  It is highly desirable to combine the full spin polarization of carriers with
modern semiconductor technology for spintronic applications. For this purpose,
one needs good crystalline ferromagnetic (or ferrimagnetic) semiconductors with
high Curie temperatures. Rutile CrO$_2$ is a half-metallic spintronic material
with Curie temperature 394 K and can have nearly-full spin polarization at room
temperature. Here, we find through first-principles investigation that when a
biaxial compressive stress is applied on rutile CrO$_2$, the density of states
at the Fermi level decreases with the in-plane compressive strain, there is a
structural phase transition to an orthorhombic phase at the strain of -5.6\%,
and then appears an electronic phase transition to a semiconductor phase at
-6.1\%. Further analysis shows that this structural transition, accompanying
the tetragonal symmetry breaking, is induced by the stress-driven distortion
and rotation of the oxygen octahedron of Cr, and the half-metal-semiconductor
transition originates from the enhancement of the crystal field splitting due
to the structural change. Importantly, our systematic total-energy comparison
indicates the ferromagnetic Curie temperature remains almost independent of the
strain, near 400 K. This biaxial stress can be realized by applying biaxial
pressure or growing the CrO$_2$ epitaxially on appropriate substrates. These
results should be useful for realizing full (100\%) spin polarization of
controllable carriers as one uses in modern semiconductor technology.
