Spin pumping effect in non-Fermi liquid metals

Spin pumping effect is a sensitive and well-established experimental method in two-dimensional (2D) magnetic materials. We propose that spin pumping effect can be a valuable probe for non-Fermi liquid (NFL) behaviors at the 2D interface of magnetic heterostructures. We show that the modulations of ferromagnetic resonance exhibit power-law scalings in frequency and temperature for NFL metals induced near a quantum critical point (QCP). At the Ising nematic QCP, we demonstrate that the enhanced Gilbert damping coefficient $\delta \alpha$ acquires negative power-law exponents in distinct frequency regimes. The exponents convey universal parameters inherited from the QCP and reflect the non-quasiparticle nature of the spin carriers in the NFL metal. At finite temperature, we show that the Gilbert damping mechanism is restored in the quantum critical regime and $\delta \alpha$ measures the temperature dependence of the correlation length. Our theoretical proposal has the potential to stimulate the development of an interdisciplinary research domain where insights from non-equilibrium spin physics in spintronics are integrated into strongly correlated matter.