Inductive detection of fieldlike and dampinglike ac inverse spin-orbit torques in ferromagnet/normal-metal bilayers

Andrew J. Berger, Eric R. J. Edwards, Hans T. Nembach, Alexy D. Karenowska, Mathias Weiler, and Thomas J. Silva

Phys. Rev. B 97, 094407 – Published 7 March 2018

Abstract

Functional spintronic devices rely on spin-charge interconversion effects, such as the reciprocal processes of electric field-driven spin torque and magnetization dynamics-driven spin and charge flow. Both dampinglike and fieldlike spin-orbit torques have been observed in the forward process of current-driven spin torque and dampinglike inverse spin-orbit torque has been well studied via spin pumping into heavy metal layers. Here, we demonstrate that established microwave transmission spectroscopy of ferromagnet/normal metal bilayers under ferromagnetic resonance can be used to inductively detect the ac charge currents driven by the inverse spin-charge conversion processes. This technique relies on vector network analyzer ferromagnetic resonance (VNA-FMR) measurements. We show that in addition to the commonly extracted spectroscopic information, VNA-FMR measurements can be used to quantify the magnitude and phase of all ac charge currents in the sample, including those due to spin pumping and spin-charge conversion. Our findings reveal that ${Ni}_{80} {Fe}_{20} /Pt$ bilayers exhibit both dampinglike and fieldlike inverse spin-orbit torques. While the magnitudes of both the dampinglike and fieldlike inverse spin-orbit torque are of comparable scale to prior reported values for similar material systems, we observed a significant dependence of the dampinglike magnitude on the order of deposition. This suggests interface quality plays an important role in the overall strength of the dampinglike spin-to-charge conversion.

Received 30 October 2017
Revised 26 January 2018
Corrected 26 September 2018

DOI:https://doi.org/10.1103/PhysRevB.97.094407

Physics Subject Headings (PhySH)

Dzyaloshinskii-Moriya interaction Ferromagnetism Inverse spin Hall effect Rashba coupling Spin Hall effect Spin current Spin pumping Spin torque Spin-orbit coupling Spintronics

Condensed Matter, Materials & Applied Physics

Corrections

26 September 2018

Correction: A sign error has been fixed in an inline equation in Sec. 3a2, in the second paragraph after Eq. (20).

Authors & Affiliations

Andrew J. Berger¹, Eric R. J. Edwards¹, Hans T. Nembach¹, Alexy D. Karenowska², Mathias Weiler^3,4, and Thomas J. Silva^1,*

¹Quantum Electromagnetics Division, National Institute of Standards and Technology, Boulder, Colorado 80305, USA
²Department of Physics, University of Oxford, Oxford, United Kingdom
³Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, Garching, Germany
⁴Physik-Department, Technische Universität München, Garching, Germany

^*thomas.silva@nist.gov

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Issue

Vol. 97, Iss. 9 — 1 March 2018

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Images

Figure 1
(a) Sample on CPW, showing out-of-plane field $H_{0}$ and sample length $l$ . The microwave driving field points primarily along $\hat{y}$ at the sample. (b) Schematic of the bilayer, with precessing magnetization $m (t)$ at time $t_{0}$ when $m = 〈 m_{x}, 0, m_{z} 〉$ . Bilayer is insulated from CPW using photoresist spacer layer (not shown). At this instant in time, $J_{e}^{F}$ (due to the Faraday effect in the NM) and $J_{e}^{SOT}$ (e.g., due to inverse Rashba-Edelstein effect) are maximal along $\pm \hat{x}$ , and $h_{y}$ is also at its maximum strength. The corresponding Oersted fields from $J_{e}^{F}$ and $J_{e}^{SOT}$ are superposed. The spin accumulation (with orientation $\hat{s}$ ) and $J_{e}^{SOT}$ are produced at the FM/NM interface. Interface normal is given by $\hat{n}$ . (c) Same as (b), except at time $t_{1}$ when $m = 〈 0, m_{y}, m_{z} 〉$ . Here, odd-symmetry SOT current $J_{o}^{SOT}$ (e.g., due to inverse spin Hall effect), and the dynamic fields $H_{o}^{SOT}$ and $H_{dipole}$ are at maximum amplitude. Note that the dipolar signal is proportional to $\partial_{t} (H_{dipole} \cdot \hat{y})$ , and not simply to $H_{dipole}$ . Spin flow direction ${\hat{Q}}_{\hat{s}}$ due to spin pumping into the NM is also shown. (d) Amplitude of driving field $h_{y}$ and different signal sources as a function of time (left), and viewed in the complex plane at time $t_{0}$ (right). Relative amplitudes not indicated. For further discussion of signal phases, see Ref. [23].
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Figure 2
Example $S_{21}$ spectrum, acquired at $f = 20.0$ GHz. (a) Raw data, with fits. Note the different background offsets of the Re and Im data (left and right axes). (b) De-embedded $Δ S_{21}$ signal.
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Figure 3
FMR spectra for FM/NM bilayers. $Re (Δ S_{21})$ at several excitation frequencies for different samples: (a) Py/Cu, (b) Cu/Py, (c) Py/Pt, and (d) Pt/Py. The change in line shape and amplitude for Py/Pt and Pt/Py clearly shows the presence of frequency-dependent inductive terms not present in the Py/Cu and Cu/Py control samples. The colored circles indicate the value of $Re (Δ S_{21}) \propto Re (L)$ when $H_{0}$ satisfies the out-of-plane FMR condition.
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Figure 4
Frequency dependence of real and imaginary inductances extracted from $S_{21}$ spectra (symbols) and fits to Eqs. (21) and (22) (lines). (a) $Re (\tilde{L})$ for all samples with $l = 8 mm$ . Zero-frequency intercept indicates the dipolar inductive coupling, while the linear slope reflects $(σ_{e}^{F} - σ_{e}^{SOT})$ . (b) $Im (\tilde{L})$ for all samples, as a function of frequency, where the linear slope is governed by $σ_{o}^{SOT}$ .
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Figure 5
$\tilde{L} (f = 0)$ and $\partial \tilde{L} / \partial f$ extracted from data as in Fig. 4 vs sample length for all samples. (a) Dipolar inductive coupling ${\tilde{L}}_{0}$ . (b) From $\partial [Re (\tilde{L})] / \partial f$ , we extract $(σ_{e}^{F} - σ_{e}^{SOT})$ . (c) From $\partial [Im (\tilde{L})] / \partial f$ , we extract $σ_{o}^{SOT}$ . Dashed lines are guides based on Eqs. (21) and (22) with values of $σ_{o}^{SOT}$ and $(σ_{e}^{F} - σ_{e}^{SOT})$ calculated as described in Sec. 3c. Several measurements were repeated to demonstrate reproducibility.
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