Procedure for numerical integration of the magnetocaloric effect

Abstract

When the magnetocaloric effect is obtained using indirect or direct techniques, the result is the isothermal entropy change ΔSiso(T,ΔH) or the adiabatic temperature change ΔTad(T,ΔH). Evaluation of the linking relation dTad=−(T/Cp)×dSiso (Cp, specific heat; T, temperature) as a way to determine the magnetocaloric effect, however, is typically not performed because it requires detailed knowledge of Cp(T,H). Here, we outline the procedure for numerical integration of the magnetocaloric effect—this is important for a physics understanding and as a practical guide on implementing the procedure. The process is notably different than the well-known method used to calculate ΔSiso from the Maxwell equation. We test the procedure by using it to calculate Cp (with dTad and dSiso as input data) and comparing it with directly measured Cp, finding excellent agreement for both first-order transition in LaFe11.6Si1.4 and second-order transition in Gd. We establish the merits and limitations of the method. In particular, the presence of a demagnetizing effect in experimental data can reduce accuracy of the method. The procedure can be applied to accurately model the magnetocaloric effect in a magnetic cooling cycle.