Spin-Hall and anisotropic magnetoresistance in ferrimagnetic Co-Gd/Pt layers

We present the Co-Gd composition dependence of the spin-Hall magnetoresistance (SMR) and anisotropic magnetoresistance (AMR) for ferrimagnetic $\mathrm{C}{\mathrm{o}}_{100-x}\mathrm{G}{\mathrm{d}}_x/\mathrm{Pt}$ bilayers. With Gd concentration $x$, its magnetic moment increasingly competes with the Co moment in the net magnetization. We find a nearly compensated ferrimagnetic state at $x=24$. The AMR changes sign from positive to negative with increasing $x$, vanishing near the magnetization compensation. On the other hand, the SMR does not vary significantly even where the AMR vanishes. These experimental results indicate that very different scattering mechanisms are responsible for AMR and SMR. We discuss a possible origin for the alloy composition dependence.

Figure 1

(a),(b) Relationship between net magnetization, Co magnetic moment, and Gd magnetic moment for (a) Co-rich Co-Gd and (b) Gd-rich Co-Gd. (c),(d) Reflection high-energy electron diffraction patterns of the (c) Co-Gd surface ($x=12$) and (d) Pt surface.

Figure 2

Measurement configurations for the angular dependence of (a) anisotropic magnetoresistance (AMR) and (b) spin-Hall magnetoresistance (SMR) of the $\mathrm{C}{\mathrm{o}}_{100-x}\mathrm{G}{\mathrm{d}}_x/\mathrm{Pt}$ bilayer. A charge current ($J_{\mathrm{c}}$) was applied along the $x$ direction. The AMR is observed when the external magnetic field (H) is rotated in the $x\text{−}z$ plane by the angle of $\gamma$. The SMR is the resistance change when H is rotated in the $y\text{−}z$ plane by an angle $\beta$.

Figure 3

Magnetization curves for the $\mathrm{C}{\mathrm{o}}_{100-x}\mathrm{G}{\mathrm{d}}_x/\mathrm{Pt}$ bilayer films with (a) $x=12$, (b) 24, (c) 25, and (d) 37, at room temperature and magnetic field H in the film plane. The longitudinal magneto-optical Kerr effect (L-MOKE) loops for (e) $x=12$, (f) 24, (g) 25, and (h) 37.

Figure 4

(a) Gd concentration ($x$) dependence of magnetization ($M$), (b) the maximum Kerr rotation angle (${\theta }_K$), and (c) the absolute value of ${\theta }_K\left(\right|{\theta }_K\left|\right)$. The solid circles represent the data for $\mathrm{Cr}/\mathrm{C}{\mathrm{o}}_{100-x}\mathrm{G}{\mathrm{d}}_x/\mathrm{Pt}$, while the open squares are those of the reference samples $\mathrm{Al}/\mathrm{C}{\mathrm{o}}_{100-x}\mathrm{G}{\mathrm{d}}_x/\mathrm{Al}$.

Figure 5

Angular ($\gamma$) dependence of the AMR of the $\mathrm{Cr}/\mathrm{C}{\mathrm{o}}_{100-x}\mathrm{G}{\mathrm{d}}_x/\mathrm{Pt}$ with (a) $x=12$, (b) 24, (c) 25, and (d) 45, and angular ($\beta$) dependence of SMR for the $\mathrm{Cr}/\mathrm{C}{\mathrm{o}}_{100-x}\mathrm{G}{\mathrm{d}}_x/\mathrm{Pt}$ with (e) $x=12$, (f) 24, (g) 25, and (h) 45. $J_{\mathrm{c}}$ was set at 0.1 mA, and $H=70\mathrm{kOe}$ was applied. The solid curves are fits by Eqs. (1) and (2).

Figure 6

(a) Gd concentration ($x$) dependence of device resistance ($R$), (b) AMR, and (c) SMR for the $\mathrm{Cr}/\mathrm{C}{\mathrm{o}}_{100-x}\mathrm{G}{\mathrm{d}}_x/\mathrm{Pt}$. The inset of (b) is a magnified plot of the AMR versus $x$.

Figure 7

Angular ($\gamma$) dependence of AMR of the reference samples $\mathrm{Al}/\mathrm{C}{\mathrm{o}}_{100-x}\mathrm{G}{\mathrm{d}}_x/\mathrm{Al}$ with (a) $x=7$ and (b) 42, and angular ($\beta$) dependence of SMR for the $\mathrm{Al}/\mathrm{C}{\mathrm{o}}_{100-x}\mathrm{G}{\mathrm{d}}_x/\mathrm{Al}$ with (c) $x=7$ and (d) 42. $J_{\mathrm{c}}$ was set to 0.1 mA, and $H=70\mathrm{kOe}$ was applied. The solid curves are fits by Eq. (1).

Figure 8

(a) Gd concentration ($x$) dependence of resistivity (${\rho }_{\mathrm{F}}$) of the present Co-Gd. (b) Comparison of the absolute values of the SMR ratios between the experiment (solid circles) and the model (solid line). (c) $G_{\mathrm{MIX}}$ calculated from the SMR ratio as a function of $x$ for the $\mathrm{Cr}/\mathrm{C}{\mathrm{o}}_{100-x}\mathrm{G}{\mathrm{d}}_x/\mathrm{Pt}$ by inverting Eq. (3).

Figure 9

Illustration of the in-plane field angular ($\alpha$) dependence of magnetoresistance, and $\alpha$ scan for the $\mathrm{Cr}/\mathrm{C}{\mathrm{o}}_{100-x}\mathrm{G}{\mathrm{d}}_x/\mathrm{Pt}$ with $x=25$. $J_{\mathrm{c}}$ was set at 0.1 mA, and $H=70\mathrm{kOe}$ was applied. The solid curve is the fit by Eq. (2) with an offset of 90 degree for $\alpha$.