  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 the
interacting electrons of materials in terms of disordered local moments (DLMs)
has produced explicit mechanisms for the drivers of these transitions and here
we study associated caloric effects in three case studies where both types of
transition are evident. Our earlier work had described FeRh's magnetic phase
diagram and large MCE. Here we present calculations of its substantial BCE and
eCE. We describe the MCE of dysprosium and find very good agreement with
experimental values for isothermal entropy ($\Delta S_{iso}$) and adiabatic
temperature ($\Delta T_{ad}$) changes over a large temperature span and
different applied magnetic field values. We examine the conditions for optimal
values of both $\Delta S_{iso}$ and $\Delta T_{ad}$ that comply with a
Clausius-Clapeyron analysis, which we use to propose a promising elastocaloric
cooling cycle arising from the unusual dependence of the entropy on temperature
and biaxial strain found in our third case study - the Mn$_3$GaN
antiperovskite. We explain how both $\Delta S_{iso}$ and $\Delta T_{ad}$ can be
kept large by exploiting the complex tensile strain-temperature magnetic phase
diagram which we had earlier predicted for this material and also propose that
hysteresis effects will be absent from half the caloric cycle. This rich and
complex behavior stems from the frustrated nature of the interactions among the
Mn local moments.
