Spin susceptibility in a pseudogap state with fluctuating spiral magnetic order

We compute the electron spin susceptibility in the pseudogap regime of the two-dimensional Hubbard model in the framework of a SU(2) gauge theory of fluctuating magnetic order. The electrons are fractionalized in fermionic chargons with a pseudospin degree of freedom and bosonic spinons. The chargons are treated in a renormalized mean-field theory and order in a N\'eel or spiral magnetic state in a broad range around half-filling below a transition temperature $T^*$. Fluctuations of the spin orientation are captured by the spinons. Their dynamics is governed by a non-linear sigma model, with spin stiffnesses computed microscopically from the pseudospin susceptibility of the chargons. The SU(2) gauge group is higgsed in the chargon sector, and the spinon fluctuations prevent breaking of the physical spin symmetry at any finite temperature. The electron spin susceptibility obtained from the gauge theory shares many features with experimental observations in the pseudogap regime of cuprate superconductors: the dynamical spin susceptibility $S(\mathbf{q},\omega)$ has a spin gap, the static uniform spin susceptibility $\kappa_s$ decreases strongly with temperature below $T^*$, and the NMR relaxation rate $T_1^{-1}$ vanishes exponentially in the low temperature limit if the ground state is quantum disordered. At low hole doping, $S(\mathbf{q},\omega)$ exhibits nematicity below a transition temperature $T_{\rm nem} < T^*$, and at larger hole doping in the entire pseudogap regime below $T^*$.