  We investigate novel topological magnon band crossings of pyrochlore
antiferromagnets with all-in-all-out (AIAO) magnetic order. By general symmetry
analysis and spin-wave theory, we show that pyrochlore materials with AIAO
orders can host Weyl magnons under external magnetic fields or uniaxial
strains. Under a small magnetic field, the magnon bands of the pyrochlore with
AIAO background can feature two opposite-charged Weyl points, which is the
minimal number of Weyl points realizable in quantum materials and has not be
experimentally observed so far. We further show that breathing pyrochlores with
AIAO orders can exhibit Weyl magnons upon uniaxial strains. These findings
apply to any pyrochlore material supporting AIAO orders, irrespective of the
forms of interactions. Specifically, we show that the Weyl magnons are robust
against direct (positive) Dzyaloshinskii-Moriya interactions. Because of the
ubiquitous AIAO orders in pyrochlore magnets including R$_2$Ir$_2$O$_7$, and
experimentally achievable external strain and magnetic field, our predictions
provide promising arena to witness the Weyl magnons in quantum magnets.

Strongly Correlated Electrons;Mesoscale and Nanoscale Physics;Materials Science