  Weyl semimetals are predicted to realize the three-dimensional axial anomaly
first discussed in particle physics. The anomaly leads to unusual transport
phenomena such as the chiral magnetic effect in which an applied magnetic field
induces a current parallel to the field. Here we investigate diagnostics of the
axial anomaly based on the fundamental equations of axion electrodynamics. We
find that materials with Weyl nodes of opposite chirality and finite energy
separation immersed in a uniform magnetic field exhibit an anomaly-induced
oscillatory magnetic field with a period set by the chemical potential
difference of the nodes. In the case where a chemical potential imbalance is
created by applying parallel electric and magnetic fields, we find a
suppression of the magnetic field component parallel to the electric field
inside the material for rectangular samples, suggesting that the chiral
magnetic current opposes this imbalance. For cylindrical geometries, we instead
find an enhancement of this magnetic field component along with an
anomaly-induced azimuthal component. We propose experiments to detect such
magnetic signatures of the axial anomaly.
