Helical ordering of spins in a superconductor

Bulaevskiǐ, L. N.; Rusinov, A.I.; Kulić, Miodrag L.

doi:10.1007/bf00115620

Cited by 66 publications

(36 citation statements)

References 10 publications

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“…Indeed, many theoretical works have tackled this issue and provided invaluable information about the interplay between AFM and unconventional SC in the coexistence state [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34] . Interestingly, as shown in Ref.…”

Section: Introductionmentioning

confidence: 99%

Induced spin-triplet pairing in the coexistence state of antiferromagnetism and singlet superconductivity: Collective modes and microscopic properties

2017

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The close interplay between superconductivity and antiferromagnetism in several quantum materials can lead to the appearance of an unusual thermodynamic state in which both orders coexist microscopically, despite their competing nature. A hallmark of this coexistence state is the emergence of a spin-triplet superconducting gap component, called π-triplet, which is spatially modulated by the antiferromagnetic wave-vector, reminiscent of a pair-density wave. In this paper, we investigate the impact of these π-triplet degrees of freedom on the phase diagram of a system with competing antiferromagnetic and superconducting orders. Although we focus on a microscopic two-band model that has been widely employed in studies of iron pnictides, most of our results follow from a Ginzburg-Landau analysis, and as such should be applicable to other systems of interest, such as cuprates and heavy fermions. The Ginzburg-Landau functional reveals not only that the π-triplet gap amplitude couples tri-linearly with the singlet gap amplitude and the staggered magnetization magnitude, but also that the π-triplet d-vector couples linearly with the magnetization direction. While in the mean field level this coupling forces the d-vector to align parallel or anti-parallel to the magnetization, in the fluctuation regime it promotes two additional collective modes -a Goldstone mode related to the precession of the d-vector around the magnetization and a massive mode, related to the relative angle between the two vectors, which is nearly degenerate with a Leggett-like mode associated with the phase difference between the singlet and triplet gaps. We also investigate the impact of magnetic fluctuations on the superconducting-antiferromagnetic phase diagram, showing that due to their coupling with the π-triplet order parameter, the coexistence region is enhanced. This effect stems from the fact that the π-triplet degrees of freedom promote an effective attraction between the antiferromagnetic and singlet superconducting degrees of freedom, highlighting the complex interplay between these two orders, which goes beyond mere competition for the same electronic states.

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Section: Introductionmentioning

confidence: 99%

Induced spin-triplet pairing in the coexistence state of antiferromagnetism and singlet superconductivity: Collective modes and microscopic properties

2017

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“…25-29 and references therein). The theoretical research has been followed by experimental confirmation of the existence of the long range triplet superconductivity [30][31][32][33][34][35][36][37][38][39].Note that the triplet component that arises in magnetic superconductors with a spiral h(r) [12,40] has zero projection of the total spin of triplet Cooper pairs S on h(r). Only near the surface of the sample, the triplet component with a nonzero projection of S on h(r) appears; it decays exponentially away from the surface [41].…”

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confidence: 99%

Nematic versus ferromagnetic spin filtering of triplet Cooper pairs in superconducting spintronics

2015

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We consider two types of magnetic Josephson junctions (JJ). They are formed by two singlet superconductors S and magnetic layers between them so that the JJ is a heterostructure of the S m /n/S m type, where S m includes two magnetic layers with non-collinear magnetization vectors. One layer is represented by a weak ferromagnet and another one-the spin filter-is either conducting strong ferromagnet (nematic or N-type JJ) or magnetic tunnel barrier with spin-dependent transparency (magnetic or M-type JJ). Due to spin filtering only fully polarized triplet component penetrates the normal n wire and provides the Josephson coupling between the superconductors S. Although both filters let to pass triplet Cooper pairs with total spin S parallel to the filter axes, the behavior of nematic and magnetic JJs is completely different. Whereas in the nematic case the charge and spin currents, I Q and I sp , do not depend on mutual orientation of the filter axes, both currents vanish in magnetic JJ in case of antiparallel filter axes, and change sign under reversing the filter direction. The obtained expressions for I Q and I sp show clearly a duality between the superconducting phase ϕ and the angle α between the exchange fields in the weak magnetic layers. PACS numbers: 74.78.Fk, 85.25.Cp, 74.45.+c Triplet Cooper pairing is known to exist in superfluid 3 He [1, 2]. As concerns superconductors, the situation is less clear. Although some indication for the triplet superconductors has been found in a number of completely different classes of materials [3][4][5], a general consensus about the existence of the triplet superconductivity in the organic metals, heavy fermions and other interesting materials investigated from this point of view has not been achieved [6,7]. In principle, the fact that the spins of the fermions of the Cooper pairs are equal to each other does not contradict the Pauli principle because the condensate wave function f (p) and the order parameter ∆ tr (p) in these triplet superconductors are odd functions of the momentum p. In contrast to the conventional BCS superconductivity, the triplet superconductivity with such a symmetry of the order parameter is sensitive to impurity scattering [8] and, therefore, it is usually strongly suppressed by disorder.However, the triplet Cooper pairs can appear already in conventional singlet superconductors provided an external magnetic (H) or an internal exchange (h) field acts on the spins of electrons. [8][9][10][11] A triplet component inevitably arises also in magnetic superconductors [12].The triplet condensate function arising from the singlet superconductivity in the presence of the magnetic or exchange field acting on spins is odd in frequency and therefore may still have an s-wave space symmetry without violating the Pauli principle. It has a component with the 0-spin projection f tr,0 ∝ 〈ĉ ↑ĉ↓ (t ) +ĉ ↓ĉ↑ (t )〉 on the direction of the field h or H but also the components with spin projection ±1. The zero projection component f tr,0 of the condensate functio...

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“…6,7,8,9,10,11) is that in most systems, most notably in both electron and hole doped 122 materials, there is a range of coexistence of SDW and superconductivity, probably up to the optimal doping level (some, however, have argued for mesoscopic phase separation on the hole-doping side 11,12 ). It was recently estimated that the magnetic moment at the Co concentration of 7% is 0.1 µ B per Fe, corresponding, roughly, to an antiferromagnetic field of the order of 50-100 meV 10 .The subject of an SDW coexisting with superconductivity has a long history, dating back to Bulaevskii et al in 1980 13 and numerous work since then. It was shown 13,14 that in a one-band BCS superconductor a spiral SDW induces a gap anisotropy that leads to gap nodes, while a collinear SDW still leads to a finite energy gap 14 .…”

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confidence: 99%

“…The subject of an SDW coexisting with superconductivity has a long history, dating back to Bulaevskii et al in 1980 13 and numerous work since then. It was shown 13,14 that in a one-band BCS superconductor a spiral SDW induces a gap anisotropy that leads to gap nodes, while a collinear SDW still leads to a finite energy gap 14 .…”

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confidence: 99%

Coexistence of superconductivity and a spin-density wave in pnictide superconductors: Gap symmetry and nodal lines

et al. 2009

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We investigate the effect of a spin-density wave (SDW) on s ± superconductivity in Fe-based superconductors. We show that, contrary to the common wisdom, no nodes open at the new, reconnected Fermi surfaces when the hole and electron pockets fold down in the SDW state, despite the fact that the s ± gap changes sign between the two pockets. Instead, the order parameter preserves its sign along the newly formed Fermi surfaces. The familiar experimental signatures of an s ± symmetry are still preserved, although they appear in a mathematically different way. For a regular s case (s ++ ) the nodes do appear in the SDW state. This distinction suggests a novel simple way to experimentally separate an s ± state from a regular s in the pnictides. We argue that recently published thermal conductivity data in the coexisting state are consistent with the s ± , but not the s ++ state. PACS numbers: 74.20.Rp, 74.25.Nf, The superconducting pnictides continue to attract great interest over a year after the original discovery. Despite more than a thousand preprints and publications, the most basic questions about pairing symmetries and mechanisms remain controversial. Early on the s ± pairing symmetry was proposed 1,2 , in which the superconducting gap function changes sign from the hole to the electron pockets, but is roughly constant on each surface. A possibility of an accidentally nodal s ± state, or a d-wave state, depending upon parameter values, was also proposed 2 , and investigated in many details recently 3 . As of now, significant experimental evidence has been accumulated in favor of the s ± proposal, and substantial theoretical effort has been devoted to the study of various properties of such a state (see Refs. 4,5 for reviews). So far, however, no one has addressed the possible modification of an s ± state due to a static spin density wave (SDW) coexisting with superconductivity. At the same time the emerging consensus among experimentalists (see Refs. 6,7,8,9,10,11) is that in most systems, most notably in both electron and hole doped 122 materials, there is a range of coexistence of SDW and superconductivity, probably up to the optimal doping level (some, however, have argued for mesoscopic phase separation on the hole-doping side 11,12 ). It was recently estimated that the magnetic moment at the Co concentration of 7% is 0.1 µ B per Fe, corresponding, roughly, to an antiferromagnetic field of the order of 50-100 meV 10 .The subject of an SDW coexisting with superconductivity has a long history, dating back to Bulaevskii et al in 1980 13 and numerous work since then. It was shown 13,14 that in a one-band BCS superconductor a spiral SDW induces a gap anisotropy that leads to gap nodes, while a collinear SDW still leads to a finite energy gap 14 . The case of the s ± superconductivity in Fe-based superconductors (FBS), on the first glance, seems quite simple: first, the SDW wave we are dealing with here is simply a collinear double-cell antiferromagnetic (AF) order, so one need not be bothered by the difference b...

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Helical ordering of spins in a superconductor

Cited by 66 publications

References 10 publications

Induced spin-triplet pairing in the coexistence state of antiferromagnetism and singlet superconductivity: Collective modes and microscopic properties

Induced spin-triplet pairing in the coexistence state of antiferromagnetism and singlet superconductivity: Collective modes and microscopic properties

Nematic versus ferromagnetic spin filtering of triplet Cooper pairs in superconducting spintronics

Coexistence of superconductivity and a spin-density wave in pnictide superconductors: Gap symmetry and nodal lines

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