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In this work, topological properties of a ferromagnetic Heisenberg model on abreathing kagome lattice are investigated extensively in the presence of  Dzyaloshinskii-Moriya interaction. While the kagome ferromagnet hosts only asingle first order topological phase, the breathing kagome system exhibitsmultiple first and second order topological phases along with theircoexistence. Magnon dispersion relation is obtained by using linear spin wavetheory. Flat band and Dirac cones are obtained in the absence of  Dzyaloshinskii-Moriya interaction. A topological phase diagram is presentedwhere several first and second order phases as well as their overlap areidentified. Values of thermal Hall conductivity for all the first order phasesare obtained. Distinct first order phases are characterized by different setsof Chern numbers in association with the necessary chiral edge states inaccordance to the first order bulk-boundary-correspondence rule. Second orderphase is characterized by polarization along with the emergence of cornerstates. Violation of the second order bulk-corner-correspondence rule has beennoted in some regions.

First and Second Order Topological Phases on Ferromagnetic Breathing Kagome Lattice