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Manganites are famous mostly for the colossal magnetoresistive effect, whichinvolves the phase separation between ferromagnetic phase and charge-orderedCE-type antiferromagnetic phases. Furthermore, manganites contain some typicalmagnetic ferroelectrics, e.g. E-type antiferromagnetic $o$-HoMnO$_3$. Here were-examined these zigzag-winding antiferromagnetic phases (CE-type and E-typeantiferromagnets) from the topological perspective. Our theoretical analysisproved that the E-type phase is a weak topological insulator belonging to the$\mathbb{Z}$ class. In momentum space, we classify the symmetries of thisphase, and find the three symmetry operators for the chiral, particle-hole, andtime-reversal symmetry. The CE-type phase can be described by theDuffin-Kemmer-Petiau algebra, implying that it is a new class of topologicalinsulator and hence extends the existing classification. The correspondingtopological end states are demonstrated via numerical calculations, which mayimplicate the experimental observed ferromagnetic edge states in manganitestrips (Nat. Commun. 6, 6179 (2015)) and may play a crucial role in thecolossal magnetoresistive effect.

Topological end states in two-orbital double-exchange model for colossal magnetoresistive manganites