Zeeman-Driven Phase Transition within the Superconducting State of κ-(BEDT-TTF)2Cu(NCS)2

C13 nuclear magnetic resonance measurements were performed on κ-(BEDT-TTF)₂Cu(NCS)₂, with the external field placed parallel to the quasi-2D conducting layers. The absorption spectrum is used to determine the electronic spin polarization M_s as a function of external field H at a temperature T=0.35K. A discontinuity in the derivative dM_s/dH at an applied field of H_s=213±3kOe is taken as evidence for a Zeeman-driven transition within the superconducting state and stabilization of inhomogeneous superconductivity.