Microscopic origin and quantitative determination of spin-current transparency at Pt–ferromagnet interfaces and the intrinsic spin Hall angle of platinum

In platinum/ferromagnet bilayers, the spin-torque-derived spin Hall angle of Pt measured by spin-torque ferromagnetic resonance depends strongly on which ferromagnet is used (about 0.11 for Pt/Co versus 0.05 for Pt/permalloy when the interface is assumed fully transparent). Zhang and co-workers (Nature Physics 11, 496–502, 2015) attributed this spread to the transparency $T$ of the Pt–ferromagnet interface to the spin Hall current, derived from the spin-mixing conductance obtained from Gilbert-damping enhancement, obtaining $T\approx 0.65$ for Pt/Co versus $T\approx 0.25$ for Pt/permalloy and an intrinsic Pt spin Hall angle of $0.19\pm 0.04$ . The literature supplies major partial results — a non-negligible imaginary part of the spin-mixing conductance, first-principles spin-memory-loss parameters for Co|Pt and permalloy|Pt, evidence that interfacial spin–orbit coupling dominates spin memory loss, and challenges to both the damping-based conductance extraction and the spin-diffusion framework — but no work quantitatively reconciles the elastic band-matching transparency picture with interfacial and bulk spin–orbit-induced spin memory loss, so the microscopic origin of the Pt/Co versus Pt/permalloy transparency difference and the intrinsic spin Hall angle of platinum remain unsettled.

Background

The spin Hall effect (SHE) is the conversion, by spin–orbit coupling, of a charge current into a transverse pure spin current; its efficiency is measured by the spin Hall angle (SHA), the ratio of spin current to charge current. In a platinum (Pt)/ferromagnet (FM) bilayer, the spin current generated in Pt exerts a spin-transfer torque on the magnetization of the FM layer, which is conveniently detected by spin-torque ferromagnetic resonance (ST-FMR): an applied radio-frequency charge current excites the ferromagnetic resonance of the FM, and rectified mixing voltages yield the torque amplitude and hence the spin-torque-derived SHA (ST-SHA). Permalloy (Py) is the disordered ferromagnetic alloy Ni $_{80}$ Fe $_{20}$ .

The efficiency with which a spin current crosses a normal-metal/ferromagnet interface is described by spin-transport theory in terms of the spin-mixing conductance $G^{\uparrow\downarrow}$ , the conductance for spin angular momentum transfer across the interface, which is generally complex; its imaginary part corresponds to spin precession-like (reactive) interfacial scattering, while its real part corresponds to dissipative angular-momentum transfer. $G^{\uparrow\downarrow}$ is commonly extracted from the enhancement of Gilbert damping (the magnetic relaxation rate) of an FM layer when a nonmagnetic layer with strong spin–orbit coupling is deposited on it, a mechanism called spin pumping: the excited magnetization pumps a spin current into the adjacent metal, whose finite spin diffusion length $\lambda$ (the length over which a spin current decays in the bulk) governs spin backflow.

Zhang, Han, Jiang, Yang and Parkin (Nature Physics 11, 496–502, 2015; preprint arXiv:1504.07929) used ST-FMR on Pt/Co and Pt/Py and observed very different ST-SHAs ( $\sim 0.11$ versus $\sim 0.05$ ) when the Pt/FM interfaces were taken to be completely transparent to spin current. Introducing an interface transparency $T$ — related to $G^{\uparrow\downarrow}$ , the Pt thickness $d$ , $\lambda$ and the Pt conductivity through their Eq. (2), with $G^{\uparrow\downarrow}$ obtained from $G_{\text{eff}}$ via their Eq. (3) — they computed $T = 0.65\pm 0.06$ for Pt/Co and $0.25\pm 0.05$ for Pt/Py from damping-enhancement measurements ( $G_{\text{eff}} = 3.96\times10^{19}$ and $1.52\times10^{19}$ m $^{-2}$ respectively, with Pt $\lambda = 14\pm 2$ Å), and normalized the ST-SHA by $T$ to obtain an intrinsic Pt spin Hall angle of $0.19\pm 0.04$ . They attributed the transparency difference to the matching of electronic bands across the interface (analogous to the interfacial origin of giant magnetoresistance), demonstrated that atomically thin ferromagnetic insertion layers strongly modulate the ST-SHA, and used Cu spacer layers to argue against a dominant role of spin memory loss — the loss of spin angular momentum to the lattice by spin-flip scattering at the interface, driven by interfacial spin–orbit coupling, in contrast to the elastic transmission considered in the transparency picture.

The analysis rests on several explicit assumptions: the imaginary part of $G^{\uparrow\downarrow}$ is taken to be much smaller than its real part; Eq. (3) assumes $\lambda$ is significantly smaller than the Pt thickness $d$ ; and the mapping from damping enhancement to $G^{\uparrow\downarrow}$ neglects other damping channels. Subsequent work questioned each of these: two-magnon scattering (a damping channel in which the uniform-precession magnon scatters into short-wavelength magnons, typically mediated by interface or defect inhomogeneity) can mimic spin-pumping damping; first-principles scattering theory (fully relativistic quantum transport calculations of interface-resolved spin currents, e.g. density-functional-based scattering theory) gives Pt spin-flip diffusion lengths near 5 nm at room temperature and substantial spin memory loss parameters at Co|Pt and Py|Pt; and the drift-diffusion model (the standard semiclassical description in which spin currents are driven by gradients of the spin accumulation) on which the $\lambda$ -based framework rests has been shown to break down for transverse spin transport in disordered Pt.

Problem Statement

Establish a quantitative, experimentally validated microscopic account of spin-current transmission at platinum–ferromagnet interfaces that explains and reconciles the physical picture of the 2015 Nature Physics study and its successors. Specifically: (1) determine the atomistic and electronic-structure origin of the large difference in spin-current transparency between Pt/Co and Pt/permalloy (and the Pt/Co $_{1-x}$ Ni $_x$ alloy series), that is, the relative contributions of elastic transmission from electronic band matching across the interface, interfacial spin–orbit-coupling-induced spin-flip scattering (spin memory loss), and bulk spin–orbit-coupling mechanisms; (2) establish the role of the imaginary part of the spin-mixing conductance $G^{\uparrow\downarrow}$ , neglected in the original transparency analysis, both in the definition of the transparency and in the extraction of $G^{\uparrow\downarrow}$ from Gilbert-damping enhancement (which must also be disentangled from two-magnon and other extraneous damping channels); (3) settle the validity of the spin-diffusion treatment behind the transparency mapping — the assumption that the spin diffusion length $\lambda$ is significantly smaller than the Pt thickness $d$ , the value of $\lambda$ for Pt, and whether the reported breakdown of the drift-diffusion framework for transverse spin transport in disordered Pt invalidates that treatment at the Pt thicknesses, growth conditions and temperatures relevant to the ST-FMR and damping measurements, and what measurement or calculation would settle the question; and (4) quantitatively disentangle elastic (transmission) from inelastic (spin-flip) interfacial spin-current processes for these interfaces — Pt/Co, Pt/permalloy and the Pt/Co $_{1-x}$ Ni $_x$ series. The four parts are jointly required to resolve the task, and each is an independently checkable sub-question whose separate resolution settles only that sub-question. Together they must yield an account whose quantitative predictions agree with the published ST-FMR, Gilbert-damping and spin-pumping measurements for these interfaces. Other heavy-metal/ferromagnet interfaces and device-relevant multilayer stacks lie outside the scope of these four parts. The common objective of all four parts is to fix, within a validated microscopic and experimental framework, the interfacial parameters governing spin-current transmission and thereby the intrinsic spin Hall angle of platinum.

References

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