We realize resonant driving of the magnetization precession by monochromatic phonons in a thin ferromagnetic layer embedded into a phononic Fabry-Pérot resonator. A femtosecond laser pulse excites resonant phonon modes of the structure in the 10−40 GHz frequency range. By applying an external magnetic field, we tune the precession frequency relative to the frequency of the phonons localized in the cavity and observe an enormous increase in the amplitude of the magnetization precession when the frequencies of free magnetization precession and phonons localized in the cavity are equal. The continual miniaturization of magnetic devices down to the nanometer scale has opened new horizons in data storage [1], computing [2,3], sensing [4,5], and medical technologies [6]. Progress in nanomagnetism is stimulated by emerging technologies, where methods to control magnetic excitations on the nanometer spatial and picosecond temporal scales include optical [7,8], electrical [8], and micromechanical [9] techniques. To realize ultrafast nanomagnetism on the technological level, new physical principles to efficiently induce and control magnetic excitations are required, and this remains a challenging task. A new basic approach to this problem would be to explore nanoscale magnetic resonance phenomena-resonant driving and monitoring of magnetic excitations-which is widely used nowadays in traditional magnetism for microscopy, medicine, and spectroscopy. The typical frequencies f M of the magnetic resonances [e.g., the ferromagnetic resonance (FMR) in ferromagnetic and ferrimagnetic materials] are in the GHz and sub-THz frequency ranges. The traditional methods to scan magnetic excitations at these frequencies use microwaves, but due to the requirement of massive microwave resonators providing long wavelength radiation, they cannot provide high-speed control of magnetization locally on the nanoscale.Among various emerging techniques in nanomagnetism, the application of stress to magnetostrictive ferromagnetic layers has been shown to be an effective, low-power method for controlling magnetization: Applying in-plane stress in stationary experiments enables irreversible switching of the magnetization vector [10]; the injection of picosecond strain pulses induces free precession of the magnetization [11]; excitation of quantized elastic waves in a membrane enables driving of the magnetization at GHz phonon frequencies [12]; and surface acoustic waves can be used to control the magnetic dynamics in ferromagnetic nanostructures [13][14][15]. In the present Rapid Communication, we examine the interaction of a high-frequency (10−40 GHz) magnetic resonance in a magnetostrictive ferromagnetic film with an elastic harmonic excitation in the form of a localized phonon mode, and demonstrate how this interaction becomes significantly stronger at resonance conditions. Our device consists of a ferromagnetic layer embedded into a phonon Fabry-Pérot (FP) cavity. Such a cavity possesses quantized resonances for elastic waves (i.e., phonons) at f...