Exploring strong electronic correlations in the breathing kagome metal <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Fe</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mi>Sn</mml:mi></mml:mrow></mml:math>

Kagome metals have emerged as pivotal materials in condensed matter physics due to their unique geometric arrangement and intriguing electronic properties. Understanding the origin of magnetism in these materials, particularly in iron-rich Fe-Sn binary compounds such as <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:msub><a:mi>Fe</a:mi><a:mn>3</a:mn></a:msub><a:mi>Sn</a:mi></a:mrow></a:math>, holds a significant importance, as they represent potential candidates for permanent magnets with a high Curie temperature and a strong magnetic anisotropy. In the present study, we employ density functional theory and dynamical mean-field theory to analyze the electronic structure and magnetic properties of <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:msub><b:mi>Fe</b:mi><b:mn>3</b:mn></b:msub><b:mi>Sn</b:mi></b:mrow></b:math>. Our investigation reveals the presence of several nearly flat bands and Weyl nodes at low excitation energies. The inclusion of local correlation effects is shown to push these features even closer to the Fermi energy, which may be important for their manipulation via external stimuli. Regarding magnetism, the Hubbard-like interaction leads to an increase of orbital polarization at the expenses of a minor reduction of the spin moment. The magnetic anisotropy energy exhibits a strong dependence on the particular choice of the Coulomb interaction parameters. Additionally, our detailed analysis of the interatomic exchange interactions indicates a significant contribution from the antisymmetric exchange, i.e., the Dzyaloshinskii-Moriya interaction, which showcases the existence of magnetic chirality in the system. Overall, our investigation highlights a strong interplay between the flat bands near the Fermi level, the local Coulomb interaction, and the triangular geometry of the lattice, which plays a crucial role in driving the magnetic properties of this material.