  Ni-Mn-based Heusler alloys, in particular all-d-metal Ni(-Co)-Mn-Ti, are
highly promising materials for energy-efficient solid-state refrigeration as
large multicaloric effects can be achieved across their magnetostructural
martensitic transformation. However, no comprehensive study on the crucially
important transition entropy change $\Delta s_t$ exists so far for
Ni(-Co)-Mn-Ti. Here, we present a systematic study analyzing the composition
and temperature dependence of $\Delta s_t$. Our results reveal a substantial
structural entropy change contribution of approximately 65 J(kgK)$^{-1}$, which
is compensated at lower temperatures by an increasingly negative entropy change
associated with the magnetic subsystem. This leads to compensation temperatures
$T_{comp}$ of 75 K and 300 K in Ni$_{35}$Co$_{15}$Mn$_{50-y}$Ti$_{y}$ and
Ni$_{33}$Co$_{17}$Mn$_{50-y}$Ti$_{y}$, respectively, below which the
martensitic transformations are arrested. In addition, we simultaneously
measured the responses of the magnetic, structural and electronic subsystems to
the temperature- and field-induced martensitic transformation near $T_{comp}$,
showing an abnormal increase of hysteresis and consequently dissipation energy
at cryogenic temperatures. Simultaneous measurements of magnetization and
adiabatic temperature change $\Delta T_{ad}$ in pulsed magnetic fields reveal a
change in sign of $\Delta T_{ad}$ and a substantial positive and irreversible
$\Delta T_{ad}$ up to 15 K at 15 K as a consequence of increased dissipation
losses and decreased heat capacity. Most importantly, this phenomenon is
universal, it applies to any first-order material with non-negligible
hysteresis and any stimulus, effectively limiting the utilization of their
caloric effects for gas liquefaction at cryogenic temperatures.
