Our new work of spin Hall nano-oscillator entitled “Dynamical mode coexistence and chaos in the nano-gap spin Hall nano-oscillator” is recently published in Phy. Rev. B [Lina Chen, Kaiyuan Zhou, S. Urazhdin, Wencong Jiang, Y. W. Du, and R. H. Liu*, Phys. Rev. B 100, 104436 (2019)]. Congratulations to Dr. Chen. In this paper, we utilize microwave spectroscopy to study the auto-oscillation modes in the nanogap spin Hall nano-oscillators based on Permalloy/Pt bilayers. We show that two distinct spin-wave modes appear in such oscillators, regardless of the magnetic film thicknesses or the size of the electrode gap. We identify the primary mode as a nonlinear self-localized bullet soliton localized at the center of the gap between the electrodes, which is excited over a broad range of currents, field magnitudes, and orientations. The secondary high-frequency mode appears at higher currents and coexists with the primary bullet mode. Micromagnetic modeling shows that this mode is stabilized by the dipolar field of the bullet, and its spatial profile exhibits two maxima offset from the center of the gap in two opposite directions collinear with the field. Simulations also suggest chaotic dynamics that emerges at large currents due to the incoherent coupling between the two modes. Our results demonstrate the possibility to induce and control complex nonlinear dynamical phenomena in spin Hall oscillators, which can be utilized in the emergent neuromorphic and reservoir computing applications. This work is collaborated with Prof. Sergei Urazhdin, Department of Physics, Emory Universty, USA.