Orbital-Selective Diffuse Magnetic Fluctuations in Sr$_2$RuO$_4$: a Unified Theoretical Picture

The quasi-two-dimensional material Sr$_2$RuO$_4$ is a paradigmatic example of a correlated system that exhibits unconventional superconductivity and intriguing magnetic properties. The interplay between these two effects and the resulting strength and nature of spin fluctuations and their role for the properties of the compound have sparked significant debates. Here, elaborating a theory that self-consistently incorporates spatial magnetic fluctuations into a realistic many-body description, we show that these fluctuations significantly reduce many-body correlations in the system, thereby preventing magnetic ordering in Sr$_2$RuO$_4$, in agreement with experimental observations. Our conclusion is supported by a theoretical calculation of the spin susceptibility that closely matches the experimental results. We obtain finite peaks at the incommensurate wave vectors, a broad dome-shaped structure centered around the $\Gamma$ point and a diminished magnetic response at the edges of the BZ. We identify the orbital character of the unusual dome structure as resulting predominantly from the 2D-like $xy$-orbital, which is believed to be responsible for the superconductivity.