Effect of doping and lattice dynamics in competing structural phases of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>LaSb</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math>

The layered rare-earth diantimonides, $R{\mathrm{Sb}}_{2}$, ($R$ = lanthanide element) composed of Sb square-net sheets exhibit diverse structural phases with distinct stacking configurations which can be tuned by the growth temperature, stoichiometry, and pressure. The recent discovery by Llanos et al. [Nano Lett. 24, 8518 (2024)] of a novel monoclinic polymorph of ${\mathrm{LaSb}}_{2}$ raises the important question as to why ${\mathrm{LaSb}}_{2}$ has been synthesized in the orthorhombic phase in previous experimental studies. We have employed first-principles electronic structure calculations to investigate the effect of charge doping and phonon entropy on the relative stability between four competing structural phases of ${\mathrm{LaSb}}_{2}$: the ${\mathrm{SmSb}}_{2}$-type, the ${\mathrm{YbSb}}_{2}$-type, the MBE-grown monoclinic, and our novel theoretically predicted orthorhombic structures (space group No. 58, $Pnnm$). The calculations reveal that the ${\mathrm{SmSb}}_{2}$-type orthorhombic phase is stabilized by electron doping that can presumably occur during bulk growth conditions such as Sb-rich flux, intrinsic vacancy formation, etc. However, the phonon entropy is found to reduce the free energy of the monoclinic phase faster than that of the orthorhombic phase with increasing temperature, indicating that the monoclinic phase becomes more stable at high temperatures. We also present the dynamical instabilities in two well-known structures with or without strain that qualitatively explain the pressure-dependent charge density waves of ${\mathrm{LaSb}}_{2}$. This research aims to shed light on the microscopic mechanisms underlying the complex and competing structural phases and resulting transitions in the family of $R{\mathrm{Sb}}_{2}$ systems.