- Open Access
Large Tunable Thermoelectric Effects in Superconducting Spin Valves with Commercially Available Materials
PRX Energy 4, 033003 – Published 16 July, 2025
DOI: https://doi.org/10.1103/xbgg-gttc
Abstract
Recent studies have revealed magnetically controllable thermoelectric effects in superconductor/ferromagnet (S/F) structures. A tunable cryogenic thermoelectric generator needs not only a high conversion factor between electricity and heat, but also a large change in the thermoelectric output when switching the magnetic state of the device. However, the reported modifications in thermoelectric power are either minimal, involve superconductors with relatively low critical temperatures (below 1 K), or do not utilize commercially available spintronic materials. Here, we experimentally measure and numerically model thermoelectric effects in fully epitaxial ferromagnet/superconductor/ferromagnet (F/S/F) junctions based on commercially available easily grown materials, as well as their dependence on the magnetic configuration of the ferromagnetic (F) electrodes. We observe sizeable Seebeck coefficients for the parallel alignment of the F electrodes, reaching values of about 100 K. Importantly, we find a decrease of the thermoelectric signal of more than an order of magnitude when switching from a parallel to an antiparallel configuration, constituting a large thermoelectric spin-valve effect. Theoretical modeling based on a self-consistent nonequilibrium Keldysh-Usadel Green’s function theory, combined with micromagnetic simulations, qualitatively reproduce the experimental findings. The thermoelectric effect is optimized when there is a large spin-dependent electron-hole asymmetry in the superconductor combined with spin-dependent transmission through the interfaces. These findings pave the way for the development of efficient and versatile cryogenic thermoelectric heat engines.
Physics Subject Headings (PhySH)
Popular Summary
Thermoelectric cooling enables many applications, but at very low temperatures thermoelectric materials typically perform poorly. Therefore, better material platforms that yield efficient thermoelectricity under cryogenic conditions are needed. Here, the authors present experimental studies of thermoelectric effects in superconductor/ferromagnet junctions based on commercially available, easily grown materials. They observe a large Seebeck coefficient exceeding 100 microvolt/Kelvin that changes by an order of magnitude upon switching the magnetic alignment of the system. This approach paves the way for developing efficient and magnetically controllable localized cryogenic cooling.
Article Text
Supplemental Material
References (66)
- G. Benenti, G. Casati, K. Saito, and R. S. Whitney, Fundamental aspects of steady-state conversion of heat to work at the nanoscale, Phys. Rep. 694, 1 (2017).
- F. S. Bergeret, M. Silaev, P. Virtanen, and T. T. Heikkilä, Colloquium: Nonequilibrium effects in superconductors with a spin-splitting field, Rev. Mod. Phys. 90, 041001 (2018).
- F. G. Aliev, V. V. Kozyrkov, V. V. Moshchalkov, R. V. Scolozdra, and K. Durcewski, Narrow band in the intermetallic compounds M (), Zeit. Phys. Cond. Mat. 80, 353 (1990).
- A. Ojha, R. K. Sabat, and S. Bathula, Advancement in half-Heusler thermoelectric materials and strategies to enhance the thermoelectric performance, Mater. Sci. Semicond. Process. 171, 107996 (2024).
- T. M. Tritt, Thermoelectric phenomena, materials, and applications, Ann. Rev. Mat. Res. 41, 433 (2011).
- J. Wei, L. Yang, Z. Ma, P. Song, M. Zhang, J. Ma, F. Yang, and X. Wang, Review of current high-ZT thermoelectric materials, J. Mater. Sci. 55, 12642 (2020).
- Z. Soleimani, S. Zoras, B. Ceranic, S. Shahzad, and Y. Cui, A review on recent developments of thermoelectric materials for room-temperature applications, Sustainable Energy Technol. Assess. 37, 100604 (2020).
- X.-L. Shi, J. Zou, and Z.-G. Chen, Advanced thermoelectric design: From materials and structures to devices, Chem. Rev. 120, 7399 (2020).
- S. Irfan, Z. Yan, and S. Bashir Khan, Advancements in thermoelectric materials: A comprehensive review, Mater. Sci. Energy Technol. 7, 349 (2024).
- J. Feng, J. Li, and R. Liu, Low-temperature thermoelectric materials and applications, Nano Energy 126, 109651 (2024).
- S. R. Harutyunyan, V. H. Vardanyan, A. S. Kuzanyan, V. R. Nikoghosyan, S. Kunii, K. S. Wood, and A. M. Gulian, Thermoelectric cooling at cryogenic temperatures, Appl. Phys. Lett. 83, 2142 (2003).
- J. T. Muhonen, M. Meschke, and J. P. Pekola, Micrometre-scale refrigerators, Rep. Progr. Phys. 75, 046501 (2012).
- T. Heikkilä, M. Silaev, M. Virtanen, and F. S. Bergeret, Thermal, electric and spin transport in superconductor/ferromagnetic-insulator structures, Prog. Surf. Sci. 94, 100540 (2019).
- P. Machon, M. Eschrig, and W. Belzig, Nonlocal thermoelectric effects and nonlocal onsager relations in a three-terminal proximity-coupled superconductor-ferromagnet device, Phys. Rev. Lett. 110, 047002 (2013).
- A. Ozaeta, P. Virtanen, F. S. Bergeret, and T. T. Heikkilä, Predicted very large thermoelectric effect in ferromagnet-superconductor junctions in the presence of a spin-splitting magnetic field, Phys. Rev. Lett. 112, 057001 (2014).
- S. Kolenda, M. J. Wolf, and D. Beckmann, Observation of thermoelectric currents in high-field superconductor-ferromagnet tunnel junctions, Phys. Rev. Lett. 116, 097001 (2016).
- P. O. Sukhachov, E. W. Hodt, and J. Linder, Thermoelectric effect in altermagnet-superconductor junctions, Phys. Rev. B 110, 094508 (2024).
- G. Marchegiani, A. Braggio, and F. Giazotto, Nonlinear thermoelectricity with electron-hole symmetric systems, Phys. Rev. Lett. 124, 106801 (2020).
- G. Germanese, F. Paolucci, G. Marchegiani, A. Braggio, and F. Giazotto, Bipolar thermoelectric Josephson engine, Nat. Nanotechnol. 17, 1084 (2022).
- F. Meng, J. Xu, X. Liu, and O. Dahlsten, Quantum harvester enables energy transfer without randomness transfer or dissipation, ArXiv:2406.08054.
- M. Bilokur, S. Gopalakrishnan, and S. Majidy, Thermodynamic limitations on fault-tolerant quantum computing, ArXiv:2411.12805.
- T. T. Heikkilä, R. Ojajärvi, I. J. Maasilta, E. Strambini, F. Giazotto, and F. S. Bergeret, Thermoelectric radiation detector based on superconductor-ferromagnet systems, Phys. Rev. Appl. 10, 034053 (2018).
- A. Rajapaksha, S. D. Gunapala, and M. Premaratne, Enhanced thermal rectification in coupled qutrit-qubit quantum thermal diode, APL Quantum 1, 046123 (2024).
- C. I. L. de Araujo, P. Virtanen, M. Spies, C. Gonzlaez-Orellana, M. I. Kerschbaumer, C. Rogero, T. T. Heikkilä, F. Giazotto, and E. Strambini, Superconducting spintronic heat engine, Nat. Commun. 15, 4823 (2024).
- J. A. Ouassou, C. González-Ruano, D. Caso, F. G. Aliev, and J. Linder, Complete magnetic control over the superconducting thermoelectric effect, Phys. Rev. B 106, 094514 (2022).
- C. González-Ruano, D. Caso, J. A. Ouassou, C. Tiusan, Y. Lu, J. Linder, and F. G. Aliev, Observation of magnetic state dependent thermoelectricity in superconducting spin valves, Phys. Rev. Lett. 130, 237001 (2023).
- See the Supplemental Material at http://link.aps.org/supplemental/10.1103/xbgg-gttc for additional details on the experimental characterization of the samples, modeling of the temperature profile, micromagnetic simulations, quasiclassical theory, and the temperature dependence of the thermoelectric effect. The Supplemental Material also includes Refs. [50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66].
- I. Martínez, C. Tiusan, M. Hehn, M. Chshiev, and F. G. Aliev, Symmetry broken spin reorientation transition in epitaxial // layers with competing anisotropies, Sci. Rep. 8, 9463 (2018).
- C. González-Ruano, L. G. Johnsen, D. Caso, C. Tiusan, M. Hehn, N. Banerjee, J. Linder, and F. G. Aliev, Superconductivity-induced change in magnetic anisotropy in epitaxial ferromagnet-superconductor hybrids with spin-orbit interaction, Phys. Rev. B 102, 020405 (2020).
- B. Kochelaev, L. Tagirov, and M. Khusainov, Spatial dispersion of spin susceptibility of conduction electrons in a superconductor, Zh. Eksp. Teor. Fiz. 76, 578 (1979).
- M. Khusainov, Multicritical points in the phase diagrams of layered ferromagnet-superconductor structures, Zh. Eksp. Teor. Fiz. 109, 524 (1996).
- A. Di Bernardo, S. Komori, G. Livanas, G. Divitini, P. Gentile, M. Cuoco, and J. W. A. Robinson, Nodal superconducting exchange coupling, Nat. Mater. 18, 1194 (2019).
- P. Tuero, C. González-Ruano, Y. Lu, C. Tiusan, and F. G. Aliev, Spin texture and spin-orbit coupling contributions in spin-triplet superconductivity, Phys. Rev. B 110, 094504 (2024).
- J. M. Rowell and W. L. McMillan, Electron interference in a normal metal induced by superconducting contracts, Phys. Rev. Lett. 16, 453 (1966).
- N. E. Alekseevskii, V. M. Sakosarenko, K. Blüthner, and H.-J. Köhler, Superconducting properties of vanadium films, Phys. Status Solidi (a) 34, 541 (1976).
- S. S. P. Parkin, C. Kaiser, A. Panchula, P. M. Rice, B. Hughes, M. Samant, and S.-H. Yang, Giant tunneling magnetoresistance at room temperature with (100) tunnel barriers, Nat. Mater. 3, 862 (2004).
- S. Yuasa, T. Nagahama, A. Fukushima, Y. Suzuki, and K. Ando, Giant room-temperature magnetoresistance in single-crystal // magnetic tunnel junctions, Nat. Mater. 3, 868 (2004).
- J. M. De Teresa, A. Barthélémy, A. Fert, J. P. Contour, F. Montaigne, and P. Seneor, Role of metal-oxide interface in determining the spin polarization of magnetic tunnel junctions, Science 286, 507 (1999).
- X. Feng, O. Bengone, M. Alouani, I. Rungger, and S. Sanvito, Interface and transport properties of /// and //// magnetic tunneling junctions, Phys. Rev. B 79, 214432 (2009).
- I. Martínez, P. Högl, C. González-Ruano, J. P. Cascales, C. Tiusan, Y. Lu, M. Hehn, A. Matos-Abiague, J. Fabian, I. Žutić, and F. G. Aliev, Interfacial spin-orbit coupling: A platform for superconducting spintronics, Phys. Rev. Appl. 13, 014030 (2020).
- A. Vansteenkiste, J. Leliaert, M. Dvornik, M. Helsen, F. García-Sánchez, and B. Van Waeyenberge, The design and verification of MuMax3, AIP Adv. 4, 107133 (2014).
- B. Dieny and M. Chshiev, Perpendicular magnetic anisotropy at transition metal/oxide interfaces and applications, Rev. Mod. Phys. 89, 025008 (2017).
- J. C. Slonczewski, Conductance and exchange coupling of two ferromagnets separated by a tunneling barrier, Phys. Rev. B 39, 6995 (1989).
- W. Belzig, F. K. Wilhelm, C. Bruder, G. Schön, and A. D. Zaikin, Quasiclassical Green’s function approach to mesoscopic superconductivity, Superlattices Microstruct. 25, 1251 (1999).
- J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Theory of superconductivity, Phys. Rev. 108, 1175 (1957).
- K. D. Usadel, Generalized diffusion equation for superconducting alloys, Phys. Rev. Lett. 25, 507 (1970).
- C. González-Ruano Iriarte, Ph.D. thesis, Doctorate School in Condensed Matter Physics, Nanoscience and Biophysics, Universidad Autónoma de Madrid, 2023, https://repositorio.uam.es/handle/10486/711139.
- M. Eschrig, A. Cottet, W. Belzig, and J. Linder, General boundary conditions for quasiclassical theory of superconductivity in the diffusive limit: Application to strongly spin-polarized systems, New J. Phys. 17, 083037 (2015).
- http://webs.fmc.uam.es/magnetrans.group/.
- C. Tiusan, F. Greullet, M. Hehn, F. Montaigne, S. Andrieu, and A. Schuhl, Spin tunnelling phenomena in single-crystal magnetic tunnel junction systems, J. Phys.: Condens. Matter 19, 165201 (2007).
- C. R. Anoop, R. K. Singh, R. R. Kumar, M. Jayalakshmi, T. Antony Prabhu, K. Thomas Tharian, and S. V. S. Narayana Murty, A review on steels for cryogenic applications, Mater. Perform. Charact. 10, 16 (2021).
- J. W. Gardner and A. C. Anderson, Effect of neutron irradiation on the low-temperature specific heat and thermal conductivity of magnesium oxide, Phys. Rev. B 23, 1988 (1981).
- B. K. Chakal’skii, N. A. Red’ko, S. S. Shalyt, and V. M. Azhazha, Thermal conductivity of pure vanadium in normal, superconducting, and mixed states, Sov. Phys.—JETP 48, 665 (1978).
- K. Balcerek, R. Wawryk, Cz. Marucha, J. Rafalowicz, and L. Krajczyk, Thermal conductivity and electrical resistivity of pure polycrystalline cobalt in the temperature range 2.5–30 K, Int. J. Thermophys. 17, 1475 (1996).
- W. H. Butler, X.-G. Zhang, T. C. Schulthess, and J. M. MacLaren, Spin-dependent tunneling conductance of sandwiches, Phys. Rev. B 63, 054416 (2001).
- C. D. Graham, Magnetocrystalline anisotropy constants of iron at room temperature and below, Phys. Rev. 112, 1117 (1958).
- L. P. Gorkov, On the energy spectrum of superconductors, Sov. Phys.—JETP 34, 505 (1958).
- W. Belzig, F. K. Wilhelm, C. Bruder, G. Schön, and A. D. Zaikin, Quasiclassical Green’s function approach to mesoscopic superconductivity, Superlatt. Microstruct. 25, 1251 (1999).
- V. Chandrasekhar, Superconductivity: Conventional and Unconventional Superconductors (Springer-Verlag, Berlin, 2008), p. 279, chapter 8.
- G. Eilenberger, Transformation of Gorkov’s equation for type II superconductors into transport-like equations, Z. Phys. 214, 195 (1968).
- N. Schopohl and K. Maki, Quasiparticle spectrum around a vortex line in a -wave superconductor, Phys. Rev. B 52, 490 (1995).
- A. Konstandin, J. Kopu, and M. Eschrig, Superconducting proximity effect through a magnetic domain wall, Phys. Rev. B 72, 140501(R) (2005).
- J. A. Ouassou, T. D. Vethaak, and J. Linder, Voltage-induced thin-film superconductivity in high magnetic fields, Phys. Rev. B 98, 144509 (2018).
- N. M. Chtchelkatchev, T. I. Baturina, A. Glatz, and V. M. Vinokur, Physical Properties of Nanosystems: Synchronized Andreev Transmission in Chains of SNS Junctions (Springer, Yalta, 2009), p. 87, chapter 7.
- H. Shimada, K. Miyawaki, A. Hagiwara, K. Takeda, and Y. Mizugaki, Characterization of superconducting single-electron transistors with small // Josephson junctions, Supercond. Sci. Technol. 27, 115015 (2014).
- N. Ligato, G. Marchegiani, P. Virtanen, E. Strambini, and F. Giazotto, High operating temperature in -based superconducting quantum interference proximity transistors, Sci. Rep. 7, 8810 (2017).
