Anisotropic Josephson coupling of $d$ vectors in triplet superconductors arising from frustrated spin textures

We demonstrate that coupling itinerant electrons to a noncollinear classical exchange field can induce anisotropic Josephson coupling between superconducting $d$ vectors, analogous to the Dzyaloshinskii-Moriya and $\mathrm{\Gamma }$-type interactions in magnetism. Using perturbative methods, we analyze an $s$-$d$ model on a geometrically frustrated lattice. Noncollinear local spin textures generate spin triplet pairing correlations and can favor spatially varying superconducting order due to anisotropic Josephson couplings between $d$ vectors, endowing a ``pliability’’ to the pairing order that competes with the superfluid stiffness. For nonunitary pairing, this spatial texture of $d$ vectors can give rise to anomalous vortices in the absence of an external magnetic field. We further predict a Josephson diode effect with efficiency proportional to the spin chirality of the underlying magnetic texture. These results establish a link between frustrated magnetism and spatial textures of triplet superconducting pairing, with implications for a range of materials such as Mn${}_3$Ge and $4H_b$-TaS${}_2$, where superconductivity can be proximity-induced or intrinsic.