Effect of a magnetic field on the magnetostructural phase transition in ${\mathrm{Gd}}_5({\mathrm{Si}}_x{\mathrm{Ge}}_{1-x}{)}_4$

The first-order magnetostructural phase transition in ${\mathrm{Gd}}_5({\mathrm{Si}}_x{\mathrm{Ge}}_{1-x}{)}_4$ alloys with $x<~0.5$ and the related entropy change $\Delta S$ are analyzed from high-field magnetization curves up to 23 T, and differential scanning calorimetry up to 5 T. The variation of the transition field $H_t$ with the transition temperature $T_t$ is discussed for fields up to 23 T for the $x<~0.5$ range. From these data, the ratio ${\mathrm{dH}}_t{/dT}_t,$ which is related to the strength of the magnetoelastic coupling, is obtained as a function of x. We show that $\Delta S$ obtained from the Clausius-Clapyeron equation and the Maxwell relation are equivalent for all compositions $(0\mathrm{}<~x<~0.5),$ provided the Maxwell relation is evaluated only within the transition region. The T and H dependences of $\Delta S$ are accounted for by modeling the T and H dependences of the magnetization outside the transition.