Interplay of spin-orbit torque and thermoelectric effects in ferromagnet/normal-metal bilayers

Can Onur Avci, Kevin Garello, Mihai Gabureac, Abhijit Ghosh, Andreas Fuhrer, Santos F. Alvarado, and Pietro Gambardella

Phys. Rev. B 90, 224427 – Published 31 December 2014

Abstract

We present harmonic transverse voltage measurements of current-induced thermoelectric and spin-orbit torque (SOT) effects in ferromagnet/normal-metal bilayers, in which thermal gradients produced by Joule heating and SOT coexist and give rise to ac transverse signals with comparable symmetry and magnitude. Based on the symmetry and field dependence of the transverse resistance, we develop a consistent method to separate thermoelectric and SOT measurements. By addressing first ferromagnet/light-metal bilayers with negligible spin-orbit coupling, we show that in-plane current injection induces a vertical thermal gradient whose sign and magnitude are determined by the resistivity difference and stacking order of the magnetic and nonmagnetic layers. We then study ferromagnet/heavy-metal bilayers with strong spin-orbit coupling, showing that second harmonic thermoelectric contributions to the transverse voltage may lead to a significant overestimation of the antidamping SOT. We find that thermoelectric effects are very strong in Ta(6 nm)/Co(2.5 nm) and negligible in Pt(6 nm)/Co(2.5 nm) bilayers. After including these effects in the analysis of the transverse voltage, we find that the antidamping SOTs in these bilayers, after normalization to the magnetization volume, are comparable to those found in thinner Co layers with perpendicular magnetization, whereas the fieldlike SOTs are about an order of magnitude smaller.

Received 26 August 2014
Revised 11 November 2014

DOI:https://doi.org/10.1103/PhysRevB.90.224427

Authors & Affiliations

Can Onur Avci^1,*, Kevin Garello¹, Mihai Gabureac¹, Abhijit Ghosh¹, Andreas Fuhrer², Santos F. Alvarado¹, and Pietro Gambardella¹

¹Department of Materials, ETH Zürich, Hönggerbergring 64, CH-8093 Zürich, Switzerland
²IBM Research - Zurich, Säumerstrasse 4, CH-8803 Rüschlikon, Switzerland

^*can.onur.avci@mat.ethz.ch

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Vol. 90, Iss. 22 — 1 December 2014

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Images

Figure 1
(a) Experimental setup and coordinate system. Oscillations of the magnetization due to (b) the fieldlike SOT and Oersted field $(T_{FL} + T_{Oe})$ , and (c) antidamping SOT $(T_{AD})$ induced by an ac current. (d) Schematic of the vertical thermal gradient produced by an in-plane current. Simulations of the (e) first harmonic and (f)–(h) second harmonic transverse resistance corresponding to (f) fieldlike torque, (g) antidamping torque, and (h) ANE due to an ac current.
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Figure 2
(a) $R_{H}^{ω}$ and (b) $R_{H}^{2 ω}$ measured for Ti/Co, Cu/Co, and Co layers. (c) $R_{FL}^{2 ω}$ component of the second harmonic signal obtained by subtraction of the $cos φ$ fits performed by taking into account the symmetry considerations given in Sec. 2d. (d) Comparison of $R_{H}^{2 ω}$ for Cu/Co and Co/Cu inverted stacks. All the measurements are performed at $j = 10^{7} {A / cm}^{2}$ and $B_{ext} = 200$ mT, except for the inverted Co/Cu sample for which $B_{ext} = 80$ mT in order to show data with comparable Oersted and ANE contributions. A small constant offset due to misalignment of the Hall branches is subtracted from all first and second harmonic signals.
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Figure 3
(a) $cos φ$ contribution of $R_{H}^{2 ω}$ normalized to the value recorded at $B_{ext} = 240$ mT as a function of the external field for Ti/Co and Co. (b) $R_{FL}^{2 ω}$ as a function of the inverse external field. (c) $cos φ$ signal amplitudes (electric field in the main panel, resistance in inset) as a function of the injected current density.
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Figure 4
(a) $R_{x y}^{ω}$ of Pt/Co and (b) Ta/Co measured at 162 mT. The solid line is a $sin (2 φ)$ fit of the experimental data. (c), (d) Top panels: $R_{x y}^{2 ω}$ of Pt/Co (c) and Ta/Co (d) for 2 different applied fields. Middle panels: $R_{AD}^{2 ω} + R_{\nabla T}^{2 ω}$ . Bottom panels: $R_{FL}^{2 ω}$ . A small constant offset due to misalignment of the Hall branches has been subtracted from the $R_{x y}^{ω}$ and $R_{x y}^{2 ω}$ signals.
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Figure 5
External field dependence of (a) $R_{AD}^{2 ω} + R_{\nabla T}^{2 ω}$ and (b) $R_{FL}^{2 ω}$ in Pt/Co, Ta/Co, and Co normalized to the values at $B_{ext} = 162$ mT. (c) $R_{AD}^{2 ω} + R_{\nabla T}^{2 ω}$ and (d) $R_{FL}^{2 ω}$ as a function of the inverse of the static fields acting against the current-induced field in each case [see Eq. (6)].
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Figure 6
FL and AD torques as a function of the external field in (a) Pt/Co and (b) Ta/Co bilayers. The current density is $j = 10^{7} {A / cm}^{2}$ in both samples. The hatched gray area encloses unreliable data due to incomplete saturation of the magnetization. The shaded green area in (b) shows the range of the Oersted field in Ta/Co, depending on the current distribution within the bilayer.
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