2026/07/24 by Andrea Grimaldi, Denys Slobodianiuk, Eleonora Raimondo +7
#cond-mat.mes-hall
Parametric pumping is a powerful tool for the excitation, amplification, and processing of oscillations and waves of different nature. In general, parametric resonance can occur when the pumping frequency fp and eigenfrequency of a linear mode (or wave) f0 satisfy the relation fp=2f0/n (n=1,2,3,...). While such parametric resonance is well known in mechanical, superconductive, and quantum systems, in magnetic and spintronic systems only the lowest (n=1) parametric resonance at double the spin wave mode frequency fp=2f0 was thoroughly studied and explored. Here, using a theoretical analysis based on both micromagnetic simulations and an analytical model, we show the emergence of resonances at fractional frequencies fp=2f0/n (with n>10) in spintronic diodes driven by the simultaneous action of ac spin-transfer torque (STT, current densities < 106 A/cm2) and voltage-controlled magnetic anisotropy (VCMA, effective anisotropy fields < 50 mT). The analytical model shows that parametric magnetization dynamics is irreducible to the standard Mathieu model of a parametric oscillator and demonstrates the crucial role of VCMA-driven mode frequency modulation: together with parametric coupling, it results in higher-order odd (n=3,5,7,...) fractional resonances, observed above certain VCMA pumping threshold, while simultaneous action with linear STT drive produces thresholdless even (n=4,6,8,...) resonances. This higher-order parametric dynamics is not restricted to VCMA pumping and opens new directions for the application of spintronic diodes for nonlinear signal processing and electromagnetic energy harvesting.