The magnetic entropy change [ΔSM(T;H)] around the phase transition temperature TC is investigated
by the scaling method for Fe0:5Co0:5Si, which exhibits a skyrmion phase below TC. The
parameters of ΔSM(T;H) exhibit field dependent behaviors. The ΔSM(T;H) curves under high
field can be well scaled into a single universal curve independent of external field and temperature.
However, ΔSM(T;H) curves under low field become divergent just below TC, which indicates a
characteristic of first-order transition. The scaling investigation of ΔSM(T;H) curves indicates
that the phase transition in Fe0:5Co0:5Si is of a weak first-order type in low field region, while it is
driven into a second-order one under high field. This weak first-order phase transition in low field
region resembles that in typical skyrmion system MnSi which is caused by the critical fluctuation.
The result suggests that critical fluctuation plays an important role in the phase transition and
formation of skyrmion state.