Spin susceptibility as a probe of the gap structure in triplet superconductors

We present a theoretical framework for analyzing the spin susceptibility of nodal spin-triplet superconductors across both the zero-field and finite-field regimes, emphasizing its implications for Knight-shift and magnetotropic-susceptibility experiments. Starting from a general expression for the static susceptibility, we derive the zero-temperature sum rule showing that the residual spin susceptibilities satisfy Σ_i χ_ii(0) = 2 χ_N and demonstrate its robustness under strong Fermi-surface anisotropy. We then incorporate the effects of supercurrents in the vortex state through a semiclassical Doppler shift of quasiparticle energies, showing how field-dependent changes in longitudinal and transverse susceptibilities encode information on nodal directions, d-vector orientation, and the modification of the sum rule at finite field. Applying this approach to a realistic tight-binding model of UTe₂, we evaluate the field-dependent susceptibility for candidate orthorhombic triplet states (B_1u, B_2u, B_3u) and identify distinctive signatures that differentiate them. Our results demonstrate that finite-field Knight-shift and magnetotropic-susceptibility measurements provide a diagnostic for the spin and orbital structure of heavy-fermion triplet superconductors.