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The spin Coulomb drag effect, arising from the exchange of momentum betweenelectrons of opposite spins, plays a crucial role in the spin transport ofinteracting electron systems and can be characterized by theexchange-correlation (XC) kernel in the spin channel $K_{\rm XC}^-(q,\omega)$.Using the state-of-the-art Variational Diagrammatic Monte Carlo approach, wecompute the Matsubara-frequency-resolved spin XC kernel $K_{\rmXC}^-(q,i\omega_n)$ for the three-dimensional uniform electron gas atsufficiently low temperatures with high precision. In the long-wavelengthlimit, we identified a singular behavior of the form $A(i\omega_n)/q^2$,confirming the theoretically predicted ultranonlocal behavior associated withspin Coulomb drag. Analysis of this structure in the low frequency regionenables precise determination of two crucial parameters characterizing the spinCoulomb drag effect: the spin mass enhancement factor and spin diffusionrelaxation time. We observe a significant trend of increasing enhancement ofthe spin mass factor with decreasing electron density, and provide clearevidence for the suppression of spin diffusion at low temperatures. Thesequantitative findings advance our understanding of Coulomb interaction effectson spin transport and provide essential parameters for time-dependent densityfunctional theory and spintronics applications.

Matsubara-Frequency-Resolved Spin Exchange-Correlation Kernel for the Three-Dimensional Uniform Electron Gas