Quantitative determination of the order phase transitions of multicaloric materials: The validity of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si141.svg" display="inline" id="d1e208"> <mml:mi>n</mml:mi> </mml:math> -overshoot

Caloric materials have a significant response (adiabatic temperature change or isothermal entropy change) in the vicinity of a phase transition, with the magnitude and characteristics of this response being strongly dependent on the nature of the transition. It is therefore important to be able to quantitatively ascertain the order of the transition (first or second order) to predict if the phase transformation implies a significant hysteresis, which is detrimental from the application point of view. In the case of magnetocalorics, the overshoot above two of the exponent n , describing the field dependence of the isothermal entropy change, has been demonstrated to be a suitable fingerprint of first order phase transitions. In this work, we demonstrate that the criterion holds for multicaloric materials in which the magnetocaloric transformation is altered by pressure. • Addressing traditional cooling & heating systems is crucial for energy concerns today. • Multicaloric materials offer an alternative to conventional refrigerants. • These materials respond to stimuli like magnetic, structural, and pressure changes. • Magnitude of caloric effects closely linked to the order of phase transitions. • A criterion reported to identify first-order phase transitions in these materials.