Temperature-Dependent Spin Transport and Current-Induced Torques in Superconductor-Ferromagnet Heterostructures

M. Müller, L. Liensberger, L. Flacke, H. Huebl, A. Kamra, W. Belzig, R. Gross, M. Weiler, and M. Althammer

Phys. Rev. Lett. 126, 087201 – Published 22 February 2021

Abstract

We investigate the injection of quasiparticle spin currents into a superconductor via spin pumping from an adjacent ferromagnetic metal layer. To this end, we use NbN- ${Ni}_{80} {Fe}_{20} (Py)$ heterostructures with a Pt spin sink layer and excite ferromagnetic resonance in the Permalloy layer by placing the samples onto a coplanar waveguide. A phase sensitive detection of the microwave transmission signal is used to quantitatively extract the inductive coupling strength between the sample and the coplanar waveguide, interpreted in terms of inverse current-induced torques, in our heterostructures as a function of temperature. Below the superconducting transition temperature $T_{c}$ , we observe a suppression of the dampinglike torque generated in the Pt layer by the inverse spin Hall effect, which can be understood by the changes in spin current transport in the superconducting NbN layer. Moreover, below $T_{c}$ we find a large fieldlike current-induced torque.

Received 30 July 2020
Revised 1 December 2020
Accepted 21 January 2021

DOI:https://doi.org/10.1103/PhysRevLett.126.087201

Physics Subject Headings (PhySH)

Spintronics Superconductivity

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

M. Müller ^1,2,*, L. Liensberger^1,2, L. Flacke ^1,2, H. Huebl ^1,2,3, A. Kamra⁴, W. Belzig ⁵, R. Gross ^1,2,3, M. Weiler^1,2,‡, and M. Althammer ^1,2,†

¹Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, 85748 Garching, Germany
²Physik-Department, Technische Universität München, 85748 Garching, Germany
³Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, 80799 München, Germany
⁴Center for Quantum Spintronics, Department of Physics, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
⁵Fachbereich Physik, Universität Konstanz, 78457 Konstanz, Germany

^*Corresponding author. manuel.mueller@wmi.badw.de
^†Corresponding author. matthias.althammer@wmi.badw.de
^‡Present address: Fachbereich Physik and Landesforschungszentrum OPTIMAS, Technische Universität Kaiserslautern, Gottlieb-Daimler-Straße 46, 67663 Kaiserslautern, Germany.

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Issue

Vol. 126, Iss. 8 — 26 February 2021

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Images

Figure 1
(a) Layer stack of samples investigated in this Letter. Numbers show the layer thicknesses in nm. For bbFMR, the samples are mounted facedown on top of a coplanar waveguide. (b) Sketch of the measurement geometry for in-plane bbFMR and schematic illustration for the generation of the charge current density $J_{q}^{iSHE}$ by ac iSHE. The ac flux $H^{iSHE}$ generated by $J_{q}^{iSHE}$ is coupled into the CPW. In (c) and (d), the change in complex transmission is plotted versus the applied external field $μ_{0} H_{ext}$ both slightly above and below $T_{c}$ for sample B ( $T_{c} = 9.0 K$ ). Both the FMR amplitude and phase exhibit clear changes in the SC state. The lines in (c) and (d) represent Polder susceptibility $χ$ fits to Eq. (S21).
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Figure 2
Inductive coupling parameters for sample B with the stack sequence Pt (5 nm)–NbN (16 nm)–Py (6 nm)– ${TaO}_{x}$ (2 nm) plotted as a function of reduced temperature around $T_{c}$ . In (a), we plot the real (triangles) and imaginary (squares) parts of the inductive coupling offset ${\tilde{L}}_{0}$ . The lines indicate the scaled superfluid condensate density $n_{s}$ following BCS theory. In (b), we show the real (triangles) and imaginary (squares) parts of the complex linear frequency dependence $Δ {\tilde{L}}_{j}$ of the normalized inductance $\tilde{L}$ . The error bars originate from fitting the extracted raw data for $\tilde{L}$ with Eq. (1).
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Figure 3
(a) Dampinglike current-induced torque conductivity $σ_{d}$ plotted as a function of $T / T_{c}$ . In the normal state, the samples containing Pt exhibit large positive $σ_{d}$ due to the iSHE in Pt. Below $T_{c}$ , all samples exhibit a very similar decay of $σ_{d}$ with decreasing $T$ irrespective of Pt spin sink layer. (b) Temperature dependence of the Gilbert damping $α$ in the SC state as a function of $T / T_{c}$ . The apparent decrease of $α$ is due to the suppression of spin pumping into the SC due to the freeze-out of thermally excited quasiparticles. The error bars originate from fitting the extracted raw data for $\tilde{L}$ with Eq. (S42) (a) and Eq. (S17) for $Δ H (f)$ (b).
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Figure 4
(a) Extracted fieldlike current-induced torque $σ_{f}$ plotted as a function of $T / T_{c}$ . Due to a complex surface impedance $Z_{eff} (ω)$ in the SC, the Faraday contribution $σ_{f}^{Faraday}$ creates an offset in $Im (\tilde{L})$ and only affects $σ_{f}$ above $T_{c}$ . We marked the corresponding temperature range with an orange background. In the SC state, we detect a substantial positive $σ_{f}$ . (b) Change in $Im (\tilde{L})$ in the SC state due to SC Faraday currents. The error bars in (a) and (b) originate from fitting the extracted raw data for $(\tilde{L})$ with Eq. (S42).
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