Anomalous Hall Effect in Bismuth Iron Oxide

Bandyopadhyay, Sumanta (2014) Anomalous Hall Effect in Bismuth Iron Oxide. Masters thesis, Indian Institute of Science Ed- ucation and Research Kolkata.

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Abstract

Bismuth iron oxide (BFO) is a well known Mott insulator with type-II multiferroic properties. It is an canted antiferromagnetic material with ferro-electricity in the system. Due to ferro-electricity, it also has topological excitations like domain walls and vortices. Two recent studies has shown an enhanced conductivity at the vortex core and domain walls. In both cases no change is observed in the bulk of the system. We suspect this to be a signal of a topological insulator. i.e, BFO may be an Mott insulator but it also has topological properties at some points near the Fermi surface. This fact is consistent with the fact that bismuth has very high spin-orbit coupling (SOC). Further, The same group showed only those domain walls conduct where the polarization vector ips. We have showed in this thesis that, at those points both the parity and time reversal symmetries are broken. These are the conditions a system needs to exhibit anomalous Hall effect (AHE). Our claim is the increased conductivity in the system insinuates to anomalous Hall phase in the system. In order to probe the depth of our claim, we inspect a minimalistic tight binding model on bismuth and iron bands in the lattice. This shows the emergence of topological insulator phase. Near the Fermi surface we took the bands with non-zero topological invariant and construct a field theory around it. The emergence of massive Dirac fermion from the effective model, explains the coupled multi-ferroic nature along with the AHE in the system. In this process, we have also seen two dimensional Dirac electron gas (2-DEG) emerges near the domain wall. This gives a new way to construct 2-DEG system. We have also studied the robustness of AHE phase in the presence of BCS instability in a 2-DEG system. In the presence of the ferromagnetic Rashba in the mean field level, BCS instability gives rise to a novel AHE in the system. This phenomena vanishes when the BCS gap sets to zero. We showed this novel AHE is remains in the system when a phase transition happens from BCS superconductor to topological superconductor. This part is done in the collaboration with Narayan Mohanta, a PhD in IIT-Kgp and Prof. Argha Taraphder of IIT-Kgp. The robustness of this phase in the presence of disorder is also been studied.

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