Observation of Magnetic State Dependent Thermoelectricity in Superconducting Spin Valves

César González-Ruano, Diego Caso, Jabir Ali Ouassou, Coriolan Tiusan, Yuan Lu, Jacob Linder, and Farkhad G. Aliev

Phys. Rev. Lett. 130, 237001 – Published 7 June 2023

Abstract

Superconductor-ferromagnet tunnel junctions demonstrate giant thermoelectric effects that are being exploited to engineer ultrasensitive terahertz radiation detectors. Here, we experimentally observe the recently predicted complete magnetic control over thermoelectric effects in a superconducting spin valve, including the dependence of its sign on the magnetic state of the spin valve. The description of the experimental results is improved by the introduction of an interfacial domain wall in the spin filter layer interfacing the superconductor. Surprisingly, the application of high in-plane magnetic fields induces a double sign inversion of the thermoelectric effect, which exhibits large values even at applied fields twice the superconducting critical field.

Received 2 December 2022
Revised 3 March 2023
Accepted 8 May 2023

DOI:https://doi.org/10.1103/PhysRevLett.130.237001

Physics Subject Headings (PhySH)

Spintronics Superconductors Thermal batteries

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

César González-Ruano ¹, Diego Caso ¹, Jabir Ali Ouassou ², Coriolan Tiusan^3,4, Yuan Lu ⁴, Jacob Linder², and Farkhad G. Aliev ^5,*

¹Departamento Física de la Materia Condensada C-III, Universidad Autónoma de Madrid, Madrid 28049, Spain
²Center for Quantum Spintronics, Department of Physics, Norwegian University of Science and Technology, NO-M7T9Q Trondheim, Norway
³Department of Solid State Physics and Advanced Technologies, Faculty of Physics, Babes-Bolyai University, Cluj Napoca 400114, Romania
⁴Institut Jean Lamour, Nancy Universitè, 54506 Vandoeuvre-les-Nancy Cedex, France
⁵Departamento Física de la Materia Condensada C-III, Instituto Nicolás Cabrera (INC) and Condensed Matter Physics Institute (IFIMAC), Universidad Autónoma de Madrid, Madrid 28049, Spain

^*Corresponding author. farkhad.aliev@uam.es

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Issue

Vol. 130, Iss. 23 — 9 June 2023

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Images

Figure 1
(a) Sketch of the $S / F / F$ junctions when heated by a LED. (b) Typical conductance-bias curves measured at $0.07 T_{c}$ at three different applied IP magnetic fields. (c) Normalized superconducting gap depth ( $S_{gap}$ ) taken from $G (V)$ curves vs applied IP and OOP magnetic fields. (d) Typical tunneling magnetoresistance (TMR) curves measured with IP magnetic field at $V = 5 mV$ and $T = 0.3 K$ . The numbers indicate the order of the field sweeping and resistance changes.
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Figure 2
Thermoelectric response of a $S / F / F$ junction measured under a rotation and fixed values of the applied magnetic field at $T = 0.3 K$ . (a) TE response at $H = 70 Oe$ for in-plane rotations of the magnetic field at $V_{LED} = 7.3 V$ ( $Δ T \approx 113 mK$ ), below and above $T_{c}$ . The tunnel magnetoresistance of the spin valve is also displayed against the rotation angle. (b) Response in the P configuration of the spin-valve stack. (c) Same experiment for the AP configuration. The TE voltage changes its sign and intensity depending not directly on the applied field, but on the saturation of the soft F layer. The related analysis is shown in panel (d), where the average value of the TE voltage is plotted against the measured resistance for the P (blue, upper horizontal axis) and AP (red, lower horizontal axis) configurations. For the P state, a lower resistance implies a better polarization, while in the AP state the polarization is better with a higher resistance.
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Figure 3
Thermoelectric voltage of an $S / F / F$ junction demonstrating sign inversion at high fields in the AP state (a) and P state (b). (c) Color map of the recorded TE voltage $Δ V$ as a function of the temperature difference $Δ T$ and the applied in-plane field $H$ for the same junction, indicating the P and AP states.
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Figure 4
(a) Thermoelectric voltage of an $S / F / F$ and $S / F$ junction at $V_{LED} = 7.3 V$ ( $Δ T \approx 113 mK$ ) vs applied in-plane field at $T = 0.3 K$ . The high-field sign inversion is achieved in both samples, and the TE effect is maintained with increasing in-plane fields up to 30 kOe. The inset displays the measured TE voltage in the $S / F / F$ junction under out-of-plane field. At $H = H_{c}$ , superconductivity and its associated TE voltage vanish. (b) TE inversion field and polarization against the maximum TMR value for all the $S / F / F$ junctions under study.
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Figure 5
(a) Sketch of the system modelled, with the superconducting (SC) and ferromagnetic (FM) layers indicating the relevant values and calculations used in each one. (b) Definitions of angles $θ$ and $φ$ with respect to the field directions in the model. (c)–(e) Numerical results for the magnetically dependent thermoelectric voltage $Δ V (φ)$ . Blue and red correspond to positive and negative voltages, while the radius in each plot is $| Δ V | = 0.04 Δ / e$ where $e$ is the elementary charge. The three plots correspond to (c) $θ = 0$ , $P_{1} = P_{2} = 80 %$ ; (d) $θ = 0$ , $P_{1} = 60 %$ , $P_{2} = 80 %$ ; (e) $θ = π / 4$ , $P_{1} = 60 %$ , $P_{2} = 80 %$ .
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