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arXiv:2311.12563 · Physical review. B./Physical review. B

Thermal Hall conductivity of a valence bond solid phase in the square lattice J1−J2 antiferromagnet Heisenberg model with a Dzyaloshinskii-Moriya interaction

Lucas S. Buzo, R. L. Doretto

Published Apr 3, 2024• 5 citations
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Abstract

We calculate the thermal Hall conductivity ${\ensuremath{\kappa}}_{xy}$ for the columnar valence bond solid phase of a two-dimensional frustrated antiferromagnet. In particular, we consider the square lattice spin-$1/2\phantom{\rule{4pt}{0ex}}{J}_{1}\text{\ensuremath{-}}{J}_{2}$ antiferromagnetic Heisenberg model with an additional Dzyaloshinskii-Moriya interaction between the spins and in the presence of an external magnetic field. We concentrate on the intermediate parameter region of the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ model, where a quantum paramagnetic phase is stable, and consider a Dzyaloshinskii-Moriya vector pattern associated with the couplings between the spins in the ${\mathrm{CuO}}_{2}$ planes of the ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6}$ compound. We describe the columnar valence bond solid phase within the bond-operator formalism, which allows us to map the Heisenberg model into an effective interacting boson model written in terms of triplet operators. The effective boson model is studied within the harmonic approximation, and the triplon excitation bands of the columnar valence bond solid phase are determined. We then calculate the Berry curvature and the Chern numbers of the triplon excitation bands and, finally, determine the thermal Hall conductivity due to triplons as a function of the temperature. We find that the Dzyaloshinskii-Moriya interaction yields a finite Berry curvature for the triplon bands, but the corresponding Chern numbers vanish. Although the triplon excitations are topologically trivial, the thermal Hall conductivity of the columnar valence bond solid phase in the square lattice antiferromagnet is finite at low temperatures. Our results complement a previous study by Samajdar et al., Phys. Rev. B 99, 165126 (2019) concerning the thermal Hall effect due to spinons of a spin-liquid phase on a square lattice. We also comment on the relations of our results with a no-go condition for a thermal Hall effect previously derived for ordered magnets by Katsura et al., Phys. Rev. Lett. 104, 066403 (2010).

DOI
10.1103/physrevb.109.134405

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The large thermal Hall conductivity recently detected in Mott insulating cuprates has been attributed to chiral neutral spin excitations. A quantum spin liquid (QSL) with Majorana excitations, Chern number $\ifmmode\pm\else\textpm\fi{}4$ and large thermal Hall conductivity is found to be an excited state of a frustrated Heisenberg model on the square lattice. Using a Majorana mean-field theory and exact diagonalizations, we explore two possible routes to achieve this chiral QSL, an orbital magnetic-field effect and spin-orbit couplings as present in cuprates. In particular, we show how only the orbital magnetic field allows this topological phase to be the ground state, while it remains an excited state of the Majorana mean field under the Dzyaloshinskii-Moriya terms. A large quantized low-temperature thermal Hall effect can be induced in our model of Mott insulating cuprates by the orbital effect of an applied magnetic field.