Giant thermophase in ferromagnetic Josephson junctions F. Giazotto, 1, * T. T. Heikkil¨ a, 2,3, † and F. S. Bergeret 4,5, ‡ 1 NEST, Instituto Nanoscienze-CNR and Scuola Normale Superiore, I-56127 Pisa, Italy 2 Department of Physics and Nanoscience Center, P.O. Box 35 (YFL), FI-40014 University of Jyv¨ askyl¨ a, Finland 3 Low Temperature Laboratory, Aalto University, P.O. Box 15100, FI-00076 AALTO, Finland 4 Centro de F´ ısica de Materiales (CFM-MPC), Centro Mixto CSIC-UPV/EHU, Manuel de Lardizabal 4, E-20018 San Sebasti´ an, Spain 5 Donostia International Physics Center (DIPC), Manuel de Lardizabal 5, E-20018 San Sebasti´ an, Spain Thermoelectric currents in superconductors are often shorted by supercurrents which generate a phase gradient, a thermophase, inside the superconductor. As suggested a long time ago by Ginzburg [1], a bimetallic supercon- ducting loop constrains the possible phase gradients, and allows observation of thermoelectric effects via magnetic fields arising from circulating currents manipulated by temperature differences. Measurements of such circulat- ing currents [2] were larger than that predicted by theory by several orders of magnitude, a discrepancy that is yet to be explained [3, 4]. Here we propose an alternative way to produce a huge thermophase in a SQUID loop consisting of a conventional superconductor in a spin-polarized con- tact with a superconductor-ferromagnet bilayer. The re- sulting thermophase can be close to π /2 across the contact, several orders of magnitude larger than in conventional Josephson junctions [5, 6]. Such a giant thermophase could be used for detecting tiny temperature differences, for instance, generated by radiation coupling to one of the superconductors. We consider a Josephson junction (see Fig. 1a) consisting of two superconductors S L and S R tunnel coupled through a ferromagnetic insulator (FI) and a non-magnetic (I) barrier. The FI has different transmissivities for spin-up and spin down electrons and therefore acts as a spin-filter.[7] The interac- tion between the conduction electrons in S L with the localized magnetic moments of the FI leads to an effective spin-splitting field h in the left electrode that decays away from the interface over the superconducting coherence length ξ 0 .[8] The thin I layer placed on the right side of the FI prevents such a spin- splitting field to be induced in S R [9, 10]. We assume that the thickness t L of S L is smaller than ξ 0 so that the induced h is spatially uniform across the entire S L layer [11]. The junction is temperature biased, so that T L,R is the temperature in S L,R , respectively, and ϕ th denotes the phase difference between the superconducting order parameters induced by such a tempera- ture difference. We focus on the static (i.e., time-independent) regime so that a dc Josepson current can flow in response to the applied thermal gradient but no thermovoltage develops across the junction. In order to analyze the setup, we generalize the calculation of [12] to the case of two superconductors. The total electric current I flowing through the junction is given by the sum of the quasiparticle (I qp ) and the Josephson contribution (I J ) I = I qp + I J = I qp + I c sin ϕ th , (1) a b FIG. 1. Thermally-biased ferromagnetic Josephson junction and the proposed experimental setup.(a) Sketch of a generic S-FI-I-S Josephson junction discussed in the text. It consists of two identical superconductors, S L and S R , tunnel-coupled by a ferromagnetic in- sulator FI and a non-magnetic barrier I. The direct contact between FI and S L leads to an induced exchange field in the latter, while the non-magnetic barrier prevents such a field to appear in S R . T L and T R are the temperature in S L and S R , respectively, whereas ϕ th de- notes the thermophase originated from thermally biasing the Joseph- son junction. t L is the thickness of S L .(b) Scheme of a detection setup consisting of a temperature-biased superconducting quantum interference device (SQUID) based on the previous junction. Super- conducting electrodes tunnel-coupled to S L and S R serve either as heaters (h) or thermometers (th), and allow one to impose and de- tect a temperature gradient across the SQUID. The magnitude of the induced ϕ th can be determined by measuring variations of the super- current (I circ ) circulating in the interferometer through a conventional dc SQUID inductively coupled to the first ring. M denotes the mu- tual inductance between the loops, and Φ ext is the external applied magnetic flux. where I c is the critical supercurrent. The current contribution proportional to cos ϕ th [13] does not contribute, since it does not possess any thermoelectric response, and it would require a finite voltage. The explicit forms for I qp and I c in Eq. (1) can be obtained from the expressions for the current through arXiv:1403.1231v1 [cond-mat.mes-hall] 5 Mar 2014