Quantifying Spin-Orbit Torques in Antiferromagnet--Heavy-Metal Heterostructures

Quantifying Spin-Orbit Torques in Antiferromagnet–Heavy-Metal Heterostructures

Egecan Cogulu, Hantao Zhang, Nahuel N. Statuto, Yang Cheng, Fengyuan Yang, Ran Cheng, and Andrew D. Kent

Phys. Rev. Lett. 128, 247204 – Published 17 June 2022

Abstract

The effect of spin currents on the magnetic order of insulating antiferromagnets (AFMs) is of fundamental interest and can enable new applications. Toward this goal, characterizing the spin-orbit torques (SOTs) associated with AFM–heavy-metal (HM) interfaces is important. Here we report the full angular dependence of the harmonic Hall voltages in a predominantly easy-plane AFM, epitaxial $c$ -axis oriented $α − {Fe}_{2} O_{3}$ films, with an interface to Pt. By modeling the harmonic Hall signals together with the $α − {Fe}_{2} O_{3}$ magnetic parameters, we determine the amplitudes of fieldlike and dampinglike SOTs. Out-of-plane field scans are shown to be essential to determining the dampinglike component of the torques. In contrast to ferromagnetic–heavy-metal heterostructures, our results demonstrate that the fieldlike torques are significantly larger than the dampinglike torques, which we correlate with the presence of a large imaginary component of the interface spin-mixing conductance. Our work demonstrates a direct way of characterizing SOTs in AFM-HM heterostructures.

Received 20 December 2021
Accepted 2 June 2022

DOI:https://doi.org/10.1103/PhysRevLett.128.247204

Physics Subject Headings (PhySH)

Antiferromagnetism Magnetization dynamics Spin Hall magnetoresistance Spin dynamics Spin torque

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Egecan Cogulu ¹, Hantao Zhang ², Nahuel N. Statuto¹, Yang Cheng³, Fengyuan Yang³, Ran Cheng ^2,4, and Andrew D. Kent ¹

¹Center for Quantum Phenomena, Department of Physics, New York University, New York 10003, USA
²Department of Electrical and Computer Engineering, University of California, Riverside, California 92521, USA
³Department of Physics, The Ohio State University, Columbus, Ohio 43210, USA
⁴Department of Physics and Astronomy, University of California, Riverside, California 92521, USA

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Vol. 128, Iss. 24 — 17 June 2022

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Images

Figure 1
(a) Transverse measurement configuration showing the Pt Hall cross with $5 μ m$ channel width. An ac current $J_{ac}$ is applied in the $\hat{x}$ direction, and the transverse voltage $V_{x y}$ is measured with a lock-in amplifier. (b) Modeling geometry. $D$ represents both the DMI vector and the hard axis direction that defines the easy plane. $m_{1}$ and $m_{2}$ are the sublattice moments and $H$ is the external magnetic field. The spin accumulation $σ_{ac}$ is in the $\hat{y}$ direction. The resulting spin-orbit torques on the sublattice moments are decomposed into fieldlike ( $τ_{FL}$ ) and dampinglike components ( $τ_{DL}$ ).
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Figure 2
Angular dependence of first and second harmonic (columns) resistance signals in $X Y$ , $X Z$ , and $Y Z$ scans (rows) at $μ_{0} H = 3 T$ . The current amplitudes are $100 μ A$ and 1.5 mA in the first and second harmonic measurements, respectively. The blue dots are the data points whereas, the red line is the fit resulting from our model that is described in the main text. The geometry of magnetic field scans in the three principal planes ( $X Y$ , $X Z$ , and $Y Z$ scans) and the definition of the angles $α$ , $β$ , and $γ$ are shown at the top. The magnitude of longitudinal SMR is approximately 0.02% and it is consistent with studies on similar AFM-HM systems [24, 28].
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Figure 3
Separating Hall effect and spin Seebeck effect contributions. (a) Field dependence of the first harmonic response in $Y Z$ scan, from 0 to 8 T as indicated by the legend. (b) The Hall effect in the first harmonic $Y Z$ scan (a), as a function of applied field. The linear trend line supports the claim that the origin of the signal is the ordinary Hall effect. (c) Field dependence of the second harmonic response in the $X Y$ scan, which shares the same legend as (a). (d) Antiferromagnetic spin Seebeck effect (SSE) separated from fieldlike SOT in the second harmonic $X Y$ scan (c), as a function of applied field. The fieldlike component scales as $1 / H$ , whereas the SSE component scales linearly with $H$ .
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Figure 4
(a) Imaginary (left) and real (right) parts of the spin mixing conductance ( $g = g_{r} + i g_{i}$ ) of an AFM-NM interface. The scale is indicated by the shared color bar on the right, with units of $ℏ$ per unit area $a^{2}$ on the interface, where $a$ is the lattice constant. (b) Ratio of $| g_{i} |$ to $| g_{r} |$ . As $λ$ approaches zero $| g_{i} |$ dominates over $| g_{r} |$ . The dashed line shows $| g_{i} | = | g_{r} |$ , which separates the fieldlike torque dominating region ( $g_{i} > g_{r}$ ) on the left from the dampinglike torque dominating region ( $g_{r} > g_{i}$ ) on the right. The color bar scale is logarithmic in this case. The inset shows a line cut of $g_{r}$ and $g_{i}$ vs $λ$ at $δ = 0.25$ . Even though they both approach zero as $λ$ goes to zero, $g_{r}$ decreases faster than $g_{i}$ and their ratio $g_{i} / g_{r}$ diverges.
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