductance. (See the Supplementary Material (Fig. S1) for the details of the extraction of the resistivity.) The resistivity of the Pt and Co layers shows a significant thickness dependence most likely due to increased interface scattering when the thickness is reduced 6,23,29 .
The MR of the Pt/Co bilayers are shown in Fig. 2. We measure the resistance (R XX ) of the Hall bars while rotating the magnetic field in the y-z plane. We define the angle between the magnetic field (H) and the z-axis within the y-z plane as j (see Fig. 1(a)). The j dependence of R XX is fitted with a sinusoidal function "" = $ 1 − '( )*+ , cos 2 + $ . From hereafter, we refer to Δ 456 as the SMR even though it may contain contributions from other MR effects. Δ 456 is plotted as a function of the Pt thickness (d Pt ) and Co thickness (t Co ) in Figs. 2(a-e) and 2(f-i), respectively. The phase offset j 0 is nearly zero for all films. R 0 is used to estimate the sheet conductance G XX .
For a given Co thickness, the characteristics of the Pt thickness dependence of Δ 456 is similar to what has been reported previously in similar systems 5 To illustrate the unusual characteristics of the Δ 456 found in the Pt/Co bilayers, we fit the Pt thickness dependence of the normalized Δ 456 with the drift-diffusion model.  8 1 − 1 cosh 8 8 (1) where l N is the spin diffusion length of the HM layer. l N and q SH are the fitting parameters and the resulting fitted curves are shown in Fig. 3(a). The agreement between the experimental results and Eq. (1) are quite good.
In Fig. 3(b) and 3(c), we show the Co thickness dependence of l N and q SH obtained from the fitting. We find that l N shows little dependence on t Co whereas q SH increases with increasing t Co .
The estimated q SH does not seem to saturate with Co thickness of ~7 nm and the maximum value reported previously 8,9,33 . We thus consider the large Δ 456 /x N found in Pt/Co bilayers is likely due to bulk spin transport in the Co layer.
Since the SMR increases with increasing Co thickness, one may consider spin current generation within the Co layer via excitations of magnons. Magnon is the main carrier of spin current in ferromagnetic insulators (FI) and causes the spin Seebeck effect in HM/FI structures 34 . Any magnon related effect, however, will be suppressed by application of large magnetic field or by lowering the measurement temperature 35 . We have thus studied the field and temperature dependence of the SMR of Pt/Co bilayers for selected films. and z-(R XX Z ) axes and took their difference, i.e., The temperature dependence of Δ 456 is plotted in Fig. 4  Representative values of the calculated IJK are shown in the supplementary material (Fig. S4).
In We have also studied the MR within the x-z plane which provides information on the so-called anisotropic interface magnetoresistance 22-24 (for clarity of notation, we denote such MR as IMR instead of AIMR used in Ref. 22 ). R XX is measured while the magnetic field is rotated in the x-z plane. The angle between the magnetic field and the z-axis within the x-z plane is defined as g.
We fit the g dependence of R XX using a sinusoidal function "" = $ 1 − '( h*+ , cos 2 + $ . Δ j56 is plotted as a function of Co thickness (t Co ) in Fig. 5(a). The large t Co limit of Δ j56 normalized by the current flowing in the Co layer, i.e.
'( h*+ k5j Y , gives the anisotropic magnetoresistance (AMR) of bulk Co (R AMR ) whereas changes at smaller t Co reflect contribution from the interface(s). In Fig. 5(b), we plot vs. 1 lm . The y-axis intercept of the linear fitting in the appropriate lm range, as shown in Fig. 5(b), gives R AMR . We find that R AMR for films with different Pt thickness are nearly the same (R AMR~1 .6%), which is close to what has been reported previously 41 . IMR is obtained by the following relation, VJK ≡ The Pt thickness dependence of VJK is plotted in Fig. 5(c). As reported previously 21,23,24 , VJK increases with decreasing lm .
Although the microscopic mechanism is not clear, one may assume 23 47,48 , and may influence the MR by means of anisotropic scattering. As the microscopic origin of the such effect remains to be identified, further investigation is required to clarify its presence.
In summary, we have studied the Pt and Co thickness dependence of spin Hall magnetoresistance), the magnetoresistance within the plane transverse to the current flow, in Pt/Co bilayers. We find SMR that increases with increasing Co thickness, which cannot be fully accounted for even if the anomalous Hall and spin Hall effects of the Co layer are considered.
Other effects that may contribute to the MR are evaluated to assess their influence on the SMR.
We find that the so-called anisotropic interface magnetoresistance and the magnetoresistance due to texture induced anisotropic scattering cannot describe the large SMR observed here. Further investigation is required to clarify the origin of the SMR in HM/Co bilayers.

Supplementary Material
The

S3. Anomalous Hall resistance
The Pt layer thickness dependence of the anomalous Hall resistance R AHE is shown in Fig. S3.

S4. Model calculations
The Pt and Co layer thickness dependence of +,-calculated using Eq. (2) of the main text is shown in Fig. S4, Fig. S4 show +,-calculated with the same parameters as above but with q F =0 and q AH =0.

S5. Influence of IMR on SMR
In order to evaluate how IMR influences the SMR, we subtract IMR from Δ /01 and extract SMR with the assumption that IMR in the y-z plane has the same magnitude with that of x-z plane. To model the system, we assume that the resistance change due to SMR occurs in the HM layer (e.g. Pt) whereas the change caused by the IMR takes place within the FM layer (e.g. Co).
One can therefore consider a parallel circuit that describes the magnetoresistance due to SMR and IMR as the following. We define the change in the current when the magnetic field is applied along the y-axis and z-axis as Δ . As noted above, Δ can be divided into two components, changes that occur in the FM layer (Δ $3 ) and the HM layer (Δ 43 ).
From the parallel circuit model, we obtain Δ can be expressed using the average film resistivity and its change Δ due to the field application along y and z, film thickness t=d N +t F and the voltage V applied across the films as: