The Magnetocaloric Entropy Budget: A Counting Bound on Magnetic Refrigeration, Applied to Gd, Gd5Si2Ge2, La(Fe,Si)13 and MnFe(P,As)

The isothermal entropy change of a magnetic refrigerant is bounded by the total magnetic entropy of its spin system, R ln(2J+1) per mole of magnetic ions. The budgets for Gd, Gd5Si2Ge2, LaFe11.4Si1.6 and MnFeP0.45As0.55 are 109.95, 87.53, 128.83 and 114.11 J/kg/K; the largest canonical published entropy changes at 0-5 T (9.8, 18.0, 19.4, 18.0 J/kg/K) use 8.9%, 20.6%, 15.1% and 15.8% of the budgets per cycle. A reported spike of 138 J/kg/K for LaFe11.5Si1.5 at 1 GPa exceeds its budget of 129.5 J/kg/K and cannot be a purely magnetic entropy change. Cooling-power ceilings at 1 Hz and Dulong-Petit lattice bounds on the adiabatic temperature change are computed for all four materials. All numbers are produced by the archived Python script from stated inputs.