Magnetization-dependent inverse spin Hall effect in compensated ferrimagnet TbCo alloys

A. Yagmur, S. Sumi, H. Awano, and K. Tanabe

Phys. Rev. B 103, 214408 – Published 2 June 2021

Abstract

In this paper, we demonstrate the magnetization-dependent inverse spin Hall effect (MD-ISHE) in ${Tb}_{x} {Co}_{100 - x} / Pt / Y_{3} {Fe}_{5} O_{12}$ devices using the spin Seebeck effect. It was found that a thermally injected spin current is precessed around the magnetization of the ${Tb}_{x} {Co}_{100 - x}$ alloy before it is converted into a charge current. Furthermore, the sign of the MD-ISHE voltage was found to depend on the Co magnetic moment direction, whereas the sign and magnitude of the conventional ISHE voltage are independent of the ${Tb}_{x} {Co}_{100 - x}$ magnetization direction. Meanwhile, the spin rotation angle was estimated to be ∼12% in ${Tb}_{x} {Co}_{100 - x} / Pt$ . Our findings demonstrate that perpendicularly magnetized ${Tb}_{x} {Co}_{100 - x}$ supplies additional symmetry to the ISHE and provides advantages in terms of tailoring the sign of the spin-current polarization through adjusting the alloy composition.

Received 1 March 2021
Revised 19 April 2021
Accepted 10 May 2021

DOI:https://doi.org/10.1103/PhysRevB.103.214408

Physics Subject Headings (PhySH)

Inverse spin Hall effect Spin Seebeck effect Spin-orbit coupling Spintronics Thermomagnetic effects

Ferrimagnets Magnetic multilayers Transition-metal rare-earth alloys

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

A. Yagmur ^*, S. Sumi, H. Awano , and K. Tanabe

Toyota Technological Institute, Nagoya 468-8511, Japan

^*ayagmur@toyota-ti.ac.jp

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Vol. 103, Iss. 21 — 1 June 2021

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Figure 1
(a) Schematic of the inverse spin Hall effect (ISHE), where an injected spin-current $J_{s}$ is converted into a charge-current $J_{c}$ depending on the cross product of $J_{s}$ and spin-polarization $σ$ . (b) Schematic of the magnetization-dependent ISHE (MD-ISHE), where an injected $J_{s}$ is converted into a $J_{c}$ depending on the cross product of $J_{s}, σ$ , and magnetization M. Schematics of the measurement condition for (c) the ISHE, where the applied magnetic field H was applied along the $x$ direction (orthogonal to the electrodes) and (d) the MD-ISHE, where the H was applied along the $y$ direction (parallel to the electrodes) for the TbCo/Pt/YIG samples. Here, $M^{TbCo}, M^{YIG}, \nabla T$ , and $V$ represent the magnetization of the TbCo alloy and YIG, the applied temperature gradient, and the induced voltage signal, respectively.
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Figure 2
Vibrating sample magnetometry hysteresis loops measured for the ${Tb}_{14} {Co}_{86} / Pt / YIG$ sample in (a) the in-plane direction and (b) the out-of-plane direction.
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Figure 3
$V$ as a function of $H_{x}$ at $Δ T = 8 K$ for the ${Tb}_{14} {Co}_{86} / Pt / YIG$ sample, where the TbCo magnetization was aligned along (a) the $+ z$ direction ( $+ M^{TbCo}$ ) and (b) the $- z$ direction ( $- M^{TbCo}$ ). $V$ as a function of $H_{y}$ at $Δ T = 8 K$ for the ${Tb}_{14} {Co}_{86} / Pt / YIG$ sample where the TbCo magnetization was aligned along (c) the $+ z$ direction ( $+ M^{TbCo}$ ) and (d) the $- z$ direction ( $- M^{TbCo}$ ). (e) Pure magnetization-dependent inverse spin Hall effect (MD-ISHE) $V$ as a function of $H_{y}$ at $Δ T = 8 K$ for the ${Tb}_{14} {Co}_{86} / Pt / YIG$ sample, where the TbCo magnetization was aligned along the $+ z$ direction, obtained by subtracting the (d) data from those in (c) and dividing the result by two. (f) $Δ T$ dependence of the $V$ signal in the $+ M^{TbCo}, - M^{TbCo}$ , and pure MD-ISHE conditions at $H_{y} = + 400 Oe$ for the ${Tb}_{14} {Co}_{86} / Pt / YIG$ sample.
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Figure 4
$V$ as a function of $H_{x}$ at $Δ T = 8 K$ for the ${Tb}_{14} {Co}_{86} / Pt / Si O_{2} / Si$ sample where the TbCo magnetization was aligned along (a) the $+ z$ direction ( $+ M^{TbCo}$ ) and (b) the $- z$ direction ( $- M^{TbCo}$ ). $V$ as a function of $H_{x}$ at $Δ T = 8 K$ for the ${Tb}_{14} {Co}_{86} / Pt / Si O_{2} / Si$ sample where the TbCo magnetization was aligned along (c) the $+ z$ direction ( $+ M^{TbCo}$ ) and (d) the $- z$ direction ( $- M^{TbCo}$ ).
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Figure 5
(a)–(d) Polar magneto-optical Kerr effect (PMOKE) loops for the ${Tb}_{x} {Co}_{100 - x}$ (19 nm)/Pt(1 nm)/YIG samples, where $x = 14$ , 16, 23, and 25, respectively. (e)–(h) The $V$ in the ${Tb}_{x} {Co}_{100 - x}$ /Pt/YIG samples, where $x = 14$ , 16, 23, and 25, respectively, as a function of $H_{x}$ at $Δ T = 8 K$ with the TbCo magnetization saturated along the $+ z$ direction ( $+ M^{TbCo}$ ). (i)–(l) The $V$ in the ${Tb}_{x} {Co}_{100 - x} / Pt / YIG$ samples, where $x = 14$ , 16, 23, and 25, respectively, as a function of $H_{y}$ at $Δ T = 8 K$ , where the $- M^{TbCo}$ data were subtracted from the $+ M^{TbCo}$ data and the result divided by two.
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Figure 6
(a) $V$ and (b) | $V$ | as a function of Tb composition $x %$ in the ${Tb}_{x} {Co}_{100 - x}$ /Pt/YIG samples at $H_{y} = + 400 Oe$ and $Δ T = 8 K$ . (c) The sheet resistance ( $R_{s}$ ) of the ${Tb}_{x} {Co}_{100 - x}$ alloys as a function of Tb concentration $x %$ . (d) $| V | / R_{s}$ as a function of Tb composition $x %$ in the ${Tb}_{x} {Co}_{100 - x}$ /Pt/YIG samples at $H_{y} = + 400 Oe$ and $Δ T = 8 K$ . (e) $| V | / R_{s}$ as a function of Tb composition $x %$ in the ${Tb}_{x} {Co}_{100 - x}$ /Pt/YIG samples at $H_{x} = + 400 Oe$ and $Δ T = 8 K$ . (f) $| θ_{R} | (= | θ_{MD - SH} / θ_{S H} | \times 100$ ) as a function of Tb composition $x %$ in the ${Tb}_{x} {Co}_{100 - x}$ /Pt/YIG samples.
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