Superconducting proximity effect and long-ranged triplets in dirty metallic antiferromagnets Eirik Holm Fyhn1Arne Brataas1Alireza Qaiumzadeh1and Jacob Linder1 1Center for Quantum Spintronics Department of Physics Norwegian

2025-05-02 0 0 381.2KB 5 页 10玖币

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Superconducting proximity eﬀect and long-ranged triplets in dirty metallic antiferromagnets

Eirik Holm Fyhn,

Arne Brataas,

Alireza Qaiumzadeh,

and Jacob Linder

Center for Quantum Spintronics, Department of Physics, Norwegian

University of Science and Technology, NO-7491 Trondheim, Norway

(Dated: May 30, 2023)

Antiferromagnets have no net spin-splitting on the scale of the superconducting coherence length. Despite

this, antiferromagnets have been observed to suppress superconductivity in a similar way as ferromagnets, a

phenomenon that still lacks a clear understanding. We ﬁnd that this eﬀect can be explained by the role of impurities

in antiferromagnets. Using quasiclassical Green’s functions, we study the proximity eﬀect and critical temperature

in diﬀusive superconductor-metallic antiferromagnet bilayers. The non-magnetic impurities acquire an eﬀective

magnetic component in the antiferromagnet. This not only reduces the critical temperature but also separates the

superconducting correlations into short-ranged and long-ranged components, similar to ferromagnetic proximity

systems.

Introduction: Antiferromagnets and superconductors

both have prominent roles in condensed matter physics [

–

]. Separately, they are both theoretically interesting due to

their diﬀerent types of quantum order [

–

]. They are also

technologically useful: superconductors in part because of

their perfect diamagnetism and dissipationless current [

and antiferromagnets because of their ultrafast dynamics [

], negligible stray-ﬁeld and considerable magnetotransport

eﬀects [

]. However, while materials with superconducting or

magnetic properties can be interesting on their own, new physics

and applications can be found in systems that combine both. For

instance, combining superconductivity and ferromagnetism in

mesoscopic heterostructures is now a well-established method

to produce odd-frequency superconductivity and long-range

spin-triplet superconductivity [

]. The latter can carry

dissipationless spin-currents, giving superconductors a unique

role in the ﬁeld of spintronics [2].

Superconductor-antiferromagnet (SC-AF) heterostructures

have been studied both theoretically and experimentally [

–

], but much less than their ferromagnetic counterparts. As a

result, much remains to be fully understood about SC-AF het-

erostructures. For instance, experiments show that proximity

to antiferromagnets can severely suppress the superconduct-

ing critical temperature [

–

]. This suppression is much

stronger than the prediction by the theoretical models which

considered the AFs to be similar to normal metals due to their

lack of uncompensated magnetic moments [

–

]. In fact, the

suppression has been reported to be even larger than the suppres-

sion seen in ferromagnetic junctions [

]. Various proposals

have been suggested to explain this suppression, such as ﬁnite

spin-splitting coming from uncompensated interfaces [

], the

possibility of magnetic impurities having been infused into the

superconductor during sample preparation [

], or the complex

spin structure of the speciﬁc antiferromagnetic materials used

in the experiments [29].

More recently, in a theoretical study of superconductor-

antiferromagnetic insulator bilayers with compensated inter-

faces, Bobkov et al.

[32]

suggested that a band-gap opening

mechanism together with the induction of spin-triplet Cooper

pairs could explain the suppression. As these eﬀects are smaller

when the mean free path is shorter, they argued that the sup-

pression would be larger for cleaner systems, but noted that a

fully detailed analysis of the roles of impurities and AF length

should consider a metallic AF.

Here, we study the proximity eﬀect in diﬀusive supercon-

ductor (SC)-antiferromagnetic metal (AFM) bilayers using our

newly derived quasiclassical framework [

]. Interestingly, our

results show that the suppression of superconductivity is not

larger for clean systems, but that impurity scattering is in fact

the dominant mechanism for superconductivity suppression in

metallic AFs. The reason is that the sublattice-spin coupling in

the antiferromagnet gives the non-magnetic impurities an eﬀec-

tive magnetic component. These eﬀective magnetic impurities

are detrimental to superconductivity, except for spin-triplet

superconductivity with spin aligned orthogonal to the Néel

vector. As a result, dirty AFMs work as superconductivity ﬁl-

ters letting only spin-triplet superconductivity with orthogonal

spin-projection to the Néel vector pass through. After studying

the critical temperature in SC/AFM bilayers, we show how the

superconducting correlations penetrate into the antiferromag-

netic metal, as well as the inverse proximity eﬀect. Moreover,

we show how the long-range spin-triplet components can be

induced by either uncompensated or magnetic interfaces with

magnetic misalignment relative to the AFM Néel vector.

Theory: To study SC-AFM bilayers, we employ the quasi-

classical Keldysh formalism derived in [

]. It is valid under

the assumption that the Fermi wavelength is short compared to

the coherence length and the mean free path, and the chemical

potential,

𝜇

, is much larger than all other energy scales in the

system, except possibly the exchange energy between localized

spins and conducting electrons,

𝐽

. Note that

|𝐽/𝜇|<1

, since

|𝜇|=√𝐽2+𝑡2

, where

𝑡

is the hopping parameter evaluated at

the Fermi surface. We also assume the dirty limit, meaning

that the system is diﬀusive, and that there is no electromag-

netic vector potential. In this case, the quasiclassical Green’s

function ˇ𝑔solves [33]

𝑖∇ · ˇ

𝒋+𝜏𝑧(𝜀+𝑖𝛿) + ˆ

Δ+𝑖𝐽2

2𝜏imp 𝜇2𝜎𝑧𝜏𝑧ˇ𝑔𝜎𝑧𝜏𝑧,ˇ𝑔=0.(1)

Here,

𝒋

is the matrix current,

𝜏𝑧

and

𝜎𝑧

are Pauli matrices

in Nambu- and spin-space, respectively,

𝜀

is energy,

𝛿

is the

Dynes parameter,

𝜏imp

is the elastic impurity scattering time

and

Δ = Δ𝑖𝜏𝑦

, under the assumption that the gap parameter

is real. The spin-quantization axis is chosen to be parallel

arXiv:2210.09325v3 [cond-mat.supr-con] 28 May 2023

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Superconductingproximityeffectandlong-rangedtripletsindirtymetallicantiferromagnetsEirikHolmFyhn,1ArneBrataas,1AlirezaQaiumzadeh,1andJacobLinder11CenterforQuantumSpintronics,DepartmentofPhysics,NorwegianUniversityofScienceandTechnology,NO-7491Trondheim,Norway(Dated:May30,2023)Antiferromagnetshavenon...

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Superconducting proximity effect and long-ranged triplets in dirty metallic antiferromagnets Eirik Holm Fyhn1Arne Brataas1Alireza Qaiumzadeh1and Jacob Linder1 1Center for Quantum Spintronics Department of Physics Norwegian

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