  Half-metals are ferromagnets hosting spin-polarized conducting carriers and
crucial for spintronics applications. The chromium spinel HgCr2Se4 represents a
unique type of half-metal, which features a half-metal to semiconductor
transition (HMST) and exhibits colossal magnetoresistance (CMR) across the
ferromagnetic-paramagnetic (FM-PM) transition. Using angle-resolved
photoemission spectroscopy (ARPES), we find that the Fermi surface of n-type
HgCr2Se4 (n-HgCr2Se4) consists of a single electron pocket which moves above
the Fermi level (EF) upon the FM-PM transition, leading to the HMST. Such a
Lifshitz transition manifests a giant band splitting which originates from the
exchange interaction unveiled with a specific chemical nonstoichiometry. The
exchange band splitting and the chemical nonstoichiometry are two key
ingredients to the HMST and CMR, consistent with our ab-initio calculation. Our
findings provide spectroscopic evidences of the electronic origin of the
anomalous properties of HgCr2Se4, which address the unique phase transition in
half-metals.
