The Magnetocaloric Properties Around the Second-Order Magnetic Transition in $$\hbox {Ni}_{2}\hbox {Mn}_{1.4}\hbox {In}_{\mathrm{0.6-x}}\hbox {R}_{\mathrm{x}} (\hbox {R}= \hbox {Si, Ge, Al})$$ Ni 2 Mn 1.4 In 0.6 - x R x ( R = Si, Ge, Al )

By combining the first-principles with Monte Carlo method, we investigate the magnetic exchange interactions and the magnetic entropy changes in the vicinity of the second-order transition in $${\hbox {Ni}}_{2}{\hbox {Mn}}_{1.4}{\hbox {In}}_{0.6}{\hbox {(R)}}\,{\hbox {(R}}= \hbox {Si, Ge, Al})$$ alloys with R substituting for In atoms. The results show that the substitution of R for In atoms can lead to the reduction of the Curie temperature and an increase in the total magnetic moments of the systems. The Si substitution gives rise to the increase in the magnetic entropy changes, whereas the Ge and Al substitutions make the entropy change decrease. In addition, our calculated Curie temperatures for $$\hbox {Ni}_{2}\hbox {Mn}_{1.4}\hbox {In}_{\mathrm{0.6-x}}\hbox {Si}_{\mathrm{x}} (x = 0.04, 0.08, 0.12, 0.16)$$ are in good agreement with available experimental results.