Altermagnetic superconducting diode effect from non-collinear compensated magnetism in Mn$_3$Pt

TL;DR

The paper develops a symmetry-guided theory for the superconducting diode effect in Mn$_3$Pt proximitized by a conventional superconductor, showing that noncollinear altermagnetic textures produce spin-split bands with zero net magnetization and give rise to a nonreciprocal critical current via proximity-induced, finite-momentum pairing. Using a tight-binding breathing kagome model and an explicit treatment of the proximity coupling, it demonstrates how the two current channels (superconducting and altermagnetic) contribute nonreciprocally to the total current, with the altermagnetic channel providing a robust nonreciprocity even at $oldsymbol{M}=0$ once spin-orbit coupling is included. The angular dependence of the diode efficiency distinguishes the competing T1 and T2 magnetic orders, predicting zeros of $ta( heta)$ fixed by mirror symmetries and delivering quantitative estimates of the diode effect strength (a few percent) consistent with experiments. The work provides a framework for designing altermagnet–superconductor hybrids with tunable nonreciprocal transport and suggests directional transport as a diagnostic for altermagnetic states. Additionally, it offers detailed derivations of the proximity-induced order parameters, the effective free energy minimization, and the altermagnet particle-particle bubble, enabling systematic exploration of SDE in related noncollinear altermagnetic systems.

Abstract

Altermagnets have recently emerged as a distinct class of magnetic systems that exhibit spin splitting of electronic bands while retaining zero net magnetization. This unique combination makes them a promising platform for time-reversal symmetry-breaking superconducting phenomena, although identifying concrete material platforms remains an important open challenge. Here, we develop a theory for the superconducting diode effect observed experimentally in a Mn$_3$Pt-superconductor heterostructure. Using both a symmetry analysis and model calculations on the breathing kagome lattice, we show how the altermagnetic spin textures in Mn$_3$Pt generate a spin splitting of the electronic bands that remains magnetization-free even in the presence of spin-orbit coupling and, upon taking into account the proximity coupling across the interface, produces a superconducting diode effect. We also demonstrate that the angular dependence of the critical current provides a probe of the magnetic order. We hope that our work will contribute to the understanding and further discovery of candidate materials for novel altermagnet-superconductor hybrid devices.

Figures (9)

• Figure 1: Noncollinear altermagnetic platform for a superconducting diode effect. (a) Crystal structure of Mn$_3$Pt, where Mn moments form a breathing kagome lattice in the $(111)$ plane (blue: Mn, brown: Pt). (b) Mn$_3$Pt altermagnet proximitized by a conventional superconductor, giving rise to a SDE with nonreciprocal critical currents, $I_c^+ \neq I_c^-$. (c,d) Two compensated magnetic orders of Mn$_3$Pt: the T1 phase (c) and the T2 phase (d). The T2 phase enables a SDE while retaining zero net magnetization.
• Figure 2: Normal state bands and Fermi surface spin textures for the T2 phase. (a) Band structure along $\Gamma$–$M$–$K$–$\Gamma$ without spin-orbit coupling ($\lambda = \lambda' = 0)$, showing an altermagnetic spin splitting. (b) Same as (a) but with a staggered spin-orbit coupling on the two kagome triangles $(\lambda\neq\lambda')$. (c),(d) Fermi surfaces and Fermi-surface spin textures at the chemical potential indicated in (a) and (b) by a blue line.
• Figure 3: Momentum-dependence of particle-particle bubbles and superconducting order parameters. (a) Particle-particle bubble of the superconductor, $\Pi_{\text{SC}}(\boldsymbol q)$, with a single maximum at $\boldsymbol q=0$. (b) Particle-particle bubble of the altermagnet, $\Pi_{\text{AM}}(\boldsymbol q)$, showing three $C_3$-related maxima at finite momenta. (c) Renormalized order parameter of the superconductor, $|\Delta_{\boldsymbol q}|^{2}$. (d) Proximity-induced supercondcuting order parameter in the altermagnet, $|\bar{\Delta}_{\boldsymbol q}|^{2}$, whose maxima occur at finite momenta, indicating finite-momentum pairing.
• Figure 4: Angular dependence of the superconducting diode effect. (a) Angular dependence of the forward and reverse critical currents, $I_c^\pm(\theta)$ (left), and the corresponding diode efficiency, $\eta(\theta)$ (right), for the T2 phase. The critical currents are normalized by $I_{\mathrm{max}}=\max_{\theta}\{I_c^\pm(\theta)\}$. (b) Same quantities for the T1 phase. The angular directions for which $\eta(\theta)=0$ differ between T1 and T2, providing a possible way to distinguish between the two phases.
• Figure 5: Magnetic-field dependence of the superconducting diode effect. (a) Critical currents as a function of out-of-plane magnetic field, $B$, for the altermagnetic [left, highly nonreciprocal, from second term in Eq. (\ref{['Eq9']})] and the superconducting [right, nearly reciprocal, first term in Eq. (\ref{['Eq9']})] contributions. The critical currents are normalized by $I_{c,\mathrm{AM}}^{+}(B=0)$ and $I_{c,\mathrm{SC}}^{+}(B=0)$, respectively. The current bias is applied along $\theta=90^\circ$ and the critical field is denoted by $B_{c2}$. (b) Diode efficiency, $\eta$, as a function of the magnetic field, $B$. The efficiency increases with $B$ as the reciprocal supercurrent contribution is progressively suppressed, which enhances the relative weight of the nonreciprocal supercurrent carried by the altermagnet.