  The behavior of conduction electrons on magnetic structures has been
intensely investigated. A typical example is the anomalous Hall effect in a
ferromagnet. However, distinguishing various anomalous and normal Hall signals
induced from the time-reversal symmetry (TRS) broken by their magnetic
structure or applied magnetic field is delicate. In this study, we present a
method to investigate TRS broken by the magnetic structure by analyzing
magnetic quantum oscillations (MQOs). As is known, if a material is
nonmagnetic, the MQO phases can only be two distinct values of 0 or $\pi$ from
the orbits. When the magnetic structure breaks the TRS, the MQO phase deviates
from these values, and the deviation is called the anomalous phase. We observed
the anomalous phase in Fe-doped NbSb2, where magnetic Fe impurities break the
TRS. The phase of a high-doped sample largely deviates from the phases of
low-doped and pristine samples, indicating the anomalous phase. In MQOs,
different types of magnetic structures afford different field dependence to the
phase; this makes it easy to discern different magnetic structures, which
respond differently with magnetic fields. This method can complement the Hall
measurement and will provide useful information by itself for studying the
magnetic structure of materials.
