Enhancement of Electronic Spin Susceptibility in Pauli Limited Unconventional Superconductors

We calculate the wave-vector dependent electronic spin susceptibility \(\chi_{\alpha\beta}(\mathbf q, \mathbf H_0)\) of a d-wave superconductor in uniform magnetic field \(\mathbf{H}_0\) with Pauli pair-breaking. We find that the transverse component of the susceptibility tensor can be greater than its normal state value; the longitudinal component also slightly increases but in a very limited range of \(q\)s. We identify several wave vectors \(\{\mathbf q_\perp,\mathbf q_\parallel\}\), that correspond to the maxima of either \(\chi_\perp\) or \(\chi_\parallel\). We compare our results with available data on the high-field phase in heavy-fermion CeCoIn\(_5\).