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Spin susceptibility in a pseudogap state with fluctuating spiral magnetic order

Paulo Forni1, Pietro M. Bonetti2, Henrik Müller-Groeling1, Demetrio Vilardi1, and Walter Metzner1

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Phys. Rev. B 113, 045144 – Published 26 January, 2026

DOI: https://doi.org/10.1103/zm7b-jdzf

Abstract

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 Néel 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 nonlinear 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(q,ω) has a spin gap, the static uniform spin susceptibility κs decreases strongly with temperature below T*, and the NMR relaxation rate T1−1 vanishes exponentially in the low temperature limit if the ground state is quantum disordered. At low hole doping, S(q,ω) exhibits nematicity below a transition temperature Tnem<T*, and at larger hole doping in the entire pseudogap regime below T*.

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Phys. Rev. B 113, 045144– Published 26 January, 2026
  • Received 18 August 2025
  • Revised 2 November 2025
  • Accepted 8 December 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by Max Planck Society.

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