The evolution of thermodynamic properties through the interconvertibility process between Lieb and kagome lattices is explored in the presence of a magnetic field and intrinsic spin-orbit coupling (ISOC). Both lattices share similar crystallographic characteristics that allow for description by a generic tight-binding model with one control parameter $\theta$ mapping the transition lattice stages ($\pi /2\le \theta \le 2\pi /3$), being Lieb ($\theta =\pi /2$) and kagome ($\theta =2\pi /3$) the limiting cases. The magnetic field applied perpendicularly to the monolayer Lieb-kagome system causes a Zeeman splitting of the band structure, and the ISOC lifts the band degeneracy. The density of states, band structures, specific heat, static spin susceptibility, internal energy, and Helmholtz energy are computed for different temperature values, magnetic field amplitudes, and ISOC strengths through the various evolutionary stages of Lieb-kagome lattices. Our numerical calculations show (i) a metal-to-semiconductor phase transition induced by the applied magnetic field for the case of non-null ISOC; (ii) that the Schottky peak increases its intensity the higher the magnetic field amplitude and also when the $\theta$ value increases between Lieb to kagome lattices; (iii) that the paramagnetic susceptibility at low temperature is strongly $\theta$ dependent, exhibiting lower values the higher the $\theta$ value; and (iv) that kagome lattice presents the lower internal energy at $T=0$, meaning to be the most stable thermodynamically investigated structure between the interconvertible lattices in the range from Lieb to kagome.

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• Flat bands
• Thermodynamics
• 2-dimensional systems
• Kagome lattice
• Two-dimensional electron system
• Tight-binding model