Absence of spin Hall magnetoresistance in $\mathrm{Pt}/{\left(\mathrm{CoNi}\right)}_n$ multilayers

We have systematically studied the magnetoresistance effect in $\mathrm{Pt}/{\left(\mathrm{CoNi}\right)}_n$ multilayers featured with perpendicular magnetic anisotropy and fcc (111) texture. Angular dependence of the magnetoresistance, including high-order cosine terms, was found in the plane perpendicular to the electrical current, which can be attributed to the geometrical size effects and the anisotropic interface magnetoresistance effect. However, the contribution from spin Hall magnetoresistance (SMR) is absent. The spin Hall angle of Pt was evaluated by spin-torque ferromagnetic resonance measurements, and the theoretical magnitude of SMR in our samples was estimated to be one order higher than the accuracy of our experiments. The absence of SMR in our multilayers indicates that the Elliott-Yafet spin relaxation of itinerant electrons in the ferromagnetic metal is crucial when studying the spin transport in all-metallic heterostructures.

Figure 1

(a) Out-of-plane x-ray measurement of $\mathrm{Ta}\left(3\right)/\mathrm{Pt}\left(10\right)/{[\mathrm{Co}\left(0.3\right)/\mathrm{Ni}\left(0.4\right)]}_n/\mathrm{Ta}\left(3\right)$ for $n$ ranging from 2 to 12. The dashed lines at 39.7° and 44.5° represent the expected positions of unstrained Pt (111) and CoNi (111) peaks, respectively. (b), (c) Rocking curves around Pt (111) and ${\left[\mathrm{Co}/\mathrm{Ni}\right]}_{12}$ (111). (d) The blue cycles are the dependence of the peak intensity ratio of ${\left[\mathrm{Co}/\mathrm{Ni}\right]}_n$ and Pt on the number of repetitions $n$. The black line is a straight line through the origin that was fitted to our results.

Figure 2

(a), (b) The loops of abnormal Hall resistance when a magnetic field was applied along the film normal and plane of $n=8$. The inset in (b) shows local enlarged data from 1.6 to 6 kOe, and the curve is the result of fitting using Eq. (1). (c) The black circles represent the dependence of the effective PMA field on the repetition number, which can be well fitted by $A/n+B$ (A and B are constants) as the curve shows. (d) The triangle represents the perpendicular anisotropy energy per unit area, and the red line denotes a linear fitting.

Figure 3

Magnetoresistance curves of $\mathrm{Pt}/{\left[\mathrm{Co}/\mathrm{Ni}\right]}_n$ structures. (a) Illustration of the $\mathrm{Ta}/\mathrm{Pt}/{\left[\mathrm{Co}/\mathrm{Ni}\right]}_n/\mathrm{Ta}$ sample structure and coordinate system of the experiment. (b) Resistivity ρ vs orientation of magnetization for three samples with different repetitions. The rotation of magnetization M is performed in the film plane ($\beta ={90}^{\circ }$, black cycles) and in the plane perpendicular to the current j ($\alpha ={90}^{\circ }$, red cycles). (c) Individual cos ${}^{2n}\beta$ contributions to ρ(β) for $n=12$. (d) Polar plot of ρ(β) for these three samples.

Figure 4

The thickness-dependent magnetoresistance after corrections of dead layer. (a)$\mathrm{\Delta }{\rho }_{xy,\mathrm{CoNi}}/{\rho }_{\mathrm{CoNi}}$ (b)$\mathrm{\Delta }{\rho }_{yz,\mathrm{CoNi}}^{\left(2\right)}/{\rho }_{\mathrm{CoNi},}$ and (c)$\mathrm{\Delta }{\rho }_{yz,\mathrm{CoNi}}^{\left(4\right)}/{\rho }_{\mathrm{CoNi}}$ as a function of the thickness of CoNi. The symbols represent experimental data, while solid black lines represent fitting lines. The dashed red lines represent the contribution of AIMR [the contribution of A in Eq. (6)]. The GSE contribution is a constant that is independent of the thickness [the contribution of C in Eq. (6)], which is indicated by a thinner solid straight line in (b). The blue dotted lines indicate the linear contribution, which corresponds to B in Eq. (6).

Figure 5

(a) ST-FMR spectrum of $n=7$ sample measured at 45° in plane with a microwave injection of 18 GHz, which includes antisymmetric (blue curve) and Lorentz symmetric (red curve) line shapes. (b) Angular dependence of $U_{\mathrm{s}}$ and $U_{\mathrm{a}}$ at 18 GHz in the $xy$ plane. (c) Fitting the spin Hall angle (${\theta }_{\mathrm{SH}}$) according to Eq. (9). (d) The dependence of the $xy$ plane magnetoresistance, the theoretical value of SMR, and the experimental value of AIMR on the thickness of CoNi are put together for comparison.