Magnetic and structural entropy contributions to the multicaloric effects in Ni-Mn-Ga-Cu

We have studied the multicaloric properties of a Ni-Mn-Ga-Cu alloy. In this alloy, application of magnetic field and uniaxial stress shift its martensitic transition towards higher temperatures which results in synergic magnetocaloric and elastocaloric effects. By a proper numerical treatment of the calorimetric curves obtained under applied magnetic field and uniaxial stress we have obtained the entropy $S(T,{\ensuremath{\mu}}_{0}H,\ensuremath{\sigma})$ as a function of the magnetic field, uniaxial stress, and temperature over the whole phase space under study. We have determined the different entropy contributions to the multicaloric effect in this alloy, and noticeably we have evidenced the role played by the interplay between magnetic and vibrational degrees of freedom. A comparison between single caloric and multicaloric effects shows that appropriate combinations of magnetic field and stress reduce the magnitude of the specific field required to obtain a given value of the isothermal entropy and adiabatic temperature changes. For example, at 299 K, to achieve an entropy change ($\mathrm{\ensuremath{\Delta}}S$) of $\ensuremath{-}14$ J ${\mathrm{kg}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$, a magnetic field of $\ensuremath{\sim}2.5$ T or a uniaxial stress of 19 MPa are required, while a combination of dual fields of (1 T, 12 MPa) yields to the same value of $\mathrm{\ensuremath{\Delta}}S$. Moreover, the maximum adiabatic temperature change is enlarged up to 9.4 K by the dual fields, higher than the value obtained by a single field ($\ensuremath{\sim}7$ K). The advantage of multicaloric effect is particularly relevant at low magnetic fields which are achievable by permanent magnets. Our findings open new avenues for using multicaloric materials in novel refrigeration technologies.