Finite-momentum mixed singlet-triplet pairing in chiral antiferromagnets induced by even-parity spin texture

Abstract

Non-relativistic spin-splitting in unconventional antiferromagnets has garnered much attention for its promising spintronic applications and open fundamental questions. Here, we uncover a unique even-parity spin texture in chiral non-collinear antiferromagnets, exemplified using a kagome lattice. We consider two distinct types of electrons in the system: one with Schrödinger-like dispersion and the other exhibiting Dirac-like behavior. Remarkably, we show that, for both electron types, this spin texture induces an exotic coexistence of opposite-spin singlet and equal-spin triplet Cooper pairs with finite momentum when proximity-coupled to conventional superconductors. The triplet pairing arises from the intrinsic spin rotation of the antiferromagnet and does not require net magnetization or spin-orbit coupling. Moreover, we identify an unprecedented and tunable phase difference between singlet and triplet pairings, controllable through junction orientation. This mixed pairing state can be experimentally probed via damped oscillations in order parameters and 0-$π$ transitions in Josephson junctions. Additionally, we analyze the effect of out-of-plane spin canting, elucidating its role in generating spin-polarized supercurrents, and discuss Mn$_3$Ga and Mn$_3$Ge to test our predictions.

Figures (10)

• Figure 1: (a) Crystal structure of the kagome antiferromagnet with a $120^\circ$ cAFM order. The arrows on the three sublattices $A,B,C$ indicate the local magnetic moments. ${\bm a}_1$ and ${\bm a}_2$ are nearest-neighbor vectors. (b) Creation mechanism of mixed singlet and equal-spin triplet pairing. For illustration, we consider the spins along $x$-direction and thus have two Cooper pairs with opposite center-of-mass momenta $\pm Q$. (c) Band structure along high symmetry lines in the absence (dashed) and presence (solid) of cAFM order. The inset shows the first Brillouin zone with the high symmetry points indicated. (d) Even-parity spin texture of the lowest band in the Brillouin zone. Parameters are $t=1$ and $J=0.3t$.
• Figure 2: (a) Singlet amplitude $\mathcal{F}_0$ (in units of $t^{-1}$) as a function of frequency $\omega$ and position $x$ (in units of unit-cell layers) in the cAFM. Inset sketches the SC-cAFM junction oriented in $x$-direction. (b) Same as (a) but for equal-spin triplet pairing amplitudes, $\mathcal{F}_t=i\mathcal{F}_{\uparrow\uparrow}=-i\mathcal{F}_{\downarrow\downarrow}$. (c) $\mathcal{F}_0$ (red) and $\mathcal{F}_t$ (blue) as functions of $x$ in the cAFM for $J=0$ and $\omega=0.1\Delta$. (d) Same as (c) but for a finite cAFM order ($J=0.5t$). (e) $\mathcal{F}_0$ (red) and $\mathcal{F}_t$ (blue) as functions of $\omega$ for $x=80$.
• Figure 3: (a) Schematic of out-of-plane canting on the cAFM and the band structure near the band edge. (b) Spin-singlet (back) and equal-spin-triplet amplitudes (red and blue), $\mathcal{F}_0$, $\mathcal{F}_{\uparrow\uparrow}$ and $\mathcal{F}_{\downarrow\downarrow}$ (in units of $t^{-1}$), as functions of position $x$ in the cAFM under out-of-plane spin canting (i.e., $J=0.5t$ and $M_z=0.1t$). (c) $\max(|\mathcal{F}_{\uparrow\uparrow}|)$, $\max(|\mathcal{F}_{\downarrow\downarrow}|)$ and their difference as functions of canting strength $M_z$. (d) $\max(|\mathcal{F}_{\uparrow\uparrow}|)/\max(|\mathcal{F}_{\downarrow\downarrow}|)$ as a function of $M_z$. Other parameters: $\mu=\mu_S=-2t$, $\omega=0.01t$ and $\Delta=0.05t$.
• Figure A1: (a) Band structure near the band edge at the $\Gamma$ point. The Cooper pairing occurs predominantly between the two Fermi surfaces, leading to finite-momentum Cooper pairs. The spin textures of the Fermi surfaces are indicated by the arrows. (b) Band structure near the band center at the $K/K'$ point. The Cooper pairing occurs predominately between different valleys. (c) Schematic for the SC/cAFM setup. The proximity-induced pairing correlations exhibit damped oscillations near the interface. (d) Periodicity of oscillations as a function of the chemical potential $|\mu_\Gamma|$ ($|\mu_K|$) measured from the band edge (center). Parameters are $t=1$ and $J=0.3t$.
• Figure A2: (a) Critical Josephson current $I_c$ as a function of chemical potential $\mu$ in the cAFM for $L=80$. The cyan shadow indicates the regions for the $\pi$-state, while the white regions correspond to the $0$-state of the Josephson junction. (b) Current-phase relation for $\mu=-2t$ and $-2.3t$ [corresponding to the two colored stars in (a)], respectively. (c) $I_c$ (orange) as a function of junction length $L$ for $\mu_N=-2t$. We plot the result (back curve) for a smaller AFM strength $J=0.3t$ for comparison. (d) Current-phase relation for $L=15$ and $40$ [corresponding to the two colored stars in (c)], respectively. Other parameters are $\mu_S=-2t$, $J=0.6t$, $\Delta=0.05t$ and $k_BT=0.02\Delta$.