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We analyze theoretically a common experimental process used to obtain themagnetic contribution to the specific heat of a given magnetic material. In theprocedure, the specific heat of a non-magnetic analog is measured and used tosubtract the non-magnetic contributions, which are generally dominated by thelattice degrees of freedom in a wide range of temperatures. We calculate thelattice contribution to the specific heat for the magnetic compounds GdMIn$_5$(M = Co, Rh) and for the non-magnetic YMIn$_5$ and LaMIn$_5$ (M = Co, Rh),using density functional theory based methods. We find that the bestnon-magnetic analog for the subtraction depends on the magnetic material and onthe range of temperatures. While the phonon specific heat contribution ofYRhIn$_5$ is an excellent approximation to the one of GdCoIn$_5$ in the fulltemperature range, for GdRhIn$_5$ we find a better agreement with LaCoIn$_5$,in both cases, as a result of an optimum compensation effect between masses andvolumes. We present measurements of the specific heat of the compoundsGdMIn$_5$ (M = Co, Rh) up to room temperature where it surpasses the valueexpected from the Dulong-Petit law. We obtain a good agreement between theoryand experiment when we include anharmonic effects in the calculations.

Lattice specific heat for the RMIn$_5$ (R = Gd, La, Y, M = Co, Rh) compounds: non-magnetic contribution subtraction