Spatially Inhomogeneous Triplet Pairing Order and Josephson Diode Effect Induced by Frustrated Spin Textures

We show that frustrated spin textures can generate anisotropic Josephson couplings between $d$ vectors that can stabilize spatially varying pairing orders in spin triplet superconductors. These couplings depend on the relative orientation of $d$ vectors, analogous to Dzyaloshinskii-Moriya and $\Gamma$-type interactions in magnetism, leading to an effective ``pliability'' of the pairing order that competes with superfluid stiffness. Such couplings cannot originate from spin-orbit coupling; rather, they can arise, for example, when itinerant electrons are coupled to a local exchange field composed of frustrated spin moments. Using a $T$-matrix expansion, we show that coupling to a local exchange field leads to an effective tunneling of itinerant electrons that is dependent on the underlying spin configurations at the barrier between superconducting grains. Furthermore, Josephson tunneling through frustrated spin textures can produce a Josephson diode effect. The diode effect originates either from nonvanishing spin chirality in the barrier, or from antisymmetric Josephson coupling between noncollinear $d$ vectors, both of which break inversion and time-reversal symmetries.