Consideration of thermal Hall effect in undoped cuprates

A recent observation of the thermal Hall effect of magnetic origin in underdoped cuprates calls for critical reexamination of low-energy magnetic dynamics in an undoped antiferromagnetic compound on square lattice, where traditional, renormalized spin-wave theory was believed to work well. Using the Holstein-Primakoff boson formalism, we find that magnon-based theories can lead to finite Berry curvature in the magnon band once the Dzyaloshinskii-Moriya spin interaction is taken into account explicitly, but fail to produce nonzero thermal Hall conductivity. Assuming accidental doping by impurities and magnon scattering off of such impurity sites fails to predict skew scattering at the level of the Born approximation. Local formation of skyrmion defects is also found incapable of generating the magnon thermal Hall effect. Turning to a spinon-based scenario, we write down a simple model by adding spin-dependent diagonal hopping to the well-known p-flux model of spinons. The resulting two-band model has a Chern number in the band structure, and generates thermal Hall conductivity whose magnetic field and temperature dependencies mimic closely the observed thermal Hall signals. In disclaimer, there is no firm microscopic basis of this model and we do not claim to have found an explanation of the data, but given the unexpected nature of the experimental observation, it is hoped this work could serve as a step towards reaching some level of understanding.