Triplet correlations in superconductor/antiferromagnet heterostructures: dependence on type of antiferromagnetic ordering

TL;DR

This work develops a generalized two-sublattice Green’s function framework to study proximity-induced triplet correlations in superconductor/antiferromagnet heterostructures with arbitrary two-sublattice AF order. It combines analytical results for homogeneous AF–superconductor systems with Bogoliubov–de Gennes simulations in 2D and 3D to quantify triplet components and superconducting order-parameter suppression across S/AF interfaces. A key finding is that checkerboard Néel triplet correlations dominate in collinear compensated G-type AF near half-filling, while layered A-type and C-type AFs fail to generate sizable Néel triplets and often only produce weak conventional triplets whose presence depends on the AF orientation relative to the interface. The results have practical implications for selecting AF materials and constructing effective homogeneous models in superconducting spintronics, suggesting layered AFs can minimize unwanted triplet proximity effects and guiding device design and interpretation.

Abstract

In recent years, a number of studies have predicted the emergence of a nontrivial proximity effect in superconductor/antiferromagnet (S/AF) heterostructures. This effect is of considerable interest for the efficient integration of antiferromagnetic materials into the fields of superconducting spintronics and electronics. A key element of this proximity effect is the Neel triplet correlations, initially predicted for S/AF heterostructures with checkerboard G-type antiferromagnetic ordering. However, various forms of antiferromagnetic ordering exist, and an important open question concerns the generalization of these results to such cases. In this paper, we develop a theory of the proximity effect in S/AF heterostructures with arbitrary two-sublattice antiferromagnetic ordering, aiming to clarify which antiferromagnets are capable of inducing triplet correlations and what structure these correlations may exhibit. We show that, in S/AF heterostructures with collinear compensated antiferromagnets, the dominant superconducting triplet correlations are of the checkerboard Neel type, as originally predicted for G-type antiferromagnets. In contrast, layered Neel triplet correlations, although potentially generated by layered antiferromagnets, are significantly weaker. Consequently, in S/AF heterostructures with layered antiferromagnetic ordering, the proximity-induced triplet correlations may exhibit either a checkerboard Neel or a conventional ferromagnetic structure, depending on the specific antiferromagnet and its orientation relative to the S/AF interface.

Figures (4)

• Figure 1: 2D Fermi surfaces for normal state of antiferromagnetic superconductors with different types of magnetic ordering. $h$ is assumed to be small and disregarded in the figures. A square crystal lattice is assumed. For all panels the Fermi surface sheets originating from $\xi_{1(2)}=0$ are shown in red (blue) color. (a) G-type AF order, $\mu=-0.02t$, the next-nearest-neighbor hopping element $t_2 = 0$. (b) G-type AF order, $t_2=0.01t$, $\mu=0$. (c) G-type AF order, $\mu=-t$, $t_2=0$. (d) A-type AF order, $\mu=0.2t$, $t_2 = 0$. (e) G-type AF order, $t=0.02t_2$, $\mu=0.2t_2$. (f) G-type AF order, $t=0.02t_2$, $\mu=1.5t_2$.
• Figure 2: Triplet correlations at 2D magnet/superconductor interfaces with different types of magnetic order in the magnetic material. Each cell represents one site. The system is infinite along the $y$-axis. The full number of sites along the $x$-axis is $N_{AF}=4$ for the magnetic part and $N_S=15$ for the superconducting part, as it is shown in the figures. The amplitude of the triplet correlations calculated according to Eq. (\ref{['triplet_total']}) is shown by color. The magnet occupies 4 left rows of the system, the type of magnetic ordering is shown by arrows. $F^s_0$ is the amplitude of singlet correlations, calculated according to Eq. (\ref{['triplet_total']}) for the isolated superconductor. The superconducting OP of the isolated superconductor $\Delta_0=0.035t$, $h=0.04t$, $\Omega_D=0.5t$, $T=0.005t$, $\mu=0$.
• Figure 3: Triplet correlations at 3D magnet/superconductor interfaces with different types of magnetic order in the magnetic material. Each cell represents one site. The system is infinite in the $(y,z)$-plane. The real size of the system along the $x$-axis is shown in the figures. The amplitude of the triplet correlations calculated according to Eq. (\ref{['triplet_total']}) is shown by color. The magnet occupies 4 left planes of the system, the type of magnetic ordering is shown by arrows. $h=0.05t$, other parameters are the same as Fig. \ref{['fig:2D']}.
• Figure 4: Superconducting order parameter as a function of the exchange field of the magnet. The value of the OP is averaged over all superconducting sites. Different curves correspond to different 3D superconductor/magnet heterostructures presented in Fig. \ref{['fig:3D']}. Black - S/F heterostructure [Fig. \ref{['fig:3D']}(a)]; blue - S/AF heterostructure with $G$-type AF [Fig. \ref{['fig:3D']}(b)]; green - S/AF heterostructure with $A$-type AF with normal to the layers oriented along the $x$-axis [Fig. \ref{['fig:3D']}(d)]; red - S/AF heterostructure with $A$-type AF with normal to the layers oriented along the $z$-axis [Fig. \ref{['fig:3D']}(c)]. $\Delta_0=0.035t$, $\Omega_D=0.5t$, $T=0.005t$, $\mu=0$.