Comparative determination of Y₃Fe₅O₁₂/Pt interfacial spin mixing conductance by spin-Hall magnetoresistance and spin pumping

Spin transfer across interfaces in heterostructured materials is critically important for spintronics applications, such as magnetic data storage and memory devices as well as future spin-based information processing technology.¹ In recent years, the extensive research activities in ferromagnetic resonance (FMR) and thermally-driven spin pumping from a ferromagnet (FM) into a nonmagnetic material (NM) as well as spin Hall magnetoresistance (SMR) in an NM layer on an FM insulator have attracted significant interests in the concept of interfacial spin mixing conductance (⁠$g↑↓$⁠) at FM/NM interfaces.^2–15 The magnitude of $g↑↓$⁠, which depends on the band structures of the FM and NM, determines the ability of the FM/NM interface to conduct spin currents. However, the experimental measurement of $g↑↓$ is nontrivial due to the sensitivity of $g↑↓$ to the film and interfacial quality. Two methods have been predominantly used to determine $g↑↓$ at FM/NM interfaces: (1) measuring the enhancement of the Gilbert damping constant (α) in the FM excited by FMR spin pumping^5,7,16,17 and (2) measuring the spin Hall magnetoresistance.^9–11 These two independent and complementary techniques probe the same interfacial spin conduction phenomenon but have rarely been exploited together to characterize the same interface. In this paper, we report the measurement of $g↑↓$ for the Y₃Fe₅O₁₂ (YIG)/Pt interface using both FMR spin pumping and SMR, which give comparably high interfacial spin mixing conductances, independently confirming the excellent spin conductivity of the YIG/Pt interface.

Epitaxial YIG thin films were deposited on the (111)-oriented Gd₃Ga₅O₁₂ (GGG) substrates using an off-axis, ultrahigh vacuum (UHV) sputtering technique developed for the epitaxial growth of single-crystalline films of complex materials.^18–22 These YIG films exhibit excellent crystalline and surface quality, as characterized by high-resolution X-ray diffraction (XRD) and atomic force microscopy (AFM).^21,23 A representative 2θ-ω XRD scan of a 20-nm YIG film shown in Fig. 1(a) demonstrates phase purity and pronounced Laue oscillations. The out-of-plane lattice constant of the YIG film, c = 12.393 Å, is very close to the bulk value of 12.376 Å. The AFM image of the YIG film shown in Fig. 1(b) reveals the root-mean-square (rms) roughness of 0.15 nm over an area of 1 × 1 m. The efficiency of spin transfer across YIG/Pt interfaces depends on the crystalline ordering of YIG, as well as the smoothness and cleanliness of the interface, and thus determines the magnitudes of both spin pumping and SMR.

Our study of SMR and FMR spin pumping was performed on YIG films with 5 nm thick Pt layers deposited on top. Figure 1(c) shows a room temperature magnetic hysteresis loop of a YIG(20 nm)/Pt(5 nm) bilayer with an in-plane magnetic field H measured by a LakeShore vibrating sample magnetometer (VSM), which exhibits a square loop with sharp reversal and a coercivity H_c = 0.78 ± 0.05 Oe. For the SMR measurements, we patterned the YIG/Pt bilayer into a standard Hall bar structure using photolithography and Ar+ ion milling.

We first measure the SMR of the YIG/Pt bilayer with the magnetic field applied in the film plane at an angle $ϕ$ with respect to the electrical current I, as illustrated in Fig. 2(a). Figure 1(d) shows the magnetic field dependence of resistance (R) and magnetoresistance (MR) calculated from MR = [R(H) – R_min]/R_min × 100% for $ϕ$ = 0° (H || I), where R_min is the minimum resistance in the MR scan. The SMR reaches a maximum value of 0.076%, which is among the largest SMR values reported in the literature,^8–10,12,14 and remains constant for |H| > 3 Oe when the magnetization M || H || I. The field range within which the resistance changes coincides with the re-magnetization process of the YIG film, as shown in Fig. 1(c). The resistance minima at H = ± (0.63 ± 0.05) Oe match well with the coercivity H_c = 0.78 Oe determined from Fig. 1(c), which indicates that at H = H_c, the magnetization is most orthogonal with the field, resulting in the minimum in resistance.

Figure 2(b) shows the dependence of SMR on in-plane field angle $ϕ$⁠. Here, each data point is obtained from individual SMR loops like that shown in Fig. 1(d). At $ϕ$ = 0° and 180° where the field and current are collinear, MR is maximum at 0.076%. At $ϕ$ = 45°, MR decreases to approximately 0; while at $ϕ$ = 90°, the sign of MR changes to negative. The sin²$ϕ$ dependence on in-plane angle shown by the blue curve in Fig. 2(b) can be understood as follows. For a thin Pt layer exhibiting strong spin-orbit coupling, the applied charge current, in conjunction with the spin Hall effect (SHE), generates spin accumulation in the Pt layer near the YIG/Pt interface, whose spin polarization $σ$ is parallel to the surface and perpendicular to I. The spin polarized electrons in Pt coupled to the YIG magnetization via exchange interaction and their spin angular momentum is absorbed via spin transfer torque, thus suppressing the spin current reflection at YIG/Pt interface. The spin current absorption is maximum when $σ$ ⊥ M and minimum when $σ$ || M. Consequently, as a result of the combined effect of SHE and inverse spin Hall effect (ISHE), SMR is maximized when M is perpendicular to $σ$ and minimized when they are parallel.

The in-plane angular dependence of SMR cannot exclude a possible contribution from anisotropic magnetoresistance (AMR) if the Pt atoms near the interface become partially magnetized due to the proximity effect, which also follows a similar angular dependence. Proximity effect induced AMR can be diagnosed by observing the variation of the magnetoresistance, as the applied magnetic field is rotated from in-plane to out-of-plane, as described by angle $γ$ between H and I, as illustrated in the inset of Fig. 3(a). As H rotates from in-plane (⁠$γ$ = 0°) to out-of-plane (⁠$γ$ = 90°), $σ$ and M remain perpendicular. If the observed magnetoresistance predominantly arises from SMR, it should remain constant as a function of $γ$⁠; it will vary as sin²$γ$ if AMR is the dominant effect. Figure 3(a) shows that the MR is approximately independent of $γ$⁠, ranging between 0.08% and 0.09%. This indicates that the observed magnetoresistance results mainly come from SMR induced by the spin current absorption and reflection at the YIG/Pt interface.

Figure 3(b) shows the MR hysteresis loop for $γ$ = 90° in an out-of-plane field, which exhibits an MR value of 0.09%. The field dependence of MR follows the out-of-plane magnetization hysteresis loops shown in Fig. 3(c), both becoming constant above a saturation field of 1850 ± 50 Oe, which is the demagnetizing field (4πM_eff) of the YIG film. The feature at small field [<100 Oe; see inset of Fig. 3(b)] is due to the magnetic switching of the in-plane magnetization, when the field is not perfectly aligned in the out-of-plane direction. Considering that the magnetic field is slightly misaligned from $γ$ = 90° in the xz plane, the projection of H on the x-axis determines when the magnetization should switch. The switching field of 48.5 ± 0.5 Oe evident in the inset of Fig. 3(b) is consistent with the small opening in the magnetization hysteresis loop in Fig. 3(c). Given that H_c = 0.78 Oe, as shown in Fig. 1(c), the actual field angle is estimated to be $γ$ = 89.1°, i.e., 0.9° off from the film normal.

The MR curve in Fig. 3(b) shows a quadratic field-dependence for H < 1850 Oe. This is likely due to the fact that in the out-of-plane geometry, the orientation of the magnetization is between $γ$ = 0° and 90°, when the field is smaller than the demagnetizing field. Assuming that M lies in the xz plane, we can calculate the z-component of M to be H/4πM_eff. Considering that the z-component of M is responsible for spin-transfer torque and spin reflection at the interface that led to SMR, we fit the region of H < 1850 Oe in Fig. 3(b) by (H/4πM_eff)², as shown by the green curve that agrees well with the experimental data. Similar quadratic behavior has previously been observed in the out-of-plane AMR for Heusler films.²⁰ 

We can determine the interfacial spin mixing conductance (⁠$g↑↓$⁠) at the YIG/Pt interface from our measured SMR. Theoretically,¹¹ the maximal variation of SMR (⁠$ΔR/R$⁠) corresponds to the rotation of M from $M∥σ to M⊥σ:$

where $G=e2hg↑↓$⁠; θ_SH, λ, d, and $ρ$ are the spin Hall angle, spin diffusion length, thickness, and electrical resistivity of the Pt layer, respectively. Previously, we have determined $θSH$ = 0.10 ± 0.01 and $λ$ = 7.3 ± 0.8 nm for Pt from spin pumping measurements.²⁴ Using d = 5 nm, $ρ$ = 4.8 × 10⁻⁷$Ω$ m and MR = 0.076% [from Fig. 1(d)] in Eq. (1), we obtain G = (3.5 ± 1.0) × 10¹⁴$Ω−1$ m⁻² that corresponds to $g↑↓$ = (9.0 ± 2.6) × 10¹⁸ m⁻². We note that Eq. (1) is based on the difference between the resistance when M || x and that when M || y for $ϕ$ = 0°; while our value of MR is obtained from MR = [R(H) – R_min]/R_min × 100%. R(H) at a high, saturating field is the resistance when M || x; however, R_min is not necessarily the resistance when the magnetization is aligned along the +y or −y direction. The actual minimum resistance might be lower than the R_min measured in Fig. 1(d). Thus, the 0.076% should be considered the lower bound of SMR.

In order to independently verify the value of the interfacial spin mixing conductance obtained from SMR, we compare it to the same parameter determined from its closely related process, FMR spin pumping. The interfacial spin mixing conductance can be determined from the enhancement of the Gilbert damping constant α,^25–27 

where $4πMs$⁠, $tYIG$⁠, $g$⁠, and $μB$ are the YIG saturation magnetization, YIG film thickness, Landé $g$ factor and Bohr magneton, respectively. The Gilbert damping constant can be accurately determined from the microwave frequency (f) dependence of the FMR linewidth (⁠$ΔH$⁠) using a microstrip transmission line. Figure 4 shows the $ΔH$ vs. f plots for a bare YIG(20 nm) film and the YIG(20 nm)/Pt(5 nm) bilayer, both of which exhibit a linear dependence following:²⁸ 

where ΔH_inh is the inhomogeneous broadening and γ is the gyromagnetic ratio. The least-squares fit to the data in Fig. 4 yield $αYIG$ = (9.1 ± 0.6) × 10⁻⁴ and $αYIG/Pt$ = (4.5 ± 0.3) × 10⁻³. Using Eq. (2), we obtain $g↑↓$ = (6.9 $±$ 0.6) $×$ 10¹⁸m⁻² from spin pumping, which is a little smaller than the (9.0 ± 2.6) × 10¹⁸m⁻² determined from the SMR measurement; the two values agree with each other within experimental uncertainty. The agreement between two complementary techniques on a high interfacial spin mixing conductance demonstrates the high efficiency of spin transmission at the YIG/Pt interface in both directions. Furthermore, the SMR analysis using Eq. (1) provides additional evidence supporting the accuracy of spin Hall angle determined for Pt by FMR spin pumping.²⁴ 

In conclusion, we studied spin Hall magnetoresistance in a YIG(20 nm)/Pt(5 nm) bilayer and measured a large SMR up to 0.09%. A high YIG/Pt interfacial spin mixing conductance of (9.0 ± 2.6) × 10¹⁸m⁻² is extracted from the SMR, which agrees with the value of (6.9 ± 0.6)×10¹⁸m⁻² obtained from the enhancement of the Gilbert damping induced by FMR spin pumping within experimental uncertainty. This result confirms that the same interfacial spin mixing conductance dictates the spin transmission efficiency of two reciprocal processes, i.e., spin Hall effect enabled spin-torque transfer from Pt → YIG and spin pumping from YIG → Pt.

The work was primarily supported by the U.S. Department of Energy (DOE) under the Grants Nos. DE-SC0001304 and DE-FG02-03ER46054. Partial support is provided by the Center for Emergent Materials, an NSF-funded MRSEC, under Grant No. DMR-1420451, Lake Shore Cryotronics Inc., and the NanoSystems Laboratory at the Ohio State University.