We compute the electron spin susceptibility in the pseudogap regime of the two-dimensional Hubbard model using an SU(2) gauge theory of fluctuating magnetic order. In this framework, electrons fractionalize into fermionic chargons and bosonic spinons. The chargons, treated within a renormalized mean-field theory, develop Néel or spiral pseudospin order below a crossover temperature $T^*$, while spinon fluctuations are described by a nonlinear sigma model with microscopically computed stiffnesses. These fluctuations Higgs the SU(2) gauge field and prevent long-range spin symmetry breaking at any finite temperature.

Our results capture key features of pseudogap phenomenology. We find a spin gap in $S(\mathbf{q}, \omega)$, a strong suppression of the uniform spin susceptibility $\kappa_s$ below $T^*$, and an exponentially suppressed NMR relaxation rate $T_1^{-1}$ at low temperatures in the quantum disordered regime. At low hole doping, the dynamic structure factor develops nematic anisotropy below a temperature $T_{\mathrm{n}\mathrm{e}\mathrm{m}}<T^{\ast }$, which persists over a broad doping range. Our results further indicate a peak in the spin-lattice relaxation rate $(T_1 T)^{-1}$ near the nematic transition.