  Around discontinuous (first-order) magnetic phase transitions the strong
caloric response of materials to the application of small fields is widely
studied for the development of solid-state refrigeration. Typically strong
magnetostructural coupling drives such transitions and the attendant
substantial hysteresis dramatically reduces the cooling performance. In this
context we describe a purely electronic mechanism which pilots a first-order
paramagnetic-ferromagnetic transition in divalent lanthanide compounds and
which explains the giant non-hysteretic magnetocaloric effect recently
discovered in a Eu$_2$In compound. There is positive feedback between the
magnetism of itinerant valence electrons and the ferromagnetic ordering of
local $f$-electron moments, which appears as a topological change to the Fermi
surface. The origin of this electronic mechanism stems directly from Eu's
divalency, which explains the absence of a similar discontinuous transition in
Gd$_2$In.
