Magnetocaloric effect, magnetothermal and elastic properties of SmFe₃ and ErFe₃ compounds

We report on the temperature and field dependences of magnetization, magnetic specific heat, and magnetic entropy of the ferromagnetic \({{\text{SmFe}}}_{3}\) ${\text{SmFe}}_3$ ( \({T}_{C}\) $T_C$  ≈ 655 K) and ferrimagnetic \({{\text{ErFe}}}_{3}\) ${\text{ErFe}}_3$ ( \({T}_{C}\) $T_C$  ≈ 600 K, compensation temperature ≈ 230 K) compounds using the mean-field theory (MFT). The magnetocaloric effect (MCE), namely, the isothermal change in entropy (∆S_m) and the adiabatic change in temperature (∆T_ad), is determined using the well-known Maxwell relation. Density Functional Theory (DFT), as implemented in the WIEN2k electronic code, is used to perform the ab-initio calculation of the elastic constants, bulk and shear moduli, and density-of-states. Using the electronic coefficient of specific heat ( \({\upgamma }_{{\text{e}}}\) ${\mathrm{\gamma }}_{\text{e}}$ ) and the Debye temperature ( \({\uptheta }_{{\text{D}}}\) ${\mathrm{\theta }}_{\text{D}}$ ), the electronic and lattice contributions to the total specific heat and total entropy are computed, respectively. The ferrimagnetic \({{\text{ErFe}}}_{3}\) ${\text{ErFe}}_3$ exhibits both direct and inverse MCE, while \({{\text{SmFe}}}_{3}\) ${\text{SmFe}}_3$ exhibits only direct MCE effects. For \({{\text{SmFe}}}_{3}\) ${\text{SmFe}}_3$ , the maximum \(\Delta {{\text{S}}}_{{\text{m}}}\) $\mathrm{\Delta }{\text{S}}_{\text{m}}$ for a 7T field change is approximately 1.29 J/mol K. For the same field change, the maximum direct and inverse | \(\Delta {{\text{S}}}_{{\text{m}}}\) $\mathrm{\Delta }{\text{S}}_{\text{m}}$ | for \({{\text{ErFe}}}_{3}\) ${\text{ErFe}}_3$ are approximately 0.69 and 0.74 J/mol K, respectively. At their respective Curie temperatures, SmFe₃ and ErFe₃ exhibit adiabatic temperature changes of about 8 and 5 K, respectively, for a 7 T field change. The Arrott plots and universal curves, along with specific aspects of the thermomagnetic and magnetocaloric properties, are used to examine the order of the magnetic phase transition in these two systems.