Enhanced reversibility of the magnetoelastic transition in (Mn,Fe)2(P,Si) alloys via minimizing the transition-induced elastic strain energy

•Generalized relationship: hysteresis v.s. transition-induced elastic strain energy.•Hysteresis reduced by 91% after replacement of Fe by 4 at.% Mo in (Mn,Fe)2(P,Si).•Reversible adiabatic temperature change enhanced by 500 via 4 at.% Mo substitution.•Spin-lattice-electron coupling dominate magnetoelastic transition in (Mn,Fe)2(P,Si).