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 δα 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 δα 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.
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