A Fermi Surface Driven Spiral Spin Liquid
EuAg$_4$Sb$_2$ is a model material to study the interplay of electronic and spin texture degrees of freedom, exhibiting numerous multi-$q$ magnetic textures coupled with the electronic properties. It is generally understood that some combination of conduction-electron mediated interactions, frustration, and higher order interactions are responsible for complex incommensurate spin textures in centrosymmetric lanthanide materials. Here, we refine an effective model of the magnetic interactions in EuAg$_4$Sb$_2$ through measurements of diffuse magnetic neutron scattering above the ordering temperature. These diffuse measurements reveal a ring of fluctuating spin modulations that reflects a manifold of nearly degenerate propagation vectors known as a spiral spin liquid (SSL). We further identify that this approximate $U$(1) symmetric SSL emerges from magnetic interactions mediated by a quasi-2D hole pocket and exhibits critical scaling of the spatial correlations. Further, Monte Carlo simulations reveal excellent agreement with experiment and provide a comprehensive understanding of the phase diagram. This study emphasizes the connection between the rich spin textures in this material, the electronic structure, and spin liquidity$\unicode{x2014}$uncovering new insights into design principles for nano-scale spin texture materials with advantageous intertwined electronic, magnetic, and topological properties, and new mechanisms for generating the physics of spiral spin liquids.