The space-group approach to the wavefunction of a Cooper pair is extended to Shubnikov groups of type III and applied to newly discovered nearly ferromagnetic superconductor UTe2. A nonunitary triplet SOP (superconducting order parameter), manifested experimentally, was obtained for Shubnikov group m'm'm . The nodal structure of triplet nonunitary SOP is investigated and it was shown that in the case of Shubnikov III symmetry nodal structure of ESP (equal spin pairing) state is in some cases unstable, i.e. changes when a complex phase winding is added. The irreducible corepresentations of a Cooper pair wave function corresponding to m'm'm symmetry and to all experimental data for UTe2 are identified.
The superconducting state in uranium compounds UGe2, URhGe and UCoGe is formed at temperatures far below the Curie temperature pointing on nonconventional nature of superconductivity in these materials - namely the superconductivity with triplet pairing. The emergence of superconductivity is accompanied by the slight magnetization expulsion typical for the type-II superconductors. Following classic Abrikosov paper I develop the theory of type-II superconductivity in application to two-band ferromagnetic metal with equal spin triplet pairing.
We study the Josephson effect in planar $SF_1F_2S$ junctions that consist of conventional $s$-wave superconductors ($S$) connected by two metallic monodomain ferromagnets ($F_1$ and $F_2$) with arbitrary transparency of interfaces. We solve the scattering problem in the clean limit based on the Bogoliubov-de Gennes equation for both spin-singlet and odd in frequency spin-triplet pairing correlations. We calculate numerically the Josephson current-phase relation $I(ϕ)$. While the first harmonic of $I(ϕ)$ is completely generated by spin-singlet and short-range spin-triplet superconducting correl…
The theory of triplet superconductivity in ferromagnetic metals based on electron-electron interaction by spin fluctuation exchange is developed. The equations for the upper critical field temperature dependence are derived. In contrast to the similar equations for the superconductivity in two band metals they contain the pairing amplitudes and the Fermi velocities depending on magnetic field. The critical field behaviour near the critical temperature and at T = 0 is established analytically.
A ferromagnetic insulator (FI) in contact with a superconductor (S) is known to induce a spin splitting of the BCS density of states at the FI/S interface. This spin splitting causes the Cooper pairs to reduce their singlet-state correlations and acquire odd-in-frequency triplet correlations. We consider a diffusive FI/S bilayer with a sharp magnetic domain wall in the FI and study the local quasiparticle density of states and triplet superconducting correlations. In the case of collinear alignment of the domains, we obtain analytical results by solving the Usadel equation. For a small enough …
Josephson junctions containing three ferromagnetic layers with non-collinear magnetizations between adjacent layers carry spin-triplet supercurrent under certain conditions. The signature of the spin-triplet supercurrent is a relatively slow decay of the maximum supercurrent as a function of the thickness of the middle ferromagnetic layer. In this work we focus on junctions where the middle magnetic layer is a [Co/Pd]$_N$ multilayer with perpendicular magnetic anisotropy (PMA), while the outer two layers have in-plane anisotropy. We compare junctions where the middle PMA layer is or is not con…
The lengthscale over which supercurrent from conventional BCS, $s$-wave, superconductors ($S$) can penetrate an adjacent ferromagnetic ($F$) layer depends on the ability to convert singlet Cooper pairs into triplet Cooper pairs. Spin aligned triplet Cooper pairs are not dephased by the ferromagnetic exchange interaction, and can thus penetrate an $F$ layer over much longer distances than singlet Cooper pairs. These triplet Cooper pairs carry a dissipationless spin current and are the fundamental building block for the fledgling field of superspintronics. Singlet-triplet conversion by inhomogen…
Since the discovery of the long-range superconducting proximity effect, the interaction between spin-triplet Cooper pairs and magnetic structures such as domain walls and vortices has been the subject of intense theoretical discussions, while the relevant experiments remain scarce. We have developed nanostructured Josephson junctions with highly controllable spin texture, based on a disk-shaped Nb/Co bilayer. Here, the vortex magnetization of Co and the Cooper pairs of Nb conspire to induce long-range triplet (LRT) superconductivity in the ferromagnet. Surprisingly, the LRT correlations emerge…
The spin-triplet state is most likely realized in uranium ferromagnetic superconductors, UGe2, URhGe, UCoGe. The microscopic coexistence of ferromagnetism and superconductivity means that the Cooper pair should be realized under the strong internal field due the ferromagnetism, leading to the spin-triplet state with equal spin pairing. The field-reinforced superconductivity, which is observed in all three materials when the ferromagnetic fluctuations are enhanced, is one of the strong evidences for the spin-triplet superconductivity. We present here the results of a newly discovered spin-tripl…
Spin-triplet Supercurrent through Inhomogeneous Ferromagnetic Trilayers
最近的一个实验[J。a. Robinson，J. D. S. Witt和M. G. Blamire，Science，\textbf{329}，5987（2010）]，我们在此研究通过由夹在两个常规s波超导体之间的Ho $\mid$ Co $\mid$ Ho三层组成的非均匀铁磁区域建立远程自旋三重态超电流的可能性。我们利用一个完整的数值解中的扩散制度的运输和研究的超电流的各种实验相关配置的铁磁三层的行为。我们获得定性非常好的协议与实验数据的行为的超电流作为一个函数的宽度的Co层，$L_\text{Co}$。此外，我们发现了一个合成的0-$π$振荡叠加快速振荡时，改变的Ho层的宽度，特别是在Ho的螺旋磁化织构。我们无法重现在该制度中实验观察到的超电流中的异常峰，但注意到所获得的结果对Ho层中的精确磁化分布非常敏感，这可能是我们的模型与实验报告数据之间存在差异的原因。我们还研究了超导系统中的本质上不均匀的Ho铁磁体取代畴壁铁磁体，并发现类似的行为在Ho $\mid$ Co $\mid$ Ho的情况下。此外，我们提出了一种新型的磁性约瑟夫森结，它只包括一个畴壁铁磁体和一个均匀的铁磁层，除了简单的磁化曲线，还提供了一个可调的远程自旋三重态超电流。最后，我们讨论了我们的研究结果的一些实验方面。
We study theoretically the proximity effect in a ferromagnetic semiconductor with Rashba spin-orbit interaction. The exchange potential generates opposite-spin-triplet Cooper pairs which are transformed into equal-spin-triplet pairs by the spin-orbit interaction. In the limit of strong spin-orbit interaction, symmetry of the dominant Cooper pair depends on the degree of disorder in a ferromagnet. In the clean limit, spin-singlet $s$-wave Cooper pairs are the most dominant because the spin-momentum locking stabilizes a Cooper pair consisting of a time-reversal partner. In the dirty limit, on th…
Coupling a conventional s-wave superconductor to a ferromagnet allows, via the proximity effect, to generate superconducting triplet correlations. This feature can be employed to achieve a superconducting triplet spin-valve effect in superconductor-ferromagnet (SF) hybrid structures, for example by switching the magnetizations of the ferromagnets between parallel and antiparallel configurations in F1SF2 and SF1F2 trilayers, or in SF bilayers with both Rashba and Dresselhaus SOC. It was recently reported that geometric curvature can control the generation of long ranged triplets. We use this pr…
The study of superconductor-ferromagnet interfaces has generated great interest in the last decades, leading to the observation of spin-aligned triplet supercurrents and 0-pi transitions in Josephson junctions where two superconductors are separated by an itinerant ferromagnet. Recently, spin-filter Josephson junctions with ferromagnetic barriers have shown unique transport properties, when compared to standard metallic ferromagnetic junctions, due to the intrinsically nondissipative nature of the tunneling process. Here we present the first extensive characterization of spin polarized Josephs…
Triplet supercurrents in multilayer ferromagnetic Josephson junctions with misaligned magnetization can penetrate thicker ferromagnetic barriers compared to the singlet component. Although the static properties of these junctions have been extensively studied, the dynamic characteristics remain largely unexplored. Here we report a comprehensive electrodynamic characterization of multilayer ferromagnetic Josephson junctions composed of Co and Ho. By measuring the temperature-dependent current-voltage characteristics and the switching current distributions down to 0.3 K, we show that phase dynam…
