A high-amplitude microwave magnetic field localized at the nanoscale is a desirable tool for various applications within the rapidly developing field of nanomagnetism. Here, we drive magnetization precession by coherent phonons in a metal ferromagnetic nanograting and generate ac-magnetic induction with extremely high amplitude (up to 10 mT) and nanometer scale localization in the grating grooves. We trigger the magnetization by a laser pulse which excites localized surface acoustic waves. The developed technique has prospective uses in several areas of research and technology, including spatially resolved access to spin states for quantum technologies.The exploration of magnetism at the nanoscale continues to be a rapidly developing field. Magnetic recording with ultrahigh densities [1] for data storage, magnetic resonant imaging with nanometer resolution [2, 3] for medicine and biology, addressing the magnetic states of atoms [4][5][6][7][8] for quantum computing, and ultrasensitive magnetic sensing [9] are the most prominent examples within the multifaceted research field of nanomagnetism. Most of the proposed concepts and prototypes utilize oscillating (ac-) magnetic fields with frequencies from millions up to hundreds of billions of cycles per second (10 6 -10 11 Hz). The oscillating magnetic fields are used to override the coercivity of ferromagnetic grains [10], to set atomic magnetic moments to a desired state [2,3,9], and to encode quantum information into spin states [4][5][6][7][8]11]. These examples utilize conventional methods for the generation of ac-magnetic fields: an external rf-generator in combination with a microwire [2][3][4][5][9][10][11] or a microwave cavity [6][7][8]11]. This methodology cannot be applied at the nanometer scale. A key breakthrough would be nanoscale generation of high-amplitude, monochromatic ac-magnetic fields. This would open the possibility to address neighboring nano-objects, e.g. spin qubits, independently, and to reduce the energy consumption in magnetic devices. It is however a challenging task to reach this goal because current technologies do not allow one to control the frequency, bandwidth and amplitude of an ac-magnetic field on the nanoscale.An efficient way to generate a high-frequency ac magnetic field is to induce coherent magnetization precession in a ferromagnet. The magnetization of ferromagnetic metals may be as large as 2 T. Precessional motion with frequencies of 10 GHz allows the generation of highamplitude microwave magnetic fields on the picosecond time scale. The magnetization precession can be driven by dc-spin polarized currents [12]. This approach is realized in microwave generators based on spin torque nanooscillators, but has severe limitations, e.g. in combining large amplitudes and high frequencies [13]. Coherent phonons, bulk [14,15] or surface [16,17] acoustic waves, have been successfully used for exciting the magnetization precession in ferromagnetic films. The effect of a surface acoustic wave (SAW) on the magnetic order in a ferromag...