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Spin-Polarized Supercurrents for Spintronics

A feature article in the January issue of Physics Today1 by Matthias Eschrig, senior lecturer at Royal Holloway University of London and senior scientist at the Appleton-Rutherford Laboratory in the UK, describes developments leading to the discovery of spin-polarized supercurrents and highlights key theoretical ideas, including the role of a quantum mechanical effect identified by Northwestern researchers for the conversion of spin-singlet Cooper pairs into spin-triplet pairs. As the author notes the “marriage between superconductivity and ferromagnetism is opening the door for new spin-based applications.”  [PDF version]

Spin Mixing: Conversion of Spin Singlet Pairs to Spin Triplet Cooper Pairs

The past decade has seen a rapid development in the design and fabrication of new materials which have zero-resistance supercurrents that are also magnetically aligned like a ferromagnet. Spin-polarized supercurrents can now be transmitted over long distances, providing a controllable source of spin, and  thus the transfer of spin-torque for the manipulation of quantum states of nano-scale magnets. A key idea underlying the operation of superconducting-ferromagnetic structures for the production of long-range spin-polarized supercurrents was identified by Taku Tokuyasu and James Sauls at Northwestern and Dierk Rainer at Bayreuth University in Germany (TSR).† Their theoretical work2 showed that when a conventional, non-magnetic superconducting film, such as Al, is placed in electrical contact with a ferromagnetic material, even an ferromagnetic insulator such as EuO, that the internal magnetic field of the ferromagnet (the “exchange field”) can penetrate into the superconductor over distances of order a micron. The mechanism responsible for the spin polarization in the superconductor is an interplay between two fundamental features of quantum mechanics: (i) “quantum tunneling”, which in the context of a ferromagnetic-superconducting (FS) interface refers to the probability of the electron pairs in the superconductor to penetrate the the energy barrier between the superconductor and the ferromagnet, and (ii) “quantum coherence”, the unique feature of a quantum system to be in a state with two or more possible outcomes any instant of time.

Specifically, TSR found that when a conventional superconductor, which is formed from electron pairs in a pure spin-singlet state, ↑↓ − ↓↑ (total spin S = 0), is placed in contact with a ferromagnet that penetration of electrons into the classically forbidden region of the ferromagnetic exchange field forces the electron pairs in the superconductor into a quantum superposition, cos ϑ (↑↓ − ↓↑) + sin ϑ (↑↓ + ↓↑) , of spin-singlet electron pairs (↑↓ − ↓↑) and spin-triplet (S = 1) electron pairs (↑↓ + ↓↑). They dubbed the effect “spin mixing” and showed that it leads to a number of observable effects in the superconductor, including the generation of an exchange field within the superconductor, observable as a spin-splitting, eVex = (hvf/2d) tan ϑ, in the standard NIS tunneling conductance spectroscopy based on an oxide tunneling barrier separating a normal metallic lead and a superconducting film of thickness d and Fermi velocity vf. The spin-mixing angle, ϑ, was shown to depend on the ratio of the exchange energy of the ferromagnet, hex, to the Fermi energy of the superconductor, Ef, ϑ ≈ 2hex/Ef for a small band gap ferromagnetic insulator. The Physics Today article describes many of the key theoretical predictions and observations for both FS proximity junctions and related SFS Josephson junctions.

The ``Twist’’ - Generating Polarized Spin-Triplet Cooper Pairs

Recent theoretical efforts have focussed on developing mechanisms based on FS structures that can be used to produce long-range voltage-controllable superconducting spin currents. One approach requires polarized spin-triplet electron pairs. Eschrig and collaborators3,4 used the spin-mixing effect of an FS bi-layer to generate spin-triplet pairs in the state, (↑↓ + ↓↑), but add a twist by coupling the FS bi-layer (magnetization m1 || z) to a ferromagnetic metal (magnetization m2|| x) or a “half-metal” (a ferromagnetic metal in which only one spin band is conducting). The triplet state is an ``equal-spin pairing state’’ along the orthogonal direction x, i.e.(↑↓ + ↓↑) = (⇉ + ⇇). Thus, when the magnetizations of the two ferromagnets are misaligned, ferromagnet m2 rotates and projects the (↑↓ + ↓↑) triplet pairs into polarized triplet pairs, which for a half-metal is the triplet-spin state (⇉) along m2. The net result is the generation of long-range spin-polarized supercurrents. Another approach proposed by Erhai Zhao and J. A. Sauls utilizes two misaligned FS bi-layers coupled by a non-magnetic conductor. In this geometry Andreev states form by constructive interference between an electron-like and a retro-reflected hole-like excitation in the conductor confined by the two FS elements. The combination of the spin-mixing effect and the twist effect from misalignment leads to long-range spin-polarized currents carried by the Andreev states and to spin-transfer torques acting on the two misaligned ferromagnets.5,6

Experimental Breakthrough - Spin-Polarized Josephson Currents

The first experimental breakthrough came with the report of Keizer et al.7 of Josephson supercurrents between two spin-singlet superconducting electrodes (NbTiN) separated by a wide region of the half-metal CrO2. This experiment was followed by intense theoretical and experimental efforts to optimize FS heterostructures for the generation of spin-polarized supercurrents. Several laboratories have now observed long-range spin supercurrents by employing inhomogeneous FS multi-layer structures. Recent experimental observations of spin-polarized supercurrents from laboratories at Penn State, Michigan State, Leiden and Cambridge Universities will be highlighted during an invited session at the March Meeting of the American Physical Society in Dallas, March 21-25.9

The Future - Towards Superconducting Spintronics

These experiments open up the possibilities for new FS structures and devices utilizing long-range spin-polarized supercurrents for both basic research and for applications. At the fundamental level will be the search for an exotic superconducting phase with ``odd-frequency pairing’’ in which electrons are correlated as bound pairs only when observed at different times!8 Readily available spin-polarized supercurrents open up new possibilities for voltage-controlled spintronic devices with long-range transport of spin-torque and long spin coherence times, important features for spin-based quantum devices.

Acknowledgements

The earlier research on “spin mixing” and spin polarization in ferromagnetic-superconducting bi-layers was supported by the National Science Foundation through the Materials Research Center at Northwestern. Current research on quantum transport in superconducting-ferromagnetic Josephson junctions and arrays is supported by the National Science Foundation through DMR grant 0805277.

References:

  1. Spin-polarized Supercurrents for Spintronics, Physics Today, 64, pp. 43–49, (2011), M. Eschrig.
  2. Proximity Effect of a Ferromagnetic Insulator in Contact with a Superconductor, Phys. Rev. B, 38, 8823, (1988), T. A. Tokuyasu, J. A. Sauls, and D. Rainer.
  3. Theory of Half-Metal-Superconductor Heterostructures, Phys. Rev. Lett., 90, 137003, (2003), M. Eschrig, J. Kopu, J. C. Cuevas, and G. Schön.
  4. Triplet supercurrents in clean and disordered half-metallic ferromagnets, Nature Physics, 4, pp. 138–143, (2008), M. Eschrig and T. Löfwander.
  5. Dynamics of Spin Transport in Voltage-biased Josephson Junctions, Phys. Rev. Lett., 98, 206601, (2007), E. Zhao and J. A. Sauls.
  6. Theory of Nonequilibrium Spin Transport and Spin Transfer Torque in Superconducting-Ferromagnetic Nanostructures, Phys. Rev. B 78, 174511 (2008), E. Zhao and J. A. Sauls.
  7. A spin triplet supercurrent through the half-metallic ferromagnet CrO2, Nature, 439, 825, (2006), R. S. Keizer, S. T. B. Goennenwein, T. M. Klapwijk, G. Miao, G. Xiao, and A. Gupta.
  8. Odd triplet superconductivity and related phenomena in superconductor-ferromagnet structures, Rev. Mod. Phys., 77, pp. 1321–1373, (2005), R. S. Bergeret, A. F. Volkov, and K. B. Efetov.
  9. APS March Meeting Session H1: Spin-Triplet Supercurrents in Superconductor/Ferromagnet/Superconductor Josephson Junctions
†James Sauls is Professor of Physics at Northwestern University. Taku Tokuyasu received his PhD in physics in 1990 under his supervision. Tokuyasu also has a PhD in Computer Science from UC Berkeley, and is now a Computational Biologist at the Cancer Research Center of the University of California, San Francisco. Dierk Rainer was a frequent visitor and collborator with the condensed matter group at Northwestern from 1987-2005. He was Professor of Physics at Bayreuth University in Germany until his retirement in 2005. Erhai Zhao received his PhD in physics in 2006 working under the direction of James Sauls. He is now Associate Professor of Physics at George Mason University in Virginia.
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