  We study the mechanism how critical end points of first-order valence
transitions are controlled by a magnetic field. We show that the critical
temperature is suppressed to be a quantum critical point (QCP) by a magnetic
field and unexpectedly the QCP exhibits nonmonotonic field dependence in the
ground-state phase diagram, giving rise to emergence of metamagnetism even in
the intermediate valence-crossover regime. The driving force of the
field-induced QCP is clarified to be cooperative phenomena of Zeeman effect and
Kondo effect, which create a distinct energy scale from the Kondo temperature.
This mechanism explains peculiar magnetic response in CeIrIn5 and metamagnetic
transition in YbXCu4 for X=In as well as sharp contrast between X=Ag and Cd.
