  An ideal Weyl semimetal with a single pair of Weyl points (WPs) may be
generated by splitting a single Dirac point (DP) through the breaking of
time-reversal symmetry by magnetic order. However, most known Dirac semimetals
possess a pair of DPs along an axis that is protected by crystalline symmetry.
Here, we demonstrate that a single pair of WPs may also be generated from a
pair of DPs. Using first-principles band structure calculations, we show that
inducing ferromagnetism in the AFM Dirac semimetal EuCd2As2 generates a single
pair of WPs due to its half-metallic nature. Analysis with a low-energy
effective Hamiltonian shows that this ideal Weyl semimetal is obtained in
EuCd2As2 because the DPs are very close to the zone center and the
ferromagnetic exchange splitting is large enough to push one pair of WPs to
merge and annihilate at Gamma while the other pair survives. Furthermore, we
predict that alloying with Ba at the Eu site can stabilize the ferromagnetic
configuration and generate a single pair of Weyl points without application of
a magnetic field.
