Spin Hall Magnetoresistance in Metallic Bilayers

Junyeon Kim, Peng Sheng, Saburo Takahashi, Seiji Mitani, and Masamitsu Hayashi

Phys. Rev. Lett. 116, 097201 – Published 29 February 2016

Abstract

Spin Hall magnetoresistance (SMR) is studied in metallic bilayers that consist of a heavy metal (HM) layer and a ferromagnetic metal (FM) layer. We find a nearly tenfold increase of SMR in $W / CoFeB$ compared to previously studied HM/ferromagnetic insulator systems. The SMR increases with decreasing temperature despite the negligible change in the W layer resistivity. A model is developed to account for the absorption of the longitudinal spin current to the FM layer, one of the key characteristics of a metallic ferromagnet. We find that the model not only quantitatively describes the HM layer thickness dependence of SMR, allowing accurate estimation of the spin Hall angle and the spin diffusion length of the HM layer, but also can account for the temperature dependence of SMR by assuming a temperature dependent spin polarization of the FM layer. These results illustrate the unique role a metallic ferromagnetic layer plays in defining spin transmission across the $HM / FM$ interface.

Received 4 September 2015

DOI:https://doi.org/10.1103/PhysRevLett.116.097201

Physics Subject Headings (PhySH)

Magnetoresistance Spin Hall effect

Bilayer films

Sputtering Transport techniques

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Junyeon Kim¹, Peng Sheng¹, Saburo Takahashi², Seiji Mitani¹, and Masamitsu Hayashi^1,*

¹National Institute for Materials Science, Tsukuba 305-0047, Japan
²Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan

^*hayashi.masamitsu@nims.go.jp

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Vol. 116, Iss. 9 — 4 March 2016

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Images

Figure 1
(a) Schematic illustration of the system including the definition of the coordinate axis. (b),(c) Magnetic moment per unit volume ( $M / V$ ) plotted as a function of the HM layer thickness for $W / CoFeB / MgO$ (b) and $Ta / CoFeB / MgO$ (c). (d),(e) The HM layer thickness dependence of the magnetic anisotropy energy ( $K_{EFF}$ ) for $W / CoFeB / MgO$ (d) and $Ta / CoFeB / MgO$ (e). Black squares and red circles represent results of as deposited and annealed films, respectively.
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Figure 2
(a),(b) The longitudinal resistance $R_{X X}$ plotted against magnetic field oriented along the $x$ axis (black squares), $y$ axis (red circles), and $z$ axis (blue triangles) for the as deposited (a) and annealed (b) W underlayer films. The W underlayer thickness is $\sim 3.3$ (a) and $\sim 3.6 nm$ (b).
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Figure 3
(a),(b) Inverse of the film sheet resistance $1 / {R_{X X}}^{0}$ ( $L / w$ ) plotted as a function of HM layer thickness for $W / CoFeB / MgO$ (a) and $Ta / CoFeB / MgO$ (b). The solid lines are linear fit to the data. (c),(d) Spin Hall magnetoresistance $Δ R_{X X}^{SMR} / R_{X X}^{0}$ plotted against the HM layer thickness for $W / CoFeB / MgO$ (c) and $Ta / CoFeB / MgO$ (d). The solid lines show the fitting results using model $B$ [ $g_{F} \neq 0$ in Eq. (1)]. Model $A$ [ $g_{F} = 0$ in Eq. (1)] returns similar curves. Parameters used in the fitting are the following: Model $A$ , $Re [G_{MIX}] = 10^{15} Ω^{- 1} {cm}^{- 2}$ . Model $B$ , $P = 0.72$ , $ρ_{F} = 160 μ Ω cm$ , $t_{F} = 1 nm$ , $λ_{F} = 1 nm$ , $Re [G_{MIX}] = 10^{15} Ω^{- 1} {cm}^{- 2}$ . For both models, $ρ_{N}$ is obtained from Table 1. (a)–(d) Black squares and red circles represent results of as deposited and annealed films, respectively.
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Figure 4
(a) W layer thickness dependence of the spin Hall magnetoresistance $Δ R_{X X}^{SMR} / R_{X X}^{0}$ for the annealed W underlayer films measured at different temperatures. The solid lines show fitting results with model $B$ . (b) The maximum $| Δ R_{X X}^{SMR} / R_{X X}^{0} |$ (red squares) and the resistivity ( $ρ_{N}$ ) of the $W$ underlayer (black circles) plotted as a function of measurement temperature. (c) Temperature dependence of the spin Hall angle ( $θ_{SH}$ ) and the spin diffusion length ( $λ_{N}$ ) of the W layer estimated from fitting the results of (a) using model $A$ [ $g_{F} = 0$ in Eq. (1)]. $ρ_{N} = 125 μ Ω cm$ , $Re [G_{MIX}] = 10^{15} Ω^{- 1} {cm}^{- 2}$ are used in the fitting with model $A$ . (d) Temperature dependence of the spin polarization ( $P$ ) of the ferromagnetic layer obtained from fitting the results of (a) with model $B$ [ $g_{F} \neq 0$ in Eq. (1)]. $ρ_{N} = 125 μ Ω cm$ , $| θ_{SH} | = 0.27$ and $λ_{N} = 1.26 nm$ are fixed to their room temperature value, $ρ_{F} = 160 μ Ω cm$ , $t_{F} = 1 nm$ , $λ_{F} = 1 nm$ , $Re [G_{MIX}] = 10^{15} Ω^{- 1} {cm}^{- 2}$ are assumed in the fitting with model $B$ . The error bars indicate the fitting errors.
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