  As novel topological phases in correlated electron systems, we have found two
examples of non-ferromagnetic states that exhibit a large anomalous Hall
effect. One is the chiral spin liquid compound Pr$_{2}$Ir$_{2}$O$_{7}$, which
exhibits a spontaneous Hall effect in a spin liquid state due to spin ice
correlation. The other is the chiral antiferromagnets Mn$_{3}$Sn and Mn$_{3}$Ge
that exhibit a large anomalous Hall effect at room temperature. The latter
shows a sign change of the anomalous Hall effect by a small change in the
magnetic field by a few 100 G, which should be useful for various applications.
We will discuss that the magnetic Weyl metal states are the origin for such a
large anomalous Hall effect observed in both the spin liquid and
antiferromagnet that possess almost no magnetization.
