  The nature of the magnetic transition, critical scaling of magnetization, and
magnetocaloric effect in Mn$_{1+x}$Fe$_{4-x}$Si$_{3}$ ($ x =$ 0 to 1) are
studied in detail. Our measurements show no thermal hysteresis across the
magnetic transition for the parent compound which is in contrast with the
previous report and corroborate the second order nature of the transition. The
magnetic transition could be tuned continuously with Mn substitution at the Fe
site. The Mn substitution leads to a linear increase in the unit cell volume
and a slight reduction in the effective moment. A detailed critical analysis of
the magnetization data for $x = 0.0$ and 0.2 is performed in the critical
regime using the modified Arrott plots, Kouvel-Fisher plot, universal curve
scaling, and scaling analysis of magnetocaloric effect. The magnetization
isotherms follow modified Arrott plots with critical exponent ($\beta \simeq
0.308$, $\gamma \simeq 1.448$, and $\delta \simeq 5.64$) for the parent
compound ($x=0.0$) and ($\beta \simeq 0.304$, $\gamma \simeq 1.445$, and
$\delta \simeq 5.64$) for $x = 0.2$. The Kouvel-Fisher and universal scaling
plots of the magnetization isotherms further confirm the reliability of our
critical analysis and values of the exponents. These values of the critical
exponents are found to be same for both the parent and doped samples which do
not fall under any of the standard universality classes. A reasonable
magnetocaloric effect $\Delta S_{\rm m}\simeq-6.67$~J/Kg-K and -5.84~J/Kg-K for
$x= 0.0$ and 0.2 compounds, respectively, with a huge relative cooling power
($RCP \sim 700$~J/Kg) for 9~T field change is observed. The universal scaling
of magnetocaloric effect further mimics the second order character of the
magnetic transition. The obtained critical exponents from the critical analysis
of magnetocaloric effect agree with the values deduced from the magnetic
isotherm analysis.

Materials Science