Spin transfer torque ferromagnetic resonance induced spin pumping in the Fe/Pd bilayer system

A. Kumar, S. Akansel, H. Stopfel, M. Fazlali, J. Åkerman, R. Brucas, and P. Svedlindh

Phys. Rev. B 95, 064406 – Published 8 February 2017

Abstract

Inconsistencies in estimates of the spin Hall angle ( $θ_{S H}$ ) and spin diffusion length ( $λ_{S D}$ ) of nonmagnetic (NM) layers using the spin transfer torque ferromagnetic resonance (ST-FMR) in ferromagnetic FM/NM bilayer structures are attributed to the inverse spin Hall effect (ISHE) and interfacial parameter contributions, interface spin transparency, interfacial anisotropic magnetoresistance, and effective spin-mixing conductance. These contributions in Fe(10 nm)/Pd(2–8 nm) bilayer structures have been probed employing the simultaneous detection of ST-FMR and ISHE in conjunction with in-plane FMR measurements. The interfacial contributions are found to increase with an increase in Pd layer thickness ( $t_{N M}$ ), which can be linked to the spin pumping effect in conjunction with spin backflow. Correcting the $t_{N M}$ dependence of the ST-FMR spectra for the interfacial and ISHE contributions prior to estimating $θ_{S H}$ and $λ_{S D}$ of the Pd layer, the estimated values are found to be $0.10 \pm 0.03$ and $5.4 \pm 1.2 nm$ , respectively.

Received 9 November 2016
Revised 13 January 2017

DOI:https://doi.org/10.1103/PhysRevB.95.064406

Physics Subject Headings (PhySH)

Spin current Spin transfer torque Spintronics

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

A. Kumar^1,*, S. Akansel¹, H. Stopfel², M. Fazlali³, J. Åkerman³, R. Brucas¹, and P. Svedlindh^1,†

¹Department of Engineering Sciences, Uppsala University, Box 534, SE-751 21 Uppsala, Sweden
²Department of Physics and Astronomy, Uppsala University, Box 516, SE-751 20 Uppsala, Sweden
³Department of Physics, University of Gothenburg, SE-41296 Göteborg, Sweden

^*Ankit.Kumar@angstrom.uu.se
^†Peter.Svedlindh@angstrom.uu.se

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Vol. 95, Iss. 6 — 1 February 2017

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Images

Figure 1
(a) Layout of the low-noise ST-FMR setup employed to measure ST-FMR and FMR spectra. Left and right picoprobes are used to record the signal along and transverse to $I_{R F}$ , respectively. (b) Schematic of ST-torque-induced precession of the magnetization $\vec{m}$ around its equilibrium direction at the driving frequency ω and phase delay $φ_{0}$ . Applied field ${\vec{H}}_{d c}$ is at 45 deg (α) to the direction of $I_{R F}$ , ψ is the angle of $\vec{m}$ with respect to the XY plane, and θ is the cone angle. $τ_{S T T}$ , $τ_{H}$ , and, $τ_{α}$ are ST torque, fieldlike torque, and dampinglike torque, respectively. (c) Geometry of the Fe/Pd bilayer patterned structure in which ST-FMR is measured along and transverse to $I_{R F}$ .
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Figure 2
Experimental data points and simulated (red line) specular XRR profiles for all samples.
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Figure 3
(a) Room temperature in-plane FMR spectra of the Fe(10 nm)/Pd(4 nm) sample recorded at different frequencies. Red lines correspond to fitted Lorentzian derivative functions to extract the line-shape parameters. (b) Linewidth vs frequency of all samples $Fe (10 nm) / Pd (t_{N M} = 2, 4, 6, 8 nm)$ ; fits according to Eq. (1) are shown as red lines. (c) Frequency vs resonance field for all samples $Fe (10 nm) / Pd (t_{N M} = 2, 4, 6, 8 nm)$ ; fits according to Kittel's equation [Eq. (2)] are shown as red lines. Inset shows $t_{N M}$ -dependent $μ_{0} M_{eff}$ values extracted from the fits and $μ_{0} M_{s}$ values extracted using magnetometry. (d) $t_{N M}$ -dependent effective Gilbert's damping constant fitted using Eq. (3) to extract the values of the real spin-mixing conductance and spin diffusion length. Inset shows the $t_{N M}$ dependence of the effective spin-mixing conductance and interface transparency of the $Fe / Pd (t_{N M})$ bilayer system.
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Figure 4
ST-FMR spectra for the Fe(10 nm)/Pd(4 nm) bilayer sample recorded (a) along $I_{R F}$ , (c) transverse to $I_{R F}$ scanning the magnetic field on the negative side, and (b) along $I_{R F}$ , (d) transverse to $I_{R F}$ scanning the magnetic field on the positive side. Red lines correspond to fits using Eq. (6), and insets show the power-dependent changes in the symmetric contribution to the spectrum recorded at 7 GHz.
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Figure 5
Symmetric-to-antisymmetric voltage ratio vs $t_{N M}$ observed (a) along $I_{R F}$ and (c) transverse to $I_{R F}$ . Linewidth vs frequency for the $Fe (10 nm) / Pd (t_{N M} = 2, 4, 6, 8 nm)$ samples recorded (b) along $I_{R F}$ and (d) transverse to $I_{R F}$ . Red lines correspond to fits using Eq. (1) to estimate effective Gilbert's damping constant values. (e) Effective Gilbert's damping constant vs $t_{N M}$ recorded along and transverse to $I_{R F}$ .
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Figure 6
(a) Ellipticity correction factor, (b) $J_{S} / J_{C}^{N M}$ , (c) $η$ ( $V_{ST - FMR}^{sym}$ weight factor due to ST-FMR), and (d) ISHE and interface transparency corrected $J_{S} / J_{C}^{N M}$ vs $t_{N M}$ .
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