Relation between spin Hall effect and anomalous Hall effect in $3d$ ferromagnetic metals

Relation between spin Hall effect and anomalous Hall effect in $3 d$ ferromagnetic metals

Yasutomo Omori, Edurne Sagasta, Yasuhiro Niimi, Martin Gradhand, Luis E. Hueso, Fèlix Casanova, and YoshiChika Otani

Phys. Rev. B 99, 014403 – Published 3 January 2019

Abstract

We study the mechanisms of the spin Hall effect (SHE) and anomalous Hall effect (AHE) in $3 d$ ferromagnetic metals [Fe, Co, permalloy $({Ni}_{81} {Fe}_{19}$ ; Py), and Ni] by varying their resistivities and temperature. At low temperatures where the phonon scattering is negligible, the skew scattering coefficients of the SHE and AHE in Py are related to its spin polarization. However, this simple relation breaks down for Py at higher temperatures as well as for the other ferromagnetic metals at any temperature. We find that, in general, the relation between the SHE and AHE is more complex, with the temperature dependence of the SHE being much stronger than that of AHE.

Received 29 June 2018

DOI:https://doi.org/10.1103/PhysRevB.99.014403

Physics Subject Headings (PhySH)

Anomalous Hall effect Spin Hall effect Spin current Spin polarization

Metals

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Yasutomo Omori¹, Edurne Sagasta², Yasuhiro Niimi^1,3,*, Martin Gradhand⁴, Luis E. Hueso^2,5, Fèlix Casanova^2,5, and YoshiChika Otani^1,6,†

¹Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan
²CIC nanoGUNE, 20018 Donostia-San Sebastian, Basque Country, Spain
³Department of Physics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan
⁴H. H. Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, United Kingdom
⁵IKERBASQUE, Basque Foundation for Science, 48011 Bilbao, Basque Country, Spain
⁶RIKEN-CEMS, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan

^*niimi@phys.sci.osaka-u.ac.jp
^†yotani@issp.u-tokyo.ac.jp

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Vol. 99, Iss. 1 — 1 January 2019

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Images

Figure 1
(a) Intuitive schematic of the SHE and the AHE in FM. Spin and charge accumulations appear in the transverse direction with respect to the incident current $I_{C}$ and are detected as the SHE and the AHE, respectively. (b) Schematic of a lateral spin valve for the spin absorption method to measure the ISHE in FM. The magnetic field $H$ is applied along the Cu wire. (c) Inverse spin Hall resistance $R_{ISHE}$ of the middle Py wire (20 nm in thickness) as a function of $H$ at 10 K using the configuration shown in (b). The ISHE signal $(Δ R_{ISHE})$ is defined in the figure. (d) Anomalous Hall resistance $R_{AHE}$ of Py as a function of $H$ at 10 K. The AHE signal $(Δ R_{AHE})$ is defined in the figure. The inset shows a part of a Hall bar for the AHE measurement. The magnetic field $H$ is applied perpendicular to the plane. Compared to the SHE configuration, the field direction is rotated by $90^{\circ}$ .
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Figure 2
(a) Spin Hall resistivity $- ρ_{x y}^{SHE}$ and (b) anomalous Hall resistivity $- ρ_{x y}^{AHE}$ in Py as a function of $ρ_{x x, 0}$ at 10 K. The solid lines are the best fits with Eq. (2). The same symbol is used in (a) and (b) if the Py deposition is done at the same time for the SHE and AHE samples. The dotted line in (b) indicates $- ρ_{x y}^{AHE} = 0$ .
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Figure 3
(a) Spin Hall angle $θ_{SHE}$ and (b) anomalous Hall angle $θ_{AHE}$ measured at 10 K as a function of the number of electrons in the outermost shell. The thickness of the the $3 d$ FMs is 20 nm. The dotted lines in (a) and (b) indicate $θ_{H} = 0$ .
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Figure 4
The temperature dependence of (a) spin Hall resistivity $- ρ_{x y}^{SHE}$ and (b) anomalous Hall resistivity $- ρ_{x y}^{AHE}$ in four FMs (Py, Fe, Co, and Ni). The thickness of the four FMs is 20 nm both for the SHE and AHE measurements.
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Figure 5
Spin Hall resistivity $- ρ_{x y}^{SHE}$ and anomalous Hall resistivity $- ρ_{x y}^{AHE}$ in four FMs (Fe, Co, Py, and Ni) at finite temperatures. $- ρ_{x y}^{SHE}$ as a function of $ρ_{x x, T}$ in (a) Fe, (c) Co, (e) Py, and (g) Ni. Anomalous Hall resistivity $- ρ_{x y}^{AHE}$ as a function of $ρ_{x x, T}$ in (b) Fe, (d) Co, (f) Py, and (h) Ni. $ρ_{x x, T}$ varies by changing temperature from 10 to 300 K. The solid lines are the best fits of the data to Eq. (3). The thickness of the four FMs is 20 nm both for SHE and AHE measurements except for the inset in (e). The inset in (e) shows $- ρ_{x y}^{SHE}$ of 5-nm-thick Py wire. For the fitting with Eq. (3), the same parameter $β_{1}^{SHE} = - 10.1 (\times 10^{3} Ω^{- 1} {cm}^{- 1})$ was used both for 20-nm and 5-nm-thick Py wires.
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