Magnetic insulators, such as yttrium iron garnet (Y$_3$Fe$_5$O$_{12}$), are ideal materials for ultra-low power spintronics applications due to their low energy dissipation and efficient spin current generation and transmission. Recently, it has been realized that spin dynamics can be driven very effectively in micrometer-sized Y$_3$Fe$_5$O$_{12}$/Pt heterostructures by spin-Hall effects. We demonstrate here the excitation and detection of spin dynamics in Y$_3$Fe$_5$O$_{12}$/Pt nanowires by spin-torque ferromagnetic resonance. The nanowires defined via electron-beam lithography are fabricated by conventional room temperature sputtering deposition on Gd$_3$Ga$_5$O$_{12 }$ substrates and lift-off. We observe field-like and anti-damping-like torques acting on the magnetization precession, which are due to simultaneous excitation by Oersted fields and spin-Hall torques. The Y$_3$Fe$_5$O$_{12}$/Pt nanowires are thoroughly examined over a wide frequency and power range. We observe a large change in the resonance field at high microwave powers, which is attributed to a decreasing effective magnetization due to microwave absorption. These heating effects are much more pronounced in the investigated nanostructures than in comparable micron-sized samples. By comparing different nanowire widths, the importance of geometrical confinements for magnetization dynamics becomes evident: quantized spin-wave modes across the width of the wires are observed in the spectra. Our results are the first stepping stones toward the realization of integrated magnonic logic devices based on insulators, where nanomagnets play an essential role.
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