The magnetic field-induced changes in the conductivity of metals are the subject of intense interest, both for revealing new phenomena and as a valuable tool for determining their Fermi surface. Here, we report a hitherto unobserved magnetoresistive
effect in ultra-clean layered metals, namely a negative longitudinal magnetoresistance that is capable of overcoming their very pronounced orbital one. This effect is correlated with the inter-layer coupling disappearing for fields applied along the so-called Yamaji angles where the inter-layer coupling vanishes. Therefore, it is intrinsically associated with the Fermi points in the field-induced quasi-one-dimensional electronic dispersion, implying that it results from the axial anomaly among these Fermi points. In its original formulation, the anomaly is predicted to violate separate number conservation laws for left- and right-handed chiral- (e.g. Weyl) fermions. Its observation in PdCoO$_2$, PtCoO$_2$ and Sr$_2$RuO$_4$ suggests that the anomaly affects the transport of clean conductors, particularly near the quantum limit.
