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We describe magneto-, baro- and elastocaloric effects (MCEs, BCEs and eCEs)in materials which possess both discontinuous (first-order) and continuous(second-order) magnetic phase transitions. Our ab initio theory of theinteracting electrons of materials in terms of disordered local moments (DLMs)has produced explicit mechanisms for the drivers of these transitions and herewe study associated caloric effects in three case studies where both types oftransition are evident. Our earlier work had described FeRh's magnetic phasediagram and large MCE. Here we present calculations of its substantial BCE andeCE. We describe the MCE of dysprosium and find very good agreement withexperimental values for isothermal entropy ($\Delta S_{iso}$) and adiabatictemperature ($\Delta T_{ad}$) changes over a large temperature span anddifferent applied magnetic field values. We examine the conditions for optimalvalues of both $\Delta S_{iso}$ and $\Delta T_{ad}$ that comply with aClausius-Clapeyron analysis, which we use to propose a promising elastocaloriccooling cycle arising from the unusual dependence of the entropy on temperatureand biaxial strain found in our third case study - the Mn$_3$GaNantiperovskite. We explain how both $\Delta S_{iso}$ and $\Delta T_{ad}$ can bekept large by exploiting the complex tensile strain-temperature magnetic phasediagram which we had earlier predicted for this material and also propose thathysteresis effects will be absent from half the caloric cycle. This rich andcomplex behavior stems from the frustrated nature of the interactions among theMn local moments.

Caloric effects around phase transitions in magnetic materials described by ab initio theory: The electronic glue and fluctuating local moments