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Recent work has shown that optical magnetism, generally considered a challenging light-matter interaction, can be significant at the nanoscale. In particular, the dielectric nanostructures that support magnetic Mie resonances are low-loss and versatile optical magnetic elements that can effectively manipulate the magnetic field of light. However, the narrow magnetic resonance band of dielectric Mie resonators is often overshadowed by the electric response, which prohibits the use of such nanoresonators as efficient magnetic nanoantennas. Here, we design and fabricate a silicon (Si) truncated cone magnetic Mie resonator at visible frequencies and excite the magnetic mode exclusively by a tightly focused azimuthally polarized beam. We use photoinduced force microscopy to experimentally characterize the local electric near-field distribution in the immediate vicinity of the Si truncated cone at the nanoscale and then create an analytical model of such structure that exhibits a matching electric field distribution. We use this model to interpret the PiFM measurement that visualizes the electric near-field profile of the Si truncated cone with a superior signal-to-noise ratio and infer the magnetic response of the Si truncated cone at the beam singularity. Finally, we perform a multipole analysis to quantitatively present the dominance of the magnetic dipole moment contribution compared to other multipole contributions into the total scattered power of the proposed structure. This work demonstrates the excellent efficiency and simplicity of our method of using Si truncated cone structure under APB illumination compared to other approaches to achieve dominant magnetic excitations.