  We propose that the topological semimetal features can co-exist with
ferromagnetic ground state in vanadium-phosphorous-oxide $\beta$-V$_2$OPO$_4$
compound from first-principles calculations. In this magnetic system with
inversion symmetry, the direction of magnetization is able to manipulate the
symmetric protected band structures from a node-line type to a Weyl one in the
presence of spin-orbital-coupling. The node-line semimetal phase is protected
by the mirror symmetry with the reflection-invariant plane perpendicular to
magnetic order. Within mirror symmetry breaking due to the magnetization along
other directions, the gapless node-line loop will degenerate to only one pair
of Weyl points protected by the rotational symmetry along the magnetic axis,
which are largely separated in momentum space. Such Weyl semimetal phase
provides a nice candidate with the minimum number of Weyl points in a condensed
matter system. The results of surface band calculations confirm the non-trivial
topology of this proposed compound. This findings provide a realistic candidate
for the investigation of topological semimetals with time-reversal symmetry
breaking, particularly towards the realization of quantum anomalous Hall effect
in Weyl semimetals.

Materials Science;Mesoscale and Nanoscale Physics